diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml
index 90e08ff..02a5948 100644
--- a/.github/workflows/main.yml
+++ b/.github/workflows/main.yml
@@ -23,6 +23,9 @@ jobs:
- name: Install R and dependencies (Python 3.13 only)
if: matrix.python-version == '3.13'
run: |
+ # Install R from CRAN repo (rpy2 requires R >= 4.5 for R_getVar symbol)
+ wget -qO- https://cloud.r-project.org/bin/linux/ubuntu/marutter_pubkey.asc | sudo gpg --dearmor -o /usr/share/keyrings/cran-archive-keyring.gpg
+ echo "deb [signed-by=/usr/share/keyrings/cran-archive-keyring.gpg] https://cloud.r-project.org/bin/linux/ubuntu $(lsb_release -cs)-cran40/" | sudo tee /etc/apt/sources.list.d/cran.list
sudo apt-get update
sudo apt-get install -y r-base r-base-dev libtirpc-dev
- name: Install R packages (Python 3.13 only)
diff --git a/.github/workflows/pr_code_changes.yaml b/.github/workflows/pr_code_changes.yaml
index 5b6dc7b..15a8323 100644
--- a/.github/workflows/pr_code_changes.yaml
+++ b/.github/workflows/pr_code_changes.yaml
@@ -68,6 +68,9 @@ jobs:
- name: Install R and dependencies (Python 3.14 only)
if: matrix.python-version == '3.14'
run: |
+ # Install R from CRAN repo (rpy2 requires R >= 4.5 for R_getVar symbol)
+ wget -qO- https://cloud.r-project.org/bin/linux/ubuntu/marutter_pubkey.asc | sudo gpg --dearmor -o /usr/share/keyrings/cran-archive-keyring.gpg
+ echo "deb [signed-by=/usr/share/keyrings/cran-archive-keyring.gpg] https://cloud.r-project.org/bin/linux/ubuntu $(lsb_release -cs)-cran40/" | sudo tee /etc/apt/sources.list.d/cran.list
sudo apt-get update
sudo apt-get install -y r-base r-base-dev libtirpc-dev
- name: Install R packages (Python 3.14 only)
diff --git a/README.md b/README.md
index a5a817f..9c2f2e9 100644
--- a/README.md
+++ b/README.md
@@ -7,7 +7,7 @@ Microimpute is a Python package for imputing variables from one survey dataset o
- **Statistical Matching**: distance-based matching to find similar donor observations
- **Ordinary Least Squares (OLS)**: linear regression imputation
- **Quantile Regression**: models conditional quantiles instead of the conditional mean
-- **Quantile Random Forests (QRF)**: non-parametric, tree-based quantile estimation
+- **Quantile Regression Forests (QRF)**: non-parametric, tree-based quantile estimation
- **Mixture Density Networks (MDN)**: neural network with a Gaussian mixture output
## Autoimpute
diff --git a/docs/index.md b/docs/index.md
index 979a4c6..63a8008 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -5,7 +5,7 @@ Microimpute is a Python package for imputing variables from one survey dataset o
The package currently supports:
- Hot Deck Matching
- Ordinary Least Squares (OLS) Linear Regression
-- Quantile Random Forests (QRF)
+- Quantile Regression Forests (QRF)
- Quantile Regression
- Mixture Density Networks (MDN)
diff --git a/docs/models/qrf/index.md b/docs/models/qrf/index.md
index 170ec9a..630d6d1 100644
--- a/docs/models/qrf/index.md
+++ b/docs/models/qrf/index.md
@@ -1,4 +1,4 @@
-# Quantile Random Forests
+# Quantile Regression Forests
The `QRF` model uses an ensemble of decision trees to predict different quantiles of the target variable distribution. This allows it to model non-linear relationships while estimating uncertainty across the conditional distribution.
@@ -8,7 +8,7 @@ QRF handles both numerical and categorical variables. For numerical targets, it
## How it works
-Quantile Random Forests build on standard random forests using the `quantile_forest` package. The method constructs an ensemble of decision trees, each trained on a bootstrapped sample of the data (bagging). At each split, only a random subset of features is considered, which introduces diversity among trees and reduces overfitting.
+Quantile Regression Forests build on standard random forests using the `quantile_forest` package. The method constructs an ensemble of decision trees, each trained on a bootstrapped sample of the data (bagging). At each split, only a random subset of features is considered, which introduces diversity among trees and reduces overfitting.
Unlike standard random forests that aggregate predictions into averages, QRF retains the full predictive distribution from each tree and estimates quantiles directly from this empirical distribution.
diff --git a/docs/models/qrf/qrf-imputation.ipynb b/docs/models/qrf/qrf-imputation.ipynb
index 6f66353..2c56a0f 100644
--- a/docs/models/qrf/qrf-imputation.ipynb
+++ b/docs/models/qrf/qrf-imputation.ipynb
@@ -4,13 +4,13 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "# Quantile Random Forest (QRF) imputation\n",
+ "# Quantile Regression Forest (QRF) imputation\n",
"\n",
- "This notebook demonstrates how to use Microimpute's `QRF` imputer to impute values using Quantile Random Forests. QRF extends traditional random forests to predict the entire conditional distribution of a target variable.\n",
+ "This notebook demonstrates how to use Microimpute's `QRF` imputer to impute values using Quantile Regression Forests. QRF extends traditional random forests to predict the entire conditional distribution of a target variable.\n",
"\n",
"## Variable type support\n",
"\n",
- "The QRF model automatically handles both numerical and categorical variables. For numerical targets, it applies quantile random forests. For categorical targets (strings, booleans, or numerically-encoded categorical variables), it switches to using a random forest classifier. This automatic adaptation happens internally without requiring any manual configuration.\n",
+ "The QRF model automatically handles both numerical and categorical variables. For numerical targets, it applies quantile regression forests. For categorical targets (strings, booleans, or numerically-encoded categorical variables), it switches to using a random forest classifier. This automatic adaptation happens internally without requiring any manual configuration.\n",
"\n",
"The QRF model supports sequential imputation with a single object and workflow. Pass a list of `imputed_variables` with all variables you want to impute, and the model imputes them sequentially. This means that previously imputed variables will serve as predictors for subsequent variables, capturing complex dependencies between the imputed variables.\n",
"\n",
@@ -584,7 +584,7 @@
"qrf_imputer = QRF()\n",
"\n",
"# Fit the model with our training data\n",
- "# This trains a quantile random forest model\n",
+ "# This trains a quantile regression forest model\n",
"fitted_qrf_imputer = qrf_imputer.fit(\n",
" X_train,\n",
" predictors,\n",
@@ -2023,7 +2023,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "This scatter plot compares actual observed values with those imputed by a Quantile Random Forest (QRF) model, providing a visual assessment of imputation accuracy. Each point represents a data record, with the x-axis showing the true value and the y-axis showing the model’s predicted value. The red dashed line represents the ideal 1:1 relationship, where predictions perfectly match actual values. Most points cluster around this line, suggesting that the QRF model effectively captures the underlying structure of the data. Importantly, the model does not appear to systematically over- or under-predict across the range, and while performance at the extremes may be weaker, the overall pattern indicates that QRF provides a reasonably accurate and unbiased approach to imputing missing values. Additionally, it is important to consider the characteristics of the diabetes dataset, which seems to show a strong linear relationship between predictors and the imputed variable. QRF's behavior suggests strength in accurately imputing variables for datasets when such linearity assumptions do not hold."
+ "This scatter plot compares actual observed values with those imputed by a Quantile Regression Forest (QRF) model, providing a visual assessment of imputation accuracy. Each point represents a data record, with the x-axis showing the true value and the y-axis showing the model’s predicted value. The red dashed line represents the ideal 1:1 relationship, where predictions perfectly match actual values. Most points cluster around this line, suggesting that the QRF model effectively captures the underlying structure of the data. Importantly, the model does not appear to systematically over- or under-predict across the range, and while performance at the extremes may be weaker, the overall pattern indicates that QRF provides a reasonably accurate and unbiased approach to imputing missing values. Additionally, it is important to consider the characteristics of the diabetes dataset, which seems to show a strong linear relationship between predictors and the imputed variable. QRF's behavior suggests strength in accurately imputing variables for datasets when such linearity assumptions do not hold."
]
},
{
@@ -3636,7 +3636,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "This plot visualizes the prediction intervals produced by the Quantile Random Forest (QRF) model for imputing total serum cholesterol values across ten data records. Each vertical bar represents an 80% (light gray) or 40% (dark gray) prediction interval, capturing the model's estimated range of plausible values based on the Q10–Q90 and Q30–Q70 quantiles, respectively. Red dots mark the model's median predictions (Q50), while black dots show the actual observed values. In most cases, the true values fall within the wider intervals, indicating that the QRF model is appropriately capturing uncertainty in its imputation. The fact that the intervals are sometimes asymmetrical around the median reflects the model’s flexibility in estimating skewed or heteroskedastic distributions. Overall, the plot demonstrates that the QRF model not only provides accurate point estimates but also yields informative prediction intervals that account for uncertainty in the imputed values."
+ "This plot visualizes the prediction intervals produced by the Quantile Regression Forest (QRF) model for imputing total serum cholesterol values across ten data records. Each vertical bar represents an 80% (light gray) or 40% (dark gray) prediction interval, capturing the model's estimated range of plausible values based on the Q10–Q90 and Q30–Q70 quantiles, respectively. Red dots mark the model's median predictions (Q50), while black dots show the actual observed values. In most cases, the true values fall within the wider intervals, indicating that the QRF model is appropriately capturing uncertainty in its imputation. The fact that the intervals are sometimes asymmetrical around the median reflects the model’s flexibility in estimating skewed or heteroskedastic distributions. Overall, the plot demonstrates that the QRF model not only provides accurate point estimates but also yields informative prediction intervals that account for uncertainty in the imputed values."
]
},
{
diff --git a/microimpute/models/__init__.py b/microimpute/models/__init__.py
index b243aa6..4b14f6e 100644
--- a/microimpute/models/__init__.py
+++ b/microimpute/models/__init__.py
@@ -6,7 +6,7 @@
Available models:
- OLS: ordinary least squares regression with bootstrapped quantiles
- - QRF: quantile random forest for non-parametric quantile regression
+ - QRF: quantile regression forest for non-parametric quantile regression
- QuantReg: linear quantile regression model
- Matching: statistical matching/hot-deck imputation (optional, requires rpy2)
- MDN: Mixture Density Network for probabilistic imputation
diff --git a/microimpute/models/mdn.py b/microimpute/models/mdn.py
index f42ffaf..aac265e 100644
--- a/microimpute/models/mdn.py
+++ b/microimpute/models/mdn.py
@@ -268,6 +268,12 @@ def fit(
col for col in X.columns.tolist() if col not in categorical_cols
]
+ # Cast continuous columns to float64 to avoid pandas 3.x
+ # LossySetitemError when pytorch_tabular's scaler writes
+ # normalized float values back into integer-typed columns.
+ for col in continuous_cols:
+ train_data[col] = train_data[col].astype("float64")
+
# Configure data
data_config = DataConfig(
target=[y.name],
@@ -351,6 +357,12 @@ def predict(self, X: pd.DataFrame, n_samples: int = 1) -> np.ndarray:
# Put model in eval mode
self.model.model.eval()
+ # Cast continuous columns to float64 for pandas 3.x compat
+ X = X.copy()
+ for col in self.model.config.continuous_cols:
+ if col in X.columns:
+ X[col] = X[col].astype("float64")
+
# Create inference dataloader
test_loader = self.model.datamodule.prepare_inference_dataloader(X)
@@ -466,6 +478,12 @@ def fit(
col for col in X.columns.tolist() if col not in categorical_cols
]
+ # Cast continuous columns to float64 to avoid pandas 3.x
+ # LossySetitemError when pytorch_tabular's scaler writes
+ # normalized float values back into integer-typed columns.
+ for col in continuous_cols:
+ train_data[col] = train_data[col].astype("float64")
+
# Configure data
data_config = DataConfig(
target=[y.name],
@@ -541,6 +559,12 @@ def predict(
Predicted values as Series, or dict with probabilities if
return_probs=True.
"""
+ # Cast continuous columns to float64 for pandas 3.x compat
+ X = X.copy()
+ for col in self.model.config.continuous_cols:
+ if col in X.columns:
+ X[col] = X[col].astype("float64")
+
# Get predictions with probabilities
preds_df = self.model.predict(X, ret_logits=False)
diff --git a/microimpute/models/qrf.py b/microimpute/models/qrf.py
index b7617e3..3f46c5f 100644
--- a/microimpute/models/qrf.py
+++ b/microimpute/models/qrf.py
@@ -482,7 +482,7 @@ class QRF(Imputer):
"""
Quantile Regression Forest model for imputation.
- This model uses a Quantile Random Forest to predict quantiles.
+ This model uses a Quantile Regression Forest to predict quantiles.
The underlying QRF implementation is from the quantile_forest package.
"""
diff --git a/paper/bibliography/references.bib b/paper/bibliography/references.bib
index 93e70d5..146f0e7 100644
--- a/paper/bibliography/references.bib
+++ b/paper/bibliography/references.bib
@@ -17,14 +17,14 @@ @article{bishop1994mixture
year = {1994}
}
-@incollection{bourguignon2006microsimulation,
- title = {Microsimulation as a tool for evaluating redistribution policies},
- author = {Bourguignon, Fran{\c{c}}ois and Spadaro, Amedeo},
- booktitle = {Journal of Economic Inequality},
- volume = {4},
- number = {1},
- pages = {77--106},
- year = {2006},
+@article{bourguignon2006microsimulation,
+ title = {Microsimulation as a tool for evaluating redistribution policies},
+ author = {Bourguignon, Fran{\c{c}}ois and Spadaro, Amedeo},
+ journal = {Journal of Economic Inequality},
+ volume = {4},
+ number = {1},
+ pages = {77--106},
+ year = {2006},
publisher = {Springer}
}
diff --git a/paper/figures/models_dist_comparison.png b/paper/figures/models_dist_comparison.png
index 747de68..e67bfd9 100644
Binary files a/paper/figures/models_dist_comparison.png and b/paper/figures/models_dist_comparison.png differ
diff --git a/paper/figures/models_ssi_reform_comparison.png b/paper/figures/models_ssi_reform_comparison.png
index 357c613..5128abc 100644
Binary files a/paper/figures/models_ssi_reform_comparison.png and b/paper/figures/models_ssi_reform_comparison.png differ
diff --git a/paper/imputing-from-scf-to-cps.ipynb b/paper/imputing-from-scf-to-cps.ipynb
index 92882d2..40ff4ef 100644
--- a/paper/imputing-from-scf-to-cps.ipynb
+++ b/paper/imputing-from-scf-to-cps.ipynb
@@ -69,7 +69,7 @@
"name": "stderr",
"output_type": "stream",
"text": [
- "100%|██████████| 1/1 [00:03<00:00, 3.07s/it]\n"
+ "100%|██████████| 1/1 [00:00<00:00, 1.08it/s]\n"
]
},
{
@@ -496,7 +496,7 @@
},
{
"cell_type": "code",
- "execution_count": 27,
+ "execution_count": 6,
"id": "1de6e0ea",
"metadata": {},
"outputs": [
@@ -23504,22981 +23504,22981 @@
"opacity": 0.7,
"type": "histogram",
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{
@@ -46506,11 +46506,11 @@
"width": 2
},
"mode": "lines",
- "name": "Weighted Median: $205,353",
+ "name": "Weighted Median: $205,247",
"type": "scatter",
"x": [
- 5.312500888804604,
- 5.312500888804604
+ 5.312277543733134,
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],
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0,
@@ -46528,7 +46528,7 @@
"size": 11
},
"showarrow": false,
- "text": "Unweighted:
Median: $405,955
Mean: $95,774
Weighted:
Median: $205,353
Mean: $34,788",
+ "text": "Unweighted:
Median: $405,955
Mean: $95,774
Weighted:
Median: $205,247
Mean: $33,949",
"x": 0.98,
"xanchor": "right",
"xref": "paper",
@@ -47587,7 +47587,7 @@
"\n",
"After harmonizing the two datasets, the `autoimpute` function from `microimpute` can be used to transfer wealth information from the SCF to the CPS. This powerful function streamlines the imputation process by automating hyperparameter tuning, method selection, validation, and application.\n",
"\n",
- "Behind the scenes, `autoimpute` evaluates multiple statistical approaches, including Quantile Random Forest, Ordinary Least Squares, Quantile Regression, and Statistical Matching. It performs cross-validation to determine which method most accurately captures the relationship between the predictor variables and wealth measures in the SCF data. The function then applies the best-performing method to generate synthetic wealth values for CPS households.\n",
+ "Behind the scenes, `autoimpute` evaluates multiple statistical approaches, including Quantile Regression Forest, Ordinary Least Squares, Quantile Regression, and Statistical Matching. It performs cross-validation to determine which method most accurately captures the relationship between the predictor variables and wealth measures in the SCF data. The function then applies the best-performing method to generate synthetic wealth values for CPS households.\n",
"\n",
"By enabling hyperparameter tuning, the function can optimize each method's parameters, further improving imputation accuracy. This automated approach saves considerable time and effort compared to manually testing different imputation strategies, while ensuring the selection of the most appropriate method for this specific imputation task."
]
@@ -47601,7 +47601,7 @@
{
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+ "model_id": "42a90159262444b5a43a1e1f9db22319",
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"output_type": "stream",
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- "[Parallel(n_jobs=-1)]: Done 2 out of 5 | elapsed: 1.8min remaining: 2.7min\n",
- "[Parallel(n_jobs=-1)]: Done 3 out of 5 | elapsed: 1.8min remaining: 1.2min\n",
- "[Parallel(n_jobs=-1)]: Done 5 out of 5 | elapsed: 1.8min finished\n",
+ "[Parallel(n_jobs=-1)]: Done 2 out of 5 | elapsed: 4.2min remaining: 6.2min\n",
+ "[Parallel(n_jobs=-1)]: Done 3 out of 5 | elapsed: 4.2min remaining: 2.8min\n",
+ "[Parallel(n_jobs=-1)]: Done 5 out of 5 | elapsed: 4.2min finished\n",
"[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.\n",
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- "[Parallel(n_jobs=-1)]: Done 5 out of 5 | elapsed: 0.4s finished\n",
+ "[Parallel(n_jobs=-1)]: Done 2 out of 5 | elapsed: 0.9s remaining: 1.3s\n",
+ "[Parallel(n_jobs=-1)]: Done 3 out of 5 | elapsed: 0.9s remaining: 0.6s\n",
+ "[Parallel(n_jobs=-1)]: Done 5 out of 5 | elapsed: 1.0s finished\n",
"[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.\n",
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- "[Parallel(n_jobs=-1)]: Done 3 out of 5 | elapsed: 10.5s remaining: 7.0s\n",
- "[Parallel(n_jobs=-1)]: Done 5 out of 5 | elapsed: 11.6s finished\n",
- "[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 6.3min\n",
- "[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 25.9min\n",
- "[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 32.6min finished\n",
+ "[Parallel(n_jobs=-1)]: Done 2 out of 5 | elapsed: 31.0s remaining: 46.4s\n",
+ "[Parallel(n_jobs=-1)]: Done 3 out of 5 | elapsed: 33.3s remaining: 22.2s\n",
+ "[Parallel(n_jobs=-1)]: Done 5 out of 5 | elapsed: 34.2s finished\n",
+ "[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 10.9min\n",
+ "[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 44.7min\n",
+ "[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 55.3min finished\n",
"[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.\n",
- "[Parallel(n_jobs=-1)]: Done 2 out of 5 | elapsed: 23.9s remaining: 35.9s\n",
- "[Parallel(n_jobs=-1)]: Done 3 out of 5 | elapsed: 24.0s remaining: 16.0s\n",
- "[Parallel(n_jobs=-1)]: Done 5 out of 5 | elapsed: 24.1s finished\n"
+ "[Parallel(n_jobs=-1)]: Done 2 out of 5 | elapsed: 38.6min remaining: 57.9min\n",
+ "[Parallel(n_jobs=-1)]: Done 3 out of 5 | elapsed: 38.6min remaining: 25.7min\n",
+ "[Parallel(n_jobs=-1)]: Done 5 out of 5 | elapsed: 38.8min finished\n"
]
}
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"alignmentgroup": "True",
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Quantiles=%{x}
Quantile loss=%{y}",
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"alignmentgroup": "True",
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Quantiles=%{x}
Quantile loss=%{y}",
@@ -48082,25 +48082,25 @@
],
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@@ -48166,8 +48166,8 @@
"type": "line",
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"x1": 18.5,
- "y0": 0.5984294993742812,
- "y1": 0.5984294993742812
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@@ -48179,8 +48179,8 @@
"type": "line",
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- "y1": 2.3370932792219534
+ "y0": 2.2319890681358983,
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@@ -49329,7 +49329,7 @@
{
"data": {
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- "model_id": "d103a104d35740df9fdc5a69bf715eb2",
+ "model_id": "397e93a773a74c0f99771e8713bb4cd1",
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{
"data": {
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- "model_id": "f25825859ed54cfcbad1519fad5c81e5",
+ "model_id": "b81bb51fa838489f8c4aa8750f562907",
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},
@@ -49593,10 +49593,10 @@
"0 networth wasserstein_distance 1.217437e+14\n",
"Model: Matching, distribution similarity: \n",
" Variable Metric Distance\n",
- "0 networth wasserstein_distance 1.194086e+06\n",
+ "0 networth wasserstein_distance 1.189243e+06\n",
"Model: MDN, distribution similarity: \n",
" Variable Metric Distance\n",
- "0 networth wasserstein_distance 8.476211e+14\n"
+ "0 networth wasserstein_distance 2.639191e+14\n"
]
}
],
@@ -49627,7 +49627,79 @@
},
{
"cell_type": "code",
- "execution_count": 30,
+ "execution_count": 29,
+ "id": "s98ouh00z1",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Trimming to [-76,757, 494,947,126] (1st-99th percentile of SCF net worth)\n",
+ "Donor records: 22,975 total, 459 dropped (2.0%)\n",
+ "\n",
+ "Model: best_method, receiver dropped: 227 of 18,395 (1.2%)\n",
+ " trimmed distribution similarity: \n",
+ " Variable Metric Distance\n",
+ "0 networth wasserstein_distance 892190.030085\n",
+ "Model: OLS, receiver dropped: 23 of 18,395 (0.1%)\n",
+ " trimmed distribution similarity: \n",
+ " Variable Metric Distance\n",
+ "0 networth wasserstein_distance 742528.269654\n",
+ "Model: QuantReg, receiver dropped: 76 of 18,395 (0.4%)\n",
+ " trimmed distribution similarity: \n",
+ " Variable Metric Distance\n",
+ "0 networth wasserstein_distance 650018.336012\n",
+ "Model: Matching, receiver dropped: 306 of 18,395 (1.7%)\n",
+ " trimmed distribution similarity: \n",
+ " Variable Metric Distance\n",
+ "0 networth wasserstein_distance 1.209626e+06\n",
+ "Model: MDN, receiver dropped: 61 of 18,395 (0.3%)\n",
+ " trimmed distribution similarity: \n",
+ " Variable Metric Distance\n",
+ "0 networth wasserstein_distance 150888.884985\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Robustness check: trimmed Wasserstein distances (excluding top/bottom 1%)\n",
+ "# This verifies that the method ranking is not driven by extreme-tail leverage.\n",
+ "\n",
+ "p1 = np.percentile(scf_data[\"networth\"], 1)\n",
+ "p99 = np.percentile(scf_data[\"networth\"], 99)\n",
+ "\n",
+ "donor_mask = (scf_data[\"networth\"] >= p1) & (scf_data[\"networth\"] <= p99)\n",
+ "donor_dropped = len(scf_data) - donor_mask.sum()\n",
+ "\n",
+ "print(f\"Trimming to [{p1:,.0f}, {p99:,.0f}] (1st-99th percentile of SCF net worth)\")\n",
+ "print(\n",
+ " f\"Donor records: {len(scf_data):,} total, {donor_dropped:,} dropped ({donor_dropped / len(scf_data) * 100:.1f}%)\\n\"\n",
+ ")\n",
+ "\n",
+ "for model, imputations in autoimpute_results.imputations.items():\n",
+ " receiver_mask = (imputations[\"networth\"] >= p1) & (imputations[\"networth\"] <= p99)\n",
+ " receiver_dropped = len(imputations) - receiver_mask.sum()\n",
+ "\n",
+ " print(\n",
+ " f\"Model: {model}, \"\n",
+ " f\"receiver dropped: {receiver_dropped:,} of {len(imputations):,} ({receiver_dropped / len(imputations) * 100:.1f}%)\"\n",
+ " )\n",
+ " print(\n",
+ " f\" trimmed distribution similarity: \\n{\n",
+ " compare_distributions(\n",
+ " donor_data=pd.DataFrame(scf_data['networth'][donor_mask]),\n",
+ " receiver_data=pd.DataFrame(imputations['networth'][receiver_mask]),\n",
+ " donor_weights=scf_data['wgt'][donor_mask],\n",
+ " receiver_weights=cps_data['household_weight'][receiver_mask],\n",
+ " imputed_variables=imputed_variables,\n",
+ " )\n",
+ " }\"\n",
+ " )"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
"id": "643cb47d",
"metadata": {},
"outputs": [],
@@ -49784,7 +49856,7 @@
" go.Histogram(\n",
" x=donor_log,\n",
" nbinsx=200,\n",
- " opacity=0.3,\n",
+ " opacity=0.5,\n",
" name=\"SCF (weighted)\",\n",
" marker_color=donor_color,\n",
" histnorm=\"percent\",\n",
@@ -49799,7 +49871,7 @@
" go.Histogram(\n",
" x=model_log,\n",
" nbinsx=200,\n",
- " opacity=0.75,\n",
+ " opacity=0.6,\n",
" name=model_name.replace(\" imputations\", \"\"),\n",
" marker_color=model_color,\n",
" histnorm=\"percent\",\n",
@@ -49919,7 +49991,7 @@
},
{
"cell_type": "code",
- "execution_count": 17,
+ "execution_count": 18,
"id": "1dd3d40f",
"metadata": {},
"outputs": [
@@ -49949,7 +50021,7 @@
"==================================================\n",
"Model: Matching\n",
"==================================================\n",
- " Matching hyperparameters: {'dist_fun': 'Mahalanobis', 'k': 9}\n",
+ " Matching hyperparameters: {'dist_fun': 'Mahalanobis', 'k': 4}\n",
"\n",
"==================================================\n",
"Model: MDN\n",
@@ -49989,7 +50061,7 @@
},
{
"cell_type": "code",
- "execution_count": 31,
+ "execution_count": 28,
"id": "4f9709f4",
"metadata": {},
"outputs": [
@@ -73018,7 +73090,7 @@
},
"name": "SCF (weighted)",
"nbinsx": 200,
- "opacity": 0.3,
+ "opacity": 0.5,
"showlegend": false,
"type": "histogram",
"x": [
@@ -96008,7 +96080,7 @@
},
"name": "OLS",
"nbinsx": 200,
- "opacity": 0.75,
+ "opacity": 0.6,
"showlegend": true,
"type": "histogram",
"x": [
@@ -114460,7 +114532,7 @@
},
"name": "SCF (weighted)",
"nbinsx": 200,
- "opacity": 0.3,
+ "opacity": 0.5,
"showlegend": false,
"type": "histogram",
"x": [
@@ -137450,7 +137522,7 @@
},
"name": "QuantReg",
"nbinsx": 200,
- "opacity": 0.75,
+ "opacity": 0.6,
"showlegend": true,
"type": "histogram",
"x": [
@@ -155902,7 +155974,7 @@
},
"name": "SCF (weighted)",
"nbinsx": 200,
- "opacity": 0.3,
+ "opacity": 0.5,
"showlegend": false,
"type": "histogram",
"x": [
@@ -178892,7 +178964,7 @@
},
"name": "Matching",
"nbinsx": 200,
- "opacity": 0.75,
+ "opacity": 0.6,
"showlegend": true,
"type": "histogram",
"x": [
@@ -178902,26 +178974,26 @@
-4.599000074357238,
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+ 5.316545828525807,
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"showlegend": false,
"type": "scatter",
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@@ -238786,7 +238858,7 @@
},
"name": "SCF (weighted)",
"nbinsx": 200,
- "opacity": 0.3,
+ "opacity": 0.5,
"showlegend": false,
"type": "histogram",
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},
"name": "QRF",
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@@ -280358,7 +280430,7 @@
"size": 10
},
"showarrow": false,
- "text": "Median: $174,186
Mean: $16,484",
+ "text": "Median: $174,101
Mean: $16,948",
"x": 7,
"xanchor": "right",
"xref": "x4",
@@ -280374,7 +280446,7 @@
"size": 10
},
"showarrow": false,
- "text": "Median: $251,020
Mean: $102,775",
+ "text": "Median: $227,495
Mean: $113,224",
"x": 7,
"xanchor": "right",
"xref": "x5",
@@ -281597,7 +281669,7 @@
},
{
"cell_type": "code",
- "execution_count": 19,
+ "execution_count": 20,
"id": "839cff5a",
"metadata": {},
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@@ -281638,16 +281710,16 @@
],
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],
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],
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@@ -282783,7 +282855,7 @@
},
{
"cell_type": "code",
- "execution_count": 20,
+ "execution_count": 21,
"id": "9bcee9aa",
"metadata": {},
"outputs": [],
@@ -282831,7 +282903,7 @@
},
{
"cell_type": "code",
- "execution_count": 21,
+ "execution_count": 22,
"id": "m2mx0oepixj",
"metadata": {},
"outputs": [
@@ -282930,7 +283002,7 @@
},
{
"cell_type": "code",
- "execution_count": 32,
+ "execution_count": 23,
"id": "2d9552bb",
"metadata": {},
"outputs": [
@@ -282946,8 +283018,8 @@
"--------------------------------------------------------------------------------\n",
"OLS 11,342,398 100.46 738 153.3%\n",
"QuantReg 8,262,234 74.58 752 111.7%\n",
- "Matching 11,116,984 90.18 676 150.2%\n",
- "MDN 9,075,249 79.61 731 122.6%\n",
+ "Matching 11,016,779 89.95 680 148.9%\n",
+ "MDN 9,778,097 86.88 740 132.1%\n",
"QRF 12,083,642 102.83 709 163.3%\n",
"Baseline (no wealth) 19,769,600 152.59 643 267.2%\n",
"--------------------------------------------------------------------------------\n",
@@ -282986,8 +283058,8 @@
"y": [
11342398.18111819,
8262234.327414215,
- 11116984.209978282,
- 9075248.530094802,
+ 11016778.97514552,
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12083641.52855222,
19769600.46492593
],
@@ -283018,8 +283090,8 @@
"y": [
100.45850661794287,
74.57541569154087,
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@@ -284217,12 +284289,12 @@
"\n",
"The **SSI Savings Penalty Elimination Act** (S. 1234 / H.R. 2540, introduced April 2025) is a bipartisan bill that would raise the resource limits to $10,000 for individuals and $20,000 for couples, with future CPI indexing. This reform provides a natural test case for wealth imputation: simulating the effect of raising resource limits *requires* household-level wealth data, since the reform changes which households pass the resource test.\n",
"\n",
- "Below, we simulate SSI outcomes under both current law and the reformed thresholds for each imputation method. The difference — additional recipients and expenditure — represents the estimated reform impact. We also simulate the reform under the baseline (no wealth) scenario, where resources default to $0. Because every household already passes the resource test under current law in the baseline, raising the thresholds has *zero effect* — demonstrating that this reform is literally un-simulable without imputed wealth data."
+ "Below, we simulate SSI outcomes under both current law and the reformed thresholds for each imputation method. The difference — additional recipients and expenditure — represents the estimated reform impact. We also simulate the reform under the baseline (no wealth) scenario, where resources default to $0. Because every household already passes the resource test under current law in the baseline, raising the thresholds has *zero effect* — demonstrating that this reform literally cannot be simulated without imputed wealth data."
]
},
{
"cell_type": "code",
- "execution_count": 23,
+ "execution_count": 24,
"id": "owl35osuah",
"metadata": {},
"outputs": [
@@ -284325,7 +284397,7 @@
},
{
"cell_type": "code",
- "execution_count": 24,
+ "execution_count": 25,
"id": "abdmvy9sddj",
"metadata": {},
"outputs": [
@@ -284341,13 +284413,13 @@
"----------------------------------------------------------------------------------------------------\n",
"OLS 11.34M 15.57M 4.22M 24.10 37.2%\n",
"QuantReg 8.26M 8.37M 0.11M 0.99 1.3%\n",
- "Matching 11.12M 12.96M 1.85M 10.41 16.6%\n",
- "MDN 9.08M 9.78M 0.71M 4.84 7.8%\n",
+ "Matching 11.02M 12.86M 1.85M 10.41 16.8%\n",
+ "MDN 9.78M 10.91M 1.13M 9.09 11.6%\n",
"QRF 12.08M 12.71M 0.63M 3.39 5.2%\n",
"Baseline (no wealth) 19.77M 19.77M 0.00M 0.00 0.0%\n",
"----------------------------------------------------------------------------------------------------\n",
"\n",
- "Baseline (no wealth) reform impact = 0: without wealth data, this reform is un-simulable.\n"
+ "Baseline (no wealth) reform impact = 0: without wealth data, this reform is cannot be simulated.\n"
]
}
],
@@ -284407,13 +284479,13 @@
"print(\"-\" * 100)\n",
"print(\n",
" \"\\nBaseline (no wealth) reform impact = 0: \"\n",
- " \"without wealth data, this reform is un-simulable.\"\n",
+ " \"without wealth data, this reform is cannot be simulated.\"\n",
")"
]
},
{
"cell_type": "code",
- "execution_count": 34,
+ "execution_count": 31,
"id": "ikwu2p4d4hj",
"metadata": {},
"outputs": [
@@ -284449,8 +284521,8 @@
"y": [
11342398.18111819,
8262234.327414215,
- 11116984.209978282,
- 9075248.530094802,
+ 11016778.97514552,
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12083641.52855222
],
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@@ -284480,8 +284552,8 @@
"y": [
15566883.581850216,
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+ 12864400.6310274,
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],
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@@ -284511,8 +284583,8 @@
"y": [
100.45850661794287,
74.57541569154087,
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+ 89.95321699560878,
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@@ -284542,11 +284614,30 @@
"y": [
124.5603771981509,
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+ 100.36657634436568,
+ 95.9753232255853,
106.2176830370023
],
"yaxis": "y2"
+ },
+ {
+ "line": {
+ "color": "black",
+ "dash": "dash",
+ "width": 1
+ },
+ "mode": "lines",
+ "name": "Admin total (current law)",
+ "showlegend": true,
+ "type": "scatter",
+ "x": [
+ null
+ ],
+ "xaxis": "x",
+ "y": [
+ null
+ ],
+ "yaxis": "y"
}
],
"layout": {
@@ -284576,30 +284667,17 @@
"y": 1,
"yanchor": "bottom",
"yref": "paper"
- },
- {
- "showarrow": false,
- "text": "Admin total (current law)",
- "x": 1,
- "xanchor": "right",
- "xref": "x domain",
- "y": 7400000,
- "yanchor": "bottom",
- "yref": "y"
- },
- {
- "showarrow": false,
- "text": "Admin total (current law)",
- "x": 1,
- "xanchor": "right",
- "xref": "x2 domain",
- "y": 59.6,
- "yanchor": "bottom",
- "yref": "y2"
}
],
"barmode": "group",
"height": 500,
+ "legend": {
+ "orientation": "v",
+ "x": 1.02,
+ "xanchor": "left",
+ "y": 0.95,
+ "yanchor": "top"
+ },
"paper_bgcolor": "#FAFAFA",
"plot_bgcolor": "#FAFAFA",
"shapes": [
@@ -285449,7 +285527,7 @@
}
},
"title": {
- "text": "SSI savings penalty elimination act: Reform impact by imputation method"
+ "text": "SSI Savings Penalty Elimination Act: Reform impact by imputation method"
},
"width": 950,
"xaxis": {
@@ -285571,8 +285649,6 @@
" line_dash=\"dash\",\n",
" line_color=\"black\",\n",
" line_width=1,\n",
- " annotation_text=\"Admin total (current law)\",\n",
- " annotation_position=\"top right\",\n",
" row=1,\n",
" col=1,\n",
")\n",
@@ -285610,19 +285686,37 @@
" line_dash=\"dash\",\n",
" line_color=\"black\",\n",
" line_width=1,\n",
- " annotation_text=\"Admin total (current law)\",\n",
- " annotation_position=\"top right\",\n",
" row=1,\n",
" col=2,\n",
")\n",
"\n",
+ "fig.add_trace(\n",
+ " go.Scatter(\n",
+ " x=[None],\n",
+ " y=[None],\n",
+ " mode=\"lines\",\n",
+ " line=dict(dash=\"dash\", color=\"black\", width=1),\n",
+ " name=\"Admin total (current law)\",\n",
+ " showlegend=True,\n",
+ " ),\n",
+ " row=1,\n",
+ " col=1,\n",
+ ")\n",
+ "\n",
"fig.update_layout(\n",
- " title=(\"SSI savings penalty elimination act: Reform impact by imputation method\"),\n",
+ " title=(\"SSI Savings Penalty Elimination Act: Reform impact by imputation method\"),\n",
" width=PLOT_CONFIG[\"width\"] + 200,\n",
" height=PLOT_CONFIG[\"height\"] - 100,\n",
" paper_bgcolor=PLOT_CONFIG[\"paper_bgcolor\"],\n",
" plot_bgcolor=PLOT_CONFIG[\"plot_bgcolor\"],\n",
" barmode=\"group\",\n",
+ " legend=dict(\n",
+ " orientation=\"v\",\n",
+ " yanchor=\"top\",\n",
+ " y=0.95,\n",
+ " xanchor=\"left\",\n",
+ " x=1.02,\n",
+ " ),\n",
")\n",
"fig.update_xaxes(\n",
" showgrid=PLOT_CONFIG[\"showgrid_x\"],\n",
@@ -285649,6 +285743,14 @@
")\n",
"fig.show()"
]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "bf3b69ab",
+ "metadata": {},
+ "outputs": [],
+ "source": []
}
],
"metadata": {
diff --git a/paper/macros.tex b/paper/macros.tex
deleted file mode 100644
index 0925fff..0000000
--- a/paper/macros.tex
+++ /dev/null
@@ -1,4 +0,0 @@
-% Custom commands and mathematics macros
-\newcommand{\policyengine}{\textsc{PolicyEngine}}
-\newcommand{\cps}{\textsc{CPS}}
-\newcommand{\puf}{\textsc{SCF}}
\ No newline at end of file
diff --git a/paper/main.pdf b/paper/main.pdf
index 6eb6047..1a74ed1 100644
Binary files a/paper/main.pdf and b/paper/main.pdf differ
diff --git a/paper/main.tex b/paper/main.tex
index 414c243..abfa7e3 100644
--- a/paper/main.tex
+++ b/paper/main.tex
@@ -1,24 +1,26 @@
-\documentclass[12pt]{article}
+\documentclass[11pt]{article}
+\usepackage{mathptmx} % Times New Roman font
+\usepackage{setspace} % Line spacing control
\usepackage{graphicx}
\usepackage{amsmath}
-\usepackage[round]{natbib} % Keep round option
-\usepackage{hyperref}
+\usepackage[round]{natbib}
\usepackage{booktabs}
\usepackage{geometry}
\usepackage{xcolor}
\usepackage{float}
+\usepackage{caption} % Caption formatting
+\usepackage{footmisc} % Footnote size control (before hyperref)
+\usepackage[hyphens]{url} % Allow URL line breaks at hyphens
+\usepackage{hyperref}
-% Draft notice in title
-\newcommand{\draftnote}{\textbf{[DRAFT]}}
-
-% Set citation style in preamble
-\bibpunct{(}{)}{;}{a}{,}{,} % Move here
-\setcitestyle{authoryear,round} % Move here
+\captionsetup{font=small,labelfont=bf}
+\renewcommand{\footnotelayout}{\fontsize{10}{12}\selectfont}
-\input{macros}
+\bibpunct{(}{)}{;}{a}{,}{,}
+\setcitestyle{authoryear,round}
-\geometry{margin=1in}
+\geometry{margin=1.5in}
\hypersetup{
colorlinks=true,
linkcolor=blue,
@@ -28,19 +30,17 @@
}
-\title{$\texttt{microimpute}$: Benchmarking Cross-Survey Imputation Methods for U.S. Household Wealth}
-% Define the \samethanks command
-\newcommand*\samethanks[1][\value{footnote}]{\footnotemark[#1]}
-
-% Define authors with the same affiliation
+\title{\texttt{microimpute}: Benchmarking Cross-Survey Imputation Methods for U.S. Household Wealth}
\author{
María Juaristi\thanks{Minerva University, PolicyEngine}
}
-\date{\today}
+\date{}
\begin{document}
+\onehalfspacing
\maketitle
+\vspace{-3em}
\input{sections/abstract}
\input{sections/introduction}
@@ -51,7 +51,9 @@
\input{sections/discussion}
\input{sections/conclusion}
-\bibliographystyle{plainnat}
+\input{sections/disclosures}
+
+\bibliographystyle{apalike}
\bibliography{./bibliography/references}
\clearpage
diff --git a/paper/sections/abstract.tex b/paper/sections/abstract.tex
index 4dcb08e..aa164a0 100644
--- a/paper/sections/abstract.tex
+++ b/paper/sections/abstract.tex
@@ -1,3 +1,6 @@
\section*{Abstract}
-Microdata surveys often lack variables needed for policy analysis, requiring imputation from richer donor surveys, yet no standardized tools exist for comparing imputation methods and selecting the best approach for a given dataset. We introduce $\texttt{microimpute}$, an open-source Python package for benchmarking, tuning, and automatically selecting among multiple imputation methods. We apply it to impute U.S. household wealth from the Survey of Consumer Finances (SCF) onto the Current Population Survey (CPS). Evaluating five methods (Quantile Random Forests, Ordinary Least Squares, Quantile Regression, Hot Deck Matching, and Mixture Density Networks) through a 5-fold cross-validation, we find that QRF reduces average quantile loss by 76\% relative to the worst-performing method and by 7\% relative to the next-best method (Hot Deck Matching), owing to its ability to model non-linear relationships between demographic predictors and wealth. Its Wasserstein distance to the donor distribution is 24\% lower than Matching's. A simulation of the Supplemental Security Income Savings Penalty Elimination Act shows what is at stake: without imputed wealth, the microsimulation overestimates SSI recipients by 167\%, and the reform is entirely un-simulable. Cross-dataset benchmarking across six additional domains, however, revealsthat no single method dominates universally. QRF performs best when relationships are non-linear, Hot Deck Matching better preserves marginal distributions by drawing directly from the donor pool, and OLS remains competitive when relationships are approximately linear. Imputation method selection should therefore be empirically driven rather than prescribed, which motivates tools like $\texttt{microimpute}$ for systematic comparison.
\ No newline at end of file
+Microdata surveys often lack variables needed for policy analysis, requiring imputation from richer donor surveys, yet no standardized tools exist for comparing imputation methods and selecting the best approach for a given dataset. We introduce \texttt{microimpute}, an open-source Python package for benchmarking, tuning, and automatically selecting among multiple imputation methods. We apply it to impute U.S. household wealth from the Survey of Consumer Finances (SCF) onto the Current Population Survey (CPS). Evaluating five methods (Quantile Regression Forests (QRF), Ordinary Least Squares, Quantile Regression, Hot Deck Matching, and Mixture Density Networks) through a 5-fold cross-validation, we find that QRF reduces average quantile loss by 75\% relative to the worst-performing method and by 6\% relative to the next-best method (Hot Deck Matching), owing to its ability to model nonlinear relationships between demographic predictors and wealth. Its Wasserstein distance to the donor distribution is 24\% lower than Matching's. A simulation of the Supplemental Security Income Savings Penalty Elimination Act demonstrates the practical importance of imputation: without imputed wealth, the microsimulation overestimates baseline SSI recipients by 167\%, and the policy reform cannot be simulated. Cross-dataset benchmarking across six additional domains, however, reveals that no single method dominates universally. QRF performs best when relationships are nonlinear, Hot Deck Matching better preserves marginal distributions by drawing directly from the donor pool, and OLS remains competitive when relationships are approximately linear. Imputation method selection should therefore be empirically driven rather than prescribed, which motivates tools like \texttt{microimpute} for systematic comparison.
+
+\vspace{1em}
+\noindent\textbf{Keywords:} microsimulation, statistical matching, wealth imputation, quantile regression forests
\ No newline at end of file
diff --git a/paper/sections/appendix_benchmarking.tex b/paper/sections/appendix_benchmarking.tex
index d546fae..38ecf9a 100644
--- a/paper/sections/appendix_benchmarking.tex
+++ b/paper/sections/appendix_benchmarking.tex
@@ -1,12 +1,12 @@
\section{Cross-Dataset Benchmarking}\label{app:benchmarking}
-To validate \texttt{microimpute} across diverse domains beyond the SCF-CPS wealth imputation use case, we conduct a cross-dataset benchmarking exercise using six publicly available regression datasets from the OpenML AutoML Benchmark regression suite \citep{vanschoren2014openml}, spanning different domains, sample sizes, and dimensionalities.
+To validate $\texttt{microimpute}$ across domains beyond the SCF-CPS wealth imputation use case, we conduct a cross-dataset benchmarking exercise using six publicly available regression datasets from the OpenML AutoML Benchmark regression suite \citep{vanschoren2014openml}, spanning different domains, sample sizes, and dimensionalities.
\subsection{Datasets}
Table~\ref{tab:benchmark_datasets} summarizes the datasets used in this analysis.
-\begin{table}[h]
+\begin{table}[H]
\centering
\caption{Datasets used for cross-dataset benchmarking.}
\label{tab:benchmark_datasets}
@@ -14,12 +14,12 @@ \subsection{Datasets}
\toprule
Dataset & Domain & Rows & Target Variable \\
\midrule
- space\_ga & Voting/demographics & 3,107 & ln(VOTES/POP) \\
- elevators & Aircraft control & 16,599 & Goal \\
- brazilian\_houses & Real estate & 10,692 & total\_(BRL) \\
- onlinenewspopularity & News/media & 39,644 & shares \\
- abalone & Marine biology & 4,177 & Class\_number\_of\_rings \\
- house\_sales & Real estate & 21,613 & price \\
+ \texttt{space\_ga} & Voting/demographics & 3,107 & \texttt{ln(VOTES/POP)} \\
+ \texttt{elevators} & Aircraft control & 16,599 & \texttt{Goal} \\
+ \texttt{brazilian\_houses} & Real estate & 10,692 & \texttt{total\_(BRL)} \\
+ \texttt{onlinenewspopularity} & News/media & 39,644 & \texttt{shares} \\
+ \texttt{abalone} & Marine biology & 4,177 & \texttt{Class\_number\_of\_rings} \\
+ \texttt{house\_sales} & Real estate & 21,613 & \texttt{price} \\
\bottomrule
\end{tabular}
\end{table}
@@ -32,7 +32,7 @@ \subsection{Results}
Table~\ref{tab:benchmark_wasserstein} reports the Wasserstein distance for each method on each dataset, with lower values indicating better distributional recovery.
-\begin{table}[h]
+\begin{table}[H]
\centering
\caption{Wasserstein distance by method and dataset. Bold values indicate the best-performing method for each dataset.}
\label{tab:benchmark_wasserstein}
@@ -41,12 +41,12 @@ \subsection{Results}
\toprule
Dataset & Matching & QRF & OLS & QuantReg & MDN \\
\midrule
- space\_ga & 0.011 & \textbf{0.010} & 0.027 & 0.098 & 0.050 \\
- elevators & \textbf{0.0002} & 0.0003 & 0.001 & 0.002 & 0.020 \\
- brazilian\_houses & 120.5 & \textbf{27.2} & 99.4 & 112.4 & 3,378.6 \\
- onlinenewspopularity & \textbf{239.9} & 783.7 & 2,777.1 & 2,376.8 & 2,038.0 \\
- abalone & \textbf{0.003} & 0.003 & 0.004 & 0.003 & 0.040 \\
- house\_sales & \textbf{8,797.8} & 12,576.6 & 41,862.3 & 64,725.3 & 544,730.4 \\
+ \texttt{space\_ga} & 0.011 & \textbf{0.010} & 0.027 & 0.098 & 0.050 \\
+ \texttt{elevators} & \textbf{0.0002} & 0.0003 & 0.001 & 0.002 & 0.020 \\
+ \texttt{brazilian\_houses} & 120.5 & \textbf{27.2} & 99.4 & 112.4 & 3,378.6 \\
+ \texttt{onlinenewspopularity} & \textbf{239.9} & 783.7 & 2,777.1 & 2,376.8 & 2,038.0 \\
+ \texttt{abalone} & \textbf{0.003} & 0.003 & 0.004 & 0.003 & 0.040 \\
+ \texttt{house\_sales} & \textbf{8,797.8} & 12,576.6 & 41,862.3 & 64,725.3 & 544,730.4 \\
\bottomrule
\end{tabular}%
}
@@ -54,7 +54,7 @@ \subsection{Results}
Table~\ref{tab:benchmark_ranks} summarizes the mean rank of each method across all six datasets.
-\begin{table}[h]
+\begin{table}[H]
\centering
\caption{Mean rank across all six benchmarking datasets (lower is better).}
\label{tab:benchmark_ranks}
@@ -71,6 +71,6 @@ \subsection{Results}
\end{tabular}
\end{table}
-Matching achieves the best Wasserstein distance on four of six datasets and the lowest mean rank overall (1.67), followed closely by QRF (1.83). QRF performs best on space\_ga and brazilian\_houses, the latter of which exhibits complex nonlinear relationships between predictors and house prices. OLS and Quantile Regression occupy middle ranks, while MDN consistently ranks last, likely reflecting a combination of the relatively small sample sizes in these datasets and the hyperparameter sensitivity of neural network-based approaches.
+Matching achieves the best Wasserstein distance on four of six datasets and the lowest mean rank overall (1.67), followed closely by QRF (1.83). QRF performs best on \texttt{space\_ga} and \texttt{brazilian\_houses}, the latter of which exhibits complex nonlinear relationships between predictors and house prices. OLS and Quantile Regression occupy middle ranks, while MDN consistently ranks last, likely reflecting a combination of the relatively small sample sizes in these datasets and the hyperparameter sensitivity of neural network-based approaches.
With only six datasets, the rank differences between methods, particularly the narrow gap between Matching (1.67) and QRF (1.83), should be interpreted cautiously; they are not statistically robust to the inclusion or exclusion of individual datasets. The relative rankings here also differ from the main SCF-CPS analysis, where QRF achieves the lowest quantile loss. This is consistent with the expectation that method performance depends on dataset characteristics, and it supports the case for empirically comparing methods on each new dataset rather than relying on a single approach.
diff --git a/paper/sections/appendix_robustness.tex b/paper/sections/appendix_robustness.tex
index fb840e0..64caf1a 100644
--- a/paper/sections/appendix_robustness.tex
+++ b/paper/sections/appendix_robustness.tex
@@ -1,12 +1,12 @@
\section{Predictor Importance Analysis for SCF-CPS Imputation}\label{app:robustness}
-To assess the relative contribution of each predictor variable to the quality of wealth imputation, we conduct two complementary analyses using the QRF model on the SCF data: a leave-one-out analysis and a progressive inclusion analysis. These analyses use six of the seven predictor variables from the main experimental setup; \texttt{own\_children\_in\_household} is excluded because it was not available in the SCF preprocessing for this robustness analysis. The results help evaluate which shared variables between the SCF and CPS are most informative for imputing net worth.
+To assess the relative contribution of each predictor variable to the quality of wealth imputation, we conduct two complementary analyses using the QRF model on the SCF data: a leave-one-out analysis and a progressive inclusion analysis. These analyses use all seven predictor variables from the main experimental setup. The results help evaluate which shared variables between the SCF and CPS are most informative for imputing net worth.
\subsection{Leave-one-out analysis}
-We measure the impact of each predictor by excluding it from the QRF model and observing the resulting increase in average quantile loss relative to the full model (baseline loss: 1,661,723, computed on the original dollar scale rather than the asinh-transformed scale used in Section~5). Table~\ref{tab:leave_one_out} reports the results.
+We measure the impact of each predictor by excluding it from the QRF model and observing the resulting increase in average quantile loss relative to the full model (baseline loss: 1,572,392, computed on the original dollar scale rather than the asinh-transformed scale used in Section~\ref{sec:results}). Table~\ref{tab:leave_one_out} reports the results.
-\begin{table}[h]
+\begin{table}[H]
\centering
\caption{Leave-one-out predictor importance for QRF wealth imputation. Relative impact measures the percentage increase in average quantile loss when the predictor is excluded.}
\label{tab:leave_one_out}
@@ -14,25 +14,26 @@ \subsection{Leave-one-out analysis}
\toprule
Predictor Removed & Avg Quantile Loss & Loss Increase & Relative Impact \\
\midrule
- interest\_dividend\_income & 3,596,108 & 1,934,385 & 116.4\% \\
- employment\_income & 2,219,377 & 557,654 & 33.6\% \\
- age & 2,189,845 & 528,122 & 31.8\% \\
- pension\_income & 1,875,120 & 213,397 & 12.8\% \\
- race & 1,728,080 & 66,358 & 4.0\% \\
- is\_female & 1,698,452 & 36,729 & 2.2\% \\
+ interest\_dividend\_income & 3,240,984 & 1,668,592 & 106.1\% \\
+ employment\_income & 2,011,280 & 438,888 & 27.9\% \\
+ age & 1,948,840 & 376,448 & 23.9\% \\
+ pension\_income & 1,691,464 & 119,072 & 7.6\% \\
+ own\_children\_in\_household & 1,661,722 & 89,330 & 5.7\% \\
+ race & 1,614,550 & 42,158 & 2.7\% \\
+ is\_female & 1,584,438 & 12,046 & 0.8\% \\
\midrule
- Baseline (all predictors) & 1,661,723 & --- & --- \\
+ Baseline (all predictors) & 1,572,392 & --- & --- \\
\bottomrule
\end{tabular}
\end{table}
-Interest and dividend income is by far the most important predictor, with its removal more than doubling the quantile loss (116.4\% increase). Employment income and age contribute substantially as well (33.6\% and 31.8\% increases, respectively). Pension income has a moderate effect (12.8\%), while race and gender contribute relatively little to imputation accuracy (4.0\% and 2.2\%).
+Interest and dividend income is by far the most important predictor, with its removal more than doubling the quantile loss (106.1\% increase). Employment income and age contribute substantially as well (27.9\% and 23.9\% increases, respectively). Pension income has a moderate effect (7.6\%), while own children in household, race, and gender contribute relatively little to imputation accuracy (5.7\%, 2.7\%, and 0.8\%).
\subsection{Progressive inclusion analysis}
We complement the leave-one-out results by adding predictors one at a time, following the importance ordering determined by the leave-one-out analysis (Table~\ref{tab:leave_one_out}), and measuring the marginal improvement at each step. Table~\ref{tab:progressive_inclusion} reports the results.
-\begin{table}[h]
+\begin{table}[H]
\centering
\caption{Progressive predictor inclusion for QRF wealth imputation. Predictors are added in order of importance, and marginal improvement measures the reduction in average quantile loss from adding each predictor.}
\label{tab:progressive_inclusion}
@@ -40,18 +41,19 @@ \subsection{Progressive inclusion analysis}
\toprule
Step & Predictor Added & Avg Quantile Loss & Marginal Improvement \\
\midrule
- 1 & interest\_dividend\_income & 5,037,628 & --- \\
- 2 & age & 2,752,098 & 2,285,529 \\
- 3 & employment\_income & 1,932,222 & 819,876 \\
- 4 & pension\_income & 1,737,197 & 195,025 \\
- 5 & race & 1,704,094 & 33,103 \\
- 6 & is\_female & 1,685,442 & 18,652 \\
+ 1 & interest\_dividend\_income & 5,041,057 & --- \\
+ 2 & age & 2,755,527 & 2,285,529 \\
+ 3 & employment\_income & 1,935,651 & 819,876 \\
+ 4 & pension\_income & 1,740,627 & 195,025 \\
+ 5 & own\_children\_in\_household & 1,636,122 & 104,505 \\
+ 6 & race & 1,588,425 & 47,696 \\
+ 7 & is\_female & 1,572,392 & 16,033 \\
\bottomrule
\end{tabular}
\end{table}
-The progressive analysis confirms the leave-one-out findings. The first three predictors (interest/dividend income, age, and employment income) account for the majority of imputation accuracy, with diminishing returns from additional demographic variables. All six predictors together yield the lowest quantile loss (1,685,442), indicating that each variable contributes positively, though the marginal gains from race and gender are small. The small difference between this value and the leave-one-out baseline (1,661,723) reflects variation across cross-validation fold assignments and random seeds between the two analyses.
+The progressive analysis confirms the leave-one-out findings. The first three predictors (interest/dividend income, age, and employment income) account for the majority of imputation accuracy, with diminishing returns from additional variables. All seven predictors together yield the lowest quantile loss (1,572,392), indicating that each variable contributes positively, though the marginal gains from own children in household, race, and gender are small.
\subsection{Implications for the Conditional Independence Assumption}
-The strong predictive power of the shared financial variables, particularly interest and dividend income, employment income, and pension income, is consistent with, though not sufficient evidence for, the plausibility of the CIA in the SCF-CPS matching context. These variables capture the main dimensions of household financial position available in both surveys. The fact that they collectively explain a large share of the variation in net worth suggests that the common variables $X$ may be sufficient to render the target variable $Y$ (wealth) approximately conditionally independent of variables $Z$ unique to the CPS, though this assumption remains fundamentally untestable as discussed in Section~2.2.
+The strong predictive power of the shared financial variables, particularly interest and dividend income, employment income, and pension income, is consistent with, though not sufficient evidence for, the plausibility of the CIA in the SCF-CPS matching context. These variables capture the main dimensions of household financial position available in both surveys. The fact that they collectively explain a large share of the variation in net worth suggests that the common variables $X$ may be sufficient to render the target variable $Y$ (wealth) approximately conditionally independent of variables $Z$ unique to the CPS, though this assumption remains fundamentally untestable as discussed in Section~\ref{sec:cia}.
diff --git a/paper/sections/background.tex b/paper/sections/background.tex
index ef7cbe0..9b41a54 100644
--- a/paper/sections/background.tex
+++ b/paper/sections/background.tex
@@ -1,4 +1,4 @@
-\section{Background}
+\section{Background}\label{sec:background}
This section defines the statistical matching problem and describes the imputation methods in \texttt{microimpute}. We begin with the formal problem definition and the assumption underlying all statistical matching procedures, then discuss the relationship to missing data mechanisms, and finally describe each of the five imputation methods.
@@ -30,9 +30,9 @@ \subsection{The Conditional Independence Assumption}\label{sec:cia}
This assumption states that the target variable $Y$ (from the donor) and any variables $Z$ unique to the receiver are independent, conditional on the common variables $X$ \citep{dorazio2006statistical}. In other words, once we account for the shared covariates, knowing $Z$ provides no additional information about $Y$.
-The CIA is fundamentally untestable because $Y$ and $Z$ are never jointly observed in either data source. Its plausibility depends on the richness of the common variables $X$. When $X$ captures the key determinants of both $Y$ and $Z$, the assumption is more likely to hold. In practice, researchers must rely on substantive knowledge to assess whether the available common variables are sufficient to render $Y$ and $Z$ conditionally independent.
+The CIA is fundamentally untestable because $Y$ and $Z$ are never jointly observed in either data source. Its plausibility depends on the richness of the common variables $X$. When $X$ captures the key determinants of both $Y$ and $Z$, the assumption is more likely to hold. In practice, researchers must rely on their knowledge to assess whether the available common variables are sufficient to render $Y$ and $Z$ conditionally independent.
-Violations of the CIA lead to biased estimates of the joint distribution of $(Y, Z)$ in the synthetic file. However, if the research question concerns only the marginal distribution of $Y$ in the receiver population, the CIA is not strictly required. What matters is that the conditional distribution $P(Y|X)$ is correctly specified and that $X$ has sufficient overlap between donor and receiver files \citep{dorazio2021statistical}.
+Violations of the CIA lead to biased estimates of the joint distribution of $(Y, Z)$ in the synthetic file. However, if the research question concerns only the marginal distribution of $Y$ in the receiver population, the CIA is not required. What matters is that the conditional distribution $P(Y|X)$ is correctly specified and that $X$ has sufficient overlap between donor and receiver files \citep{dorazio2021statistical}.
\subsection{Missing Data Mechanisms}
@@ -46,9 +46,9 @@ \subsection{Missing Data Mechanisms}
\item \textbf{Missing Not at Random (MNAR)}: The probability of missingness depends on the unobserved values. This would occur if, for example, high-wealth individuals were systematically less likely to appear in the wealth survey.
\end{itemize}
-Under MAR, valid inference about $P(Y|X)$ can be obtained from the donor data alone, which justifies the statistical matching approach. Most imputation methods, including those implemented in \texttt{microimpute}, assume MAR. When MNAR is suspected, sensitivity analyses or methods that explicitly model the selection mechanism may be required \citep{little2002statistical}.
+Under MAR, inference about $P(Y|X)$ can be obtained from the donor data alone, which justifies the statistical matching approach. Most imputation methods, including those implemented in \texttt{microimpute}, assume MAR. When MNAR is suspected, sensitivity analyses or methods that explicitly model the selection mechanism may be required \citep{little2002statistical}.
-In statistical matching applications, an important consideration arises when the donor and receiver files come from surveys with different sampling designs. For instance, wealth surveys often oversample high-net-worth households to improve precision for this rare population, while general household surveys use designs representative of the broader population. This differential sampling can introduce a form of selection that resembles MNAR if not properly addressed. Luckily, survey weights provide a mechanism to mitigate this issue. By incorporating weights that reflect each observation's representativeness of the target population, imputation methods can adjust for known differences in sampling probabilities between the donor and receiver surveys \citep{dugoff2014generalizing}. The \texttt{microimpute} package supports the use of survey weights throughout its imputation pipeline, allowing methods to account for complex survey designs. While survey weights cannot fully address MNAR when missingness depends on unobserved values of $Y$ itself, they can substantially reduce bias arising from differential sampling designs across data sources.
+In statistical matching applications, an important consideration arises when the donor and receiver files come from surveys with different sampling designs. For instance, wealth surveys often oversample high-net-worth households to improve precision for this rare population, while general household surveys use designs representative of the broader population. This differential sampling can introduce a form of selection that resembles MNAR if not properly addressed. Luckily, survey weights provide a mechanism to mitigate this issue. By incorporating weights that reflect each observation's representativeness of the target population, imputation methods can adjust for known differences in sampling probabilities between the donor and receiver surveys \citep{dugoff2014generalizing}. The \texttt{microimpute} package supports the use of survey weights throughout its imputation pipeline, allowing methods to account for complex survey designs. While survey weights cannot fully address MNAR when missingness depends on unobserved values of $Y$ itself, they can reduce bias arising from differential sampling designs across data sources.
\subsection{Imputation Methods}
@@ -60,8 +60,8 @@ \subsubsection{Hot Deck Matching}
Hot deck methods are nonparametric and avoid distributional assumptions, making them robust when the true conditional distribution is unknown or complex \citep{dorazio2006statistical}. However, they face limitations:
\begin{itemize}
- \item \textbf{Donor scarcity}: For receiver observations in sparse regions of the covariate space suitable donors may be unavailable, which can lead to the reuse of the same donors, which can affect the accuracy in the distribution of imputed values
- \item \textbf{Discrete outputs}: Imputed values are restricted to the set of observed donor values, which may not adequately represent the continuous nature of $Y$
+ \item \textbf{Donor scarcity}: For receiver observations in sparse regions of the covariate space suitable donors may be unavailable, which can lead to the reuse of the same donors and affect the accuracy of the distribution of imputed values
+ \item \textbf{Discrete outputs}: Imputed values are restricted to the set of observed donor values, which may not represent the continuous nature of $Y$
\item \textbf{Tail behavior}: Extreme values in the receiver population may have no appropriate donors or poor matches, leading to biased imputations at the tails
\end{itemize}
@@ -105,7 +105,7 @@ \subsubsection{Quantile Regression}
where the check function $\rho_\tau(u) = u(\tau - \mathbf{1}_{u<0})$ penalizes positive and negative residuals asymmetrically.
-The \texttt{microimpute} implementation of Quantile regression also uses the \texttt{statsmodels} library. By fitting models at multiple quantiles, it can approximate the entire conditional distribution of $Y|X$. For imputation, a random quantile $\tau^* \sim \text{Uniform}(0,1)$ can be drawn, and the imputed value computed by interpolating between estimated quantile functions \citep{wei2014multiple}.
+The \texttt{microimpute} implementation of Quantile Regression also uses the \texttt{statsmodels} library. By fitting models at multiple quantiles, it can approximate the entire conditional distribution of $Y|X$. For imputation, a random quantile $\tau^* \sim \text{Uniform}(0,1)$ can be drawn, and the imputed value computed by interpolating between estimated quantile functions \citep{wei2014multiple}.
Quantile regression offers advantages over OLS:
\begin{itemize}
@@ -146,9 +146,9 @@ \subsubsection{Mixture Density Networks (MDN)}
\item \textbf{Computational cost}: Training is more expensive than parametric methods
\end{itemize}
-\subsubsection{Quantile Random Forests (QRF)}\label{sec:qrf_background}
+\subsubsection{Quantile Regression Forests (QRF)}\label{sec:qrf_background}
-Quantile Random Forests extend Random Forests to estimate conditional quantiles \citep{meinshausen2006quantile}. A standard Random Forest builds an ensemble of decision trees, each trained on a bootstrap sample, with predictions averaged across trees. QRF modifies this by retaining all training observations in each terminal node rather than just their mean.
+Quantile Regression Forests extend Random Forests to estimate conditional quantiles \citep{meinshausen2006quantile}. A standard Random Forest builds an ensemble of decision trees, each trained on a bootstrap sample, with predictions averaged across trees. QRF modifies this by retaining all training observations in each terminal node rather than just their mean.
For a new observation with covariates $x$, QRF estimates the conditional distribution function as:
\begin{equation}
@@ -184,20 +184,20 @@ \subsubsection{Quantile Random Forests (QRF)}\label{sec:qrf_background}
\subsection{Current Practice in Microsimulation}
-Statistical matching and data fusion are fundamental operations in microsimulation modeling, yet the methods employed in practice have remained relatively unchanged for decades. A review of major tax-benefit microsimulation models reveals a strong reliance on traditional imputation approaches, primarily hot deck matching and OLS-based regression.
+Statistical matching and data fusion are fundamental operations in microsimulation modeling, yet the methods employed in practice have remained relatively unchanged for decades. A review of major tax-benefit microsimulation models reveals a strong reliance on traditional imputation approaches, primarily Hot Deck Matching and OLS-based regression.
-Hot deck matching remains the dominant approach in European microsimulation. EUROMOD, the EU-wide tax-benefit model, employs a multi-stage imputation procedure combining predictive mean matching with distance-based hot deck methods to integrate consumption data from Household Budget Surveys into its EU-SILC input data \citep{sutherland2013euromod}. Hot deck methods are simple to implement and guarantee that imputed values are actual observed values from the donor file. However, as discussed above, these methods struggle with tail behavior and may not adequately capture the full conditional distribution of the target variable.
+Hot Deck Matching remains the dominant approach in European microsimulation. EUROMOD, the EU-wide tax-benefit model, employs a multi-stage imputation procedure combining predictive mean matching with distance-based hot deck methods to integrate consumption data from Household Budget Surveys into its EU-SILC input data \citep{sutherland2013euromod}. Hot deck methods are simple to implement and guarantee that imputed values are actual observed values from the donor file. However, as discussed above, these methods struggle with tail behavior and may not capture the full conditional distribution of the target variable.
-In U.S. tax policy microsimulation, regression-based approaches are more common. The Tax Policy Center employs a two-stage probit and OLS procedure for wealth imputation, first predicting the probability of holding each asset type, then predicting amounts conditional on positive holdings \citep{nunns2012tax}. Similarly, the Institute on Taxation and Economic Policy (ITEP) model relies on statistical matching between tax return data and the American Community Survey, supplemented with regression-based imputations from the Survey of Consumer Finances \citep{itep2023model}. These regression approaches assume linear relationships and normally distributed errors, assumptions frequently violated by economic variables with heavy tails and heteroscedasticity.
+In U.S. tax policy microsimulation, regression-based approaches are more common. The Tax Policy Center employs a two-stage probit and OLS procedure for wealth imputation, first predicting the probability of holding each asset type, then predicting amounts conditional on positive holdings \citep{nunns2012tax}. Similarly, the Institute on Taxation and Economic Policy (ITEP) model relies on matching tax return data to the American Community Survey, supplemented with regression-based imputations from the Survey of Consumer Finances \citep{itep2023model}. These regression approaches assume linear relationships and normally distributed errors, assumptions frequently violated by economic variables with heavy tails and heteroscedasticity.
More recent microsimulation efforts have begun incorporating administrative data through record linkage rather than statistical matching \citep{abowd2019census}, but this approach requires access to restricted data and raises privacy concerns. For researchers working with publicly available survey data, statistical matching remains the primary option, and there is room for methods that capture distributional features more effectively.
-These limitations are especially pronounced for heavy-tailed variables where the relationship with predictors varies across the distribution. Machine learning methods such as Quantile Random Forests can capture nonlinear relationships, model the entire conditional distribution, and handle heavy-tailed data without restrictive parametric assumptions, yet they have seen limited adoption in microsimulation practice. The \texttt{microimpute} package provides a common framework for comparing traditional and machine learning approaches, so that researchers can empirically evaluate which method works best for their data.
+These limitations are especially pronounced for heavy-tailed variables where the relationship with predictors varies across the distribution. Machine learning methods such as Quantile Regression Forests can capture nonlinear relationships, model the entire conditional distribution, and handle heavy-tailed data without restrictive parametric assumptions, yet they have seen limited adoption in microsimulation practice. The \texttt{microimpute} package provides a common framework for comparing traditional and machine learning approaches, so that researchers can empirically evaluate which method works best for their data.
\subsection{Supplemental Security Income as a Validation Case}
-The limitations of traditional imputation approaches have concrete consequences for downstream policy analysis. The Supplemental Security Income (SSI) program illustrates this well. SSI is a federal means-tested program for aged, blind, and disabled individuals with strict resource limits (\$2,000 for individuals, \$3,000 for couples) that have remained unchanged since 1989 \citep{ssa2023ssi}. The resource test requires household wealth and asset data that the CPS does not collect, making SSI eligibility determination dependent on imputed or heuristic wealth values.
+The limitations of traditional imputation approaches have consequences for downstream policy analysis. The Supplemental Security Income (SSI) program illustrates this well. SSI is a federal means-tested program for aged, blind, and disabled individuals with strict resource limits (\$2,000 for individuals, \$3,000 for couples) that have remained unchanged since 1989 \citep{ssa2023ssi}. The resource test requires household wealth and asset data that the CPS does not collect, making SSI eligibility determination dependent on imputed or heuristic wealth values.
-In 2024, SSI served approximately 7.4 million recipients with \$59.6 billion in federal payments \citep{ssa2024ssi}. Because different wealth imputation methods produce different wealth distributions, they directly affect which simulated households pass the resource test and therefore the resulting estimates of SSI recipient counts and expenditure. This makes SSI a particularly informative case for comparing imputation approaches, as described in Section~\ref{sec:policy_validation}.
+In 2024, SSI served approximately 7.4 million recipients with \$59.6 billion in federal payments \citep{ssa2024ssi}. Because different wealth imputation methods produce different wealth distributions, method choice affects which simulated households pass the resource test and therefore the resulting estimates of SSI recipient counts and expenditure. This makes SSI a particularly informative case for comparing imputation approaches, as described in Section~\ref{sec:policy_validation}.
-The frozen resource limits also make SSI a compelling case for policy reform analysis. In 2024 dollars, the original 1989 thresholds of \$2,000/\$3,000 are worth approximately \$4,800/\$7,200, meaning the resource test has become substantially more restrictive over time without any legislative change. The SSI Savings Penalty Elimination Act (S.~1234 / H.R.~2540), a bipartisan bill introduced in April 2025, proposes raising these limits to \$10,000 for individuals and \$20,000 for couples, with future CPI indexing \citep{ssi_spea_2025}. Simulating the impact of this reform, and determining which additional households would gain eligibility under the higher thresholds requires household-level wealth data, making it a natural application for cross-survey imputation. As we show in Section~\ref{sec:policy_validation}, the choice of imputation method produces meaningfully different estimates of this reform's impact, meaning that imputation is not merely a data preprocessing step but a modeling choice with real consequences for policy analysis.
+The frozen resource limits also make SSI a compelling case for policy reform analysis. In 2024 dollars, the original 1989 thresholds of \$2,000/\$3,000 are worth approximately \$4,800/\$7,200, meaning the resource test has become substantially more restrictive over time without any legislative change. The SSI Savings Penalty Elimination Act (S.~1234 / H.R.~2540), a bipartisan bill introduced in April 2025, proposes raising these limits to \$10,000 for individuals and \$20,000 for couples, with future CPI indexing \citep{ssi_spea_2025}. Simulating the impact of this reform, and determining which additional households would gain eligibility under the higher thresholds requires household-level wealth data, making it a natural application for cross-survey imputation. As we show in Section~\ref{sec:policy_validation}, the choice of imputation method produces different estimates of this reform's impact, meaning that imputation is not merely a data preprocessing step but a modeling choice with real consequences for policy analysis.
diff --git a/paper/sections/conclusion.tex b/paper/sections/conclusion.tex
index 362be7b..88f2e29 100644
--- a/paper/sections/conclusion.tex
+++ b/paper/sections/conclusion.tex
@@ -1,7 +1,7 @@
-\section{Conclusion}
+\section{Conclusion}\label{sec:conclusion}
-This paper has introduced $\texttt{microimpute}$, an open-source Python package for cross-survey imputation, and applied it to a substantive policy problem: imputing household wealth from the SCF onto the CPS. Comparing five imputation methods with an inverse hyperbolic sine transformation to accommodate negative and zero net worth values, we find that Quantile Random Forests achieve the strongest conditional accuracy for wealth imputation, owing to their ability to model the non-linear relationships between demographic predictors and wealth. A downstream SSI simulation confirms the practical importance of method choice. Without wealth data, the microsimulation overestimates SSI recipients by 167\%, while imputation-based approaches substantially narrow this gap. Simulating the SSI Savings Penalty Elimination Act, which would raise resource limits from \$2,000/\$3,000 to \$10,000/\$20,000, further shows that method choice directly affects policy estimates. Reform impact estimates range from 0.1 to 4.2 million additional recipients and \$1.0 to \$24.1 billion in additional expenditure depending on the imputation method. Without imputed wealth, this reform cannot be simulated at all.
+This paper has introduced \texttt{microimpute}, an open-source Python package for cross-survey imputation, and applied it to a practical policy problem: imputing household wealth from the SCF onto the CPS. Comparing five imputation methods with an inverse hyperbolic sine transformation to accommodate negative and zero net worth values, we find that Quantile Regression Forests achieve the strongest conditional accuracy for wealth imputation, owing to their ability to model the nonlinear relationships between demographic predictors and wealth. A downstream SSI simulation confirms the importance of method choice. Without wealth data, the microsimulation overestimates SSI recipients by 167\%, while imputation-based approaches narrow this gap. Simulating the SSI Savings Penalty Elimination Act, which would raise resource limits from \$2,000/\$3,000 to \$10,000/\$20,000, further shows that method choice directly affects policy estimates. Reform impact estimates range from 0.1 to 4.2 million additional recipients and \$1.0 to \$24.1 billion in additional expenditure depending on the imputation method. Without imputed wealth, this reform cannot be simulated at all.
The findings also reveal nuances about method selection. Cross-dataset benchmarking shows that QRF's advantage reflects the specific characteristics of the wealth imputation problem rather than a universal superiority, and predictor importance analysis confirms that financial variables drive the majority of imputation accuracy.
-Two broader implications follow. First, imputation method selection should be empirically driven rather than prescribed; the optimal approach depends on dataset characteristics, and standardized comparison tools are needed to support this. Second, the gap between statistical and policy-relevant evaluation metrics (QRF achieves the best quantile loss yet not the closest SSI estimates to administrative totals) points to the importance of validating imputation quality through downstream applications, not only through statistical benchmarks. Future work should expand $\texttt{microimpute}$'s method library to include gradient boosting and deep learning approaches \citep{alaa2024deep}, explore ensemble strategies that combine methods across different parts of the distribution, and address the terminal node sparsity problem that limits tree-based methods at extreme quantiles.
\ No newline at end of file
+Two broader implications follow. First, imputation method selection should be empirically driven rather than prescribed; the optimal approach depends on dataset characteristics, and standardized comparison tools are needed to support this. Second, the gap between statistical and policy-relevant evaluation metrics (QRF achieves the best quantile loss yet not the closest SSI estimates to administrative totals) points to the importance of validating imputation quality through downstream applications, not only through statistical benchmarks. Future work should expand \texttt{microimpute}'s method library to include gradient boosting and deep learning approaches \citep{alaa2024deep}, explore ensemble strategies that combine methods across different parts of the distribution, and address the terminal node sparsity problem that limits tree-based methods at extreme quantiles.
\ No newline at end of file
diff --git a/paper/sections/data.tex b/paper/sections/data.tex
index d51902a..83fabf3 100644
--- a/paper/sections/data.tex
+++ b/paper/sections/data.tex
@@ -10,10 +10,10 @@ \subsection{Survey of Consumer Finances}
\subsection{Current Population Survey}
-The Current Population Survey, conducted jointly by the U.S. Census Bureau and the Bureau of Labor Statistics, is a monthly survey of approximately 60,000 U.S. households and is the primary source of labor force statistics for the United States. The CPS uses a multistage probability-based sample designed to represent the civilian non-institutional population; on average, each sampled household represents approximately 2,500 households in the population. The Annual Social and Economic Supplement (ASEC) extends the core survey with detailed annual income data, including earnings, unemployment compensation, Social Security, pension income, interest, dividends, and other income sources. However, despite its broad coverage of income and employment, the CPS does not collect information on household wealth, assets, or liabilities, which are needed for wealth-based policy analysis. This omission motivates the need for statistical matching to transfer wealth information from the SCF onto the CPS.
+The Current Population Survey, conducted jointly by the U.S. Census Bureau and the Bureau of Labor Statistics, is a monthly survey of approximately 60,000 U.S. households and is the primary source of labor force statistics for the United States. The CPS uses a multistage probability-based sample designed to represent the civilian non-institutional population; on average, each sampled household represents approximately 2,500 households in the population. The Annual Social and Economic Supplement (ASEC) extends the survey with detailed annual income data, including earnings, unemployment compensation, Social Security, pension income, interest, dividends, and other income sources. However, despite its broad coverage of income and employment, the CPS does not collect information on household wealth, assets, or liabilities, which are needed for wealth-based policy analysis. This omission motivates the need for statistical matching to transfer wealth information from the SCF onto the CPS.
Specifically, we use the Enhanced CPS 2024 produced by PolicyEngine \citep{policyengine_us} as our receiver dataset. The Enhanced CPS extends the base CPS ASEC microdata through survey reweighting and calibration to administrative totals, improving its representativeness for tax-benefit microsimulation. The SCF 2022 financial variables are uprated to 2024 dollars using CPI adjustment factors to ensure consistency with the receiver dataset's reference year.
\subsection{Comparative analysis and characteristics for imputation}
-The SCF and CPS differ fundamentally in sampling design: the SCF employs a dual-frame approach combining a standard area-probability sample with a list sample that deliberately oversamples wealthy households, while the CPS uses a multistage area-probability household design representative of the civilian non-institutional population. This difference means that the donor and receiver surveys weight different parts of the wealth distribution differently, making proper survey weight integration during model training essential for unbiased imputation. The two surveys share a core set of demographic and income variables (age, sex, race, number of children, employment income, interest and dividend income, and pension income) but differ in detailed coverage: the SCF collects granular asset and liability data absent from the CPS, while the CPS captures labor force dynamics and program participation variables not available in the SCF. This partial overlap constrains the conditioning set available for imputation and reinforces the importance of the conditional independence assumption discussed in Section~\ref{sec:cia}. The contrasting survey designs, the heavy-tailed nature of wealth, and the limited variable overlap make the SCF-to-CPS imputation an informative test case for comparing methods. It is also directly relevant to U.S. policy microsimulation, where analyzing the distributional effects of tax and benefit reforms requires microdata that combine income, demographics, and wealth.
\ No newline at end of file
+The SCF and CPS differ in sampling design: the SCF employs a dual-frame approach combining a standard area-probability sample with a list sample that deliberately oversamples wealthy households, while the CPS uses a multistage area-probability household design representative of the civilian non-institutional population. This difference means that the donor and receiver surveys weight different parts of the wealth distribution differently, making proper survey weight integration during model training essential for unbiased imputation. The two surveys share a core set of demographic and income variables (age, sex, race, number of children, employment income, interest and dividend income, and pension income) but differ in detailed coverage: the SCF collects asset and liability data absent from the CPS, while the CPS captures labor force dynamics and program participation variables not available in the SCF. This partial overlap constrains the conditioning set available for imputation and reinforces the importance of the conditional independence assumption discussed in Section~\ref{sec:cia}. The contrasting survey designs, the heavy-tailed nature of wealth, and the limited variable overlap make the SCF-to-CPS imputation an informative test case for comparing methods. It is also directly relevant to U.S. policy microsimulation, where analyzing the distributional effects of tax and benefit reforms requires microdata that combine income, demographics, and wealth.
\ No newline at end of file
diff --git a/paper/sections/disclosures.tex b/paper/sections/disclosures.tex
new file mode 100644
index 0000000..53a97e5
--- /dev/null
+++ b/paper/sections/disclosures.tex
@@ -0,0 +1,15 @@
+\section*{Acknowledgements and Disclosures}
+
+\subsection*{Conflict of Interest}
+The authors declare no conflicts of interest.
+
+\subsection*{Funding}
+This work received no external funding.
+
+\subsection*{Data and Code Availability}
+\begin{sloppypar}
+The \texttt{microimpute} package is open-source and available at \url{https://github.com/PolicyEngine/microimpute}. The 2022 Survey of Consumer Finances is publicly available from the Federal Reserve Board (\url{https://www.federalreserve.gov/econres/scfindex.htm}). Current Population Survey data are publicly available from the U.S. Census Bureau (\url{https://www.census.gov/programs-surveys/cps.html}). The Enhanced CPS 2024 dataset used in this study is produced by PolicyEngine and available through the \texttt{policyengine-us-data} package (\url{https://github.com/PolicyEngine/policyengine-us-data}). The Jupyter notebook that reproduces all results presented in this paper is available in the repository at \url{https://github.com/PolicyEngine/microimpute/blob/main/paper/imputing-from-scf-to-cps.ipynb}.
+\end{sloppypar}
+
+\subsection*{Use of Generative AI}
+Generative AI (Claude, Anthropic) was used to assist with code development and manuscript editing. The authors reviewed and take full responsibility for all content.
diff --git a/paper/sections/discussion.tex b/paper/sections/discussion.tex
index 3600d45..9706977 100644
--- a/paper/sections/discussion.tex
+++ b/paper/sections/discussion.tex
@@ -1,28 +1,28 @@
-\section{Discussion}
+\section{Discussion}\label{sec:discussion}
-This paper has evaluated five imputation methods within the \texttt{microimpute} framework, finding that Quantile Random Forests offer meaningful advantages for the SCF-to-CPS wealth imputation application. By preserving the full conditional distribution of wealth, QRF captures statistical properties of wealth data that traditional methods miss.
+This paper has evaluated five imputation methods within the \texttt{microimpute} framework, finding that Quantile Regression Forests offer advantages for the SCF-to-CPS wealth imputation application. By preserving the full conditional distribution of wealth, QRF captures statistical properties of wealth data that traditional methods miss.
\subsection{The role of \texttt{microimpute} in the analysis}
-Several design choices in \texttt{microimpute} shaped the analysis and its results. Wrapping all five methods behind a consistent API meant that performance differences in the benchmarking reflect the methods themselves, not differences in how they were implemented or tuned \citep{policyengine2025microimpute}. The \texttt{autoimpute} function automated hyperparameter tuning and method selection based on quantile loss, removing a subjective step that could otherwise bias the comparison. Using quantile loss rather than RMSE as the evaluation metric was itself consequential: its asymmetric penalty structure prioritizes accuracy at distribution tails, where symmetric metrics are insensitive to the kinds of errors that matter most for skewed variables like wealth.
+Several design choices in \texttt{microimpute} shaped the analysis and its results. Wrapping all five methods behind a consistent API meant that performance differences in the benchmarking reflect the methods themselves, not differences in how they were implemented or tuned \citep{policyengine2025microimpute}. The \texttt{autoimpute} function automated hyperparameter tuning and method selection based on quantile loss, removing a subjective step that could otherwise bias the comparison. Using quantile loss rather than RMSE as the evaluation metric was also consequential: its asymmetric penalty structure prioritizes accuracy at distribution tails, where symmetric metrics are insensitive to the kinds of errors that matter most for skewed variables like wealth.
-Two practical aspects also mattered. First, native survey weight support through stratified sampling allowed the models to train on data representative of the U.S. population despite the SCF's deliberate oversampling of wealthy households. Second, the full cross-validation pipeline, including hyperparameter tuning on the SCF for the QRF, MDN, and Matching models ran in under 45 minutes on standard hardware, making iterative experimentation practical. The package is open-source, so all algorithms and evaluation procedures can be inspected and modified \citep{policyengine2025microimpute}.
+Two practical aspects also mattered. First, native survey weight support through stratified sampling allowed the models to train on data representative of the U.S. population despite the SCF's deliberate oversampling of wealthy households. Second, the full cross-validation pipeline, including hyperparameter tuning on the SCF for the QRF, MDN, and Matching models, ran in under 90 minutes on standard hardware, making iterative experimentation practical. The package is open-source, so all algorithms and evaluation procedures can be inspected and modified \citep{policyengine2025microimpute}.
\subsection{Generalizability and predictor sensitivity}
Two supplementary analyses help contextualize the main SCF-CPS results.
-The cross-dataset benchmarking exercise (Appendix~\ref{app:benchmarking}) shows that method performance is context-dependent. QRF achieves the best Wasserstein distance on datasets with complex non-linear relationships, such as the Brazilian houses dataset and the SCF wealth imputation. Matching, by contrast, achieves the lowest Wasserstein distance on four of six benchmarking datasets and the best mean rank overall (1.67 vs.\ QRF's 1.83). This strong marginal performance follows from Matching's mechanism: drawing imputed values directly from the donor pool inherently preserves the shape and tail behavior of the original distribution, yielding low Wasserstein distances even when the conditioning on predictor values is suboptimal. But as the main SCF-CPS results show, good marginal distributions do not guarantee accurate conditional imputation. Households may receive plausible-looking wealth values that do not correctly reflect their individual characteristics. The trade-off between marginal and conditional accuracy, and the effect of differing survey designs on record matching, deserve careful attention in any application.
+The cross-dataset benchmarking exercise (Appendix~\ref{app:benchmarking}) shows that method performance is context-dependent. QRF achieves the best Wasserstein distance on datasets with complex nonlinear relationships, such as the Brazilian houses dataset and the SCF wealth imputation. Matching, by contrast, achieves the lowest Wasserstein distance on four of six benchmarking datasets and the best mean rank overall (1.67 vs.\ QRF's 1.83). This strong marginal performance follows from Matching's mechanism: drawing imputed values directly from the donor pool inherently preserves the shape and tail behavior of the original distribution, yielding low Wasserstein distances even when the conditioning on predictor values is suboptimal. But as the main SCF-CPS results show, good marginal distributions do not guarantee accurate conditional imputation. Households may receive plausible-looking wealth values that do not correctly reflect their individual characteristics. The trade-off between marginal and conditional accuracy, and the effect of differing survey designs on record matching, deserve careful attention in any application.
-OLS performs competitively on datasets where the predictor-target relationship is approximately linear (e.g., abalone, space\_ga), confirming that simpler parametric methods remain effective when their structural assumptions hold. MDN consistently ranks last across the benchmarking datasets, likely reflecting a combination of the relatively small sample sizes in these datasets and the hyperparameter sensitivity of neural network-based approaches, which require larger training sets to realize their flexibility advantage.
+OLS performs competitively on datasets where the predictor-target relationship is approximately linear (e.g., \texttt{abalone}, \texttt{space\_ga}), confirming that simpler parametric methods remain effective when their structural assumptions hold. MDN consistently ranks last across the benchmarking datasets, likely reflecting a combination of the relatively small sample sizes in these datasets and the hyperparameter sensitivity of neural network-based approaches, which require larger training sets to realize their flexibility advantage.
No single method dominates across all settings. The best choice depends on dataset size, the complexity of the predictor-target relationship, and whether the research question calls for conditional accuracy or marginal distributional fidelity. This is precisely why automated comparison matters: researchers should test methods on their own data rather than defaulting to any one approach.
-The predictor importance analysis (Appendix~\ref{app:robustness}) reveals a clear hierarchy among the variables shared between the SCF and CPS. Financial predictors, particularly interest and dividend income, employment income, and age, account for the vast majority of imputation accuracy, with interest and dividend income alone more than doubling the quantile loss when removed. Demographic variables such as race and gender contribute relatively little to imputation quality. This concentration of predictive power in financial variables has two practical implications. First, the quality of wealth imputation rests primarily on the availability and accuracy of income-related variables in both surveys; researchers lacking financial predictors would see substantially degraded results. Second, diminishing returns from additional demographic predictors suggest that a parsimonious set of well-chosen financial variables can achieve most of the attainable accuracy, as confirmed by the progressive inclusion analysis showing that the first three predictors capture the majority of achievable performance. That said, demographic variables still provide incremental improvements and should not be excluded without reason.
+The predictor importance analysis (Appendix~\ref{app:robustness}) reveals a clear hierarchy among the variables shared between the SCF and CPS. Financial predictors, particularly interest and dividend income, employment income, and age, account for the vast majority of imputation accuracy, with interest and dividend income alone more than doubling the quantile loss when removed. Demographic variables such as race and gender contribute relatively little to imputation quality. This concentration of predictive power in financial variables has two practical implications. First, the quality of wealth imputation rests primarily on the availability and accuracy of income-related variables in both surveys; researchers lacking financial predictors would see degraded results. Second, diminishing returns from additional demographic predictors suggest that a set of well-chosen financial variables can achieve most of the attainable accuracy, as confirmed by the progressive inclusion analysis showing that the first three predictors capture the majority of achievable performance. That said, demographic variables still provide incremental improvements and should not be excluded without reason.
The predictor importance and progressive inclusion tools in \texttt{microimpute} let researchers assess which variables drive imputation performance in their specific context and make informed decisions about variable selection when data are limited.
-Together, these supplementary analyses put the main results in perspective. QRF's strong performance in the SCF-CPS setting reflects the particular characteristics of the wealth imputation problem, namely a large donor dataset, highly non-linear relationships, and informative financial predictors available in both surveys. Researchers applying \texttt{microimpute} to other settings should expect method rankings to vary with dataset characteristics.
+Together, these supplementary analyses put the main results in perspective. QRF's strong performance in the SCF-CPS setting reflects the particular characteristics of the wealth imputation problem, namely a large donor dataset, highly nonlinear relationships, and informative financial predictors available in both surveys. Researchers applying \texttt{microimpute} to other settings should expect method rankings to vary with dataset characteristics.
\subsection{Reform analysis and policy uncertainty}
@@ -44,6 +44,6 @@ \subsubsection{QRF-specific challenges}
\subsubsection{Missing data assumptions}
-All imputation methods in this study operate under the assumption that wealth is missing at random (MAR) conditional on the shared predictors $X$, as formalized in Section~\ref{sec:cia}. This assumption may be violated in practice: wealthy individuals may be less likely to participate in surveys or may underreport assets, introducing missing-not-at-random (MNAR) patterns that the conditioning variables cannot fully account for \citep{andridge2010review}. The predictor exclusion analysis in Appendix~\ref{app:robustness} provides a partial sensitivity check on the plausibility of the MAR assumption. The substantial degradation in imputation quality when financial predictors are removed, particularly the 116\% increase in quantile loss when interest and dividend income is excluded, indicates that the conditioning set is doing meaningful work in explaining wealth variation, consistent with MAR plausibility. However, this analysis cannot rule out residual dependence on unobserved factors. More formal MNAR sensitivity analyses, such as pattern-mixture models or selection models applied to the imputation framework, are a natural next step. Researchers applying \texttt{microimpute} to settings where nonresponse or selection effects are suspected should consider supplementary diagnostics to assess the sensitivity of their results to departures from MAR.
+All imputation methods in this study operate under the assumption that wealth is missing at random (MAR) conditional on the shared predictors $X$, as formalized in Section~\ref{sec:cia}. This assumption may be violated in practice: wealthy individuals may be less likely to participate in surveys or may underreport assets, introducing missing-not-at-random (MNAR) patterns that the conditioning variables cannot fully account for \citep{andridge2010review}. The predictor exclusion analysis in Appendix~\ref{app:robustness} provides a partial sensitivity check on the plausibility of the MAR assumption. The substantial degradation in imputation quality when financial predictors are removed, particularly the 106\% increase in quantile loss when interest and dividend income is excluded, indicates that the conditioning set is doing meaningful work in explaining wealth variation, consistent with MAR plausibility. However, this analysis cannot rule out residual dependence on unobserved factors. More formal MNAR sensitivity analyses, such as pattern-mixture models or selection models applied to the imputation framework, are a natural next step. Researchers applying \texttt{microimpute} to settings where nonresponse or selection effects are suspected should consider supplementary diagnostics to assess the sensitivity of their results to departures from MAR.
These extensions would broaden the range of problems \texttt{microimpute} can address while preserving its current simplicity.
\ No newline at end of file
diff --git a/paper/sections/introduction.tex b/paper/sections/introduction.tex
index 864fe41..4dd5c00 100644
--- a/paper/sections/introduction.tex
+++ b/paper/sections/introduction.tex
@@ -1,19 +1,19 @@
-\section{Introduction}
+\section{Introduction}\label{sec:introduction}
Statistical matching, also known as data fusion or full variable imputation, combines information from multiple data sources that share common variables but contain different samples of units \citep{dorazio2006statistical}, a situation common across empirical research fields. In its simplest form, the problem involves a donor dataset containing both shared and unique variables and a receiver dataset containing only the shared variables, where the goal is to impute the missing variables for observations in the receiver file based on their shared characteristics \citep{dorazio2021statistical}. This framework generalizes traditional missing data imputation by recognizing that ``missingness'' can arise not only from nonresponse within a single survey but also from the structural absence of variables across distinct data sources.
Statistical matching is widely applicable in the social sciences, particularly in microsimulation modeling, where policy analysis often requires combining detailed demographic information from one survey with economic variables from another \citep{bourguignon2006microsimulation}. For instance, household surveys may capture income and consumption patterns but lack wealth data, while financial surveys provide wealth information for different samples. Constructing synthetic files that combine these variables allows more detailed policy analysis than either source alone.
-The main methodological difficulty is accurately modeling the conditional distribution of the target variable given shared predictors, as different approaches make different assumptions about this relationship. Parametric methods may be too restrictive for economic variables with heavy tails and heteroscedasticity, while nonparametric and machine learning approaches are more flexible but also more complex \citep{meinshausen2006quantile, andridge2010review}. Section~2 reviews these trade-offs in detail.
+The main methodological difficulty is accurately modeling the conditional distribution of the target variable given shared predictors, as different approaches make different assumptions about this relationship. Parametric methods may be too restrictive for economic variables with heavy tails and heteroscedasticity, while nonparametric and machine learning approaches are more flexible but also more complex \citep{meinshausen2006quantile, andridge2010review}. Section~\ref{sec:background} reviews these trade-offs in detail.
-This paper presents the \texttt{microimpute} package, a Python library implementing five statistical matching methods: Hot Deck Matching, Ordinary Least Squares, Quantile Regression, Mixture Density Networks, and Quantile Random Forests. The package provides a framework for comparing these methods through systematic benchmarking, with automated model selection based on quantile loss performance. We demonstrate the methodology through an application to wealth imputation, transferring net worth data from the Survey of Consumer Finances to the Current Population Survey. This task exemplifies the challenges of statistical matching for heavy-tailed distributions.
+This paper presents the \texttt{microimpute} package, a Python library implementing five statistical matching methods: Hot Deck Matching, Ordinary Least Squares, Quantile Regression, Mixture Density Networks, and Quantile Regression Forests. The package provides a framework for comparing these methods through systematic benchmarking, with automated model selection based on quantile loss performance. We demonstrate the methodology through an application to wealth imputation, transferring net worth data from the Survey of Consumer Finances to the Current Population Survey. This task exemplifies the challenges of statistical matching for heavy-tailed distributions.
This work provides the following contributions:
\begin{itemize}
\item An open-source implementation of five imputation methods under a common interface, allowing systematic comparison across methods
\item An automated benchmarking pipeline that evaluates distributional accuracy using quantile loss, so that researchers can select the most appropriate method for their data
- \item Empirical evidence on the relative performance of these methods for wealth imputation, suggesting that Quantile Random Forests are well-suited to heavy-tailed distributions, though method choice remains context-dependent
- \item A policy reform simulation of the SSI Savings Penalty Elimination Act, showing that imputation method choice produces meaningfully different estimates of reform impact, and that without imputed wealth data, such reforms cannot be simulated at all
+ \item Empirical evidence on the relative performance of these methods for wealth imputation, suggesting that Quantile Regression Forests are well-suited to heavy-tailed distributions, though method choice remains context-dependent
+ \item A policy reform simulation of the SSI Savings Penalty Elimination Act, showing that imputation method choice produces different estimates of reform impact, and that without imputed wealth data, such reforms cannot be simulated at all
\end{itemize}
-The remainder of this paper is organized as follows. Section 2 reviews the statistical matching problem, including its formal definition, the conditional independence assumption that underlies all matching methods, and the five imputation approaches implemented in \texttt{microimpute}. Section 3 describes our data sources. Section 4 presents the package architecture and benchmarking methodology. Section 5 reports empirical results from the wealth imputation application. Section 6 discusses implications and limitations, and Section 7 concludes.
\ No newline at end of file
+The remainder of this paper is organized as follows. Section~\ref{sec:background} reviews the statistical matching problem, including its formal definition, the conditional independence assumption that underlies all matching methods, and the five imputation approaches implemented in \texttt{microimpute}. Section~\ref{sec:data} describes our data sources. Section~\ref{sec:methodology} presents the package architecture and benchmarking methodology. Section~\ref{sec:results} reports empirical results from the wealth imputation application. Section~\ref{sec:discussion} discusses implications and limitations, and Section~\ref{sec:conclusion} concludes.
\ No newline at end of file
diff --git a/paper/sections/methodology.tex b/paper/sections/methodology.tex
index 6623906..5a0edc7 100644
--- a/paper/sections/methodology.tex
+++ b/paper/sections/methodology.tex
@@ -1,12 +1,12 @@
\section{Methodology}\label{sec:methodology}
-\subsection{$\texttt{microimpute}$ package implementation}
+\subsection{\texttt{microimpute} package implementation}
-$\texttt{microimpute}$\footnote{Documentation, implementation details, and usage examples are available at https://policyengine.github.io/microimpute/.} is an open-source Python framework for statistical matching that provides a common interface for imputing variables across survey datasets using multiple methods. While several imputation approaches exist individually, researchers have lacked a standardized tool for comparing their distributional performance on a given dataset and automatically selecting the best approach. In this study, \texttt{microimpute} is both a methodological contribution and the analytical engine behind the wealth imputation experiments described below.
+\texttt{microimpute}\footnote{Documentation, implementation details, and usage examples are available at \url{https://policyengine.github.io/microimpute/}.} is an open-source Python framework for statistical matching that provides a common interface for imputing variables across survey datasets using multiple methods. While several imputation approaches exist individually, researchers have lacked a standardized tool for comparing their distributional performance on a given dataset and automatically selecting the best approach. In this study, \texttt{microimpute} is both a methodological contribution and the analytical engine behind the wealth imputation experiments described below.
\subsubsection{Core capabilities}
-The package currently supports five imputation methods: Hot Deck Matching, Ordinary Least Squares Linear Regression (OLS), Quantile Regression, Quantile Random Forests (QRF), and Mixture Density Networks (MDN). The package is modular, so additional imputation methods can be added without modifying the existing codebase.
+The package currently supports five imputation methods: Hot Deck Matching, Ordinary Least Squares Linear Regression (OLS), Quantile Regression, Quantile Regression Forests (QRF), and Mixture Density Networks (MDN). The package is modular, so additional imputation methods can be added without modifying the existing codebase.
\subsubsection{Key features}
@@ -29,7 +29,7 @@ \subsection{Evaluation framework}
\mathcal{L}_\tau = \rho_\tau(y - \hat{Q}_\tau(y|x)) = (y - \hat{Q}_\tau(y|x)) \cdot (\tau - \mathbf{1}_{y < \hat{Q}_\tau(y|x)})
\end{equation}
-Under-prediction of an upper-tail quantile is penalized at rate $\tau$, whereas over-prediction is penalized at rate $1 - \tau$. This asymmetric structure captures directional bias, which matters when imputing highly skewed variables like wealth, where large under-estimates in the right tail must be discouraged more strongly than equal-sized over-estimates \citep{koenker1978regression}. Compared with mean-squared or mean-absolute error, which penalize errors symmetrically, quantile loss directly targets the conditional distribution and remains robust to outliers \citep{ghenis2018quantile}. Averaging over multiple quantiles $\tau \in \{0.1, 0.2, \ldots, 0.9\}$ summarizes how well the method estimates the conditional distribution across its entire range. Lower average quantile loss indicates better distributional calibration. Because quantile loss is not scale-invariant, the absolute values reported in Section~5 reflect the scale transformation applied; we supplement raw values with relative improvement percentages to aid interpretability.
+Under-prediction of an upper-tail quantile is penalized at rate $\tau$, whereas over-prediction is penalized at rate $1 - \tau$. This asymmetric structure captures directional bias, which matters when imputing highly skewed variables like wealth, where large under-estimates in the right tail must be discouraged more strongly than equal-sized over-estimates \citep{koenker1978regression}. Compared with mean-squared or mean-absolute error, which penalize errors symmetrically, quantile loss targets the conditional distribution and remains robust to outliers \citep{ghenis2018quantile}. Averaging over multiple quantiles $\tau \in \{0.1, 0.2, \ldots, 0.9\}$ summarizes how well the method estimates the conditional distribution across its entire range. Lower average quantile loss indicates better distributional calibration. Because quantile loss is not scale-invariant, the absolute values reported in Section~5 reflect the scale transformation applied; we supplement raw values with relative improvement percentages to aid interpretability.
As a complementary metric, we use the Wasserstein distance (also known as the earth mover's distance) to measure overall distributional similarity between imputed and reference distributions. Formally, for one-dimensional distributions $P$ and $Q$:
\begin{equation}
@@ -44,7 +44,7 @@ \subsection{Experimental setup}\label{sec:experimental_setup}
The \texttt{autoimpute} function orchestrates the full imputation pipeline in a single call: it tunes hyperparameters for applicable methods using the Optuna framework \citep{akiba2019optuna}, evaluates all methods through $k$-fold cross-validation on the donor data, and automatically selects the best-performing one to impute onto the receiver dataset. Using this pipeline, we evaluate all five imputation methods (QRF, OLS, Quantile Regression, Hot Deck Matching, and MDN) for net worth imputation from the SCF to the CPS.
-Prior to model training, we apply an inverse hyperbolic sine (asinh) transformation to the net worth target variable. The asinh function, $\operatorname{asinh}(x) = \ln(x + \sqrt{x^2 + 1})$, approximates the natural logarithm for large positive values while remaining well-defined for zero and negative values. This is particularly important for wealth data, where a meaningful fraction of households report negative net worth (i.e., debts exceeding assets), making a standard logarithmic transformation infeasible. The transformation compresses the extreme right tail of the wealth distribution, stabilizing variance and improving model performance across all methods. After imputation, predictions are back-transformed via the inverse function $\sinh(\cdot)$ to recover values on the original dollar scale.
+Prior to model training, we apply an inverse hyperbolic sine (asinh) transformation to the net worth target variable. The asinh function, $\operatorname{asinh}(x) = \ln(x + \sqrt{x^2 + 1})$, approximates the natural logarithm for large positive values while remaining well-defined for zero and negative values. This is important for wealth data, where a fraction of households report negative net worth (i.e., debts exceeding assets), making a logarithmic transformation infeasible. The transformation compresses the extreme right tail of the wealth distribution, stabilizing variance and improving model performance across methods. After imputation, predictions are back-transformed via the inverse function $\sinh(\cdot)$ to recover values on the original dollar scale.
This experimental design implicitly assumes that wealth is missing at random (MAR) conditional on the shared predictors $X$, i.e., that the probability of observing wealth in the donor survey does not depend on wealth itself once we condition on the demographic and financial variables available in both datasets, as formalized in Section~\ref{sec:cia}. This assumption is standard in statistical matching but may be violated in practice: wealthy households may be less likely to participate in surveys or may underreport assets, creating MNAR-like patterns that the shared predictors cannot fully capture. We return to this limitation and discuss partial sensitivity checks in Section~\ref{sec:limitations}.
@@ -61,7 +61,7 @@ \subsection{Experimental setup}\label{sec:experimental_setup}
\item Impute wealth (\texttt{networth}) onto the SCF holdout set using each method, with the remaining four folds as training data
\begin{enumerate}
\item SCF survey data weights (captured in the variable \texttt{household\_weight}) are passed into \texttt{autoimpute} for sampling
- \item Demographic and financial variables available in both surveys serve as predictors, after preprocessing for consistent variable names and encoding: \texttt{is\_female}, \texttt{age}, \texttt{race}, \texttt{own\_children\_in\_household}, \texttt{employment\_income}, \texttt{interest\_dividend\_income}, \texttt{pension\_income}
+ \item Demographic and financial variables available in both surveys serve as predictors, after preprocessing for consistent variable names and encoding: \texttt{is\_female}, \texttt{age}, \texttt{race}, \texttt{own\_\allowbreak{}children\_\allowbreak{}in\_\allowbreak{}household}, \texttt{employment\_\allowbreak{}income}, \texttt{interest\_\allowbreak{}dividend\_\allowbreak{}income}, \texttt{pension\_\allowbreak{}income}
\item Each method performs imputation at 20 equally spaced quantiles
\end{enumerate}
@@ -74,13 +74,13 @@ \subsection{Experimental setup}\label{sec:experimental_setup}
\item Retrain the selected method on the full SCF dataset and use it to perform the final imputation of net worth onto the CPS
\end{enumerate}
-This end-to-end pipeline allows for direct comparison between methods on a common evaluation framework and provides a robust assessment of relative performance. The final imputation step uses the entire SCF as training data, maximizing the information available to the selected model.
+This pipeline allows for comparison between methods on a common evaluation framework and provides a robust assessment of relative performance. The final imputation step uses the entire SCF as training data, maximizing the information available to the selected model.
The imputation from the SCF onto the CPS is then replicated for the remaining four methods with an identical setup: training on the full SCF, the same predictor variables, and imputations at the median quantile to avoid introducing bias toward a specific side of the distribution.
\subsection{Downstream policy analysis}\label{sec:policy_validation}
-While distributional metrics such as quantile loss and Wasserstein distance assess how well an imputation method recovers the statistical properties of the target variable, they do not directly capture whether differences between methods matter for downstream policy analysis. To address this, we introduce a policy analysis layer that evaluates imputation quality through its effect on a concrete policy simulation, under both current law and a proposed reform.
+While distributional metrics such as quantile loss and Wasserstein distance assess how well an imputation method recovers the statistical properties of the target variable, they do not capture whether differences between methods matter for downstream policy analysis. To address this, we introduce a policy analysis layer that evaluates imputation quality through its effect on a concrete policy simulation, under both current law and a proposed reform.
We use the Supplemental Security Income (SSI) program as the policy case. SSI is a federal means-tested program that provides cash assistance to aged, blind, and disabled individuals with limited income and resources \citep{ssa2023ssi}. SSI eligibility includes a resource test with limits of \$2,000 for individuals and \$3,000 for couples, which depends on household wealth data that the CPS does not collect.
diff --git a/paper/sections/results.tex b/paper/sections/results.tex
index d6f81d5..a9f6f1c 100644
--- a/paper/sections/results.tex
+++ b/paper/sections/results.tex
@@ -1,10 +1,10 @@
-\section{Results}
+\section{Results}\label{sec:results}
\subsection{Imputation results}
-The cross-validation results show that QRF performs well across the wealth distribution. With the asinh transformation applied to the net worth target variable, QRF achieved the lowest average quantile loss across all quantiles, outperforming OLS, Hot Deck Matching, Quantile Regression, and MDN. QRF's overall consistency across the entire distribution made it the best-performing method for wealth imputation in this setting.
+The cross-validation results show that QRF performs well across the wealth distribution. With the asinh transformation applied to the net worth target variable, QRF achieved the lowest average quantile loss across all quantiles, outperforming OLS, Hot Deck Matching, Quantile Regression (QuantReg), and MDN. QRF's overall consistency across the entire distribution made it the best-performing method for wealth imputation in this setting.
-Automated hyperparameter tuning via the Optuna framework contributed to these results. The optimal QRF configuration identified through cross-validation included 202 trees, a minimum of 1 sample per leaf, a split threshold of 5 samples, approximately 95\% of features considered at each split, and bootstrap sampling enabled. These parameters balance model complexity with generalization, preventing overfitting while still capturing non-linear relationships between demographic predictors and wealth.
+Automated hyperparameter tuning via the Optuna framework contributed to these results. The optimal QRF configuration identified through cross-validation included 202 trees, a minimum of 1 sample per leaf, a split threshold of 5 samples, approximately 95\% of features considered at each split, and bootstrap sampling enabled. These parameters balance model complexity with generalization, preventing overfitting while still capturing nonlinear relationships between demographic predictors and wealth.
\subsubsection{Quantile loss}
@@ -17,7 +17,7 @@ \subsubsection{Quantile loss}
\label{fig:quantile_loss_comparison}
\end{figure}
-We observe how QRF proves to be the best-performing model out of the five. It significantly outperforms Matching and OLS on average, while only being outperformed by QuantReg past the 80th quantile. The dashed lines in Figure~\ref{fig:quantile_loss_comparison} indicate each method's average quantile loss across all quantiles, clearly separating QRF and Matching from the remaining methods. Matching's performance presents the perfect opportunity to see the quantile loss's directional bias at work. Because Matching does not incorporate quantile information into its imputation process in any way, it will match donor and receiver units, and thus impute values identically regardless of the quantile at work. The laddering behavior observed above results from the fact that Matching's wealth imputations consistently underpredict relative to the true wealth values, and this property is increasingly favored for quantiles below the median, and increasingly penalized as quantiles approach the right end of the distribution.
+We observe how QRF proves to be the best-performing model out of the five. It outperforms all other models on average, while only being outperformed slightly by Matching in the middle of the distribution. The dashed lines in Figure~\ref{fig:quantile_loss_comparison} indicate each method's average quantile loss across all quantiles, clearly separating QRF and Matching from the remaining methods. Matching's performance illustrates the quantile loss's directional bias. Because Matching does not incorporate quantile information into its imputation process in any way, it will match donor and receiver units, and thus impute values identically regardless of the quantile at work. The laddering behavior observed above results from the fact that Matching's wealth imputations consistently underpredict relative to the true wealth values, and this property is increasingly favored for quantiles below the median, and increasingly penalized as quantiles approach the right end of the distribution.
Table~\ref{tab:avg_quantile_loss} summarizes average quantile loss across all quantiles and cross-validation folds, with relative improvement computed against the worst-performing method (MDN) as a reference.
@@ -29,20 +29,22 @@ \subsubsection{Quantile loss}
\toprule
Method & Avg Quantile Loss & Std & Improvement (\%) \\
\midrule
- QRF & 0.560 & 0.016 & 76.2 \\
- Matching & 0.601 & 0.018 & 74.4 \\
- OLS & 1.866 & 0.196 & 20.6 \\
- QuantReg & 2.104 & 0.241 & 10.4 \\
- MDN & 2.349 & 0.227 & --- \\
+ QRF & 0.560 & 0.016 & 74.9 \\
+ Matching & 0.597 & 0.015 & 73.3 \\
+ OLS & 1.866 & 0.196 & 16.4 \\
+ QuantReg & 2.104 & 0.241 & 5.7 \\
+ MDN & 2.232 & 0.212 & --- \\
\bottomrule
\end{tabular}
+ \vspace{0.5em}
+ \par\noindent\footnotesize\textit{Note:} Quantile loss values are reported on the asinh-transformed target scale and should be interpreted comparatively across methods rather than as absolute performance levels.
\end{table}
-QRF and Matching achieve substantially lower quantile loss than the remaining methods, with QRF reducing loss by 76.2\% and Matching by 74.4\% relative to MDN. The gap between these two leading methods is modest (0.560 vs.\ 0.601), while OLS, QuantReg, and MDN cluster at substantially higher loss values.
+QRF and Matching achieve substantially lower quantile loss than the remaining methods, with QRF reducing loss by 74.9\% and Matching by 73.3\% relative to MDN. The gap between these two leading methods is modest (0.560 vs.\ 0.597), while OLS, QuantReg, and MDN cluster at higher loss values.
\subsubsection{Imputed wealth distribution comparisons}
-Comparing the imputed wealth distributions against the weighted donor distribution gives a fuller picture of imputation performance beyond the quantile loss averages measured on the SCF. The distribution of wealth values imputed by QRF closely matches the original SCF distribution, suggesting that QRF performs well not only in quantile loss but also in reproducing the overall shape of the U.S. wealth distribution. Because Matching directly takes values from the donor distribution and imputes them onto the receiver, it is unsurprising that its distribution closely resembles the donor distribution. However, Matching may fail to capture the non-linear relationship between predictors and wealth, producing a marginal distribution that looks correct while assigning inaccurate values to individual households. OLS, QuantReg, and MDN fail to capture variability across the distribution and concentrate imputed values at the lower or higher ends.
+Comparing the imputed wealth distributions against the weighted donor distribution gives a fuller picture of imputation performance beyond the quantile loss averages measured on the SCF. The distribution of wealth values imputed by QRF closely matches the original SCF distribution, suggesting that QRF performs well not only in quantile loss but also in reproducing the overall shape of the U.S. wealth distribution. Because Matching directly takes values from the donor distribution and imputes them onto the receiver, it is unsurprising that its distribution closely resembles the donor distribution. However, Matching may fail to capture the nonlinear relationship between predictors and wealth, producing a marginal distribution that looks correct while assigning inaccurate values to individual households. OLS, QuantReg, and MDN fail to capture variability across the distribution and concentrate imputed values at the lower or higher ends.
\begin{figure}[H]
\centering
@@ -61,7 +63,7 @@ \subsubsection{Wasserstein distance}
\label{tab:wasserstein}
\begin{tabular}{lr}
\toprule
- Model & Wasserstein Distance \\
+ Method & Wasserstein Distance \\
\midrule
QRF & 910,299 \\
Matching & 1,192,141 \\
@@ -72,7 +74,9 @@ \subsubsection{Wasserstein distance}
\end{tabular}
\end{table}
-QRF achieves the lowest Wasserstein distance (\$910,299), confirming that its imputed distribution most closely reproduces the donor wealth distribution. To contextualize this magnitude, the 2022 SCF reports a median U.S. household net worth of approximately \$192,700 \citep{fed2023scf}; QRF's Wasserstein distance thus represents roughly 4.7 median household net worths of cumulative distributional displacement, which is small relative to the full range of the wealth distribution but non-trivial in absolute terms. Matching follows at \$1.19 million, consistent with its mechanism of drawing values directly from the donor pool. OLS produces a substantially larger distance (\$68.0 million), reflecting its compressed predictions that fail to span the full range of the wealth distribution. QuantReg and MDN exhibit Wasserstein distances several orders of magnitude larger, indicating severe distributional mismatch driven by concentrated imputed values in narrow regions.
+QRF achieves the lowest Wasserstein distance (\$910,299), confirming that its imputed distribution most closely reproduces the donor wealth distribution. To contextualize this magnitude, the 2022 SCF reports a median U.S. household net worth of approximately \$192,700 \citep{fed2023scf}; QRF's Wasserstein distance thus represents roughly 4.7 median household net worths of cumulative distributional displacement, which is small relative to the full range of the wealth distribution but non-trivial in absolute terms. Matching follows at \$1.19 million, consistent with its mechanism of drawing values directly from the donor pool. OLS produces a substantially larger distance (\$68.0 million), reflecting its compressed predictions that fail to span the full range of the wealth distribution. QuantReg and MDN exhibit Wasserstein distances several orders of magnitude larger.
+
+However, the Wasserstein distance is sensitive to extreme values, and the untrimmed ranking warrants a robustness check. After excluding observations outside the 1st--99th percentile range of the SCF net worth distribution, the ranking reverses: MDN achieves the lowest trimmed Wasserstein distance (\$151K), followed by QuantReg (\$650K), OLS (\$743K), QRF (\$892K), and Matching (\$1.21M). Notably, MDN and QuantReg drop only 0.3\% and 0.4\% of receiver records respectively under trimming, fewer than QRF (1.2\%) or Matching (1.7\%). This indicates that their extreme untrimmed Wasserstein distances are driven by a small number of very large imputed values that dominate the metric. QRF and Matching, by contrast, are nearly unaffected by trimming (their distances change by less than 2\%), reflecting stable behavior across the full distribution even if their core distributional fit is less precise. The untrimmed Wasserstein distances in Table~\ref{tab:wasserstein} therefore reflect tail stability, and methods that appear to perform poorly may in fact model the bulk of the wealth distribution well, even if they miss important tail behavior.
\subsubsection{Distribution of wealth by disposable income decile}
@@ -97,7 +101,7 @@ \subsection{Policy analysis: SSI simulation}
\label{tab:ssi_results}
\begin{tabular}{lrrr}
\toprule
- Model & Recipients (M) & Expenditure (\$B) & Recipients \% of Admin \\
+ Method & Recipients (M) & Expenditure (\$B) & Recipients \% of Admin \\
\midrule
Admin total & 7.4 & 59.6 & 100.0\% \\
Baseline (no wealth) & 19.8 & 152.6 & 267.2\% \\
@@ -111,7 +115,7 @@ \subsection{Policy analysis: SSI simulation}
\end{tabular}
\end{table}
-Without imputed wealth data, the baseline produces 19.8 million recipients and \$152.6 billion in expenditure (267.2\% of administrative totals). All five imputation methods substantially reduce this overestimation by screening out households whose imputed wealth exceeds the resource limits. Quantile Regression yields the closest match to administrative totals (111.7\%), while QRF, despite achieving the best quantile loss, produces higher SSI estimates (163.3\%). This divergence reflects the interaction between imputation accuracy and the policy function: QRF faithfully reproduces the conditional distribution of wealth, including the substantial mass of near-zero values in the SCF, which places more households just below the eligibility threshold. QuantReg's linear compression of the wealth distribution, while statistically less accurate, coincidentally pushes more values above the threshold. The remaining overestimation across all methods reflects that SCF net worth includes assets excluded from SSI countable resources (such as the primary residence and one vehicle).
+Without imputed wealth data, the baseline produces 19.8 million recipients and \$152.6 billion in expenditure (267.2\% of administrative totals). All five imputation methods reduce this overestimation by screening out households whose imputed wealth exceeds the resource limits. Quantile Regression yields the closest match to administrative totals (111.7\%), while QRF, despite achieving the best quantile loss, produces higher SSI estimates (163.3\%). This divergence reflects the interaction between imputation accuracy and the policy function: QRF faithfully reproduces the conditional distribution of wealth, including the substantial mass of near-zero values in the SCF, which places more households just below the eligibility threshold. QuantReg's linear compression of the wealth distribution, while statistically less accurate, coincidentally pushes more values above the threshold. The remaining overestimation across all methods reflects that SCF net worth includes assets excluded from SSI countable resources (such as the primary residence and one vehicle).
\subsubsection{Policy reform: SSI Savings Penalty Elimination Act}
@@ -125,7 +129,7 @@ \subsubsection{Policy reform: SSI Savings Penalty Elimination Act}
\toprule
& \multicolumn{2}{c}{Recipients (M)} & \multicolumn{2}{c}{Expenditure (\$B)} & \multicolumn{2}{c}{Change} \\
\cmidrule(lr){2-3} \cmidrule(lr){4-5} \cmidrule(lr){6-7}
- Model & Current & Reform & Current & Reform & +Recip (M) & +Exp (\$B) \\
+ Method & Current & Reform & Current & Reform & +Recip (M) & +Exp (\$B) \\
\midrule
QuantReg & 8.3 & 8.4 & 74.6 & 75.6 & 0.1 & 1.0 \\
MDN & 9.1 & 9.8 & 79.6 & 84.5 & 0.7 & 4.8 \\
diff --git a/paper/ssi_policy_overview.md b/paper/ssi_policy_overview.md
deleted file mode 100644
index 5170f24..0000000
--- a/paper/ssi_policy_overview.md
+++ /dev/null
@@ -1,389 +0,0 @@
-# Supplemental Security Income (SSI): A Policy Overview
-
-## 1. What SSI Is
-
-### Purpose
-
-Supplemental Security Income (SSI) is a federal means-tested income
-assistance program administered by the Social Security Administration
-(SSA). It provides monthly cash payments to aged, blind, and disabled
-individuals who have limited income and resources. Unlike Social
-Security retirement and disability benefits, SSI is not based on prior
-work history or payroll tax contributions. Instead, it is funded
-through general tax revenues from the U.S. Treasury
-([SSA, 2023](https://www.ssa.gov/ssi)).
-
-SSI serves as the nation's primary cash safety net for the most
-economically vulnerable Americans who are aged or have disabilities,
-functioning as a program of last resort for individuals who cannot
-support themselves through employment and lack sufficient Social
-Security or other benefits.
-
-### History
-
-SSI was established by Title XVI of the Social Security Act and began
-making payments on January 1, 1974. The program replaced three
-earlier federal-state programs:
-
-- **Old-Age Assistance (OAA)** -- aid for the elderly poor
-- **Aid to the Blind (AB)** -- assistance for blind individuals
-- **Aid to the Permanently and Totally Disabled (APTD)** -- support
- for people with disabilities
-
-Prior to SSI, these programs were administered by individual states,
-leading to significant variation in eligibility criteria, benefit
-levels, and administrative practices. Congress created SSI to
-establish a uniform, nationwide floor of income support with
-consistent federal eligibility standards and benefit amounts
-([Congressional Research Service, 2022](https://crsreports.congress.gov/product/pdf/RL/RL32279)).
-
-### Policy Goals
-
-The core policy goals of SSI include:
-
-1. **Poverty alleviation**: Providing a minimum income floor for
- aged, blind, and disabled individuals who lack other means of
- support.
-2. **Nationwide uniformity**: Replacing the patchwork of state
- programs with consistent federal eligibility rules and benefit
- levels.
-3. **Dignity and independence**: Enabling recipients to meet basic
- needs such as food and shelter.
-4. **Administrative efficiency**: Centralizing program administration
- under the Social Security Administration.
-
-## 2. Who Qualifies for SSI
-
-### Categorical Eligibility
-
-An applicant must meet one of the following categorical requirements
-([SSA, 2023](https://www.ssa.gov/benefits/ssi/eligibility)):
-
-- **Aged**: Age 65 or older.
-- **Blind**: Visual acuity of 20/200 or less in the better eye with
- use of a correcting lens, or a visual field limitation such that
- the widest diameter subtends an angle no greater than 20 degrees.
-- **Disabled**: Inability to engage in any substantial gainful
- activity (SGA) by reason of a medically determinable physical or
- mental impairment that can be expected to result in death or that
- has lasted or can be expected to last for a continuous period of
- not less than 12 months. For children under age 18, the standard
- is having a medically determinable impairment that results in
- marked and severe functional limitations.
-
-### Income Limits
-
-SSI uses a broad definition of income that includes both earned and
-unearned income. Key exclusions and disregards include
-([20 CFR § 416.1112](https://www.law.cornell.edu/cfr/text/20/416.1112)):
-
-- **General income exclusion**: The first $20 per month of most
- unearned income (or earned income if no unearned income).
-- **Earned income exclusion**: The first $65 per month of earned
- income, plus one-half of remaining earned income.
-- **Student earned income exclusion**: Up to $2,220 per month (with
- an annual maximum of $8,950) for students under age 22 in 2023.
-
-The substantial gainful activity (SGA) level for non-blind disabled
-individuals was $1,470 per month in 2023; for blind individuals, it
-was $2,460 per month
-([SSA, 2023](https://www.ssa.gov/oact/cola/sga.html)).
-
-### Resource Limits
-
-Applicants must have countable resources below
-([20 CFR § 416.1205](https://www.law.cornell.edu/cfr/text/20/416.1205)):
-
-- **$2,000** for an individual
-- **$3,000** for a couple
-
-These limits have not been adjusted for inflation since 1989. Notable
-resource exclusions include:
-
-- The home the individual lives in (regardless of value)
-- One vehicle (generally)
-- Household goods and personal effects
-- Life insurance with a face value of $1,500 or less per person
-- Burial funds up to $1,500 per person
-
-### Citizenship and Residency Requirements
-
-Applicants generally must be:
-
-- A U.S. citizen or national, **or** in a qualified alien category
- (e.g., lawful permanent residents meeting certain conditions,
- refugees, asylees, certain trafficking victims)
-- A resident of one of the 50 states, DC, or the Northern Mariana
- Islands
-- Not absent from the country for 30 or more consecutive days
-
-## 3. Benefit Amounts
-
-### Federal Benefit Rate (FBR) for 2023
-
-The FBR is the maximum monthly federal SSI payment. For 2023
-([SSA](https://www.ssa.gov/oact/cola/SSIamts.html)):
-
-| Recipient Category | Monthly FBR | Annual FBR |
-|----------------------|-------------|-------------|
-| Eligible individual | $914 | $10,968 |
-| Eligible couple | $1,371 | $16,452 |
-
-The 2023 COLA was 8.7%, one of the largest increases in decades,
-reflecting high inflation in 2022.
-
-### How Benefits Are Calculated
-
-The SSI benefit formula
-([42 U.S.C. § 1382](https://www.law.cornell.edu/uscode/text/42/1382)):
-
-**SSI Federal Benefit = FBR - Countable Income**
-
-Where countable income is determined after applying all applicable
-exclusions. For example, for an individual with $300/month in Social
-Security and no earned income:
-
-1. Start with unearned income: $300
-2. Subtract general exclusion: $300 - $20 = $280
-3. Countable income = $280
-4. SSI benefit = $914 - $280 = **$634/month**
-
-For earned income of $500/month with no unearned income:
-
-1. Subtract general exclusion: $500 - $20 = $480
-2. Subtract earned income exclusion: $480 - $65 = $415
-3. Exclude 50% of remainder: $415 / 2 = $207.50
-4. Countable income = $207.50
-5. SSI benefit = $914 - $207.50 = **$706.50/month**
-
-### State Supplements
-
-Many states provide supplemental payments on top of the federal SSI
-benefit. Approximately 44 states and DC provide some form of state
-supplementation. In calendar year 2023, federally administered state
-supplementation totaled $3.2 billion
-([SSI Annual Statistical Report, 2023](https://www.ssa.gov/policy/docs/statcomps/ssi_asr/2023/sect01.html)).
-
-## 4. How SSI Differs from SSDI
-
-| Feature | SSI | SSDI |
-|------------------------|----------------------------------------|----------------------------------------|
-| **Funding source** | General tax revenues | Social Security trust fund |
-| **Work history** | No work history required | Must have sufficient work credits |
-| **Means test** | Yes (income and resource limits) | No means test |
-| **Benefit basis** | Need-based (FBR minus countable income)| Based on past earnings (AIME/PIA) |
-| **Health coverage** | Medicaid (automatic in most states) | Medicare (after 24-month waiting) |
-| **Age eligibility** | 65+ (aged), any age (blind/disabled) | Under full retirement age |
-| **2023 max individual**| $914/month (federal only) | $3,627/month (maximum) |
-| **Resource limits** | $2,000 / $3,000 | None |
-
-## 5. Key Statistics (Calendar Year 2023)
-
-### Recipient Population
-
-As of December 2023
-([SSI Annual Statistical Report, 2023](https://www.ssa.gov/policy/docs/statcomps/ssi_asr/2023/sect01.html)):
-
-- **Total SSI recipients**: **7,425,331** received federally
- administered payments.
-- **Aged 65 or older**: 2,402,843 (32.4%)
-- **Blind and disabled, aged 18-64**: 4,039,319 (54.4%)
-- **Blind and disabled, under 18**: 983,169 (13.2%)
-- 84% were eligible on the basis of blindness or disability.
-- 52% were female.
-
-### Program Costs
-
-From the
-[SSI Annual Statistical Report, 2023](https://www.ssa.gov/policy/docs/statcomps/ssi_asr/2023/index.html):
-
-- **Federal SSI payments (CY 2023)**: **$58.2 billion**
-- **Total payments including federally administered state
- supplements**: **~$61.4 billion** (a 6.6% increase from 2022)
-- **Federally administered state supplementation**: $3.2 billion
-
-### Average Benefits
-
-- **Average monthly payment (December 2023)**: **$675**
-
-### Concurrent Beneficiaries
-
-Approximately **2.5 million** SSI recipients also received Social
-Security (OASDI) benefits in 2023
-([SSI ASR 2023, Section 3](https://www.ssa.gov/policy/docs/statcomps/ssi_asr/2023/sect03.html)).
-
-## 6. Administrative Totals for Microsimulation Benchmarking
-
-The following table consolidates the official 2023 administrative
-statistics that serve as reference points for comparing
-microsimulation results across different imputation models. All
-figures are from the
-[SSI Annual Statistical Report, 2023](https://www.ssa.gov/policy/docs/statcomps/ssi_asr/2023/index.html)
-unless otherwise noted.
-
-| Metric | Value | Source |
-|--------|-------|--------|
-| Total SSI recipients (Dec. 2023) | **7,425,331** | [ASR 2023, Sect. 1](https://www.ssa.gov/policy/docs/statcomps/ssi_asr/2023/sect01.html) |
-| -- Aged (65+) | 2,402,843 (32.4%) | ASR 2023, Sect. 1 |
-| -- Blind/disabled, 18-64 | 4,039,319 (54.4%) | ASR 2023, Sect. 1 |
-| -- Blind/disabled, under 18 | 983,169 (13.2%) | ASR 2023, Sect. 1 |
-| Federal SSI payments (CY 2023) | **$58.2 billion** | ASR 2023, Sect. 1 |
-| Total incl. fed-admin state supplements | **~$61.4 billion** | ASR 2023, Sect. 1 |
-| Federally administered state supplements | $3.2 billion | ASR 2023, Sect. 1 |
-| Average monthly federal payment (Dec. 2023) | **$675** | ASR 2023, Sect. 1 |
-| Federal Benefit Rate -- individual (2023) | $914/month ($10,968/yr) | [SSA COLA](https://www.ssa.gov/oact/cola/SSIamts.html) |
-| Federal Benefit Rate -- couple (2023) | $1,371/month ($16,452/yr) | [SSA COLA](https://www.ssa.gov/oact/cola/SSIamts.html) |
-| Concurrent SSI + OASDI recipients | ~2.5 million | [ASR 2023, Sect. 3](https://www.ssa.gov/policy/docs/statcomps/ssi_asr/2023/sect03.html) |
-| Resource limit -- individual | $2,000 | [20 CFR § 416.1205](https://www.law.cornell.edu/cfr/text/20/416.1205) |
-| Resource limit -- couple | $3,000 | [20 CFR § 416.1205](https://www.law.cornell.edu/cfr/text/20/416.1205) |
-| General income exclusion | $20/month | [20 CFR § 416.1112](https://www.law.cornell.edu/cfr/text/20/416.1112) |
-| Earned income exclusion | $65/month + 50% of remainder | [20 CFR § 416.1112](https://www.law.cornell.edu/cfr/text/20/416.1112) |
-| SGA threshold -- non-blind (2023) | $1,470/month | [SSA](https://www.ssa.gov/oact/cola/sga.html) |
-| SGA threshold -- blind (2023) | $2,460/month | [SSA](https://www.ssa.gov/oact/cola/sga.html) |
-| PolicyEngine calibration target (Dec. 2022) | 7,407,730 | `policyengine-us` `calibration/gov/ssa/ssi/participation.yaml` |
-
-### Suggested Benchmarking Comparisons
-
-When comparing microsimulation results from datasets imputed with
-each of the five models (QRF, OLS, Quantile Regression, Statistical
-Matching, MDN), the following comparisons against administrative
-totals are most informative:
-
-1. **Total recipient count**: Compare simulated SSI take-up to the
- 7,425,331 administrative total. Differences reflect how each
- imputation model's wealth distribution affects who passes the
- resource test.
-2. **Total federal expenditures**: Compare simulated aggregate SSI
- benefits to the $58.2 billion administrative total.
-3. **Average monthly benefit**: Compare simulated average to the
- $675 administrative average.
-4. **Sanity check**: No individual's federal SSI benefit should
- exceed $914/month (individual FBR) or $1,371/month (couple FBR).
-
-**Note on calendar year vs. fiscal year**: The SSA reports SSI
-statistics on a calendar-year basis. CBO and the federal budget use
-fiscal years (October-September). The figures above are calendar
-year 2023 unless otherwise noted.
-
-**Note on point-in-time vs. annual**: Recipient counts are
-point-in-time (December 2023). Payment totals are annual cumulative
-figures for calendar year 2023.
-
-## 7. Policy Significance
-
-### SSI as an Anti-Poverty Program
-
-SSI plays a critical role in the U.S. safety net:
-
-1. **Poverty reduction**: CBPP estimates SSI lifted approximately
- 3.2 million people out of deep poverty in 2022, including roughly
- 1.1 million children
- ([CBPP, 2023](https://www.cbpp.org/research/social-security/supplemental-security-income)).
-
-2. **Gateway to health coverage**: In most states, SSI eligibility
- confers automatic Medicaid eligibility.
-
-3. **Below-poverty floor**: The maximum federal benefit ($914/month
- in 2023) falls below the federal poverty level ($1,215/month for
- an individual in 2023), meaning SSI alone does not bring
- recipients to the poverty line.
-
-### Ongoing Policy Debates
-
-- **Outdated resource limits**: The $2,000/$3,000 limits have not
- been updated since 1989 (~$4,800/$7,200 in 2023 dollars).
-- **Benefit adequacy**: The FBR is approximately 75% of the federal
- poverty guideline.
-- **Marriage penalty**: Two SSI recipients' combined couple benefit
- ($1,371) is less than two individual benefits ($1,828).
-
-### Relevance to Microsimulation
-
-SSI is particularly important for microsimulation models because:
-
-- Its means-tested structure requires detailed information about
- individual income **and assets**, making accurate data imputation
- critical.
-- SSI interacts with many other programs (Social Security, SNAP,
- Medicaid, housing assistance).
-- The CPS does not capture wealth/asset data, which is essential for
- modeling the SSI resource test. Imputing wealth from the SCF
- enables more accurate SSI microsimulation.
-- Policy proposals to modify SSI parameters (e.g., raising resource
- limits, changing income disregards) require microsimulation to
- estimate costs and distributional effects.
-
-## 8. PolicyEngine SSI Model Architecture
-
-PolicyEngine US implements SSI as a chain of person-level variables
-under `policyengine_us/variables/gov/ssa/ssi/`. The calculation
-flows as follows:
-
-```
-ssi (final benefit, Person, YEAR)
- └─ uncapped_ssi = ssi_amount_if_eligible - ssi_countable_income
- │
- ├─ ssi_amount_if_eligible (FBR lookup)
- │ ├─ Joint claim (both spouses eligible) → couple rate / 2
- │ ├─ Spousal deeming applies → couple rate (capped to
- │ │ individual FBR in ssi.py per 20 CFR §416.1163)
- │ └─ Otherwise → individual rate
- │
- ├─ ssi_countable_income
- │ ├─ ssi_marital_earned_income
- │ │ └─ Sources: employment_income, self_employment_income
- │ ├─ ssi_marital_unearned_income
- │ │ └─ Sources: pension_income, social_security,
- │ │ disability_benefits, veterans_benefits,
- │ │ workers_compensation, unemployment_compensation,
- │ │ retirement_distributions, gi_cash_assistance,
- │ │ alimony_income, child_support_received,
- │ │ dividend_income, interest_income, rental_income
- │ ├─ ssi_blind_or_disabled_working_student_exclusion
- │ ├─ ssi_unearned_income_deemed_from_ineligible_parent
- │ ├─ ssi_income_deemed_from_ineligible_spouse
- │ └─ _apply_ssi_exclusions():
- │ 1. $20/mo general exclusion (unearned first)
- │ 2. $65/mo earned income exclusion
- │ 3. 50% of remaining earned income excluded
- │
- └─ is_ssi_eligible
- ├─ is_ssi_aged_blind_disabled
- │ ├─ is_ssi_aged (age >= 65)
- │ ├─ is_blind
- │ └─ is_ssi_disabled (reported SSI receipt OR
- │ is_disabled, AND not engaged in SGA)
- ├─ meets_ssi_resource_test
- │ └─ ssi_countable_resources (INPUT VARIABLE,
- │ no formula — must be provided in data)
- │ Limit: $2,000 individual / $3,000 couple
- └─ citizenship (CITIZEN or qualified noncitizen)
-```
-
-**Key finding for imputation research**: The variable
-`ssi_countable_resources` is a stub with no formula — it must be
-provided as input data. Since the CPS does not collect wealth/asset
-data, PolicyEngine uses a `pass_rate` calibration parameter of
-**0.4** (meaning it probabilistically assumes only 40% of
-categorically eligible people pass the asset test when resources
-are unavailable). Imputing wealth from the SCF directly populates
-this variable, enabling a proper resource test rather than relying
-on the 40% heuristic. Different imputation models will produce
-different wealth distributions, directly affecting who passes the
-resource test and therefore the simulated recipient count and total
-expenditures.
-
-## Sources
-
-1. SSA. "Understanding Supplemental Security Income." [https://www.ssa.gov/ssi](https://www.ssa.gov/ssi)
-2. SSA. "SSI Eligibility Requirements." [https://www.ssa.gov/benefits/ssi/eligibility](https://www.ssa.gov/benefits/ssi/eligibility)
-3. SSA. "SSI Federal Payment Amounts." [https://www.ssa.gov/oact/cola/SSIamts.html](https://www.ssa.gov/oact/cola/SSIamts.html)
-4. SSA. "Substantial Gainful Activity." [https://www.ssa.gov/oact/cola/sga.html](https://www.ssa.gov/oact/cola/sga.html)
-5. SSA. *SSI Annual Statistical Report, 2023.* [https://www.ssa.gov/policy/docs/statcomps/ssi_asr/2023/index.html](https://www.ssa.gov/policy/docs/statcomps/ssi_asr/2023/index.html)
-6. SSA. *SSI Annual Statistical Report, 2023 -- Section 1.* [https://www.ssa.gov/policy/docs/statcomps/ssi_asr/2023/sect01.html](https://www.ssa.gov/policy/docs/statcomps/ssi_asr/2023/sect01.html)
-7. SSA. *SSI Annual Statistical Report, 2023 -- Section 3.* [https://www.ssa.gov/policy/docs/statcomps/ssi_asr/2023/sect03.html](https://www.ssa.gov/policy/docs/statcomps/ssi_asr/2023/sect03.html)
-8. Congressional Research Service. "Supplemental Security Income: An Overview." CRS Report RL32279. [https://crsreports.congress.gov/product/pdf/RL/RL32279](https://crsreports.congress.gov/product/pdf/RL/RL32279)
-9. Center on Budget and Policy Priorities. "Supplemental Security Income." [https://www.cbpp.org/research/social-security/supplemental-security-income](https://www.cbpp.org/research/social-security/supplemental-security-income)
-10. 20 CFR § 416.1112 -- Earned income we do not count. [https://www.law.cornell.edu/cfr/text/20/416.1112](https://www.law.cornell.edu/cfr/text/20/416.1112)
-11. 20 CFR § 416.1205 -- Limitation on resources. [https://www.law.cornell.edu/cfr/text/20/416.1205](https://www.law.cornell.edu/cfr/text/20/416.1205)
-12. 42 U.S.C. § 1382 -- Eligibility for benefits. [https://www.law.cornell.edu/uscode/text/42/1382](https://www.law.cornell.edu/uscode/text/42/1382)
diff --git a/tests/test_models/README.md b/tests/test_models/README.md
index f63c7f8..ce94f72 100644
--- a/tests/test_models/README.md
+++ b/tests/test_models/README.md
@@ -31,7 +31,7 @@ The tests in this directory verify that all imputation models in this package:
- Tests the model's ability to be fit to specific quantiles
- Verifies proper prediction format and structure
-- **test_qrf.py**: Tests for the Quantile Random Forest imputer model:
+- **test_qrf.py**: Tests for the Quantile Regression Forest imputer model:
- Cross-validation evaluation on the Iris dataset
- Tests model fitting with optional RandomForest hyperparameters
- Verifies prediction structure across multiple quantiles