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Quantile Regression API Reference

Module

Import: from panelbox.models.quantile import PooledQuantile, FixedEffectsQuantile, CanayTwoStep, LocationScale Source: panelbox/models/quantile/

Overview

The quantile module provides panel data quantile regression methods that go beyond mean regression to estimate the full conditional distribution:

Estimator Description Reference
PooledQuantile Pooled QR with cluster-robust inference Koenker & Bassett (1978)
FixedEffectsQuantile Penalized FE quantile regression Koenker (2004)
CanayTwoStep Two-step estimator for panel QR Canay (2011)
LocationScale Location-scale model Machado & Santos Silva (2019)
DynamicQuantile Dynamic panel quantile regression —
QuantileTreatmentEffects Quantile treatment effects —

Optional dependencies

Some quantile classes (FixedEffectsQuantile, CanayTwoStep, LocationScale, DynamicQuantile) use optional imports and may be None if dependencies are missing.

Classes

PooledQuantile

Pooled quantile regression with cluster-robust standard errors. Estimates conditional quantiles ignoring the panel structure.

Constructor

PooledQuantile(
    endog: np.ndarray | pd.Series,
    exog: np.ndarray | pd.DataFrame,
    entity_id: np.ndarray | pd.Series | None = None,
    time_id: np.ndarray | pd.Series | None = None,
    quantiles: float | np.ndarray = 0.5,
    weights: np.ndarray | pd.Series | None = None,
)
Parameter Type Default Description
endog np.ndarray \| pd.Series required Dependent variable
exog np.ndarray \| pd.DataFrame required Independent variables
entity_id np.ndarray \| pd.Series \| None None Entity identifiers (for clustering)
time_id np.ndarray \| pd.Series \| None None Time identifiers
quantiles float \| np.ndarray 0.5 Quantile(s) to estimate (0 < tau < 1)
weights np.ndarray \| pd.Series \| None None Observation weights

Methods

.fit()
def fit(
    self,
    method: str = "interior_point",
    maxiter: int = 1000,
    tol: float = 1e-6,
    se_type: str = "cluster",
    alpha: float = 0.05,
    **kwargs,
) -> PooledQuantileResults
Parameter Type Default Description
method str "interior_point" Optimization method
maxiter int 1000 Maximum iterations
tol float 1e-6 Convergence tolerance
se_type str "cluster" SE type: "cluster", "bootstrap", "iid"
alpha float 0.05 Significance level for confidence intervals

Example

from panelbox.models.quantile import PooledQuantile
import numpy as np

model = PooledQuantile(
    endog=df["wage"],
    exog=df[["education", "experience"]],
    entity_id=df["worker_id"],
    quantiles=np.array([0.25, 0.50, 0.75]),
)
result = model.fit(se_type="cluster")
print(result.summary())

FixedEffectsQuantile

Fixed Effects quantile regression using the penalized approach of Koenker (2004). Controls for entity-specific heterogeneity.

Constructor

FixedEffectsQuantile(
    endog, exog, entity_id, time_id=None,
    quantiles=0.5, weights=None,
)

Koenker (2004) approach

Uses an L1-penalty on entity effects to achieve consistent estimation. The penalty parameter controls the bias-variance tradeoff.

CanayTwoStep

Canay (2011) two-step estimator for panel quantile regression. Step 1 estimates entity effects using mean regression, Step 2 estimates quantile regression on the adjusted data.

Constructor

CanayTwoStep(
    endog, exog, entity_id, time_id=None,
    quantiles=0.5,
)

When to use Canay

Canay's estimator is computationally simpler than Koenker (2004) but requires large T. Best suited for panels with many time periods per entity.

LocationScale

Location-Scale model of Machado & Santos Silva (2019). Models both the location (conditional mean) and scale (conditional dispersion) of the distribution.

Constructor

LocationScale(
    endog, exog, entity_id, time_id=None,
    quantiles=0.5,
)

DynamicQuantile

Dynamic panel quantile regression with lagged dependent variable. Handles the incidental parameters problem in dynamic quantile settings.

QuantileTreatmentEffects

Quantile Treatment Effects (QTE) estimation for panel data. Estimates heterogeneous treatment effects across the distribution.

QuantileMonotonicity

Non-crossing constraints for multiple quantile regressions. Ensures that estimated quantile curves do not cross (monotonicity constraint).

FEQuantileComparison

Compare Fixed Effects quantile regression methods (Koenker 2004, Canay 2011, Machado-Santos Silva 2019) on the same dataset.

Base Classes

QuantilePanelModel

Base class for all panel quantile regression models.

QuantilePanelResult

Base result class for panel quantile regression.

Inference

QuantileBootstrap

from panelbox.inference.quantile import QuantileBootstrap

boot = QuantileBootstrap(model, n_bootstrap=999, method="pairs")
boot_result = boot.run()

Bootstrap inference for quantile regression models, accounting for panel structure.

BootstrapResult

Result container with bootstrap confidence intervals and standard errors.

Diagnostics

QuantileRegressionDiagnostics

from panelbox.diagnostics.quantile import QuantileRegressionDiagnostics

diag = QuantileRegressionDiagnostics(result)

Quantile-specific diagnostics including goodness-of-fit, specification tests, and graphical diagnostics.

Example: Quantile Process

import numpy as np
from panelbox.models.quantile import PooledQuantile

# Estimate across the distribution
quantiles = np.arange(0.1, 1.0, 0.1)
model = PooledQuantile(
    endog=df["income"],
    exog=df[["education", "experience", "age"]],
    entity_id=df["person_id"],
    quantiles=quantiles,
)
result = model.fit(se_type="cluster")

# Compare coefficients across quantiles
for q in quantiles:
    print(f"tau={q:.1f}: education={result.params[q]['education']:.3f}")

See Also