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Simultaneous Maximum Likelihood Estimation for Piecewise Linear Instrumental Variable Models.

Shuo Shuo Liu1, Yeying Zhu2

  • 1Department of Statistics, The Pennsylvania State University, University Park, PA 16801, USA.

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|September 23, 2022
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Summary
This summary is machine-generated.

This study introduces a generalized piecewise linear model for instrumental variable analysis, improving causal inference. The new method effectively estimates causal effects, even with complex relationships, offering robust solutions for econometrics and social sciences.

Keywords:
causal inferenceinstrumental variablespiecewise linearthresholds model

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Area of Science:

  • Econometrics
  • Causal Inference
  • Statistical Modeling

Background:

  • Endogeneity and unmeasured confounding are significant challenges in causal inference.
  • Traditional linear instrumental variable models have limitations in capturing complex relationships.

Purpose of the Study:

  • To propose a generalized piecewise linear model for instrumental variable analysis.
  • To address endogeneity and unmeasured confounding in causal inference.
  • To investigate the causal effect of education on salary.

Main Methods:

  • Utilizing a piecewise linear model to fit continuous instrumental variable and explanatory variable relationships.
  • Employing two-stage least square and limited information maximum likelihood for simultaneous estimation.
  • Analyzing the limiting distribution of estimators in specified and misspecified models.
  • Providing robust estimation of the variance-covariance matrix.

Main Results:

  • The proposed model generalizes traditional linear instrumental variable approaches.
  • Simulations demonstrate the finite sample properties of the estimation.
  • The model is applied to education-salary data to estimate the causal effect of schooling on wages.

Conclusions:

  • The piecewise linear instrumental variable model offers a flexible and robust approach to causal inference.
  • This method effectively handles complex relationships and provides reliable estimates.
  • The findings have implications for understanding the causal impact of education on economic outcomes.