Working Paper: NBER ID: w24601
Authors: Casey B. Mulligan
Abstract: When combined with the logical notion of partially interpreted functions, many nonparametric results in econometrics and statistics can be understood as statements about semi-algebraic sets. Tarski’s quantifier elimination (QE) theorem therefore guarantees that a universal algorithm exists for deducing such results from their assumptions. This paper presents the general framework and then applies QE algorithms to Jensen’s inequality, omitted variable bias, partial identification of the classical measurement error model, point identification in discrete choice models, and comparative statics in the nonparametric Roy model. This paper also discusses the computational complexity of real QE and its implementation in software used for program verification, logic, and computer algebra. I expect that automation will become as routine for abstract econometric reasoning as it already is for numerical matrix inversion.
Keywords: No keywords provided
JEL Codes: C01; C63; C65
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Assumptions (C51) | Hypotheses (C12) |
| Assumptions (C51) | Unbiased Estimation in Regression Models (C51) |
| QE identifies necessary conditions for unbiased estimation (C20) | OLS estimator unbiasedness (C51) |
| Assumptions satisfied (C29) | Hypothesis of unbiasedness satisfied (C12) |
| Certain values (D46) | Null results (C29) |
| QE identifies identified set for slope parameter (C20) | Regression coefficients (C29) |
| Regression coefficients (C29) | Identified set bounded (D52) |