Mata implementation of Gauss-Legendre quadrature in the M-estimation context: Correcting for sample-selection bias in a generic nonlinear setting

Joseph Terza

2019 Stata Conference from Stata Users Group

Abstract: Many contexts in empirical econometrics require non-closed form integration for appropriate modeling and estimation design. Applied researchers often avoid such correct but computationally demanding specifications and opt for simpler misspecified modeling designs. The presentation will detail a newly developed Mata implementation of a relatively simple numerical integration technique – Gauss-Legendre quadrature. Although this Mata code is applicable in a variety of circumstances, it was mainly written for use in M-estimation when the relevant objective function (e.g. the likelihood function) involves integration at the observation level. As inputs, the user supplies a vector-valued integrand function (e.g. a vector of sample log-likelihood integrands) and a matrix of upper and lower integration limits. The code outputs the corresponding vector of integrals (e.g. the vector of observation-specific log-likelihood values). To illustrate the use of this Mata implementation, we conduct an empirical analysis of classical sample selection bias in the estimation of wage offer regressions. We estimate a nonlinear version of the model based on the modeling approach suggested by Terza (Econometric Reviews, 2009) which requires numerical integration. This model is juxtaposed with the classical linear sample selection specification of Heckman (Annals of Economic and Social Measurement, 1976) for which numerical integration is not required.

Date: 2019-08-02
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Persistent link: https://EconPapers.repec.org/RePEc:boc:scon19:31

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