Even Simpler Standard Errors for Two-Stage Optimization Estimators: Mata Implementation via the DERIV Command

Terza (Stata J., 2016) offers a heretofore unexploited simplification (henceforth referred to as SIMPLE) of the conventional formulation for the standard errors of two-stage optimization estimators (2SOE). In that paper, SIMPLE was illustrated in the context of two-stage residual inclusion (2SRI) estimation (Terza et al., J. Health Ec., 2008). Stata/Mata implementations of SIMPLE for 2SRI estimators are detailed in Terza (Stata J., 2017). Terza (2016b) develops a variant of SIMPLE for calculating the standard errors of two-stage marginal effects estimators (2SME). Generally applicable Stata/Mata implementation of SIMPLE for 2SME is detailed in (Terza, Stata J., 2017) and compared with results from the Stata MARGINS command (for the subset of cases in which the MARGINS command is available). Although SIMPLE substantially reduces the analytic and coding burden imposed by the conventional formulation, it still requires the derivation and coding of key partial derivatives which may prove daunting for some model specifications. I detail how such analytic demands and coding requirements are virtually eliminated via the use of the Mata DERIV command. Illustrations in the 2SRI and 2SME contexts will be discussed.