Validating a user-developed bivariate pseudo-random vector generator

Testing based on simulated data is an important component of the design and assessment of a newly developed estimation method. Often, the relevant modeling context involves bivariate outcomes, for example, endogenous treatment-effect (ETE) models and nonlinear seemingly unrelated regressions (SUR). Stata offers reliable commands for univariate pseudo-random-number generators for a wide variety of probability distributions but, as is the case for all statistical software packages, does not provide similar commands for bivariate pseudodata simulation. This is of course reasonable, given the myriad of extant bivariate probability laws and the inherent technical challenges posed by the lack of a generic bivariate version of the inverse transform theorem. In such cases, it is left to the researcher to develop and implement the requisite bivariate data generator using Stata programming or Mata code. Reliability must be established before using such a user-developed simulator to generate data for assessing the feasibility, accuracy, and precision of a newly developed estimator. We propose a Mata-based approach for validating user-developed bivariate simulator reliability based on comparison of the cumulative bivariate relative frequencies for the generated data to the corresponding “true” bivariate cumulative distribution function values. Interesting illustrative examples in the ETE and SUR contexts are discussed.