برآورد فوق العاده سازگار و استنتاج در الگوهای اقتصادسنجی ساختاری با استفاده از آمار نظم فوق العاده

Data-generating processes whose distributions’ supports depend on unknown parameters arise naturally in empirical applications. In such situations the maximum-likelihood estimator is often difficult to calculate and usually has a nonstandard limiting distribution that depends on nuisance parameters. We propose an alternative estimation strategy that is typically simpler to implement than the likelihood approach and allows one to conduct inference using simulation methods. Our proposed estimators are based on the analog estimation principle and bear a striking resemblance to generalized method-of-moments estimators, although here the estimators are generally parameter consistent at rate T rather than the usual rate View the MathML source.

In a wide variety of empirical applications the support of a dependent variable's distribution depends on some or all of the unknown parameters; e.g., the job-search models in Flinn and Heckman (1982) or the procurement-auction models in Paarsch (1992). In such situations the maximum-likelihood (ML) estimator (MLE) is often difficult to calculate and usually has a nonstandard limiting distribution, making inference difficult. In particular, the MLE is often a function of extreme order statistics rather than averages, and its limiting distribution is related to the exponential distribution rather than to the normal distribution. Also the distribution of the MLE usually depends on nuisance parameters. In this paper we consider estimation and inference in such models. First, motivated by difficulties in computing values of and conducting inference for the MLE, we propose estimators based on the analogy principle. These estimators are typically simpler to compute than the MLE and retain some of the advantages that the MLE has over method-of-moments (MM) estimators (MMEs) and generalized method-of-moments (GMM) estimators (GMMEs); viz, a form of parameter superconsistency.1 Besides being easier to compute the new estimators give rise to statistics for testing parameter restrictions and model specification that have a simple, easily simulated form. In order to gauge relative bias and efficiency of the new estimators, we compare their small-sample performance with that of the MLE and some MMEs using Monte Carlo methods. Next, we compare the performance of our new estimators with that of the MLE and the MMEs in terms of inference reliability. A simulation-based inference procedure is used for the new estimators. While standard View the MathML source asymptotic normality arguments give rise to the usual inference methods for the MMEs, inferences for the MLE are conducted using resampling methods proposed in the statistics literature, in particular a parametric bootstrap method; see, for example, Efron (1982) for an introduction to bootstrap methods and Horowitz (2001) for an elaborate discussion of how such methods have been applied in econometrics. Finally, we demonstrate that our new estimators can be implemented in a straightforward manner by calculating them as well as the MLE and an MME using data from an application, Paarsch (1992). We also implement a proposed test of specification which yields qualitatively similar conclusions to those reported in Paarsch (1992). To motivate the importance of our research in terms of empirical applications in economics we consider two canonical examples of support problems which arise naturally in the labor-economic and industrial-organization literatures.

Using the analogy principle we have proposed an alternative estimation strategy which is typically simpler to implement than the MLE and which allows one to conduct inference using simulation methods to generate p-values. These two features circumvent problems with using the MLE to estimate and to perform inference concerning the parameters of models in which the support of the data-generating process depends on unknown parameters. Our proposed estimators, BEMDEs, which bear a striking resemblance to GMMEs and MDEs, are parameter consistent at rate T rather than the usual rate View the MathML source. Evidence from a small-scale Monte Carlo study suggests that the BEMDEs and their related test statistics are reasonable alternatives to the MLE and its related test statistics. A loss of accuracy exists, but the BEMDEs are typically easier to calculate. Moreover, our simulation approach to inference is both feasible and simple. For most applications of the MLE this is not true. The BEMDEs are demonstrably better than the MMEs. We have also demonstrated that our estimators are feasible in actual research by estimating the parameters of an empirical specification used by Paarsch (1992). Like Paarsch, who used other methods, we reject the empirical specification using one of our proposed specification test statistics.