Volume 4, Issue 1

We propose a new approach to statistical inference on parameters that depend on population parameters in a non-standard way. As examples we consider a parameter that is interval identified and a parameter that is the maximum (or minimum) of population parameters. In both examples we transform the inference problem into a test of a composite null against a composite alternative hypothesis involving point identified population parameters. We use standard tools in this testing problem. This setup substantially simplifies the conceptual basis of the inference problem. By inverting the Likelihood Ratio test statistic for the composite null and composite alternative inference problem, we obtain a closed form expression for the confidence interval that does not require any tuning parameter and is uniformly valid. We use our method to derive a confidence interval for a regression coefficient in a multiple linear regression with an interval censored dependent variable.

In economic applications it is often the case that the variate of interest is non-negative and its distribution has a mass-point at zero. Many regression strategies have been proposed to deal with data of this type but, although there has been a long debate in the literature on the appropriateness of different models, formal statistical tests to choose between the competing specifications are not often used in practice. We use the non-nested hypothesis testing framework of Davidson and MacKinnon (Davidson and MacKinnon 1981. “Several Tests for Model Specification in the Presence of Alternative Hypotheses.” Econometrica 49: 781–793.) to develop a novel and simple regression-based specification test that can be used to discriminate between these models.

We develop simple tests for endogenous prices arising from omitted demand factors in discrete choice models. Our approach only requires one to locate testing proxies that have some correlation with the omitted factors when prices are endogenous. We use the difference between prices and their predicted values given observed demand and supply factors. If prices are exogenous, these proxies should not explain demand given prices and other explanatory variables. We reject exogeneity if these proxies enter significantly in utility as additional explanatory variables. The tests are easy to implement as we show with several Monte Carlos and discuss for three recent demand applications.

This paper describes and applies econometric strategies for estimating regression models of economic share data outcomes where the shares may take boundary values (zero and 1) with nontrivial probability. The main focus of the paper is on the conditional mean structures of such data. The paper proposes an extension of the fractional regression methodology proposed by (Papke, L. E., and J. M. Wooldridge. 1996. “Econometric Methods for Fractional Response Variables with an Application to 401(k) Plan Participation Rates.” Journal of Applied Econometrics 11: 619–632; Papke, L. E. and J. M. Wooldridge. 2008. “Panel Data Methods for Fractional Response Variables with an Application to Test Pass Rates.” Journal of Econometrics 145: 121–133.), in univariate cross-sectional and panel contexts. The paper discusses the stochastic aspects of share definition and measurement, and summarizes important features of the existing literature on econometric strategies for share model estimation. The paper then goes on to discuss the univariate fractional regression estimation strategies proposed by Papke and Wooldridge and to extend the fractional regression approach to estimation of and inference about regression models describing the multivariate share data. Some issues involving outcome aggregation/disaggregation are considered, as is a full likelihood estimation approach based on Dirichlet-multinomial models. The paper demonstrates the workings of these various empirical strategies by estimating models of financial asset portfolio shares using data from the 2001, 2004, and 2007 US Surveys of Consumer Finances.

This paper considers the use of multiple proxy measures for an unobserved variable and contrasts the approach taken in the measurement error literature to that of the model specification literature. We find that including all available proxy variables in the regression minimizes the bias on coefficients of correctly measured variables in the regression. We derive a set of bounds for all parameters in the model, and compare these results to extreme bounds analysis. Monte Carlo simulations demonstrate the performance of our bounds relative to extreme bounds. We conclude with an empirical example from the cross-country growth literature in which human capital is measured through three proxy variables: literacy rates, and enrollment in primary and secondary school, and show that our approach yields results that contrast sharply with extreme bounds analysis.

Since the seminal paper by [Heckman, J. J. 1974. “Shadow Prices, Market Wages, and Labor Supply.” Econometrica 42: 679–694], the sample selection model has been an essential tool for applied economists and arguably the most sensitive to sources of misspecification among the standard microeconometric models involving limited dependent variables. The need for alternative methods to get consistent estimators has led to a number of estimation proposals for the sample selection model under non-normality. There is a marked dichotomy in the literature that has developed in two conceptually different directions: the bivariate normality assumption can be either replaced, by using copulae, or relaxed/removed, relying on semi- and non-parametric estimators. This paper surveys the more recent proposals on the estimation of the sample selection model that deal with distributional misspecification giving the practitioner a unified framework of both parametric and semi/non-parametric options.

The standard model of essential heterogeneity, whereby program take up depends on unobserved costs and benefits of take up, is generalized to allow the source of latent heterogeneity to influence counterfactual outcomes. The standard instrumental variables (IV) estimator is shown to still be preferable to the naïve, ordinary least squares (OLS), estimator for mean impact on the treated. However, under certain conditions, the IV estimate of the overall mean impact will be even more biased than OLS. Examples are given for stylized training, insurance and microcredit schemes.

This paper employs a Monte Carlo study to compare the performance of equal-tailed bootstrap percentile- t , symmetric bootstrap percentile- t , bootstrap percentile, and standard asymptotic confidence intervals in two distinct heteroscedastic regression models. Bootstrap confidence intervals are constructed with both the XY and wild bootstrap algorithm. Theory implies that the percentile- t methods will outperform the other methods, where performance is based on the convergence rate of empirical coverage to the nominal level. Results are consistent across models, in that in the case of the XY bootstrap algorithm the symmetric percentile- t method outperforms the other methods, but in the case of the wild bootstrap algorithm the two percentile- t methods perform similarly and outperform the other methods. The implication is that practitioners that employ the XY algorithm should utilize the symmetric percentile- t interval, while those who opt for the wild algorithm should use either of the percentile- t methods.