Simpler Standard Errors for Multi-Stage Regression-Based Estimators: Illustrations in Health Economics

With a view towards lessening the analytic and computational burden faced by researchers in empirical health economics who seek an alternative to bootstrapping for the standard errors of two-stage estimators, we offer heretofore unexploited simplifications of the typical, but somewhat daunting, textbook approach. For the most commonly encountered cases in empirical health economics – two-stage estimators that, in either stage, involve maximum likelihood estimation or the nonlinear least squares method – we show that: 1) the usual textbook formulation of the relevant asymptotic covariance can be substantially reduced in complexity; and 2) nearly all components of our simplified formulation can be retrieved as outputs from packaged regression routines (e.g., in Stata). With the applied researcher in mind, we illustrate these points with two examples in empirical health economics that involve the estimation of causal effects in the presence of endogeneity – a sampling problem that can often be solved via two-stage estimation. As a by-product of this illustrative discussion, we detail four very useful two-stage estimators (and their asymptotic standard errors) that are consistent for the model parameters in such settings, along with their corresponding multi-stage causal effect estimators (and their asymptotic standard errors)

Two-stage residual inclusion estimation: A practitioners guide to Stata implementation

Abstract. Empirical econometric research often requires implementation of nonlinear models whose regressors include one or more endogenous variables—regressors that are correlated with the unobserved random component of the model. In such cases, conventional regression methods that ignore endogeneity will likely produce biased results that are not causally interpretable. Terza, Basu, and Rathouz (2008, Journal of Health Economics 27: 531–543) discuss a relatively simple estimation method (two-stage residual inclusion) that avoids endogeneity bias, is applicable in many nonlinear regression contexts, and can easily be implemented in Stata. In this article, I offer a step-by-step protocol to implement the two-stage residual inclusion method in Stata. I illustrate this protocol in the context of a real-data example. I also discuss other examples and pertinent Stata code

Health Policy Analysis from a Potential Outcomes Perspective: Smoking During Pregnancy and Birth Weight

Most empirical research in health economics is conducted with the goal of providing scientific evidence that will serve to inform current and future health policy. The use of parametric nonlinear regression (NR) methods for empirical analysis in health economics abounds. Studies that offer clear policy-relevant interpretations of NR results are, however, rare. We offer a comprehensive policy analytic framework within which the applied researcher can: 1) clearly define the policy-relevant estimation objective; 2) consistently estimate that objective using NR methods designed to account for the possible endogeneity of the policy variable of interest; 3) conduct correct asymptotic inference; and 4) offer policy-relevant interpretations of the empirical results. For binary policies, Rubin (1974, 1977) developed the potential outcomes framework (POF). We propose a generally applicable extension of the POF (EPOF) which covers a broad range of policy analytic contexts. In particular, our EPOF accommodates: a) a non-binary policy variable of interest (Xp ); b) policy-relevant counterfactual versions of Xp that are not fixed values; and c) a policy-defining increment to Xp that is not constant. Moreover, our EPOF facilitates the use of extant nonlinear regression (NR) methods that correct for potential bias due to the endogeneity of Xp . As a case in point, we consider the analysis of potential gains in infant birth weight that may result from a prenatal smoking prevention and cessation policy which, if fully effective, would maintain zero levels of smoking for non-smokers (prevention) and convince smokers to quit before becoming pregnant (cessation). In the context of our EPOF, using endogeneity-correcting NR methods, we re-analyze the data examined by Mullahy (1997) and estimate the potential effect of the smoking prevention/cessation policy described above. The EPOF should serve as a useful guide to applied health policy analysts

Regression-Based Causal Analysis from the Potential Outcomes Perspective

Most empirical economic research is conducted with the goal of providing scientific evidence that will be informative in assessing causal relationships of interest based on relevant counterfactuals. The implementation of regression methods in this context is ubiquitous. With this as motivation, we detail a comprehensive regression-based potential outcomes framework for causal modeling, estimation and inference. This framework facilitates rigorous specification of the effect parameter of interest and makes clear the sense in which it is causally interpretable, when appropriately defined in a potential outcomes setting. It also serves to crystallize the conditions under which the effect parameter and the underlying regression parameters are identified. The consistent sample analog estimator of the effect parameter is discussed. Juxtaposing this framework with a stylized version of a commonly implemented and routinely applied modeling and estimation protocol reveals how the latter is deficient in recognizing, and fully accounting for, conditions required for identification of the relevant effect parameter and the causal interpretability of estimation results. In the context of an example, we demonstrate the conceptual advantages of this general potential outcomes framework for regression modeling by showing how it resolves fundamental shortcomings in the conventional approach to characterizing and remedying omitted variable bias

State characteristics and the location of foreign direct investment within the United States: a linear conditional logit model

Investments, Foreign - United States

State government effects on the spatial distribution of inward foreign direct investment

In a recent review of the literature, Wasylenko (1981) concluded that taxes have very little effect on interregional business location decisions. The present study examines the impact of state taxes and incentive programs on the spatial distribution of inward foreign direct investment in manufacturing. The results reveal that taxes, which were measured in various ways, deter foreign direct investment. Conversely, states providing tax incentives, financial assistance, and employment assistance tended to have larger numbers of foreign direct investments.Investments, Foreign - United States ; Taxation ; Industries

Estimating Sales for Retail Centers: An Application of the Poisson Gravity Model

The projection of total retail sales for a shopping center development is of critical importance in its valuation, in the making of investment decisions by investors, and to the retail merchants who must make location decisions. In this study, we apply the Poisson Gravity Model to forecast the number of shopping trips attracted to each of the major retail centers in the Atlanta metropolitan area. In the second stage, the estimated total retail sales for all the shopping centers covered in the study, are allocated to the individual centers, based on their estimated shopping trip shares.

Photography-based taxonomy is inadequate, unnecessary, and potentially harmful for biological sciences

The question whether taxonomic descriptions naming new animal species without type specimen(s) deposited in collections should be accepted for publication by scientific journals and allowed by the Code has already been discussed in Zootaxa (Dubois & Nemésio 2007; Donegan 2008, 2009; Nemésio 2009a–b; Dubois 2009; Gentile & Snell 2009; Minelli 2009; Cianferoni & Bartolozzi 2016; Amorim et al. 2016). This question was again raised in a letter supported by 35 signatories published in the journal Nature (Pape et al. 2016) on 15 September 2016. On 25 September 2016, the following rebuttal (strictly limited to 300 words as per the editorial rules of Nature) was submitted to Nature, which on 18 October 2016 refused to publish it. As we think this problem is a very important one for zoological taxonomy, this text is published here exactly as submitted to Nature, followed by the list of the 493 taxonomists and collection-based researchers who signed it in the short time span from 20 September to 6 October 2016