Volume 2, Issue 1

Ridder and Woutersen (Ridder, G., and T. Woutersen. 2003. “The Singularity of the Efficiency Bound of the Mixed Proportional Hazard Model.” Econometrica 71: 1579–1589) have shown that under a weak condition on the baseline hazard, there exist root-N consistent estimators of the parameters in a semiparametric Mixed Proportional Hazard model with a parametric baseline hazard and unspecified distribution of the unobserved heterogeneity. We extend the linear rank estimator (LRE) of Tsiatis (Tsiatis, A. A. 1990. “Estimating Regression Parameters using Linear Rank Tests for Censored Data.” Annals of Statistics 18: 354–372) and Robins and Tsiatis (Robins, J. M., and A. A. Tsiatis. 1992. “Semiparametric Estimation of an Accelerated Failure Time Model with Time-Dependent Covariates.” Biometrika 79: 311–319) to this class of models. The optimal LRE is a two-step estimator. We propose a simple one-step estimator that is close to optimal if there is no unobserved heterogeneity. The efficiency gain associated with the optimal LRE increases with the degree of unobserved heterogeneity.

Empirical research with Markov regime-switching models often requires the researcher not only to estimate the model but also to test for the presence of more than one regime. Despite the need for both estimation and testing, methods of estimation are better understood than are methods of testing. We bridge this gap by explaining, in detail, how to apply the newest results in the theory of regime testing, developed by Cho and White [Cho, J. S., and H. White 2007. “Testing for Regime Switching.” Econometrica 75 (6): 1671–1720.]. A key insight in Cho and White is to expand the null region to guard against false rejection of the null hypothesis due to a small group of extremal values. Because the resulting asymptotic null distribution is a function of a Gaussian process, the critical values are not obtained from a closed-form distribution such as the χ². Moreover, the critical values depend on the covariance of the Gaussian process and so depend both on the specification of the model and the specification of the parameter space. To ease the task of calculating critical values, we describe the limit theory and detail how the covariance of the Gaussian process is linked to the specification of both the model and the parameter space. Further, we show that for linear models with Gaussian errors, the relevant parameter space governs a standardized index of regime separation, so one need only refer to the tabulated critical values we present. While the test statistic under study is designed to detect regime switching in the intercept, the test can be used to detect broader alternatives in which slope coefficients and error variances may also switch over regimes.

This paper develops finite mixture models with fixed effects for two families of distributions for which the incidental parameter problem has a solution. Analytical results are provided for mixtures of Normals and mixtures of Poisson. We provide algorithms based on the expectations-maximization (EM) approach as well as computationally simpler equivalent estimators that can be used in the case of the mixtures of normals. We design and implement a Monte Carlo study that examines the finite sample performance of the proposed estimator and also compares it with other estimators such the Mundlak-Chamberlain conditionally correlated random effects estimator. The results of Monte Carlo experiments suggest that our proposed estimators of such models have excellent finite sample properties, even in the case of relatively small T and moderately sized N dimensions. The methods are applied to models of healthcare expenditures and counts of utilization using data from the Health and Retirement Study.

We provide formulae for calculating approximate p-values for the non-standard asymptotic null distributions of a variety of tests used for detecting multiple structural change in a wide range of models. Our approximations are based on simulated quantiles obtained from 100,000 replications, and the latter are more accurate than the quantiles reported in the literature by increasing the number of replications by a factor of 10. The p-value response surfaces are approximated using a parametric method proposed by Hansen and their use is illustrated with an example. Using our p-value response surfaces, it is shown that the use of Bai and Perron’s response surfaces for the critical values of these tests can lead to misleading inferences, and thus should be used with extreme caution.

This paper proposes a parametric approach to estimating a dynamic binary response panel data model that allows for endogenous contemporaneous regressors. Such a model is of particular value for settings in which one wants to estimate the effects of an endogenous treatment on a binary outcome. In order to demonstrate the usefulness of the approach, we use it to examine the impact of rural-urban migration on the likelihood that households in rural China fall below the poverty line. In this application, it is shown that migration is important for reducing the likelihood that poor households remain in poverty and that non-poor households fall into poverty. Furthermore, it is demonstrated that failure to control for unobserved heterogeneity would lead the researcher to underestimate the impact of migrant labor markets on reducing the probability of falling into poverty.

Reproducibility of economic research has attracted considerable attention in recent years. So far, the discussion has focused mainly on reproducibility of empirical analyses. This paper addresses a further aspect of reproducibility, the reproducibility of computational experiments. More specifically, we contribute to the emerging literature on reproducibility in economics along three lines: (i) we document how simulations of various types are an integral part of publications in modern econometrics, (ii) we provide some general guidelines about how to set up reproducible simulation experiments, and, finally, (iii) we provide a case study from time series econometrics that illustrates the main issues arising in connection with reproducibility, emphasizing the use of modular tools.

This paper focuses on econometrics pedagogy. It demonstrates the importance of including probability weights in regression analysis using data from surveys that do not use simple random samples (SRS). We use concrete, numerical examples and simulation to show how to effectively teach this difficult material to a student audience. We relax the assumption of simple random sampling and show how unequal probability of selection can lead to biased, inconsistent OLS slope estimates. We then explain and apply probability weighted least squares, showing how weighting the observations by the reciprocal of the probability of inclusion in the sample improves performance. The exposition is non-mathematical and relies heavily on intuitive, visual displays to make the content accessible to students. This paper will enable professors to incorporate unequal probability of selection into their courses and allow students to use best practice techniques in analyzing data from complex surveys. The primary delivery vehicle is Microsoft Excel ® . Two user-defined array functions, SAMPLE and LINESTW, are included in a prepared Excel workbook. We replicate all results in Stata ® and offer a do-file for easy analysis in Stata. Documented code in Excel and Stata allows users to see each step in the sampling and probability weighted least squares algorithms. All files and code are available at www.depauw.edu/learn/stata .