Volume 6, Issue 1

In regression discontinuity (RD) with a running variable S crossing a known cutoff c , an unexpectedly small break magnitude is due to S being a mis-measured version of the genuine running variable G . Has all been lost, and is RD useless when G≠S ? This paper proves three things. First, when P ( G=S )=0, nonparametric RD identification fails. Second, when P ( G=S )>0, although the usual RD effect on the margin E (·| G=c ) is not nonparametrically identified, the “effect on the truthful margin” E (·| G=S=c ) is. Third, under a no-selection-problem assumption, the effect on the truthful margin becomes the effect on the margin; the no-selection-problem assumption is unnecessary, as long as the effect on the truthful margin is taken as a parameter of interest.

We present a method for estimating Markov dynamic models with unobserved state variables which can be serially correlated over time. We focus on the case where all the model variables have discrete support. Our estimator is simple to compute because it is noniterative, and involves only elementary matrix manipulations. Our estimation method is nonparametric, in that no parametric assumptions on the distributions of the unobserved state variables or the laws of motions of the state variables are required. Monte Carlo simulations show that the estimator performs well in practice, and we illustrate its use with a dataset of doctors’ prescription of pharmaceutical drugs.

In this paper, we analyze the forecasting performance of a set of widely used window selection methods in the presence of data revisions and recent structural breaks. Our Monte Carlo and empirical results for U.S. real GDP and inflation show that the expanding window estimator often yields the most accurate forecasts after a recent break. It performs well regardless of whether the revisions are news or noise, or whether we forecast first-release or final values. We find that the differences in the forecasting accuracy are large in practice, especially when we forecast inflation after the break of the early 1980s.

In models estimated by (generalized) method of moments a test on coefficient restrictions can either be based on a Wald statistic or on the difference between evaluated criterion functions. From their correspondence it easily follows that the statistic used for testing instrument validity, the Sargan-Hansen overidentifying restrictions (OR) statistic, is equivalent to an exclusion restrictions test statistic for a nonunique group of regressor variables. We prove that asymptotically this is the case too for incremental OR tests. However, we also demonstrate that, despite this equivalence of test statistics, one can nevertheless distinguish between either the (in)validity of some additional instruments or the (un)tenability of particular exclusion restrictions. This, however, requires to be explicit about the adopted maintained hypothesis. It also highlights that recent warnings in the literature that overidentifying restrictions tests may mislead practitioners should not be directed towards the test, but to practitioners who do not realize that inference based on such tests is unavoidably conditional on the validity of particular just-identifying statistically untestable assumptions.

The copula graphic estimator (CGE) for competing risks models has received little attention in empirical research, despite having been developed into a comprehensive research method. In this paper, we bridge the gap between theoretical developments and applied research by considering a general class of competing risks copula models, which nests popular models such as the Cox proportional hazards model, the semiparametric multivariate mixed proportional hazards model (MMPHM), and the CGE as special cases. Analyzing the effects of a German Hartz reform on unemployment duration, we illustrate that the CGE imposes fewer restrictions on partial covariate effects than standard methods do. Differences are less evident when a more flexible difference-in-differences estimator is applied. It is also found that the MMPHM estimates react more strongly to the choice of the copula than the CGE in terms of the shape of the treatment effect function over time. Thus, the MMPHM produces less robust results in our application.

This paper develops a test for intercept homogeneity in fixed-effects one-way error component models assuming slope homogeneity. We show that the proposed test works equally well when intercepts are assumed to be either fixed (non-stochastic) or random. Moreover, this test can also be used to test for random effect vs. fixed effect although in the restrictive sense. The test is shown to be robust to cross-sectional dependence; for both weak and strong dependence. The proposed test is shown to have a standard χ 2 limiting distribution and is free from nuisance parameters under the null hypothesis. Monte Carlo simulations also show that the proposed test delivers more accurate finite sample sizes than existing tests for various combinations of N and T . Simulation study shows that F-test is either over-sized or under-sized depending on the pattern of cross-sectional dependence. The performance of Hausman test (1978), on the other hand, is quite unstable across various DGP s; and empirical size varies from 0% to the nominal sizes depending on the structure of error variance-covariance matrix. The power of the proposed test outperforms the other two tests. It is worthwhile to mention that the power of our proposed test increases with T in contrast to that of Hausman test which is known to have no power as T →∞. An empirical illustration to examine the Kuznets’ U curve hypothesis with balanced panel data of Indian states is also provided. This empirical illustration points out the efficacy and the necessity of our robust test.

This paper details implementation of the recently proposed root- n kernel density estimator of (Escanciano, J. C., and D. T. Jacho-Chávez. 2012. “n$\sqrt n $-uniformly consistent density estimation in nonparametric regression models.” Journal of Econometrics 167: 305–316.) that circumvents the slow rate of convergence of traditional nonparametric kernel density estimators. We discuss implementation issues such as bandwidth selection and controlling for heteroskedasticity. Two empirical examples are provided; we re-examine the classic study of the emerging multimodality of the cross-country distribution of income per capita, finding more local structure with this new method, and we study the distribution of lean body mass across gender, where we demonstrate robustness of the new methods to alternative bandwidth selection mechanisms.

Economists rely frequently on instrumental variables estimation to overcome biases that endogenous explanatory variables cause in ordinary least squares estimation. However, traditional instrumental variables estimators, such as two-stage least squares and limited information maximum likelihood estimation, can suffer persistent estimator biases and size-of-test biases in even very large samples if the instruments used are large in number or are only weakly correlated with an endogenous explanatory variable. This paper reviews strategies for grappling with weak instruments and with large numbers of instruments in linear regression models.

We present a review on the implementation of regularization methods for the estimation of additive nonparametric regression models with instrumental variables. We consider various versions of Tikhonov, Landweber-Fridman and Sieve (Petrov-Galerkin) regularization. We review data-driven techniques for the sequential choice of the smoothing and the regularization parameters. Through Monte Carlo simulations, we discuss the finite sample properties of each regularization method for different smoothness properties of the regression function. Finally, we present an application to the estimation of the Engel curve for food in a sample of rural households in Pakistan, where a partially linear specification is described that allows one to embed other exogenous covariates.

In this study, we review the graphical methods suggested in Davidson and MacKinnon (Davidson, Russell, and James G. MacKinnon. 1998. “Graphical Methods for Investigating the Size and Power of Hypothesis Tests.” The Manchester School 66 (1): 1–26.) that can be used to investigate size and power properties of hypothesis tests for undergraduate and graduate econometrics courses. These methods can be used to assess finite sample properties of various hypothesis tests through simulation studies. In addition, these methods can be effectively used in classrooms to reinforce students’ understanding of basic hypothesis testing concepts such as Type I error, Type II error, size, power, p-values and under-or-over-sized tests. We illustrate the procedural aspects of these graphical methods through Monte Carlo experiments, and provide the implementation codes written in Matlab and R for the classroom applications.