I study the partial identifying power of structural single-equation threshold-crossing models for binary responses when explanatory variables may be endogenous. The sharp identified set of threshold functions is derived for the case in which explanatory variables are discrete, and I provide a constructive proof of sharpness. There is special attention to a widely employed semiparametric shape restriction, which requires the threshold-crossing function to be a monotone function of a linear index involving the observable explanatory variables. The restriction brings great computational benefits, allowing calculation of the identified set of index coefficients without calculating the nonparametrically specified threshold function. With the restriction in place, the methods of the paper can be applied to produce identified sets in a class of binary response models with mismeasured explanatory variables.

Improvements in data acquisition and processing techniques have led to an almost continuous flow of information for financial data. High-resolution tick data are available and can be quite conveniently described by a continuous-time process. It is therefore natural to ask for possible extensions of financial time series models to a functional setup. In this paper we propose a functional version of the popular autoregressive conditional heteroskedasticity model. We will establish conditions for the existence of a strictly stationary solution, derive weak dependence and moment conditions, show consistency of the estimators, and perform a small empirical study demonstrating how our model matches with real data.

This paper considers the problem of testing for multiple structural changes in the persistence of a univariate time series. We propose sup-Wald tests of the null hypothesis that the process has an autoregressive unit root throughout the sample against the alternative hypothesis that the process alternates between stationary and unit root regimes. We derive the limit distributions of the tests under the null and establish their consistency under the relevant alternatives. We further show that the tests are inconsistent when directed against the incorrect alternative, thereby enabling identification of the nature of persistence in the initial regime. We also propose hybrid testing procedures that allow ruling out of stable stationary processes or ones that are subject to only stationary changes under the null, thereby aiding the researcher in interpreting a rejection as emanating from a switch between a unit root and stationary regime. The computation of the test statistics as well as asymptotic critical values is facilitated by the dynamic programming algorithm proposed in Perron and Qu (2006, Journal of Econometrics134, 373–399) which allows imposing within- and cross-regime restrictions on the parameters. Finally, we present Monte Carlo evidence to show that the proposed procedures perform well in finite samples relative to those available in the literature.

This paper studies second-order properties of the empirical likelihood overidentifying restriction test to check the validity of moment condition models. We show that the empirical likelihood test is Bartlett correctable and suggest second-order refinement methods for the test based on the empirical Bartlett correction and adjusted empirical likelihood. Our second-order analysis supplements the one in Chen and Cui (2007, Journal of Econometrics141, 492–516) who considered parameter hypothesis testing for overidentified models. In simulation studies we find that the empirical Bartlett correction and adjusted empirical likelihood assisted by bootstrapping provide reasonable improvements for the properties of the null rejection probabilities.

This paper presents computationally simple estimators for the index coefficients in a binary choice model with a binary endogenous regressor without relying on distributional assumptions or on large support conditions and yields root-n consistent and asymptotically normal estimators. We develop a multistep method for estimating the parameters in a triangular, linear index, threshold-crossing model with two equations. Such an econometric model might be used in testing for moral hazard while allowing for asymmetric information in insurance markets. In outlining this new estimation method two contributions are made. The first one is proposing a novel “matching” estimator for the coefficient on the binary endogenous variable in the outcome equation. Second, in order to establish the asymptotic properties of the proposed estimators for the coefficients of the exogenous regressors in the outcome equation, the results of Powell, Stock, and Stoker (1989, Econometrica 75, 1403–1430) are extended to cover the case where the average derivative estimation requires a first-step semiparametric procedure.

Testing for the presence of a broken linear trend when the nature of the persistence in the data is unknown is not a trivial problem, because the test needs to be both asymptotically correctly sized and consistent, regardless of the order of integration of the data. In a recent paper, Sayginsoy and Vogelsang (2011, Econometric Theory 27, 992–1025) (SV) show that tests based on fixed-b asymptotics provide a useful solution to this problem in the case where the shocks may be either weakly dependent or display strong dependence within the near-unit-root class. In this paper we analyze the performance of these tests when the shocks may be fractionally integrated, an alternative model paradigm that allows for either weak or strong dependence in the shocks. We demonstrate that the fixed-b trend break statistics converge to well-defined limit distributions under both the null and local alternatives in this case (and retain consistency against fixed alternatives), but that these distributions depend on the fractional integration parameter δ. As a result, it is only when δ is either zero or one that the SV critical values yield correctly sized tests. Consequently, we propose a procedure that employs δ-adaptive critical values to remove the size distortions in the SV test. In addition, use of δ-adaptive critical values also allows us to consider a simplification of the SV test that is (asymptotically) correctly sized across δ but can also provide a significant increase in power over the standard SV test when δ = 1.

The two-sample version of the celebrated Pearson goodness-of-fit problem has been a topic of extensive research, and several tests like the Kolmogorov-Smirnov and Cramér-von Mises have been suggested. Although these tests perform fairly well as omnibus tests for comparing two probability density functions (PDFs), they may have poor power against specific departures such as in location, scale, skewness, and kurtosis. We propose a new test for the equality of two PDFs based on a modified version of the Neyman smooth test using empirical distribution functions minimizing size distortion in finite samples. The suggested test can detect the specific directions of departure from the null hypothesis. Specifically, it can identify deviations in the directions of mean, variance, skewness, or tail behavior. In a finite sample, the actual probability of type-I error depends on the relative sizes of the two samples. We propose two different approaches to deal with this problem and show that, under appropriate conditions, the proposed tests are asymptotically distributed as chi-squared. We also study the finite sample size and power properties of our proposed test. As an application of our procedure, we compare the age distributions of employees with small employers in New York and Pennsylvania with group insurance before and after the enactment of the “community rating” legislation in New York. It has been conventional wisdom that if community rating is enforced (where the group health insurance premium does not depend on age or any other physical characteristics of the insured), then the insurance market will collapse, since only older or less healthy patients would prefer group insurance. We find that there are significant changes in the age distribution in the population in New York owing mainly to a shift in location and scale.