Comparing features of convenient estimators for binary choice models with endogenous regressors

Abstract We discuss the relative advantages and disadvantages of four types of convenient estimators of binary choice models when regressors may be endogenous or mismeasured or when errors are likely to be heteroscedastic. For example, such models arise when treatment is not randomly assigned and outcomes are binary. The estimators we compare are the two‐stage least squares linear probability model, maximum likelihood estimation, control function estimators, and special regressor methods. We specifically focus on models and associated estimators that are easy to implement. Also, for calculating choice probabilities and regressor marginal effects, we propose the average index function (AIF), which, unlike the average structural function (ASF), is always easy to estimate.     

On uniqueness of the conditional maximum likelihood estimation for a binary panel model

This paper considers an estimation method for a binary panel model with incidental parameters as individual effects. The necessary condition for the conditional maximum likelihood approach proposed by Andersen (1970) is investigated and we show that unique sufficient statistics exist only for logit models in a two-wave panel.     

Weak exogeneity in partially nonstationary models

This paper is dedicated to analysing the conditions for weak exogeneity in partially nonstationary models. After adopting a particular identification regime which is based on a triangularization of the parameters of the cointegration relations, we show that the conditions for weak exogeneity developed in the literature can be stated in terms of the parameters of the so-called structural form. This alternative presentation of the conditions permits new interpretations and provides fresh insights on how to test the exogeneity hypothesis.     

Partial identification in binary response models with nonignorable nonresponses

This study investigates the identification of parameters in semiparametric binary response models of the form y=1(x^′β+v+ε>0)$y=1(x^{\prime }\beta +v+\epsilon >0)$ when there are nonignorable nonresponses. We propose an estimation procedure for the identified set, the set of parameters that are observationally indistinguishable from the true value β$\beta$, based on the special regressor approach of Lewbel (2000). We show that the estimator for the identified set is consistent in the Hausdorff metric.     

Testing for normality in linear regression models using regression and scale equivariant estimators

In this paper we provide a general solution to the problem of controlling the probability of a type I error in normality tests for the disturbances in linear regressions when using robust-regression residuals. We show that many classes of well-known robust regression estimators belong to the class of regression and scale equivariant estimators. It is these equivariance properties that are used to reduce the nuisance parameter space under the null, from which we develop Monte Carlo and Maximized Monte Carlo tests for the null of disturbance normality. Finally, we illustrate in a simulation experiment the potential power gains from using robust-regression residuals in testing this null hypothesis.     

Inverse demand systems and choice of functional form

Barten (Empirical Economics 18 (1993) 129) recently advocated estimation of a synthetic demand system that mechanically nests four other popular differential demand models. This paper follows a similar strategy, but in the context of four inverse share-equation demand systems: The Inverse Translog Demand System (ITLDS); the Inverse Almost Ideal Demand System (IAIDS); the Inverse Lewbel Demand System (ILDS); and the Inverse Non-Separable Linear Expenditure System (INLES). Each of these specifications is artificially nested in a Hybrid Inverse Demand System (HIDS). An empirical application to three categories of quarterly U.S. meat demand data over the period 1961-1996 indicates the HIDS is a preferred specification.     

Testing for serial correlation and random effects in a two-way error component regression model

In this paper, we test the existence of serial correlation and random effects in a two-way error component regression model with panel data. Under moment conditions alone, we suggest several easily implemented tests based on the parameter estimators for artificial autoregressions modeled by the differences in residuals. Under the null hypotheses, the tests for serial correlation are two-sided and asymptotically chi-square distributed, whereas those for random effects are one-sided, and are asymptotically standard normally distributed variables. Moreover, these methods can also be used similarly to construct tests for both serial correlation and individual effects jointly, whether or not time effects are present. The proposed tests are able to detect local alternatives that are distinct from the null at the parametric rate. Monte Carlo simulations and real data applications are carried out for purposes of illustration.     

Testing for structural breaks with local smoothers: A simulation study

By means of an extensive Monte Carlo simulation study based on the design of Chen and Hong (2012) we compare the performance of the tests they proposed for parameter stability with the linearity test of Li et al. (2002) and the functional form test of Li and Wang (1998). We find that the test of Li et al. (2002) test adapted to testing for parameter stability performs favorably well in terms of size and equally well in terms of power compared with the others, whereas the test by Li and Wang has no power.     

Testing for Zipf’s law: A common pitfall

It is noted that the regression procedure commonly used when testing for Zipf’s law is erroneous.     

Testing for bivariate stochastic dominance using inequality restrictions

We propose a test of bivariate stochastic dominance within a generalized framework for testing inequality restrictions, utilizing the covariance structure of the estimates of the joint distribution functions. Monte Carlo simulations and an empirical example assess its usefulness.     

Testing of the mean reversion parameter in continuous time models

In this paper we use the approximate bias expressions developed in Yu (2012) and Bao et al. (2013) to improve the testing of the ordinary least squares or quasi-maximum likelihood estimator of the mean reversion parameter in continuous time models. We follow the approach given in Iglesias and Phillips (2005) and Chambers (2013), where if we bias correct the estimated mean reversion parameter, we can improve on the small sample properties of the testing procedure. Simulation results confirm the usefulness of this approach using a t$t$-statistic in this setting in the near unit root situation when the mean reversion parameter is approaching its lower bound. Therefore we always recommend bias correcting when applying a t$t$-statistic in practice in this context.     

Testing for structural break in Japanese demand system after the bubble era

The aims of this paper are two: to define the structural break in the Japanese demand system after the bubble era and to apply the structural break test developed by Andrews et al. (1996) within the framework of the cointegrated demand system. Our test results reject the null hypothesis of no structural break for March 1994 and then demonstrate the structural break after the bubble era. We define the concept of structural break as the time-series change in preference having the following two aspects: the change in preference for commodity prices by the decline in personal income and the change in preference regarding goods in the course of aging effect, with the improvement of living standards.     

TESTING THE SEQUENTIAL LOGIT MODEL AGAINST THE NESTED LOGIT MODEL*

In this paper, we show that the sequential logit (SL) model, in which a choice process is characterized as a sequence of independent multinomial logit models, is a limiting case of the nested logit (NL) model. For testing the SL model against the NL model, we propose Wald, likelihood ratio and Lagrange multiplier tests after suitably reparameterizing the NL model. It is found that when the NL model parameters are “weakly identified”, the Wald test severely underrejects the true model, whereas the sizes of the LR and LM tests are not significantly affected.     

Testing stochastic income convergence in seasonal heterogeneous panels

In this paper we introduce a seasonal version of the Solow–Swan growth model and acquire an empirical income convergence equation. We take this equation as a basis to investigate whether income convergence exists in an OECD sample. To do this, we propose the test statistics under various asymptotic properties for some of the seasonal frequencies in the context of nonstationary heterogeneous panels. Critical values and moments of our statistics are generated and their finite sample performances are examined via Monte Carlo simulations.     

Testing for individual and time effects in the two-way error component model with time-invariant regressors

In this paper, we focus on testing for individual and time effects in the two-way error component model with time-invariant regressors. We present the so-called FEF estimators when time-invariant regressors are exogenous and the FEF-IV estimators when one or more of time-invariant variables are endogenous, and obtain their asymptotic properties under some mild conditions. In the light of the moment-based test methods of Wu and Li (2014), we construct several tests for the existence of individual and time effects in the two-way error component model with time-invariant regressors. The resulting tests can be shown to have some desired properties as follows: they do not need any distributional assumptions on the error components; they do not require any assumptions on the correlation among the two random effects and the time-varying regressors; they are robust to the presence of one effect when the other one is tested. Simulation study and real data analysis are carried out for illustration of the above.     

Testing nonlinearity: Decision rules for selecting between logistic and exponential STAR models

A new LM specification procedure to choose between Logistic and Exponential Smooth Transition Autoregressive (STAR) models is introduced. The new decision rule has better properties than those previously available in the literature when the model is ESTAR and similar properties when the model is LSTAR. A simple natural extension of the usual LM-test for linearity is introduced and evaluated in terms of power. Monte-Carlo simulations and empirical evidence are provided in support of our claims.     

Financial constraints and occupational choice in Thai villages

Financial constraints and entrepreneurship are key factors affecting economic performance in developing countries. I formulate and solve a model of occupational choice with moral hazard under three alternative financial market environments: savings only, borrowing and lending with default and moral hazard constrained insurance. I use computationally efficient techniques based on mechanism design, genetic algorithms and maximum likelihood to estimate and statistically test these models of financial constraints. Using occupational choice data from Thai villages I find evidence that the saving only regime is rejected in favor of regimes allowing for borrowing and/or insurance, especially in higher-wealth data stratifications. A direct test between the borrowing and insurance regimes reveals that neither can be rejected in favor of the other. Allowing ex-ante lotteries over wealth improves the explanatory power of the model. I also find evidence for differences in the best fitting regimes by region, wealth, and access to formal credit.     

Testing for efficiency in selected developing foreign exchange markets: An equilibrium-based approach

This paper proposes an alternative way of testing FOREX efficiency for developing countries. The FOREX market will be efficient if fully reflects all available information. If this holds, the actual exchange rate will not deviate significantly from its equilibrium rate. Moreover, the spot rate should deviate from its equilibrium rate by only transitory components (i.e. it should follow a white noise process). This test is applied to three Central and Eastern European Countries — members of the EU. Considering an LSTAR model we find no evidence of nonlinear adjustment in the misalignment series. So, linear unit root tests imply that the Poland/Euro FOREX market is efficient, the Czech/Euro FOREX market is not, while the Slovak/Euro FOREX market is quasi-efficient.     

A simple and effective misspecification test for the double-hurdle model

The commonly-used version of the double-hurdle model rests on a rather restrictive set of statistical assumptions, which are very seldom tested by practitioners, mainly because of the lack of a standard procedure for doing so, although violation of such assumptions can lead to serious modelling flaws. We propose here a bootstrap-corrected conditional moment portmanteau test which is simple to implement and has good size and power properties.     

A note on tests of sphericity and cross-sectional dependence for fixed effects panel model

This paper theoretically explains why bias correction appears in two statistics recently developed by Baltagi et al. (2011, 2012), which are designed to test the sphericity and cross-sectional dependence of the errors in the fixed effects panel model respectively. Our explanation shows that the bias correction is in fact avoidable, which is demonstrated by two corresponding statistics that are newly constructed in this paper. Simulation suggests that our statistics perform as well as the two in Baltagi et al. (2011, 2012). In addition, according to the theories underlying our explanation, we extend a new sphericity test proposed by Fisher et al. (2010) to the fixed effects model. Simulation finds that the test behaves well only if both the cross-sectional and the time series dimension are large.