Improved likelihood ratio tests for cointegration rank in the VAR model

We suggest improved tests for cointegration rank in the vector autoregressive (VAR) model and develop asymptotic distribution theory and local power results. The tests are (quasi-)likelihood ratio tests based on a Gaussian likelihood, but as usual the asymptotic results do not require normally distributed innovations. Our tests differ from existing tests in two respects. First, instead of basing our tests on the conditional (with respect to the initial observations) likelihood, we follow the recent unit root literature and base our tests on the full likelihood as in, e.g., Elliott et al. (1996). Second, our tests incorporate a “sign” restriction which generalizes the one-sided unit root test. We show that the asymptotic local power of the proposed tests dominates that of existing cointegration rank tests.     

Nonparametric tests for conditional symmetry in dynamic models

This article proposes omnibus tests for conditional symmetry around a parametric function in a dynamic context. Conditional moments may not exist or may depend on the explanatory variables. Test statistics are suitable functionals of the empirical process of residuals and explanatory variables, whose limiting distribution under the null is nonpivotal. The tests are implemented with the assistance of a bootstrap method, which is justified assuming very mild regularity conditions on the specification of the center of symmetry and the underlying serial dependence structure. Finite sample properties are examined by means of a Monte Carlo experiment.     

A fast resample method for parametric and semiparametric models

We propose a fast resample method for two step nonlinear parametric and semiparametric models, which does not require recomputation of the second stage estimator during each resample iteration. The fast resample method directly exploits the score function representations computed on each bootstrap sample, thereby reducing computational time considerably. This method is used to approximate the limit distribution of parametric and semiparametric estimators, possibly simulation based, that admit an asymptotic linear representation. Monte Carlo experiments demonstrate the desirable performance and vast improvement in the numerical speed of the fast bootstrap method.     

Likelihood ratio tests for model selection of stochastic frontier models

An important issue when conducting stochastic frontier analysis is how to choose a proper parametric model, which includes choices of the functional form of the frontier function, distributions of the composite errors, and also the exogenous variables. In this paper, we extend the likelihood ratio test of Vuong, Econometrica 57(2):307–333, (1989) and Takeuchi’s, Suri-Kagaku (Math Sci) 153:12–18, (1976) model selection criterion to the stochastic frontier models. The most attractive feature of this test is that it can not only be used for testing a non-nested model, but also still be applicable even when the general model is misspecified. Finally, we also demonstrate how to apply this test to the Indian farm data used by Battese and Coelli, J Prod Anal 3:153–169, (1992), Empir Econ 20(2):325–332, (1995) and Alvarez et al., J Prod Anal 25:201–212, (2006).     

Exact permutation tests for non-nested non-linear regression models

This paper proposes exact distribution-free permutation tests for the specification of a non-linear regression model against one or more possibly non-nested alternatives. The new tests may be validly applied to a wide class of models, including models with endogenous regressors and lag structures. These tests build on the well-known J test developed by Davidson and MacKinnon [1981. Several tests for model specification in the presence of alternative hypotheses. Econometrica 49, 781–793] and their exactness holds under broader assumptions than those underlying the conventional J test. The J-type test statistics are used with a randomization or Monte Carlo resampling technique which yields an exact and computationally inexpensive inference procedure. A simulation experiment confirms the theoretical results and also shows the performance of the new procedure under violations of the maintained assumptions. The test procedure developed is illustrated by an application to inflation dynamics.     

An adaptive empirical likelihood test for parametric time series regression models

We propose an adaptive empirical likelihood (EL) test for a parametric regression model against a class of alternatives for weakly dependent time series observations. The test is formulated by maximizing a standardized version of the EL statistic over a set of smoothing bandwidths. It is demonstrated that the proposed test is able to distinguish the null hypothesis from a series of local alternatives at an optimal rate.     

Bayesian averaging,prediction and nonnested model selection

This paper studies the asymptotic relationship between Bayesian model averaging and post-selection frequentist predictors in both nested and nonnested models. We derive conditions under which their difference is of a smaller order of magnitude than the inverse of the square root of the sample size in large samples. This result depends crucially on the relation between posterior odds and frequentist model selection criteria. Weak conditions are given under which consistent model selection is feasible, regardless of whether models are nested or nonnested and regardless of whether models are correctly specified or not, in the sense that they select the best model with the least number of parameters with probability converging to 1. Under these conditions, Bayesian posterior odds and BICs are consistent for selecting among nested models, but are not consistent for selecting among nonnested models and possibly overlapping models. These findings have important bearing for applied researchers who are frequent users of model selection tools for empirical investigation of model predictions.     

Joint and marginal specification tests for conditional mean and variance models

This article proposes a class of joint and marginal spectral diagnostic tests for parametric conditional means and variances of linear and nonlinear time series models. The use of joint and marginal tests is motivated from the fact that marginal tests for the conditional variance may lead to misleading conclusions when the conditional mean is misspecified. The new tests are based on a generalized spectral approach and do not need to choose a lag order depending on the sample size or to smooth the data. Moreover, the proposed tests are robust to higher order dependence of unknown form, in particular to conditional skewness and kurtosis. It turns out that the asymptotic null distributions of the new tests depend on the data generating process. Hence, we implement the tests with the assistance of a wild bootstrap procedure. A simulation study compares the finite sample performance of the proposed and competing tests, and shows that our tests can play a valuable role in time series modeling. Finally, an application to the S&P 500 highlights the merits of our approach.     

Nonparametric identification and estimation of sample selection models under symmetry

Under a conditional mean restriction Das et al. (2003) considered nonparametric estimation of sample selection models. However, their method can only identify the outcome regression function up to a constant. In this paper we strengthen the conditional mean restriction to a symmetry restriction under which selection biases due to selection on unobservables can be eliminated through proper matching of propensity scores; consequently we are able to identify and obtain consistent estimators for the average treatment effects and the structural regression functions. The results from a simulation study suggest that our estimators perform satisfactorily.     

Markov-switching model selection using Kullback–Leibler divergence

In Markov-switching regression models, we use Kullback–Leibler (KL) divergence between the true and candidate models to select the number of states and variables simultaneously. Specifically, we derive a new information criterion, Markov switching criterion (MSC), which is an estimate of KL divergence. MSC imposes an appropriate penalty to mitigate the over-retention of states in the Markov chain, and it performs well in Monte Carlo studies with single and multiple states, small and large samples, and low and high noise. We illustrate the usefulness of MSC via applications to the U.S. business cycle and to media advertising.     

Generalized empirical likelihood tests in time series models with potential identification failure

We introduce test statistics based on generalized empirical likelihood methods that can be used to test simple hypotheses involving the unknown parameter vector in moment condition time series models. The test statistics generalize those in Guggenberger and Smith [2005. Generalized empirical likelihood estimators and tests under partial, weak and strong identification. Econometric Theory 21 (4), 667–709] from the i.i.d. to the time series context and are alternatives to those in Kleibergen [2005a. Testing parameters in GMM without assuming that they are identified. Econometrica 73 (4), 1103–1123] and Otsu [2006. Generalized empirical likelihood inference for nonlinear and time series models under weak identification. Econometric Theory 22 (3), 513–527]. The main feature of these tests is that their empirical null rejection probabilities are not affected much by the strength or weakness of identification. More precisely, we show that the statistics are asymptotically distributed as chi-square under both classical asymptotic theory and weak instrument asymptotics of Stock and Wright [2000. GMM with weak identification. Econometrica 68 (5), 1055–1096]. We also introduce a modification to Otsu's (2006) statistic that is computationally more attractive. A Monte Carlo study reveals that the finite-sample performance of the suggested tests is very competitive.     

Kuhn-Tucker,likelihood ratio and Wald tests for nonlinear models with inequality constraints on the parameters

This paper considers the problem of testing statistical hypothesis in nonlinear regression models with inequality constraints on the parameters. First, the Kuhn-Tucker test procedure is defined. Next, it is shown that the distribution of the Kuhn-Tucker, the likelihood ratio and the Wald test statistics converges to the same mixture of chi-square distributions under the null hypothesis. To illustrate these results two examples are considered: (1) the problem of testing that individual effects are missing in an error component model, and (2) the problem of testing equilibrium for a model of markets in disequilibrium.     

Nonparametric dynamic panel data models: Kernel estimation and specification testing

Motivated by the first-differencing method for linear panel data models, we propose a class of iterative local polynomial estimators for nonparametric dynamic panel data models with or without exogenous regressors. The estimators utilize the additive structure of the first-differenced model—the fact that the two additive components have the same functional form, and the unknown function of interest is implicitly defined as a solution of a Fredholm integral equation of the second kind. We establish the uniform consistency and asymptotic normality of the estimators. We also propose a consistent test for the correct specification of linearity in typical dynamic panel data models based on the _L2$L_2$ distance of our nonparametric estimates and the parametric estimates under the linear restriction. We derive the asymptotic distributions of the test statistic under the null hypothesis and a sequence of Pitman local alternatives, and prove its consistency against global alternatives. Simulations suggest that the proposed estimators and tests perform well for finite samples. We apply our new method to study the relationships among economic growth, the initial economic condition and capital accumulation, and find a significant nonlinear relation between economic growth and the initial economic condition.     

Variable selection, estimation and inference for multi-period forecasting problems

This paper conducts a broad-based comparison of iterated and direct multi-period forecasting approaches applied to both univariate and multivariate models in the form of parsimonious factor-augmented vector autoregressions. To account for serial correlation in the residuals of the multi-period direct forecasting models we propose a new SURE-based estimation method and modified Akaike information criteria for model selection. Empirical analysis of the 170 variables studied by Marcellino, Stock and Watson (2006) shows that information in factors helps improve forecasting performance for most types of economic variables although it can also lead to larger biases. It also shows that SURE estimation and finite-sample modifications to the Akaike information criterion can improve the performance of the direct multi-period forecasts.     

Nonparametric estimation of conditional distribution functions with longitudinal data and time-varying parametric models

Nonparametric estimation and inferences of conditional distribution functions with longitudinal data have important applications in biomedical studies. We propose in this paper an estimation approach based on time-varying parametric models. Our model assumes that the conditional distribution of the outcome variable at each given time point can be approximated by a parametric model, but the parameters are smooth functions of time. Our estimation is based on a two-step smoothing method, in which we first obtain the raw estimators of the conditional distribution functions at a set of disjoint time points, and then compute the final estimators at any time by smoothing the raw estimators. Asymptotic properties, including the asymptotic biases, variances and mean squared errors, are derived for the local polynomial smoothed estimators. Applicability of our two-step estimation method is demonstrated through a large epidemiological study of childhood growth and blood pressure. Finite sample properties of our procedures are investigated through simulation study.     

Quasi-maximum likelihood estimation and testing for nonlinear models with endogenous explanatory variables

I propose a quasi-maximum likelihood framework for estimating nonlinear models with continuous or discrete endogenous explanatory variables. Joint and two-step estimation procedures are considered. The joint procedure is a quasi-limited information maximum likelihood procedure, as one or both of the log likelihoods may be misspecified. The two-step control function approach is computationally simple and leads to straightforward tests of endogeneity. In the case of discrete endogenous explanatory variables, I argue that the control function approach can be applied with generalized residuals to obtain average partial effects. I show how the results apply to nonlinear models for fractional and nonnegative responses.     

Estimation and testing of Euler equation models with time-varying reduced-form coefficients

This paper studies the estimation and testing of Euler equation models in the framework of the classical two-step minimum-distance method. The time-varying reduced-form model in the first step reflects the adaptation of private agents’ beliefs to the changing economic environment. The presumed ability of Euler conditions to deliver stable parameters indexing tastes and technology is interpreted as a time-invariant second-step model. This paper shows that, complementary to and independent of one another, both standard specification test and stability test are required for the evaluation of an Euler equation. As an empirical application, a widely used investment Euler equation is submitted to examination. The empirical outcomes appear to suggest that the standard investment model has not been a success for aggregate investment.     

Cointegration,long-run structural modelling and weak exogeneity: Two models of the UK economy

Cointegration ideas as introduced by Granger in 1981 are commonly embodied in empirical macroeconomic modelling through the vector error correction model (VECM). It has become common practice in these models to treat some variables as weakly exogenous, resulting in conditional VECMs. This paper studies the consequences of different approaches to weak exogeneity for the dynamic properties of such models, in the context of two models of the UK economy, one a national-economy model, the other the UK submodel of a global model. Impulse response and common trend analyses are shown to be sensitive to these assumptions and other specification choices.     

Monotonicity of the power function and unbiasedness of some likelihood ratio tests

A natural generalization of thep-dimensional normal distribution is provided by elliptically contoured distributions. In the case of the normal distribution the likelihood ratio tests (LRT) of null-hypothesis of the form

Goodness-of-fit tests for conditional models under censoring and truncation

The problem of specification tests for conditional models is studied when the data are subject to left truncation and right censoring. A general method is applied to derive tests for the polynomial regression, the proportional hazards, the additive risks and the proportional odds models. Bootstrap versions to approximate the critical values of the test are introduced and proved to work both from a theoretical viewpoint as well as in a small simulation study.