Testing homogeneity in a random intercept model using asymptotic, posterior predictive and plug-in p-values

In this paper three statistics and three discrepancy measures with which homogeneity in the random intercept model can be investigated will be evaluated. The first two can be used to test the homogeneity of level one residual variances across level two units and the third can be used to test whether effects should be fixed or random. Each statistic and discrepancy measure will be evaluated using asymptotic (if available), posterior predictive and plug in p -values. A simulation study will be used to investigate the frequency properties of these p -values. In the discussion it will be indicated how the results obtained for the random intercept model with one explanatory variable can be useful during the construction of general two level models.     

Goodness-of-fit testing of a count time series’ marginal distribution

Popular goodness-of-fit tests like the famous Pearson test compare the estimated probability mass function with the corresponding hypothetical one. If the resulting divergence value is too large, then the null hypothesis is rejected. If applied to i. i. d. data, the required critical values can be computed according to well-known asymptotic approximations, e. g., according to an appropriate \(\chi ^2\)-distribution in case of the Pearson statistic. In this article, an approach is presented of how to derive an asymptotic approximation if being concerned with time series of autocorrelated counts. Solutions are presented for the case of a fully specified null model as well as for the case where parameters have to be estimated. The proposed approaches are exemplified for (among others) different types of CLAR(1) models, INAR(p) models, discrete ARMA models and Hidden-Markov models.     

On new variance approximations for linear models with inequality constraints

In this paper, we examine the estimation of linear models subject to inequality constraints with a special focus on new variance approximations for the estimated parameters. For models with one inequality restriction, the proposed variance formulas are exact. The variance approximations proposed in this paper can be used in regression analysis, Kalman filtering, and balancing national accounts, when inequality constraints are to be incorporated in the estimation procedure.     

Estimation with overidentifying inequality moment conditions

This paper derives limit distributions of empirical likelihood estimators for models in which inequality moment conditions provide overidentifying information. We show that the use of this information leads to a reduction of the asymptotic mean-squared estimation error and propose asymptotically uniformly valid tests and confidence sets for the parameters of interest. While inequality moment conditions arise in many important economic models, we use a dynamic macroeconomic model as a data generating process and illustrate our methods with instrumental variable estimators of monetary policy rules. The results obtained in this paper extend to conventional GMM estimators.     

Nonparametric/semiparametric estimation and testing of econometric models with data dependent smoothing parameters

We consider nonparametric/semiparametric estimation and testing of econometric models with data dependent smoothing parameters. Most of the existing works on asymptotic distributions of a nonparametric/semiparametric estimator or a test statistic are based on some deterministic smoothing parameters, while in practice it is important to use data-driven methods to select the smoothing parameters. In this paper we give a simple sufficient condition that can be used to establish the first order asymptotic equivalence of a nonparametric estimator or a test statistic with stochastic smoothing parameters to those using deterministic smoothing parameters. We also allow for general weakly dependent data.     

Nonparametric transfer function models

In this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between ‘input’ and ‘output’ time series. The transfer function is smooth with unknown functional forms, and the noise is assumed to be a stationary autoregressive-moving average (ARMA) process. The nonparametric transfer function is estimated jointly with the ARMA parameters. By modeling the correlation in the noise, the transfer function can be estimated more efficiently. The parsimonious ARMA structure improves the estimation efficiency in finite samples. The asymptotic properties of the estimators are investigated. The finite-sample properties are illustrated through simulations and one empirical example.     

A bootstrap algorithm for testing cointegration rank in VAR models in the presence of stationary variables

In this paper, a bootstrap algorithm for a reduced rank vector autoregressive (VAR) model which also includes stationary regressors, is analyzed. It is shown that the bootstrap distribution for estimating the rank converges to the distribution derived from the usual asymptotic framework. Because the asymptotic distribution will typically depend on unknown parameters, bootstrap distributions are of considerable interest in this context. The result of an application and some Monte Carlo experiments are also presented.     

Indirect estimation of large conditionally heteroskedastic factor models,with an application to the Dow 30 stocks

We derive indirect estimators of conditionally heteroskedastic factor models in which the volatilities of common and idiosyncratic factors depend on their past unobserved values by calibrating the score of a Kalman-filter approximation with inequality constraints on the auxiliary model parameters. We also propose alternative indirect estimators for large-scale models, and explain how to apply our procedures to many other dynamic latent variable models. We analyse the small sample behaviour of our indirect estimators and several likelihood-based procedures through an extensive Monte Carlo experiment with empirically realistic designs. Finally, we apply our procedures to weekly returns on the Dow 30 stocks.     

Information criteria for impulse response function matching estimation of DSGE models

We propose new information criteria for impulse response function matching estimators (IRFMEs). These estimators yield sampling distributions of the structural parameters of dynamic stochastic general equilibrium (DSGE) models by minimizing the distance between sample and theoretical impulse responses. First, we propose an information criterion to select only the responses that produce consistent estimates of the true but unknown structural parameters: the Valid Impulse Response Selection Criterion (VIRSC). The criterion is especially useful for mis-specified models. Second, we propose a criterion to select the impulse responses that are most informative about DSGE model parameters: the Relevant Impulse Response Selection Criterion (RIRSC). These criteria can be used in combination to select the subset of valid impulse response functions with minimal dimension that yields asymptotically efficient estimators. The criteria are general enough to apply to impulse responses estimated by VARs, local projections, and simulation methods. We show that the use of our criteria significantly affects estimates and inference about key parameters of two well-known new Keynesian DSGE models. Monte Carlo evidence indicates that the criteria yield gains in terms of finite sample bias as well as offering tests statistics whose behavior is better approximated by the first order asymptotic theory. Thus, our criteria improve existing methods used to implement IRFMEs.     

A score test under logistic regression models based on case–control data

We propose a score statistic to test the vector of odds ratio parameters under the logistic regression model based on case–control data. The proposed score test is based on the semiparametric profile loglikelihood function under a two-sample semiparametric model, which is equivalent to the assumed logistic regression model. The proposed score statistic has an asymptotic chi-squared distribution under the null hypothesis and an asymptotic noncentral chi-squared distribution under local alternatives to the null hypothesis. Moreover, we show that the proposed score test is asymptotically equivalent to the Wald test under the logistic regression model based on case–control data. In addition, we demonstrate that the proposed score statistic and its asymptotic distribution may be obtained by fitting the prospective logistic regression model to case–control data. We present some results on simulation and on the analysis of two real datasets.     

EL inference for partially identified models: Large deviations optimality and bootstrap validity

This paper addresses the issue of optimal inference for parameters that are partially identified in models with moment inequalities. There currently exists a variety of inferential methods for use in this setting. However, the question of choosing optimally among contending procedures is unresolved. In this paper, I first consider a canonical large deviations criterion for optimality and show that inference based on the empirical likelihood ratio statistic is optimal. Second, I introduce a new empirical likelihood bootstrap that provides a valid resampling method for moment inequality models and overcomes the implementation challenges that arise as a result of non-pivotal limit distributions. Lastly, I analyze the finite sample properties of the proposed framework using Monte Carlo simulations. The simulation results are encouraging.     

Logarithmic calibration for multiplicative distortion measurement errors regression models

In this article, we propose a new identifiability condition by using the logarithmic calibration for the distortion measurement error models, where neither the response variable nor the covariates can be directly observed but are measured with multiplicative measurement errors. Under the logarithmic calibration, the direct-plug-in estimators of parameters and empirical likelihood based confidence intervals are proposed, and we studied the asymptotic properties of the proposed estimators. For the hypothesis testing of parameter, a restricted estimator under the null hypothesis and a test statistic are proposed. The asymptotic properties for the restricted estimator and test statistic are established. Simulation studies demonstrate the performance of the proposed procedure and a real example is analyzed to illustrate its practical usage.     

Functional coefficient instrumental variables models

We consider estimation of nonparametric structural models under a functional coefficient representation for the regression function. Under this representation, models are linear in the endogenous components with coefficients given by unknown functions of the predetermined variables, a nonparametric generalization of random coefficient models. The functional coefficient restriction is an intermediate approach between fully nonparametric structural models that are ill posed when endogenous variables are continuously distributed, and partially linear models over which they have appreciable flexibility. We propose two-step estimators that use local linear approximations in both steps. The first step is to estimate a vector of reduced forms of regression models and the second step is local linear regression using the estimated reduced forms as regressors. Our large sample results include consistency and asymptotic normality of the proposed estimators. The high practical power of estimators is illustrated via both a Monte Carlo simulation study and an application to returns to education.     

Least squares, preliminary test and Stein-type estimation in general vector AR(p) models

In the general vector autoregressive process AR ( p ), multivariate least square estimation (LSE)/maximum likelihood estimation (MLE) of a subset of the parameters is considered when the complementary subset is suspected to be redundant. This may be viewed as a special case of linear constraints of autoregressive parameters. We incorporate this nonsample information in the estimation process and propose preliminary test and Stein-type estimators for the target subset of parameters. Under local alternatives their asymptotic properties are investigated and compared with those of unrestricted and restricted LSE. The dominance picture of the estimators is presented.     

Two-stage rank estimation of quantile index models

This paper estimates a class of models which satisfy a monotonicity condition on the conditional quantile function of the response variable. This class includes as a special case the monotonic transformation model with the error term satisfying a conditional quantile restriction, thus allowing for very general forms of conditional heteroscedasticity. A two-stage approach is adopted to estimate the relevant parameters. In the first stage the conditional quantile function is estimated nonparametrically by the local polynomial estimator discussed in Chaudhuri (Journal of Multivariate Analysis 39 (1991a) 246–269; Annals of Statistics 19 (1991b) 760–777) and Cavanagh (1996, Preprint). In the second stage, the monotonicity of the quantile function is exploited to estimate the parameters of interest by maximizing a rank-based objective function. The proposed estimator is shown to have desirable asymptotic properties and can then also be used for dimensionality reduction or to estimate the unknown structural function in the context of a transformation model.     

On the estimation of location parameters in the multivariate one sample and two sample problems

Summary In this paper we consider the problem of estimating the vectors of location parameters in the multivariate one sample and two sample problems. These estimators are obtained through the use of the multivariate rank order statistics such as theWilcoxon or the normal scores statistic considered by the authors inPuri, Sen [1966] andSen, Puri [1967] for the corresponding testing problems. The distribution of these estimators is shown to be symmetric with respect to the parameters being estimated. These estimators are translation invariant, robust and asymptotically normal. Their asymptotic relative efficiencies with respect to the estimators based on the vector of means and medians are discussed by applying the criterion ofWilks generalized variance [Anderson, p. 166]. In particular, it is shown that the estimators based on the multivariate normal scores statistics are asymptotically as efficient as the ones based on the method of least squares when the parent distributions are normal. Research sponsored by National Science Foundation Grant No. GP-12462, and by Research Grant, GM-12868 from the N.I.H., Public Health Service.     

Testing parameter constancy in linear models against stochastic stationary parameters

This paper considers testing parameter constancy in a linear model when the alternative is that a subset of the parameters follows a stationary vector autoregressive process of known finite order. This kind of a linear model is only identified under the alternative, which usually precludes finding a test statistic with an analytic null distribution. In the present situation, however, it is still possible to derive a test statistic with an asymptotic chi-squared distribution under the null hypothesis and this is done in the paper. The small-sample properties of the test statistic are investigated by simulation and found statisfactory. The test retains its power when the alternative to parameter constancy is a random walk parameter process.     

Solving the incomplete market model with aggregate uncertainty using a perturbation method

We use a perturbation method to solve the incomplete markets model with aggregate uncertainty described in den Haan et al. [Computational suite of models with heterogeneous agents: incomplete markets and model uncertainty. Journal of Economic Dynamics & Control, this issue]. To apply that method, we use a “barrier method” to replace the original problem with occasionally binding inequality constraints by one with only equality constraints. We replace the structure with a continuum of agents by a setting in which a single infinitesimal agent faces prices generated by a representative-agent economy. We also solve a model variant with a large (but finite) number of agents. Our perturbation-based method is much simpler and faster than other methods.     

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 testing for smooth structural changes in panel data models

Detecting and modeling structural changes in time series models have attracted great attention. However, relatively little effort has been paid to the testing of structural changes in panel data models despite their increasing importance in economics and finance. In this paper, we propose a new approach to testing structural changes in panel data models. Unlike the bulk of the literature on structural changes, which focuses on detection of abrupt structural changes, we consider smooth structural changes for which model parameters are unknown deterministic smooth functions of time except for a finite number of time points. We use nonparametric local smoothing method to consistently estimate the smooth changing parameters and develop two consistent tests for smooth structural changes in panel data models. The first test is to check whether all model parameters are stable over time. The second test is to check potential time-varying interaction while allowing for a common trend. Both tests have an asymptotic $N(0,1)$ distribution under the null hypothesis of parameter constancy and are consistent against a vast class of smooth structural changes as well as abrupt structural breaks with possibly unknown break points alternatives. Simulation studies show that the tests provide reliable inference in finite samples and two empirical examples with respect to a cross-country growth model and a capital structure model are discussed.