Smoothly mixing regressions

This paper extends the conventional Bayesian mixture of normals model by permitting state probabilities to depend on observed covariates. The dependence is captured by a simple multinomial probit model. A conventional and rapidly mixing MCMC algorithm provides access to the posterior distribution at modest computational cost. This model is competitive with existing econometric models, as documented in the paper's illustrations. The first illustration studies quantiles of the distribution of earnings of men conditional on age and education, and shows that smoothly mixing regressions are an attractive alternative to nonBayesian quantile regression. The second illustration models serial dependence in the S&P 500 return, and shows that the model compares favorably with ARCH models using out of sample likelihood criteria.     

Econometric analysis of jump-driven stochastic volatility models

This paper introduces and studies the econometric properties of a general new class of models, which I refer to as jump-driven stochastic volatility models, in which the volatility is a moving average of past jumps. I focus attention on two particular semiparametric classes of jump-driven stochastic volatility models. In the first, the price has a continuous component with time-varying volatility and time-homogeneous jumps. The second jump-driven stochastic volatility model analyzed here has only jumps in the price, which have time-varying size. In the empirical application I model the memory of the stochastic variance with a CARMA(2,1) kernel and set the jumps in the variance to be proportional to the squared price jumps. The estimation, which is based on matching moments of certain realized power variation statistics calculated from high-frequency foreign exchange data, shows that the jump-driven stochastic volatility model containing continuous component in the price performs best. It outperforms a standard two-factor affine jump–diffusion model, but also the pure-jump jump-driven stochastic volatility model for the particular jump specification.     

Censored regression quantiles with endogenous regressors

This paper develops a semiparametric method for estimation of the censored regression model when some of the regressors are endogenous (and continuously distributed) and instrumental variables are available for them. A “distributional exclusion” restriction is imposed on the unobservable errors, whose conditional distribution is assumed to depend on the regressors and instruments only through a lower-dimensional “control variable,” here assumed to be the difference between the endogenous regressors and their conditional expectations given the instruments. This assumption, which implies a similar exclusion restriction for the conditional quantiles of the censored dependent variable, is used to motivate a two-stage estimator of the censored regression coefficients. In the first stage, the conditional quantile of the dependent variable given the instruments and the regressors is nonparametrically estimated, as are the first-stage reduced-form residuals to be used as control variables. The second-stage estimator is a weighted least squares regression of pairwise differences in the estimated quantiles on the corresponding differences in regressors, using only pairs of observations for which both estimated quantiles are positive (i.e., in the uncensored region) and the corresponding difference in estimated control variables is small. The paper gives the form of the asymptotic distribution for the proposed estimator, and discusses how it compares to similar estimators for alternative models.     

Frequency domain estimation of temporally aggregated Gaussian cointegrated systems

This paper considers joint estimation of long run equilibrium coefficients and parameters governing the short run dynamics of a fully parametric Gaussian cointegrated system formulated in continuous time. The model allows the stationary disturbances to be generated by a stochastic differential equation system and for the variables to be a mixture of stocks and flows. We derive a precise form for the exact discrete analogue of the continuous time model in triangular error correction form, which acts as the basis for frequency domain estimation of the unknown parameters using discrete time data. We formally establish the order of consistency and the asymptotic sampling properties of such an estimator. The estimator of the cointegrating parameters is shown to converge at the rate of the sample size to a mixed normal distribution, while that of the short run parameters converges at the rate of the square root of the sample size to a limiting normal distribution.     

Pseudo conditional maximum likelihood estimation of the dynamic logit model for binary panel data

We show how the dynamic logit model for binary panel data may be approximated by a quadratic exponential model. Under the approximating model, simple sufficient statistics exist for the subject-specific parameters introduced to capture the unobserved heterogeneity between subjects. The latter must be distinguished from the state dependence which is accounted for by including the lagged response variable among the regressors. By conditioning on the sufficient statistics, we derive a pseudo conditional likelihood estimator of the structural parameters of the dynamic logit model, which is simple to compute. Asymptotic properties of this estimator are studied in detail. Simulation results show that the estimator is competitive in terms of efficiency with estimators recently proposed in the econometric literature.     

Identification with latent variables

This is an essay on a unified approach to the identifiability problem in static models with and without hidden endogenous variables. As is well known, when some of these variables are unobserved, the prior information requirements for models when all endogenous variables are observed, are still there. In addition, extra prior information that takes the place of the means and covariances of the missing variables will have to be supplied directly or indirectly by the statistical researcher. In the paper we characterize the quality and quantity of the required information for the general linear static model and apply it when the model is i) an econometric demand and supply model with missing observations on the quantity transacted, ii) a factor analysis model with observed characteristics of the test takers and iii) a LISREL Model without fixed exogenous variables. With unknown true parameters, the exact rank conditions are seldom verifiable but we do recommend an implementable check-list that is adequate for almost all parameters.     

Engel's Law Reconsidered

Engel's Law expresses a negative stochastic association of the bivariate distribution of income and food share across a population. Among the many different definitions which can be found in the statistical literature four concepts are discussed and tested: Kendall's τ, quadrant dependence, stochastic decreasing conditional food share distribution function and decreasing regression. Only the last one is used in the economic literature, yet it does not imply useful information of the underlying distribution. For linking Engels's Law to micro-economics, stronger concepts of stochastic association are needed. This motivates the empirical study of the proposed alternative concepts of negative association.     

Making a match: Combining theory and evidence in policy-oriented macroeconomic modeling

A persistent question in the development of models for macroeconomic policy analysis has been the relative role of economic theory and evidence in their construction. This paper looks at some popular strategies that involve setting up a theoretical or conceptual model (CM) which is transformed to match the data and then made operational for policy analysis. A dynamic general equilibrium model is constructed that is similar to standard CMs. After calibration to UK data it is used to examine the utility of formal econometric methods in assessing the match of the CM to the data and also to evaluate some standard model-building strategies.     

Local structural quantile effects in a model with a nonseparable control variable

I consider a semiparametric version of the nonseparable triangular model of Chesher [Chesher, A., 2003. Identification in nonseparable models. Econometrica 71, 1405–1441]. The proposed model is linear in coefficients, where the coefficients are unknown functions of unobserved latent variables. Using a control variable idea and quantile regression methods, I propose a simple two-step estimator for the coefficients evaluated at particular values of the latent variables. Under the condition that the instruments are locally relevant (i.e. they affect a particular conditional quantile of interest of the endogenous variable) I establish consistency and asymptotic normality. Simulation experiments confirm the theoretical results.     

Endogeneity in quantile regression models: A control function approach

This paper considers a linear triangular simultaneous equations model with conditional quantile restrictions. The paper adjusts for endogeneity by adopting a control function approach and presents a simple two-step estimator that exploits the partially linear structure of the model. The first step consists of estimation of the residuals of the reduced-form equation for the endogenous explanatory variable. The second step is series estimation of the primary equation with the reduced-form residual included nonparametrically as an additional explanatory variable. This paper imposes no functional form restrictions on the stochastic relationship between the reduced-form residual and the disturbance term in the primary equation conditional on observable explanatory variables. The paper presents regularity conditions for consistency and asymptotic normality of the two-step estimator. In addition, the paper provides some discussions on related estimation methods in the literature.     

Bayesian modeling of joint and conditional distributions

In this paper, we study a Bayesian approach to flexible modeling of conditional distributions. The approach uses a flexible model for the joint distribution of the dependent and independent variables and then extracts the conditional distributions of interest from the estimated joint distribution. We use a finite mixture of multivariate normals (FMMN) to estimate the joint distribution. The conditional distributions can then be assessed analytically or through simulations. The discrete variables are handled through the use of latent variables. The estimation procedure employs an MCMC algorithm. We provide a characterization of the Kullback–Leibler closure of FMMN and show that the joint and conditional predictive densities implied by the FMMN model are consistent estimators for a large class of data generating processes with continuous and discrete observables. The method can be used as a robust regression model with discrete and continuous dependent and independent variables and as a Bayesian alternative to semi- and non-parametric models such as quantile and kernel regression. In experiments, the method compares favorably with classical nonparametric and alternative Bayesian methods.     

Testing for structural change in regression quantiles

Most studies in the structural change literature focus solely on the conditional mean, while under various circumstances, structural change in the conditional distribution or in conditional quantiles is of key importance. This paper proposes several tests for structural change in regression quantiles. Two types of statistics are considered, namely, a fluctuation type statistic based on the subgradient and a Wald type statistic, based on comparing parameter estimates obtained from different subsamples. The former requires estimating the model under the null hypothesis, and the latter involves estimation under the alternative hypothesis. The tests proposed can be used to test for structural change occurring in a pre-specified quantile, or across quantiles, which can be viewed as testing for change in the conditional distribution with a linear specification of the conditional quantile function. Both single and multiple structural changes are considered. We derive the limiting distributions under the null hypothesis, and show they are nuisance parameter free and can be easily simulated. A simulation study is conducted to assess the size and power in finite samples.     

Testing for time-invariant unobserved heterogeneity in generalized linear models for panel data

Recent literature on panel data emphasizes the importance of accounting for time-varying unobservable individual effects, which may stem from either omitted individual characteristics or macro-level shocks that affect each individual unit differently. In this paper, we propose a simple specification test of the null hypothesis that the individual effects are time-invariant against the alternative that they are time-varying. Our test is an application of Hausman (1978) testing procedure and can be used for any generalized linear model for panel data that admits a sufficient statistic for the individual effect. This is a wide class of models which includes the Gaussian linear model and a variety of nonlinear models typically employed for discrete or categorical outcomes. The basic idea of the test is to compare two alternative estimators of the model parameters based on two different formulations of the conditional maximum likelihood method. Our approach does not require assumptions on the distribution of unobserved heterogeneity, nor it requires the latter to be independent of the regressors in the model. We investigate the finite sample properties of the test through a set of Monte Carlo experiments. Our results show that the test performs well, with small size distortions and good power properties. We use a health economics example based on data from the Health and Retirement Study to illustrate the proposed test.     

Restrictions on variables

Accounting identities impose exact restrictions on the endogenous variables of econometric models. Such restrictions are usually met by choosing a closing entry or by building an allocation model. Selecting a closing entry may be difficult or arbitrary, while allocation models admit little flexibility in the choice of explanatory variables and lagged adjustment schemes. This paper studies a third solution which in a sense lies inbetween: freely chosen equations for all variables are adjusted additively such that the restrictions will hold. The adjustment involves some new parameters which can be estimated simultaneously with the original parameters using Maximum Likelihood techniques.An application is provided for a financial model of the Dutch private sector. Our approach here proves superior to any choice of closing entry in the system.     

Evaluation of dynamic stochastic general equilibrium models based on distributional comparison of simulated and historical data

We take as a starting point the existence of a joint distribution implied by different dynamic stochastic general equilibrium (DSGE) models, all of which are potentially misspecified. Our objective is to compare “true” joint distributions with ones generated by given DSGEs. This is accomplished via comparison of the empirical joint distributions (or confidence intervals) of historical and simulated time series. The tool draws on recent advances in the theory of the bootstrap, Kolmogorov type testing, and other work on the evaluation of DSGEs, aimed at comparing the second order properties of historical and simulated time series. We begin by fixing a given model as the “benchmark” model, against which all “alternative” models are to be compared. We then test whether at least one of the alternative models provides a more “accurate” approximation to the true cumulative distribution than does the benchmark model, where accuracy is measured in terms of distributional square error. Bootstrap critical values are discussed, and an illustrative example is given, in which it is shown that alternative versions of a standard DSGE model in which calibrated parameters are allowed to vary slightly perform equally well. On the other hand, there are stark differences between models when the shocks driving the models are assigned non-plausible variances and/or distributional assumptions.     

A new instrumental method for dealing with endogenous selection

This paper develops a new method for dealing with endogenous selection. The usual instrumental strategy based on the independence between the outcome and the instrument is likely to fail when selection is directly driven by the dependent variable. Instead, we suggest to rely on the independence between the instrument and the selection variable, conditional on the outcome. This approach may be particularly suitable for nonignorable nonresponse, binary models with missing covariates or Roy models with an unobserved sector. The nonparametric identification of the joint distribution of the variables is obtained under a completeness assumption, which has been used recently in several nonparametric instrumental problems. Even if the conditional independence between the instrument and the selection variable fails to hold, the approach provides sharp bounds on parameters of interest under weaker monotonicity conditions. Apart from identification, nonparametric and parametric estimations are also considered. Finally, the method is applied to estimate the effect of grade retention in French primary schools.     

Identifying Conditional Conservatism

Abstract

This paper provides guidance for empiricists interested in measuring conditional conservatism and in interpreting associations of those measures with variables of interest. I begin by discussing the nature and importance of conditional conservatism and surveying the literature identifying conditional conservatism. I then describe and comment on the various limitations of asymmetric timeliness identified in the literature. Despite these limitations, I argue that asymmetric timeliness is the most direct implication of conditional conservatism, and that alternative measures that have been proposed need not capture any type of conservatism. Finally, I provide four specific suggestions for estimating asymmetric timeliness and for interpreting it as a measure of conditional conservatism.     

More on connections between Wishart and matrix GIG distributions

The paper is devoted to relations between the matrix GIG and Wishart distributions. Our basic tool in the first part is a version of the Matsumoto-Yor property for matrix variables. This approach covers the following issues: the Herz identity for the Bessel function of matrix variate argument, characterization of a class of Wishart matrices and linear transformations of the matrix GIG distribution. The Bayesian Wishart model, studied in the second part, gives an alternative definition of the matrix GIG distribution. Such a model is characterized by linearity of conditional expectations and matrix GIG conditional distribution. It is also extended to Bayesian matrix GIG models, in the framework of which an interesting independence property is proved.     

Identification and information in monotone binary models

This paper considers binary response models where errors are uncorrelated with a set of instrumental variables and are independent of a continuous regressor v$v$, conditional on all other variables. It is shown that these exclusion restrictions are not sufficient for identification and that additional identifying assumptions are needed. Such an assumption, introduced by Lewbel [Semiparametric qualitative response model estimation with unknown heteroskedasticity or instrumental variables. Journal of Econometrics 97, 145–177], is that the support of the continuous regressor is large, but we show that it significantly restricts the class of binary phenomena which can be analysed. We propose an alternative additional assumption under which β$\beta$ remains just identified and the estimation unchanged. This alternative assumption does not impose specific restrictions on the data, which broadens the scope of the estimation method in empirical work. The semiparametric efficiency bound of the model is also established and an existing estimator is shown to achieve that bound. The efficient estimator uses a plug-in density estimate. It is shown that plugging in the true density rather than an estimate is inefficient. Extensions to ordered choice models are provided.     

存在遗漏变量时的内生性研究

存在遗漏变量时回归系数的估计是计量经济学的一个重要内容。本文讨论单方程计量经济模型中随机解释变量的内生性,指出了目前的计量经济理论所存在的问题,提出了普通最小二乘估计一致性判别的新方法,并证明了存在遗漏变量情况下的普通最小二乘估计仍是一致估计。