Adjustment and unobserved heterogeneity in dynamic stochastic frontier models

Stochastic frontier models with autocorrelated inefficiency have been proposed in the past as a way of addressing the issue of temporal variation in firm-level efficiency scores. They are justified using an underlying model of dynamic firm behavior. In this paper we argue that these models could have radically different implications for the expected long-run efficiency scores in the presence of unobserved heterogeneity. The possibility of accounting for unobserved heterogeneity is explored. Random- and correlated random-effects dynamic stochastic frontier models are proposed and applied to a panel of US electric utilities.     

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.     

Spatial stochastic frontier models: accounting for unobserved local determinants of inefficiency

This paper analyzes the productivity of farms across 370 municipalities in the Center-West region of Brazil. A stochastic frontier model with a latent spatial structure is proposed to account for possible unknown geographical variation of the outputs. The paper compares versions of the model that include the latent spatial effect in the mean of output or as a variable that conditions the distribution of inefficiency, include or not observed municipal variables, and specify independent normal or conditional autoregressive priors for the spatial effects. The Bayesian paradigm is used to estimate the proposed models. As the resultant posterior distributions do not have a closed form, stochastic simulation techniques are used to obtain samples from them. Two model comparison criteria provide support for including the latent spatial effects, even after considering covariates at the municipal level. Models that ignore the latent spatial effects produce significantly different rankings of inefficiencies across agents.

Quantile regression under random censoring

Censored regression models have received a great deal of attention in both the theoretical and applied econometric literature. Most of the existing estimation procedures for either cross-sectional or panel data models are designed only for models with fixed censoring. In this paper, a new procedure for adapting these estimators designed for fixed censoring to models with random censoring is proposed. This procedure is then applied to the CLAD and quantile estimators of Powell (J. Econom. 25 (1984) 303, 32 (1986a) 143) to obtain an estimator of the coefficients under a mild conditional quantile restriction on the error term that is applicable to samples exhibiting fixed or random censoring. The resulting estimator is shown to have desirable asymptotic properties, and performs well in a small-scale simulation study.     

Linear prediction and estimation methods for regression models with stationary stochastic coefficients

A linear regression model is proposed in which the coefficient vector is a weakly stationary multivariate stochastic process. The model provides a convinient representation of a general class of nonstationary processes. Prediction and estimation methods are proposed that are linear and relatively easy to compute. The proposed procedures are illustrated by estimation of time-varying GNP multipliers of several macro policy instruments over the period 1891-1970. The results are compatible with theoretical priors and suggest that predictability of policy outcomes depends on the mixture of policy instruments.     

Semiparametric Bayesian inference for dynamic Tobit panel data models with unobserved heterogeneity

This paper develops semiparametric Bayesian methods for inference of dynamic Tobit panel data models. Our approach requires that the conditional mean dependence of the unobserved heterogeneity on the initial conditions and the strictly exogenous variables be specified. Important quantities of economic interest such as the average partial effect and average transition probabilities can be readily obtained as a by‐product of the Markov chain Monte Carlo run. We apply our method to study female labor supply using a panel data set from the National Longitudinal Survey of Youth 1979. Copyright © 2008 John Wiley & Sons, Ltd.     

Identification and estimation of nonlinear dynamic panel data models with unobserved covariates

This paper considers nonparametric identification of nonlinear dynamic models for panel data with unobserved covariates. Including such unobserved covariates may control for both the individual-specific unobserved heterogeneity and the endogeneity of the explanatory variables. Without specifying the distribution of the initial condition with the unobserved variables, we show that the models are nonparametrically identified from two periods of the dependent variable _Yit$Y_{it}$ and three periods of the covariate _Xit$X_{it}$. The main identifying assumptions include high-level injectivity restrictions and require that the evolution of the observed covariates depends on the unobserved covariates but not on the lagged dependent variable. We also propose a sieve maximum likelihood estimator (MLE) and focus on two classes of nonlinear dynamic panel data models, i.e., dynamic discrete choice models and dynamic censored models. We present the asymptotic properties of the sieve MLE and investigate the finite sample properties of these sieve-based estimators through a Monte Carlo study. An intertemporal female labor force participation model is estimated as an empirical illustration using a sample from the Panel Study of Income Dynamics (PSID).     

Identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity

We extend the identification results for nonparametric simultaneous equations models in Matzkin (2008) to situations where the observations on the vector of dependent variables might be limited, and where the number of exogenous unobservable variables is larger than the number of dependent variables.     

Partial rank estimation of duration models with general forms of censoring

In this paper we propose estimators for the regression coefficients in censored duration models which are distribution free, impose no parametric specification on the baseline hazard function, and can accommodate general forms of censoring. The estimators are shown to have desirable asymptotic properties and Monte Carlo simulations demonstrate good finite sample performance. Among the data features the new estimators can accommodate are covariate-dependent censoring, double censoring, and fixed (individual or group specific) effects. We also examine the behavior of the estimator in an empirical illustration.     

Simple solutions to the initial conditions problem in dynamic,nonlinear panel data models with unobserved heterogeneity

I study a simple, widely applicable approach to handling the initial conditions problem in dynamic, nonlinear unobserved effects models. Rather than attempting to obtain the joint distribution of all outcomes of the endogenous variables, I propose finding the distribution conditional on the initial value (and the observed history of strictly exogenous explanatory variables). The approach is flexible, and results in simple estimation strategies for at least three leading dynamic, nonlinear models: probit, Tobit and Poisson regression. I treat the general problem of estimating average partial effects, and show that simple estimators exist for important special cases. Copyright © 2005 John Wiley & Sons, Ltd.     

Option pricing with stochastic volatility models

A general class of models for derivative pricing with stochastic volatility is analyzed. We include the possibility of jumps for the paths of the asset's price and for those of its volatility. We also consider the case of correlation between the process of the asset's price and that of its volatility. In this way we are able to give a unifying view on most of the models studied in the literature. We will examine theoretical issues related to the market price of volatility risk, the equivalent martingale measures and the possibility of obtaining a numerically tractable formula for contingent claim pricing. Finally, we propose some methodologies to test the behavior of stochastic volatility models when applied to market data.     

Quasi-isotonic regression and stochastic approximation

Summary Mukerjee’s stochastic approximation procedure on a lattice is modified: at each stage of the procedure, a sample quasi-isotonic regression is calculated instead of the isotonic one, the former being defined as the least-squares fit of observations within the class of functions that are nonpositive on the left and nonnegative on the right of some point. An effective algorithm is given and a convergence theorem proven. A multidimensional version of the procedure is proposed, the question of its convergence being left open. Research supported by the Deutsche Forschungsgemeinschaft, SFB 72.     

Testing for unobserved heterogeneity in exponential and Weibull duration models

We examine the use of the likelihood ratio (LR) statistic to test for unobserved heterogeneity in duration models, based on mixtures of exponential or Weibull distributions. We consider both the uncensored and censored duration cases. The asymptotic null distribution of the LR test statistic is not the standard chi-square, as the standard regularity conditions do not hold. Instead, there is a nuisance parameter identified only under the alternative, and a null parameter value on the boundary of the parameter space, as in Cho and White (2007a). We accommodate these and provide methods delivering consistent asymptotic critical values. We conduct a number of Monte Carlo simulations, comparing the level and power of the LR test statistic to an information matrix (IM) test due to Chesher (1984) and Lagrange multiplier (LM) tests of Kiefer (1985) and Sharma (1987). Our simulations show that the LR test statistic generally outperforms the IM and LM tests. We also revisit the work of van den Berg and Ridder (1998) on unemployment durations and of Ghysels et al. (2004) on interarrival times between stock trades, and, as it turns out, affirm their original informal inferences.     

Automatic selection of unobserved components models for supply chain forecasting

For many companies, automatic forecasting has come to be an essential part of business analytics applications. The large amounts of data available, the short life-cycle of the analysis and the acceleration of business operations make traditional manual data analysis unfeasible in such environments. In this paper, an automatic forecasting support system that comprises several methods and models is developed in a general state space framework built in the SSpace toolbox written for Matlab. Some of the models included are well-known, such as exponential smoothing and ARIMA, but we also propose a new model family that has been used only very rarely in this context, namely unobserved components models. Additional novelties include the use of unobserved components models in an automatic identification environment and the comparison of their forecasting performances with those of exponential smoothing and ARIMA models estimated using different software packages. The new system is tested empirically on a daily dataset of all of the products sold by a franchise chain in Spain (166 products over a period of 517 days). The system works well in practice and the proposed automatic unobserved components models compare very favorably with other methods and other well-known software packages in forecasting terms.     

Fitting nonlinear time-series models with applications to stochastic variance models

New strategies for the implementation of maximum likelihood estimation of nonlinear time series models are suggested. They make use of recent work on the EM algorithm and iterative simulation techniques. The estimation procedures are applied to the problem of fitting stochastic variance models to exchange rate data.     

Forecasting in dynamic models with stochastic regressors

When a dependent variable y is related to present and past values of an exogenous variable x in a dynamic regression (distributed lag) model, and when x must be forecast in order to forecast y, necessary and sufficient conditions are derived in order for optimal forecasts of y to possess lower mean square error as a result of including x in the model, relative to forecasting y solely from its own past. The contribution to this forecast MSE reduction of non-invertibility in the lag distribution is assessed. Examples from econometrics and engineering are provided to illustrate the results.     

Inference in regression models with many regressors

We investigate the behavior of various standard and modified F$F$, likelihood ratio (LR$LR$), and Lagrange multiplier (LM$LM$) tests in linear homoskedastic regressions, adapting an alternative asymptotic framework in which the number of regressors and possibly restrictions grows proportionately to the sample size. When the restrictions are not numerous, the rescaled classical test statistics are asymptotically chi-squared, irrespective of whether there are many or few regressors. However, when the restrictions are numerous, standard asymptotic versions of classical tests are invalid. We propose and analyze asymptotically valid versions of the classical tests, including those that are robust to the numerosity of regressors and restrictions. The local power of all asymptotically valid tests under consideration turns out to be equal. The “exact” F$F$ test that appeals to critical values of the F$F$ distribution is also asymptotically valid and robust to the numerosity of regressors and restrictions.