Neglected dynamics in panel data models; consequences and detection in finite samples*

The bias of various estimators for static cross-section and panel data models is assessed in a simulation study, where the actual data generating process is a dynamic adjustment mechanism with random individual effects. It is concluded that the consequences of incorrectly estimating a static model can be rather serious. Therefore, it is important to have an accurate technique available for the detection of dynamics. Two exact similar tests for the presence of a lagged dependent variable in panel data models are developed; in some simulation experiments these tests outperform standard asymptotic test procedures. Empirical results on Engle curves for food illustrate the above issues.     

The effects of dynamic feedbacks on LS and MM estimator accuracy in panel data models

The finite sample behavior is analyzed of particular least squares (LS) and a range of (generalized) method of moments (MM) estimators in panel data models with individual effects and both a lagged dependent variable regressor and another explanatory variable. The latter may be affected by lagged feedbacks from the dependent variable too. Asymptotic expansions indicate how the order of magnitude of bias of MM estimators tends to increase with the number of moment conditions exploited. They also provide analytic evidence on how the bias of the various estimators depends on the feedbacks and on other model characteristics such as prominence of individual effects and correlation between observed and unobserved heterogeneity. Simulation results corroborate the theoretical findings and reveal that in small samples of models with dynamic feedbacks none of the techniques examined dominates regarding bias and mean squared error over all parametrizations examined.     

Discrete time duration models with group-level heterogeneity

Dynamic discrete choice panel data models have received a great deal of attention. In those models, the dynamics is usually handled by including the lagged outcome as an explanatory variable. In this paper we consider an alternative model in which the dynamics is handled by using the duration in the current state as a covariate. We propose estimators that allow for group-specific effect in parametric and semiparametric versions of the model. The proposed method is illustrated by an empirical analysis of job durations allowing for firm-level effects.     

2SLS and OLS in a spatial autoregressive model with equal spatial weights

The paper considers a Cliff–Ord type spatial model with a spatially lagged dependent variable and a row normalized weighting matrix with equal weights. We show that the 2SLS and OLS estimators are inconsistent unless panel data are available. The weighting matrix in question is one which would naturally be considered if all units are neighbors to each other, and there is no other reasonable or observable measure of distance between them.     

Penalty and related estimation strategies in the spatial error model

Spatial autoregressive models are powerful tools in the analysis of data sets from diverse scientific areas of research such as econometrics, plant species richness, cancer mortality rates, image processing, analysis of the functional Magnetic Resonance Imaging (fMRI) data, and many more. An important class in the host of spatial autoregressive models is the class of spatial error models in which spatially lagged error terms are assumed. In this paper, we propose efficient shrinkage and penalty estimators for the regression coefficients of the spatial error model. We carry out asymptotic as well as simulation analyses to illustrate the gain in efficiency achieved by these new estimators. Furthermore, we apply the new methodology to housing prices data and provide a bootstrap approach to compute prediction errors of the new estimators.     

Tests on the validity of static equilibrium models

This paper provides a framework to test the validity of static cost minimizing equilibrium assumptions that form the basis for much of the empirical literature on industrial production. The point of departure in our model is to allow the observed technology to be at a short-run equilibrium where firms minimize variable costs while being constrained by the utilization levels of quasi-fixed factors. The long-run equilibrium is then inferred by minimizing total costs with the optimal adjustment of quasi-fixed factor levels.We use results from the optimization problem to form tests with respect to quantities and prices. In the quantity space version, departures between the actual and the optimal long-run levels of quasi-fixed factors are tested for statistical significance. A significant non-zero departure implies the rejection of a static equilibrium specification. In the price space version, the test is cast as a comparison of the market price and the long-run shadow value of a quasi-fixed factor. Although the two versions would give identical results in the non-stochastic case, the rejection powers of these two tests are found to depend on the particular functional form chosen to represent the production process (i.e. cost function).In an application based on aggregate U.S. manufacturing where capital is taken to be quasi-fixed, we were able to reject the static equilibrium specification. These results cast doubt on the validity of a number of previous empirical studies.     

An analysis of stock market transactions data

Many studies have argued against the strict form of the efficient markets hypothesis (EMH) by concluding that a lagged relationship exists between volume and the absolute value of a price change. These studies have denied a priori the possibility of a contemporaneous relationship. If a simultaneous relationship exists then least squares with only lagged variables suffers from omitted variable bias, and least squares with contemporaneous variables may suffer from simultaneous equations bias. Investigating these possibilities, this study demonstrates that simultaneity exists and that previous findings of a lagged relationship between the variables are therefore due to specification error. System estimation techniques suggest that the price-volume relationship is recursive, with the absolute value of a price change causing volume contemporaneously, but not conversely.     

Simulation estimation of two‐tiered dynamic panel Tobit models with an application to the labor supply of married women

In this paper a computationally practical simulation estimator is proposed for the two‐tiered dynamic panel Tobit model originally developed by Cragg ( 1971 ). The log‐likelihood function simulated through procedures based on a recursive algorithm formulated by the Geweke–Hajivassiliou–Keane simulator is maximized. The simulation estimators are then applied to study the labor supply of married women. The rich dynamic structure of the labor force participation decision as well as hours worked decisions that are conditional on the participation of married women are identified by using the proposed simulation estimators. The average partial effects of the participation and hours worked decisions for married women in response to fertility decisions and increases in the husband's income are also investigated. It is found that the hypothesis that the fertility decision is exogenous and the hypothesis that the husband's income is exogenous to married women's labor supply function are both rejected in the dynamic and static two‐tiered models. Moreover, children aged between 6 and 13 years old may have a negative impact on the hours worked decision for married women that is conditional on their participation. However, these children may provide some positive incentives for married women to participate in the labor force. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Quantile regression for dynamic panel data with fixed effects

This paper studies a quantile regression dynamic panel model with fixed effects. Panel data fixed effects estimators are typically biased in the presence of lagged dependent variables as regressors. To reduce the dynamic bias, we suggest the use of the instrumental variables quantile regression method of Chernozhukov and Hansen (2006) along with lagged regressors as instruments. In addition, we describe how to employ the estimated models for prediction. Monte Carlo simulations show evidence that the instrumental variables approach sharply reduces the dynamic bias, and the empirical levels for prediction intervals are very close to nominal levels. Finally, we illustrate the procedures with an application to forecasting output growth rates for 18 OECD countries.     

Youth unemployment and terrorism in the MENAP (Middle East,North Africa,Afghanistan, and Pakistan) region

This paper builds on existing research investigating the root causes of terrorism by considering youth unemployment as a measure of economic deprivation. In particular, the study focuses on terrorism in Middle Eastern and North African (MENAP) countries and features terrorism incident count data for the period 1998–2012 using negative binomial regression models. In our exogenous model, we find that while youth unemployment tends to increase domestic terrorism, it does not have any significant effect on transnational terrorism. Given concerns about endogeneity of youth unemployment in these models, we use two kinds of corrections-instrumental variables and lagged variables. We control for endogeneity by using military expenditure, under-five mortality rate and foreign direct investment as instruments. We are not able to reject the null hypothesis that youth unemployment is exogenous. Using lagged variables, we find a similar result as noted in the exogenous specifications with regard to the effect of youth unemployment on domestic and transnational terrorism. We also find evidence that domestic terrorism tends to have a positive relationship with press freedom, religious and linguistic fractionalization, and area of the country. Transnational terrorism has a positive association with the quality of democracy and a negative association with political stability and regulatory quality. The amount of natural resources tends to be negatively associated with domestic terrorism and positively associated with transnational terrorism.     

Using stochastic growth models to understand unit roots and breaking trends

This paper provides economic underpinnings for some recent econometric models of unit roots and breaking trends. It shows that in an endogenous growth model, difference stationarity is present in every growing variable; and this phenomenon is generated by the propagation mechanism of the model. For an exogenous growth model, either difference stationarity or trend stationarity may be present, depending on the nature of external impulses. Regarding long-run growth rates, permanent changes in economic fundamentals lead to segmented trends in endogenous growth models, but only shifting trends in exogenous growth models.     

A theory of robust long-run variance estimation

Long-run variance estimation can typically be viewed as the problem of estimating the scale of a limiting continuous time Gaussian process on the unit interval. A natural benchmark model is given by a sample that consists of equally spaced observations of this limiting process. The paper analyzes the asymptotic robustness of long-run variance estimators to contaminations of this benchmark model. It is shown that any equivariant long-run variance estimator that is consistent in the benchmark model is highly fragile: there always exists a sequence of contaminated models with the same limiting behavior as the benchmark model for which the estimator converges in probability to an arbitrary positive value. A class of robust inconsistent long-run variance estimators is derived that optimally trades off asymptotic variance in the benchmark model against the largest asymptotic bias in a specific set of contaminated models.     

Time-series–cross-section Data

This article treats the analysis of 'time-series–cross-section' (TSCS) data. Such data consists of repeated observations on a series of fixed units. Examples of such data are annual observations on the political economy of OECD nations in the post-war era. TSCS data is distinguished from 'panel' data, in that asymptotics are in the number of repeated observations, not the number of units.
The article begins by treating the complications of TSCS data in an 'old-fashioned' manner, that is, as a nuisance which causes estimation difficulties. It claims that TSCS data should be analyzed via ordinary least squares with 'panel correct standard errors' rather than generalized least squares methods. Dynamics should be modeled via a lagged dependent variable or, if appropriate, a single equation error correction model.
The article then treats more modern issues, in particular, the modeling of spatial effects and heterogeneity. It also claims that heterogeneity should be assessed with 'panel cross-validation' as well as more standard tests. The article concludes with a discussion of estimation in the presence of a binary dependent variable.     

Exponentially tilted likelihood inference on growing dimensional unconditional moment models

Growing-dimensional data with likelihood function unavailable are often encountered in various fields. This paper presents a penalized exponentially tilted (PET) likelihood for variable selection and parameter estimation for growing dimensional unconditional moment models in the presence of correlation among variables and model misspecification. Under some regularity conditions, we investigate the consistent and oracle properties of the PET estimators of parameters, and show that the constrained PET likelihood ratio statistic for testing contrast hypothesis asymptotically follows the chi-squared distribution. Theoretical results reveal that the PET likelihood approach is robust to model misspecification. We study high-order asymptotic properties of the proposed PET estimators. Simulation studies are conducted to investigate the finite performance of the proposed methodologies. An example from the Boston Housing Study is illustrated.     

Formulation and estimation of dynamic models using panel data

This paper presents a statistical analysis of time series regression models for longitudinal data with and without lagged dependent variables under a variety of assumptions about the initial conditions of the processes being analyzed. The analysis demonstrates how the asymptotic properties of estimators of longitudinal models are critically dependent on the manner in which samples become large: by expanding the number of observations per person, holding the number of people fixed, or by expanding the number of persons, holding the number of observations per person fixed. The paper demonstrates which parameters can and cannot be identified from data produced by different sampling plans.     

The effect of housing and stock market wealth on consumption in emerging and developed countries

This study examines the long- and short-run relationship between private consumption, housing wealth, stock market wealth and income. In order to asses this relationship empirically, we use pooled mean group estimators of dynamic heterogeneous panel data on a sample of 30 developed and emerging economies. The sample countries are segmented into three separate panels: a developed bank-based panel, a developed market-based panel, and an emerging bank-based panel. Empirical estimates support the existence of long- and short-run stock market wealth effects in both groups of developed countries, with the effect being particularly strong in the developed market-based countries. A moderate long-run housing wealth effect is confirmed only for the developed bank-based countries, while a very strong short-run housing wealth effect is present in the developed market-based countries. As far as the emerging countries are concerned, the evidence is somewhat inconclusive, but it does seem to suggest that both wealth effects are effective in the long run, with housing wealth being more dominant.     

Nonlinear minimization estimators in the presence of cointegrating relations

In this paper, we consider estimation of a long-run and a short-run parameter jointly in the presence of nonlinearities. The theory developed establishes limit behavior of minimization estimators of the long- and short-run parameters jointly. Typically, if the long-run parameter that is present in a cointegrating relationship is estimated, its estimator will be superconsistent. Therefore, we may conjecture that the joint minimization estimation of both parameters jointly will result in the same limit distribution for the short-run parameter as if the long-run parameter was known. However, we show that unless a regularity condition holds, this intuition is false in general. This regularity condition, that clearly holds in the standard linear case, is identical to the condition for validity of a two-step Granger–Engle type procedure. Also, it is shown that if the cointegrated variables are measured in deviation from their averages, the standard asymptotic normality result (that one would obtain if the long-run parameter was known) holds.     

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.