Residual‐based IV estimation of dynamic panel data models with fixed effects

In dynamic panel regression, when the variance ratio of individual effects to disturbance is large, the system‐GMM estimator will have large asymptotic variance and poor finite sample performance. To deal with this variance ratio problem, we propose a residual‐based instrumental variables (RIV) estimator, which uses the residual from regressing Δy_i,t?1 on as the instrument for the level equation. The RIV estimator proposed is consistent and asymptotically normal under general assumptions. More importantly, its asymptotic variance is almost unaffected by the variance ratio of individual effects to disturbance. Monte Carlo simulations show that the RIV estimator has better finite sample performance compared to alternative estimators. The RIV estimator generates less finite sample bias than difference‐GMM, system‐GMM, collapsing‐GMM and Level‐IV estimators in most cases. Under RIV estimation, the variance ratio problem is well controlled, and the empirical distribution of its t‐statistic is similar to the standard normal distribution for moderate sample sizes.     

Simulation Estimation of Two‐tiered Dynamic Panel Tobit Models with an Application to the labour Supply of Married Women: A Comment

We find that the empirical results reported in Chang (Journal of Applied Econometrics 2011; 26 (5): 854–871) are contingent on the specification of the model. The use of Heckman's initial conditions combined with observed and not latent lagged dependent variables leads to a counter‐intuitive estimation of the true state dependence. The use of Wooldridge's initial conditions together with the observed lagged dependent variable and a proper modelling of censoring provides a much more natural estimate of the true state dependence parameters together with a clearer interpretation of the decision to participate in the labour market in the two‐tiered model. Copyright © 2015 John Wiley & Sons, Ltd.     

The estimation of utility‐consistent labor supply models by means of simulated scores

We consider a utility‐consistent static labor supply model with flexible preferences and a nonlinear and possibly non‐convex budget set. Stochastic error terms are introduced to represent optimization and reporting errors, stochastic preferences, and heterogeneity in wages. Coherency conditions on the parameters and the support of error distributions are imposed for all observations. The complexity of the model makes it impossible to write down the probability of participation. Hence we use simulation techniques in the estimation. We compare our approach with various simpler alternatives proposed in the literature. Both in Monte Carlo experiments and for real data the various estimation methods yield very different results. Copyright © 2008 John Wiley & Sons, Ltd.     

On solving bias‐corrected non‐linear estimation equations with an application to the dynamic linear model

In a seminal paper, Mak, Journal of the Royal Statistical Society B, 55, 1993, 945, derived an efficient algorithm for solving non‐linear unbiased estimation equations. In this paper, we show that when Mak's algorithm is applied to biased estimation equations, it results in the estimates that would come from solving a bias‐corrected estimation equation, making it a consistent estimator if regularity conditions hold. In addition, the properties that Mak established for his algorithm also apply in the case of biased estimation equations but for estimates from the bias‐corrected equations. The marginal likelihood estimator is obtained when the approach is applied to both maximum likelihood and least squares estimation of the covariance matrix parameters in the general linear regression model. The new approach results in two new estimators when applied to the profile and marginal likelihood functions for estimating the lagged dependent variable coefficient in the dynamic linear regression model. Monte Carlo simulation results show the new approach leads to a better estimator when applied to the standard profile likelihood. It is therefore recommended for situations in which standard estimators are known to be biased.     

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).     

Estimation of linear dynamic panel data models with time‐invariant regressors

We present a sequential approach to estimating a dynamic Hausman–Taylor model. We first estimate the coefficients of the time‐varying regressors and subsequently regress the first‐stage residuals on the time‐invariant regressors. In comparison to estimating all coefficients simultaneously, this two‐stage procedure is more robust against model misspecification, allows for a flexible choice of the first‐stage estimator, and enables simple testing of the overidentifying restrictions. For correct inference, we derive analytical standard error adjustments. We evaluate the finite‐sample properties with Monte Carlo simulations and apply the approach to a dynamic gravity equation for US outward foreign direct investment.     

Small‐sample bias in synthetic cohort models of labor supply

This paper investigates small‐sample biases in synthetic cohort models (repeated cross‐sectional data grouped at the cohort and year level) in the context of a female labor supply model. I use the Current Population Survey to compare estimates when group sizes are extremely large to those that arise from randomly drawing subsamples of observations from the large groups. I augment this approach with Monte Carlo analysis so as to precisely quantify biases and coverage rates. In this particular application, thousands of observations per group are required before small‐sample issues can be ignored in estimation and sampling error leads to large downward biases in the estimated income elasticity. Copyright © 2007 John Wiley & Sons, Ltd.     

A collective labor supply model with complementarities in leisure: Identification and estimation by means of panel data

We present a novel identification strategy for a collective labor supply model that allows for complementarities in leisure (i.e., individuals may enjoy leisure more in company of their spouse). Individual preferences and the Pareto weights (which capture the intra-household bargaining process) are identified by making use of panel data with couples and individuals who became a widow(er) in the observation period, along with the assumption that an individual's preferences can only change in a particular manner after the spouse's death. The change in preferences comes from changes in observable variables that can be controlled for (like mental health) and from the loss of the possibility to jointly enjoy leisure after the couple's dissolution. We apply the model to American households coming from the first nine waves of the Health and Retirement Study (1992-2008) and show that complementarities in leisure are indeed important when modeling spouses' labor supply choices.     

Autocorrelation and dynamic methodology with an application to wage determination models

A demonstration is provided of rigorous, statistical methodology whereby both the type and order of an error process can be identified in dynamic, single equation econometric models. The paper relies heavily upon maximum likelihood estimation, nested likelihood ratio tests and the overfitting or exponentially weighted procedure for model selection. An application of the methodology to a class of quarterly wage determination models is included.     

Finite‐sample comparison of alternative methods for estimating dynamic panel data models

The Wooldridge method is based on a simple and novel strategy to deal with the initial values problem in nonlinear dynamic random‐effects panel data models. The characteristic of the method makes it very attractive in empirical applications. However, its finite sample performance and robustness are not fully known as of yet. In this paper we investigate the performance and robustness of this method in comparison with an ideal case in which the initial values are known constants; the worst scenario is based on an exogenous initial values assumption, and the Heckman's reduced‐form approximation method, which is widely used in the literature. The dynamic random‐effects probit and Tobit (type I) models are used as working examples. Various designs of the Monte Carlo experiments and two further empirical illustrations are provided. The results suggest that the Wooldridge method works very well only for the panels of moderately long duration (longer than 5–8 periods). Heckman's reduced‐form approximation is suggested for short panels (shorter than 5 periods). It is also found that all the methods tend to perform equally well for panels of long duration (longer than 15–20 periods). Copyright © 2011 John Wiley & Sons, Ltd.     

R&D and subsidies at the firm level: an application of parametric and semiparametric two‐step selection models

This paper analyzes the effect of public R&D subsidies on firms' private R&D investment per employee and new product sales in German manufacturing. Parametric and semiparametric two‐step selection models are applied to this evaluation problem. The results show that the average treatment effect on the treated firms' R&D intensity is positive. The estimated effects are robust with respect to the different selection models. Further results show that publicly induced R&D spending is as productive as private R&D investment in generating new product sales. Copyright © 2008 John Wiley & Sons, Ltd.     

Comparative statics in dynamic programming models with an application to job search

This paper presents a technique for qualitative comparative statics analysis in dynamic programming models. Let the value function υ be the fixed point of a contraction mapping which depends differentiably on some exogenous parameter θ. Ten the derivative of υ with respect to θ exists and is also the fixed point of a contraction mapping. Since this derivative is the fixed point of a contraction mapping, its qualitative properties can be investigated using mathematical induction. This comparative statics methodology is illustrated with an application to a model of job search.     

Dynamic models of the labor force behavior of married women which can be estimated using limited amounts of past information

This paper examines the extent of the inadequacy of standard cross-sectional models of US labor force behavior and considers the abilities of alternative models to capture the observed continuity in the hours of work and earnings of individuals as well as in their employment histories. Both of the alternatives to the standard cross-sectional model considered in this study incorporate limited amounts of information about past work behavior that could easily be collected as part of a national population census. Using a population of 21 to 64 year old married working women taken from a 1969 through 1978 Michigan Panel Study of Income Dynamics, the variables included in the Z vector age: 1) age of the wife; 2) education of the wife; 3) state average hourly wage in manufacturing measured in 1967 dollars; and 4) unemployment rate for the state in which the wife lives. Results show that by using information about a women's hours of work and wage rate in the previous year, it may be feasible to improve on forecasts of a woman's employment and earnings behavior. For each model a separate estimate is made for wives aged 21 through 46, and for those aged 47 through 64. The dummy and difference models perform much better than the standard model, with the dummy model having the higher pseudo-chi-square statistic. These models show that systematic errors made in determining which individuals work, what they earn per hour, or how many hours they work, should result in prediction errors of the same sort year after year in the computation of annual earnings. These findings with respect to years of work and nonwork, years of part time versus full time work, and cumulative earnings over a 10 year period, confirm and extend Heckman's findings; thus, forecasting models of the work behavior of individuals should not be estimated using pure cross-sectional data. It would be important if researchers could identify what observable factors, if any, increase the likelihood that wives will alter their work behavior from what it has been in the immediate past, even if they are not able to fully understand or explain this previous work behavior.     

Bayesian analysis of the two‐part model with endogeneity: application to health care expenditure

This paper studies the effect of managed care on medical expenditure using a model in which the insurance status is assumed to be endogenous. Insurance plan choice is modeled through the multinomial probit model. The medical expenditure variable, the outcome of interest, has a significant proportion of zeros that are handled using the two‐part model, extended to handle endogenous insurance. The estimation approach is Bayesian, based on the Gibbs Sampler. The model is applied to a sample of 20 460 individuals obtained from the Medical Expenditure Panel Survey. The results provide substantial evidence of selectivity. Copyright © 2006 John Wiley & Sons, Ltd.     

Half‐panel jackknife fixed‐effects estimation of linear panels with weakly exogenous regressors

This paper considers estimation and inference in linear panel regression models with lagged dependent variables and/or other weakly exogenous regressors when N (the cross‐section dimension) is large relative to T (the time series dimension). It allows for fixed and time effects (FE‐TE) and derives a general formula for the bias of the FE‐TE estimator which generalizes the well‐known Nickell bias formula derived for the pure autoregressive dynamic panel data models. It shows that in the presence of weakly exogenous regressors inference based on the FE‐TE estimator will result in size distortions unless N/T is sufficiently small. To deal with the bias and size distortion of the FE‐TE estimator the use of a half‐panel jackknife FE‐TE estimator is considered and its asymptotic distribution is derived. It is shown that the bias of the half‐panel jackknife FE‐TE estimator is of order T^?2, and for valid inference it is only required that N/T³→0, as N,T→∞ jointly. Extension to unbalanced panel data models is also provided. The theoretical results are illustrated with Monte Carlo evidence. It is shown that the FE‐TE estimator can suffer from large size distortions when N>T, with the half‐panel jackknife FE‐TE estimator showing little size distortions. The use of half‐panel jackknife FE‐TE estimator is illustrated with two empirical applications from the literature.     

On Markov error‐correction models,with an application to stock prices and dividends

This paper considers Markov error‐correction (MEC) models in which deviations from the long‐run equilibrium are characterized by different rates of adjustment. To motivate our analysis and illustrate the various issues involved, our discussion is structured around the analysis of the long‐run properties of US stock prices and dividends. It is shown that the MEC model is flexible enough to account for situations where deviations from the long‐run equilibrium are nonstationary in one of the states of nature and allows us to test for such a possibility. An empirical specification procedure to establish the existence of MEC adjustment in practice is also presented. This is based on a multi‐step test procedure that exploits the differences between the global and local characteristics of systems with MEC adjustment. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

On the estimation of simultaneous-equations error-components models with an application to a model of developing country foreign trade

An empirical balance of payments model involving the demand and supply of imports and exports for 31 developing countries is estimated utilizing panel data over 1964-1987. In order to compute error-components 3SLS estimates of this model, which requires different instruments for different equations, we propose a generalization of the Fuller-Battese transformation to obtain GMM estimates. Our empirical results suggest that very little of the short-run adjustment in external imbalances is likely to be achieved by exchange rate policies, and most of the burden must fall on aggregate demand management.     

The effect of uncertainty and instability on dynamic economic models with an application to cournot oligopoly

Consider a dynamic discrete-time economic model in which a state-dependent payoff is earned during each period. We give conditions which ensure that a mean preserving increase in the riskiness of the model's parameters increases (or decreases) the expected payoff earned during n periods.     

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.