Incidental Parameter Bias Research Articles

The persistence of wages

This paper documents the extent to which wage persistence can be explained by permanent worker, employer, and match heterogeneity. Standard methods used to perform such decompositions for industry or racial wage gaps are inappropriate for decomposing wage persistence in dynamic panel data models because of the incidental parameter problem. When we apply these methods without bias correction, we find that the majority, 59.3 percent, of wage persistence is explained by worker heterogeneity, with employer and match heterogeneity explaining 29.7 and 11.0 percent, respectively. We evaluate three methods for addressing incidental parameter bias using a Monte Carlo study. An empirical application to Portuguese linked employer–employee data shows that the uncorrected estimates tend to understate wage persistence by around 24 to 42 percent, depending on the choice of the bias correction estimator used, and overstate the extent to which wage persistence arises from permanent unobserved heterogeneity. Furthermore, results indicate that the uncorrected estimates overstate the role of permanent worker heterogeneity, and understate the role of firm heterogeneity.

Adversarial Inference Is Efficient

We study properties of the adversarial framework, introduced in Kaji, Manresa and Pouliot (2020). We show that the adversarial inference with an oracle classifier is statistically efficient. In addition, we study the finite sample properties of the adversarial estimation framework for the autoregressive parameter of a linear dynamic fixed effects panel data model with Gaussian errors. Unlike maximum likelihood, but similarly as other minimum distance estimators, the adversarial estimators do not suffer from the incidental parameter bias. In our simulations, using a one-hidden-layer neural network as discriminator delivers the estimates with smallest root mean squared error.

Informal pay gaps in good and bad times: Evidence from Russia

Informal work is traditionally large in Russia and has further increased in the recent years. We explore the implications of this shift in terms of wage dynamics. Our characterization is based on the estimation of informal pay gaps at the mean and along the wage distribution, relying on the Russian Longitudinal Monitoring Survey for 2003–2017. Our approach comprises three original features: we rely on unconditional quantile effects of informality, we incorporate quantile-specific fixed effects using a tractable approach, and we suggest a treatment of the incidental parameter bias. Over the whole period, informal wage penalties are relatively small and do not suggest heavily segmented labor markets, even at low wage levels. Yet, in the past decade, a substantial negative selection into informal employment and self-employment has taken place, on average and especially at low earnings. Economic downturns and labor market policies have likely contributed to the shakeout of less productive workers in the formal sector, making the low-tier informal sector more of a last resort.

Market Pricing of Fundamentals at the Shanghai Stock Exchange: Evidence from a Dividend Discount Model with Adaptive Expectations

We study market pricing of fundamentals at the Shanghai Stock Exchange, incorporating possible irrational pricing behavior with adaptive expectation. Using panel data of listed stocks to overcome the limited information in aggregate time series data, we estimated key parameters of the price elasticity of dividends and the expectation adjustment based on a linear dynamic panel data model. We use a major subset of stocks with stationary real prices and cash flows and apply methods that correct for incidental parameter bias. The resulting price elasticity of dividends is about 0.46 (0.35) based on annual (quarterly) data, which is sizable given high PD (PE) ratios in the market. Our results imply that slow expectation adjustment contributes to “bubble-like” price patterns. We also show prices significantly react to macro information related to the discount rate, but these effects are very sensitive to the information set used.

Nonlinear factor models for network and panel data

Factor structures or interactive effects are convenient devices to incorporate latent variables in panel data models. We consider fixed effect estimation of nonlinear panel single-index models with factor structures in the unobservables, which include logit, probit, ordered probit and Poisson specifications. We establish that fixed effect estimators of model parameters and average partial effects have normal distributions when the two dimensions of the panel grow large, but might suffer from incidental parameter bias. We also show how models with factor structures can be applied to capture important features of network data such as reciprocity, degree heterogeneity, homophily in latent variables, and clustering. We illustrate this applicability with an empirical example to the estimation of a gravity equation of international trade between countries using a Poisson model with multiple factors.

IV Estimation of Spatial Dynamic Panels with Interactive Effects: Large Sample Theory and an Application on Bank Attitude Toward Risk

The present paper develops a new Instrumental Variables (IV) estimator for spatial, dynamic panel data models with interactive effects under large N and T asymptotics. For this class of models, the only approaches available in the literature are based on quasi-maximum likelihood estimation. The approach put forward in this paper is appealing from both a theoretical and a practical point of view for a number of reasons. Firstly, the proposed IV estimator is linear in the parameters of interest and it is computationally inexpensive. Secondly, the IV estimator is free from asymptotic bias. In contrast, existing QML estimators suffer from incidental parameter bias, depending on the magnitude of unknown parameters. Thirdly, the IV estimator retains the attractive feature of Method of Moments estimation in that it can accommodate endogenous regressors, so long as external exogenous instruments are available. The IV estimator is consistent and asymptotically normal as N, T go to infinity, with N/T^2 going to 0 and T/N^2 tending to 0. The proposed methodology is employed to study the determinants of risk attitude of banking institutions. The results of our analysis provide evidence that the more risk-sensitive capital regulation that was introduced by the Basel III framework in 2011 has succeeded in influencing banks’ behavior in a substantial manner.

Xtspj: A command for split-panel jackknife estimation

In this article, we present a new command, xtspj, that corrects for incidental parameter bias in panel-data models with fixed effects. The correction removes the first-order bias term of the maximum likelihood estimate using the split-panel jackknife method. Two variants are implemented: the jackknifed maximum-likelihood estimate and the jackknifed log-likelihood function (with corresponding maximizer). The model may be nonlinear or dynamic, and the covariates may be predetermined instead of strictly exogenous. xtspj implements the split-panel jackknife for fixed-effects versions of linear, probit, logit, Poisson, exponential, gamma, Weibull, and negbin2 regressions. It also accommodates other models if the user specifies the log-likelihood function (and, possibly but not necessarily, the score function and the Hessian). xtspj is fast and memory efficient, and it allows large datasets. The data may be unbalanced. xtspj can also be used to compute uncorrected maximum-likelihood estimates of fixed-effects models for which no other xt (see [XT] xt) command exists.

Technical and allocative efficiency in a panel stochastic production frontier system model

• Uses a panel data stochastic frontier model with firm fixed effects and inefficiency. • Address endogeneity of inputs using economic behavior. • Models persistent allocative inefficiency. • Address incidental parameter problem. • Compute cost of technical and allocative inefficiency. In this paper, we consider a state-of-the-art panel stochastic production frontier model and estimate it using a system that includes both technical and allocative inefficiency. The system consists of the optimal input choice rule (the first-order conditions (FOCs)) under cost minimization together with the production function. The FOCs are used to take care of endogeneity of inputs. Allocative inefficiency is modeled as non-fulfillment of the FOCs. We use distributional assumptions on the noise and inefficiency components and estimate the model parameters using the maximum likelihood method. In estimating technical and allocative inefficiency components and costs therefrom we control for fixed firm-effects in each equation of the system. We also correct for the incidental parameter bias by using the half-panel jackknife estimator.

Likelihood Corrections for Two-way Models

The use of panel data models with two-way fixed effects is widespread. Incidental-parameter bias, however, invalidates inference based on the (profile) likelihood. We consider modifications to the likelihood that yield asymptotically-unbiased estimators as well as test statistics that are size correct under rectangular-array asymptotics. The modifications are widely applicable and easy to implement. Through several examples we illustrate that the modifications can lead to dramatic improvements relative to maximum likelihood, both in terms of point estimation and inference.

Fixed Effects Estimation of Large-TPanel Data Models

This article reviews recent advances in fixed effects estimation of panel data models for long panels, where the number of time periods is relatively large. We focus on semiparametric models with unobserved individual and time effects, where the distribution of the outcome variable, conditional on covariates and unobserved effects, is specified parametrically while the distribution of the unobserved effects is left unrestricted. In contrast to existing reviews on long panels, we discuss models with both individual and time effects, split-panel jackknife bias corrections, unbalanced panels, distribution and quantile effects, and other extensions. Understanding and correcting the incidental parameter bias caused by the estimation of many fixed effects are our main focuses, and the unifying theme is that the order of this bias is given by the simple formula p/ n for all models discussed, with p being the number of estimated parameters and n the total sample size.

Public Sector Wage Gaps Over the Long-Run: Evidence from Panel Administrative Data

With the increase in national debts, pay freezes are imposed for several years in the public sector of some countries, at the risk of decreasing the quality of public services. Since public wage setting policies should account for relevant comparisons with the private sector, we provide novel evidence on the public sector wage gap throughout the wage distribution in France, taking a long-term perspective. We exploit a long administrative panel dataset (1988-2013) and suggest methodological innovations. We estimate the public sector premia/penalties on the unconditional wage distribution while accounting for quantile-specific fixed effects and a jackknife correction for the potential incidental parameter bias.We find that the public wage gap is broadly negative in France, with larger penalties at the top, which contribute to a compression of the wage distribution by the public sector. We show that this compression effect is partly concealed by the incidental parameter bias. Time changes in the wage gap over 25 years are consistently explained by a mix of political and business cycles. The unobserved skill gap between sectors reveals the extent of positive selection into public jobs. It tends to decline in the 1990s, a period characterized by the growth of public employment and a move towards less selective recruitment schemes.More critically, it totally disappears among top earners in the recent period, suggesting the detrimental effect of nominal wage freeze and the absence of performance-based remuneration among public sector executives.

Dynamic labor supply adjustment with bias correction

I estimate a dynamic fixed effects hours equation for prime-age men with bias correction. Studies using household data typically find a weak response in hours of work to changes in the wage. This paper finds that rather than indicating a small elasticity of intertemporal substitution, the weak dependence of hours on wages is the result of delayed adjustment. The coefficient on the lagged dependent variable is found to be between 0.31 and 0.33, which suggests that it takes 1.5 years for an individual in the sample to adjust hours of work to a change in the wage or other preference variables, an important consideration in policy evaluation. Failure to correct for incidental parameter bias leads to underestimating this effect by more than 15%. Time-varying endogeneity of the wage is handled using a control function approach.

Bootstrap inference for linear dynamic panel data models with individual fixed effects

This paper’s main contribution is to propose and theoretically justify the application of bootstrap methods for inference in autoregressive panel data models with fixed effects. Whereas the focus of the existing literature has been on bias correcting the standard fixed effects OLS estimator (due to the well known incidental parameter bias), our focus here is on improving the quality of inference by relying on the bootstrap instead of the standard normal distribution when computing critical values for test statistics. In particular, we show by simulation that confidence intervals based on the normal distribution can be very distorted in finite samples. Instead, a bootstrap that resamples the residuals and generates the bootstrap observations recursively using the estimated autoregressive panel data model greatly reduces these distortions. We show that this recursive-design residual-based bootstrap fixed effects OLS estimator contains a built-in bias correction term that mimics the incidental parameter bias. Thus, this method can be used to approximate the bias (as well as the entire distribution) of the (biased) fixed effects OLS estimator. This is in contrast with two other methods we consider (a fixed-design residual-based bootstrap and a pairs bootstrap) whose distributions are incorrectly centered at zero. As it turns out, both the recursive-design and the pairs bootstrap are asymptotically valid when applied to the bias-corrected estimator, but the fixed-design bootstrap is not. In the simulations, the recursive-design bootstrap is the method that does best overall.

Dynamic Labor Supply Adjustment with Bias Correction

I estimate a dynamic fixed-effects hours equation for prime-age men with bias correction. Studies using household data typically find a weak response in hours of work to changes in the wage. This paper finds that, rather than indicating a small elasticity of intertemporal substitution, the weak dependence of hours on wages is the result of delayed adjustment. The coefficient on the lagged dependent variable is found to be between 0.31 and 0.33, which suggests that it takes 1.5 years for an individual in the sample to adjust hours of work to a change in the wage or other preference variables, an important consideration in policy evaluation. Failure to correct for incidental parameter bias leads to underestimating this effect by more than 15 percent. Time-varying endogeneity of the wage is handled using a control-function approach.

Bias Reduction in Nonlinear and Dynamic Panels in the Presence of Cross-Section Dependence, with a GARCH Panel Application

Nonlinear and dynamic panel models that contain individual-specific parameters are well-known to suffer from the incidental parameter bias. This bias and methods for correcting it have been studied extensively for panels with time-series dependence. However, a general analysis under cross-section dependence is missing. This paper extends the literature to dependence across both dimensions in large-N large-T panels. Our analysis is based on the integrated likelihood method which nests many common estimation approaches. We show that the composition of the first-order bias changes only under strong cross-section dependence, but not under weak or cluster-type dependence. Using bias correction techniques, we also propose a novel estimation approach for GARCH-type financial volatility modelling in small samples. Simulation analysis and a forecast exercise suggest that this method achieves success with as little as 150 time-series observations, which is much less than what is required by standard volatility estimation methods. We also use this approach to analyse the volatility characteristics of monthly hedge fund returns.

Worker Reallocation Across Occupations in Western Germany

This paper analyzes the determinants of annual worker reallocation across disaggregated occupations in western Germany for the period 1985-2003. Employing data from the German Socio-Economic Panel, the pattern of average occupational mobility is documented. Worker reallocation is found to be strongly procyclical. Its determinants at the individual level are then investigated while controlling for unobserved worker heterogeneity. A dynamic probit fixed effects model is estimated to obtain coefficients and marginal effects. The incidental parameter bias is reduced by the method proposed in Hahn and Kuersteiner (2004). An interesting finding is that workers changing occupation are about 8 to 9 percent less inclined to experience occupational mobility in the subsequent year than workers who do not change. Except for workers with only compulsory education, the impact of age on the probability of occupational change is declining in the level of education. The unemployment rate has a negative effect on the probability of occupational changes, especially for female foreigners.

Practical Use of Modified Maximum Likelihoods for Stratified Data

Stratified data arise in several settings, such as longitudinal studies or multicenter clinical trials. Between-strata heterogeneity is usually addressed by random effects models, but an alternative approach is given by fixed effects models, which treat the incidental nuisance parameters as fixed unknown quantities. This approach presents several advantages, like computational simplicity and robustness to confounding by strata. However, maximum likelihood estimates of the parameter of interest are typically affected by incidental parameter bias. A remedy to this is given by the elimination of stratum-specific parameters by exact or approximate conditioning. The latter solution is afforded by the modified profile likelihood, which is the method applied in this paper. The aim is to demonstrate how the theory of modified profile likelihoods provides convenient solutions to various inferential problems in this setting. Specific procedures are available for different kinds of response variables, and they are useful both for inferential purposes and as a diagnostic method for validating random effects models. Some examples with real data illustrate these points.