Fixed effects models with time invariant variables: a theoretical note

This paper demonstrates the equivalence between a consistent two-stage GLS estimator and the pooled OLS estimator of the coefficients on time invariant covariates in an unbalanced FE panel. In general the estimated standard errors differ between these two procedures.     

Grouped coefficients to reduce bias in heterogeneous dynamic panel models with small T

We propose the grouped coefficients estimator to reduce bias in dynamic panels with small T that have a multilevel structure to the coefficient and factor loading heterogeneity. If groups are chosen such that the within-group heterogeneity is small, then the grouped coefficients estimator can lead to substantial bias reduction compared to pooled GMM dynamic panel estimators. We also propose using a Wald test that can be used to assess whether pooled estimators suffer from heterogeneity bias. We illustrate the usefulness of grouped coefficients with an application to labour demand in which the coefficients are grouped by sub-sector. Our results suggest that the standard pooled estimates are substantially biased.     

On the estimation and forecasting of international migration: how relevant is heterogeneity across countries?

This paper performs a comparative analysis of estimation as well as of out-of-sample forecasting results of more than 20 estimators common in the panel data literature using the data on migration to Germany from 18 source countries in the period 1967–2001. Our results suggest that the choice of an estimation procedure has a substantial impact on the parameter estimates of the migration function. Out-of-sample forecasting results indicate the following: (1) the standard fixed effects estimators clearly outperforms the pooled OLS estimator, (2) both the fixed effects estimators and the hierarchical Bayes estimator exhibit the superior forecast performance, (3) the fixed effects estimators outperform GMM and other instrumental variables estimators, (4) forecasting performance of heterogenous estimators is mediocre in our data set.     

A multidimensional spatial lag panel data model with spatial moving average nested random effects errors

This paper focuses on a three-dimensional model that combines two different types of spatial interaction effects, i.e. endogenous interaction effects via a spatial lag on the dependent variable and interaction effects among the disturbances via a spatial moving average (SMA) nested random effects errors. A three-stage procedure is proposed to estimate the parameters. In a first stage, the spatial lag panel data model is estimated using an instrumental variable (IV) estimator. In a second stage, a generalized moments (GM) approach is developed to estimate the SMA parameter and the variance components of the disturbance process using IV residuals from the first stage. In a third stage, to purge the equation of the specific structure of the disturbances a Cochrane–Orcutt-type transformation is applied combined with the IV principle. This leads to the GM spatial IV estimator and the regression parameter estimates. Monte Carlo simulations show that our estimators are not very different in terms of root mean square error from those produced by maximum likelihood. The approach is applied to European Union regional employment data for regions nested within countries.     

An Improved Two‐step Regularization Scheme for Spot Volatility Estimation

We are concerned with the problem of spot volatility estimation in the presence of microstructure noise. We introduce an estimator based on the technique of multi‐step regularization. A preliminary form for such an estimator was proposed in Ogawa (2008) and was shown to work in a real‐time manner. However, the main drawback of this scheme is that it needs a lot of observation data. The aim of the present paper is to introduce an improvement to this scheme, such that the modified estimator can work more efficiently and with a data set of smaller size. The technical aspects of implementation of the proposed scheme and its performance on simulated data are analysed. The scheme is tested against other spot volatility estimators, namely a realized volatility type estimator, the Fourier estimator and three kernel estimators.     

Small Sample Properties Of Existing And New Estimators Of The Autocorrelation Coefficient And Regression Coefficients In The Context Of Ar(1) Errors

This study systematically and comprehensively investigates the small sample properties of the existing and some new estimators of the autocorrelation coefficient and of the regression coefficients in a linear regression model when errors follow an autoregressive process of order one. The new estimators of autocorrelation coefficient proposed here are based on the jackknife procedure. The jackknife procedure is applied in two alternative ways: first to the regression itself, and second to the residuals of the regression model. Next, the performance of the existing and new estimators of autocorrelation coefficient (thirty-three in total) is investigated in terms of bias and the root mean squared errors. Finally, we have systematically compared all of the estimators of the regression coefficients (again thirty-three) in terms of efficiency and their performance in hypothesis testing. We observe that the performance of the autocorrelation coefficient estimators is dependent upon the degree of autocorrelation and whether the autocorrelation is positive or negative. We do not observe a direct link between the bias and efficiency of an estimator. The performance of the estimators of the regression coefficients also depends upon the degree of autocorrelation. If the efficiency of regression estimator is of concern, then the iterative Prais-Winsten estimator should be used since it is most efficient for the widest range of independent variables and values of the autocorrelation coefficient. If testing of the hypothesis is of concern, then the estimators based on jackknife technique are certainly superior and are highly recommended. However, for negative values of the autocorrelation coefficient, the estimators based on Quenouille procedure and iterative Prais-Winsten estimator are comparable. But, for computational ease iterative Prais-Winsten estimator is recommended.

     

Estimation of Censored Regression Model: A Simulation Study

We investigate the finite sample performance of several estimators proposed for the panel data Tobit regression model with individual effects, including Honoré estimator, Hansen’s best two-step GMM estimator, the continuously updating GMM estimator, and the empirical likelihood estimator (ELE). The latter three estimators are based on more conditional moment restrictions than the Honoré estimator, and consequently are more efficient in large samples. Although the latter three estimators are asymptotically equivalent, the last two have better finite sample performance. However, our simulation reveals that the continuously updating GMM estimator performs no better, and in most cases is worse than Honoré estimator in small samples. The reason for this finding is that the latter three estimators are based on more moment restrictions that require discarding observations. In our designs, about seventy percent of observations are discarded. The insufficiently few number of observations leads to an imprecise weighted matrix estimate, which in turn leads to unreliable estimates. This study calls for an alternative estimation method that does not rely on trimming for finite sample panel data censored regression model.     

ICT growth effects at the industry level: A comparison between the US and the EU

This is an empirical study on the growth impact of Information and Communication Technologies using industry-level data for the US and the EU industries over the period 1980-2000. A panel data approach is employed to estimate the ICT effect using the system GMM and the pooled mean group panel data estimators. The results vary depending on the period, the region, and the type of industry considered. The GMM estimates suggest a significant ICT effect on growth during the 90s both in the US and in the EU. This effect for the EU was strong in the early 90s and weakened afterwards, as opposed to the US where it strengthened in the late 90s. The results of the pooled mean group estimator confirm that the long run growth contribution of ICT was significantly positive in the industries of both regions and over the entire period 1980-2000. However, it seems that the productivity effects of ICT are mainly present in the industries which are either ICT producers or heavy ICT users.     

Instrumental variable estimation of a spatial autoregressive panel model with random effects

This paper extends the instrumental variable estimators of Kelejian and Prucha (1998) and Lee (2003) proposed for the cross-sectional spatial autoregressive model to the random effects spatial autoregressive panel data model. It also suggests an extension of the Baltagi (1981) error component 2SLS estimator to this spatial panel model.     

The combined estimator approach to model transferability and updating

The idea of transferability is to employ in model estimation, fitted model parameters computed from a different data set. Thecombined estimator approach to the transferability problem is expressed as a linear combination of the unbiased direct estimators on the two data sets. The major gain is in variance reduction. The combined estimator is shown to have superior accuracy, in a Mean Square Error sense, to a unbiased direct estimator whenever the transfer bias is relatively small. A test that indicates if the combined estimator is superior to the direct estimator is provided. Variances of the direct estimators are assumed to be known. Monte Carlo experiments are performed to assess the quality of the approximations. The results show that the approximations used are highly conservative. An empirical example of the combined estimator applied to a discrete choice problem is presented.     

Cross sectional and panel estimation of convergence

Cross sectional estimation of convergence regressions is known to be hazardous if there is convergence towards heterogeneous steady state values. In this paper, Monte Carlo methods are used to investigate the implications of this parameter heterogeneity problem. The cross sectional and pooled OLS estimators are compared with a panel estimator which is unaffected by heterogeneity. If there is heterogeneity, the latter outperforms both the unconditional and conditional cross sectional and pooled OLS estimators.     

Purchasing Power Parity and aggregation bias for a developing country: The case of Mexico

This paper investigates long-run Purchasing Power Parity (PPP) between the US and Mexico. We use a panel of disaggregated price data between the US and Mexico with a long time series to look at two types of aggregation bias. The first is examined in Imbs et al. — which we refer to as estimator aggregation bias — and the second is put forth by Broda and Weinstein — hereafter, data aggregation bias. The findings indicate substantial estimator aggregation bias and data aggregation bias. Although estimates using aggregate data and imposing homogeneous coefficients provide little evidence of PPP, findings with disaggregated data and heterogeneous coefficient estimators offer strong support. The results also suggest the presence of small-sample bias as examined in Chen and Engel, but with little effect on the qualitative results. Tradable goods and non-tradable goods show little distinction in convergence rates. Estimated half-lives are lower under flexible than fixed exchange rates and indicate rapid convergence during the Mexican peso crisis.     

Unit Root Tests for Dependent Micropanels

This paper proposes a new test for the null hypothesis of panel unit roots for micropanels with short time dimensions (T) and large cross‐sections (N). There are several distinctive features of this test. First, the test is based on a panel AR(1) model allowing for cross‐sectional dependency, which is introduced by a factor structure of the initial condition. Second, the test employs the panel AR(1) model with AR(1) coefficients that are heterogeneous for finite N. Third, the test can be used both for the alternative hypothesis of stationarity and for that of explosive roots. Fourth, the test does not use the AR(1) coefficient estimator. The effectiveness of the test rests on the fact that the initial condition has permanent effects on the trajectory of a time series in the presence of a unit root. To measure the effects of the initial condition, the present paper employs cross‐sectional regressions using the first time‐series observations as a regressor and the last as a dependent variable. If there is a unit root in every individual time series, the coefficient of the regressor is equal to one. The t‐ratios for the coefficient are this paper's test statistics and have a standard normal distribution in the limit. The t‐ratios are based on the OLS estimator and the instrumental variables estimator that uses reshuffled regressors as instruments. The test proposed in this paper makes it possible to test for a unit root even at T = 2 as long as N is large. Simulation results show that test statistics have reasonable empirical size and power. The test is applied to college graduates' monthly real wage in South Korea. The number of time‐series observations for this data is only two. The null hypothesis of a unit root is rejected against the alternative of stationarity.     

A panel data model with interactive effects characterized by multilevel non-parallel factors

Current research only considers parallel factors in factor models. In this article, we provide an algorithm based on cross principal component analysis that identifies and estimates a panel data model with interactive effects characterized by multilevel and non-parallel factors. The simulation results show that our estimator is consistent, converges quickly and outperforms other estimators that identify the factor structure incorrectly.     

Semiparametric estimation of conditional mean functions with missing data

A new semiparametric estimator for estimating conditional expectation functions from incomplete data is proposed, which integrates parametric regression with nonparametric matching estimators. Besides its applicability to missing data situations due to non-response or attrition, the estimator can also be used for analyzing treatment effect heterogeneity and statistical treatment rules, where data on potential outcomes is missing by definition. By combining moments from a parametric specification with nonparametric estimates of mean outcomes in the non-responding population within a GMM framework, the estimator seeks to balance a good fit in the responding population with low bias in the non-responding population. The estimator is applied to analyzing treatment effect heterogeneity among Swedish rehabilitation programmes.

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Spatial econometric Monte Carlo studies: raising the bar

We discuss Monte Carlo methodology that can be used to explore alternative approaches to estimating spatial regression models. Our focus is on models that include spatial lags of the dependent variable, e.g., the SAR specification. A major point is that practitioners rely on scalar summary measures of direct and indirect effects estimates to interpret the impact of changes in explanatory variables on the dependent variable of interest. We argue that these should be the focus of Monte Carlo experiments. Since effects estimates reflect a nonlinear function of both \(\beta \) and \(\rho \), past studies’ focus exclusively on \(\beta \) and \(\rho \) parameter estimates may not provide useful information regarding statistical properties of effects estimates produced by alternative estimators. Since effects estimates have recently become the focus of inference regarding the significance of (scalar summary) direct and indirect impacts arising from changes in the explanatory variables, empirical measures of dispersion produced by simulating draws from the (estimated) variance–covariance matrix of the parameters \(\beta \) and \(\rho \) should be part of the Monte Carlo study. An implication is that differences in the quality of estimated variance–covariance matrices arising from alternative estimators also plays a role in determining the accuracy of inference. An applied illustration is used to demonstrate how these issues can impact conclusions regarding the performance of alternative estimators.     

Pooled Mean Group Estimation of the Bilateral Trade Balance Equation: USA vis‐à‐vis her Trading Partners

The autoregressive distributed lag model (ARDL), even though it distinguishes between the short run and the long run effect, allows both the intercepts and slopes to vary across countries. Static panel estimations, such as fixed‐effects estimation (FE), cannot distinguish between the short run and the long run behavior. To address the issue of short run heterogeneity as well as long run homogeneity of the estimated coefficients in a panel framework, the pooled mean group (PMG) estimator has gained popularity since 1999. In this paper, we estimate the bilateral trade balance model for the USA vis‐à‐vis her 19 OECD trading partners for the period 1973q1–2004q4 using the PMG estimator and find that PMG performs better than ARDL, FE, and MG estimators and provides significant and theoretically consistent results.     

The relationship between regional value-added and public capital in Finland: what do the new panel econometric techniques tell us?

This article applies recently developed panel estimation techniques to estimate the elasticity of private production with respect to public capital in a regional framework. We use the widely applied production function approach and regional data from Finland for the 1975–2004 period. In contrast to many previous studies about the productivity of public capital, we focus especially on panel estimation techniques, showing that the results from commonly applied fixed effects OLS are probably biased and sensitive to a change of estimator. To get more reliable results, we use the panel DOLS and panel DSUR estimators. The results suggest that public capital has had a positive impact on private production.     

A more general class of biased estimators of the co-efficients in linear regression

In a recent paper, Ullah and Ullah (1978) proposed a class of biased estimators, namely double k-class (k₁, k₂) for the coefficients in a linear regression model. Even though, this set of estimators contains James and Stein (1961) as a special case, in its present form, it does not contain the ridge type estimators. The aim of this note is to extend Ullah and Ullah set of estimators and then establish a relationship with the various operational ridge estimators. The conditions under which the extended set of estimators dominates the ordinary least squares estimator are analyzed.     

Long-run estimates of interfuel and interfactor elasticities

Meta-analyses of interfuel and capital-energy elasticities of substitution show that elasticity estimates are dependent on the type of data − time series, panel, or cross-section − and the estimators used. Econometric theory suggests that the between estimator might generate the best estimates of long-run elasticities but no existing estimates of elasticities of substitution have used it. Alternatively, Chirinko et al. argued in favor of estimating long-run elasticities of substitution using a long-run difference estimator. We provide estimates of China’s interfuel and interfactor elasticities of substitution using the between and long-run difference estimators. To address potential omitted variables bias, we add province level inefficiency and national technological change terms to our regression model. The results show that demand for coal and electricity in China is very inelastic, while demand for diesel and gasoline is elastic. With the exception of gasoline and diesel, there are limited substitution possibilities among the fuels. Substitution possibilities are greater between energy and labor than between energy and capital. The results are quite different to some previous studies for China but coincide well with the patterns found in meta-analyses for long-run estimates of elasticities of substitution.