Estimating Standard Errors for the Parks Model: Can Jackknifing Help?

This paper shows how to bootstrap hypothesis tests in the context of the Parks’s (1967) Feasible Generalized Least Squares estimator. It then demonstrates that the bootstrap outperforms FGLS(Parks)’s top competitor. The FGLS(Parks) estimator has been a workhorse for the analysis of panel data and seemingly unrelated regression equation systems because it allows the incorporation of cross-sectional correlation together with heteroskedasticity and serial correlation. Unfortunately, the associated, asymptotic standard error estimates are biased downward, often severely. To address this problem, Beck and Katz (1995) developed an approach that uses the Prais-Winsten estimator together with “panel corrected standard errors” (PCSE). While PCSE produces standard error estimates that are less biased than FGLS(Parks), it forces the user to sacrifice efficiency for accuracy in hypothesis testing. The PCSE approach has been, and continues to be, widely used. This paper develops an alternative: a nonparametric bootstrapping procedure to be used in conjunction with the FGLS(Parks) estimator. We demonstrate its effectiveness using an experimental approach that creates artificial panel datasets modelled after actual panel datasets. Our approach provides a superior alternative to existing estimation options by allowing researchers to retain the efficiency of the FGLS(Parks) estimator while producing more accurate hypothesis test results than the PCSE.

There is a widely application of panel data estimation in accounting and finance research. The approach is well accepted, because the pooled panel data provide rich information as compared to either cross-sections or time series data structure. However, within panel data structure, variables of interest are often cross-sectionally and serially correlated and as a result, OLS standard errors would be biased when panel data are used in the regression analysis. Several techniques, for example firm dummy variables, one-way cluster-robust standard errors, Fama-MacBeth procedure, and Newey-West procedure, are documented as a solution in analyzing panel data. These techniques to some extent correct either cross-sectional correlation or serial correlation. None is designed to deal with correlations in two dimensions (across firms and across time). With panel data structure, correlations are more likely to appear in two dimensions with both firm effects and time effects. This study suggests that two-way cluster-robust standard errors approach can correct both cross-sectional correlation and serial correlation and therefore should be considered as a better alternative in handling panel data. Nonetheless, two-way cluster-robust standard errors approach could be biased when applying to a finite sample. This study uses a real data set and constructs an empirical application of the estimation procedures of two-way cluster-robust regression estimation with and without finite-sample adjustment and the results show that finite-sample adjusted estimates are superior to unadjusted asymptotic estimates.

Panel data analysis is often faced with the issue of errors having arbitrary correlation across time for a particular individual “I” (serial correlation) and/or errors having arbitrary correlation across individuals at a moment in time (spatial correlation) with error disturbances having non constant variance. This study examined some panel data estimators in the presence of serial and spatial autocorrelation with panel heteroscedasticity. The study was done using two different sets of data simulated separately with ?=0.95 & 0.50. For each set of simulations short and long panels were considered for different sample sizes. The analysis considered two settings were rho is considered to be panel-specific (?i) and where rho is considered to be common for all panels (?). The estimators were examined based on bias, overconfidence and relative efficiency. The results produced evidence that the size of the autocorrelation coefficient ? affects the general performance of an estimator. Comparison of the estimators showed that Panel Corrected Standard Error Estimator (PCSE) produced better results than the other estimators considered in this work. But it was seen not to do very well in small samples and short panels. In terms of relative efficiency Park-Kmenta estimator was found to be more efficient that PCSE and PWLS (Panel Weighted Least Square Estimator). This paper has been able to show that the size of rho at the long run has an impact on the performance of the estimators, it showed that a small size of rho tends to increase overconfidence. The paper also revealed that Park-Kmenta estimator even with its flaws is still the most efficient estimator compared to the PCSE and PWLS. and it also substantiated the fact that PCSE performs badly in samples especially when N>T.

This paper modifies the Hausman and Taylor (1981) panel data estimator to allow for serial correlation in the remainder disturbances. It demonstrates the gains in efficiency of this estimator versus the standard panel data estimators that ignore serial correlation using Monte Carlo experiments.

Pentair Inc, USA

The bootstrap: Some large sample theory and connections with robustness

Passive systems, which completely depend on natural phenomena such as gravity, conduction and convection to accomplish the safety functions, are increasingly being used in new generation nuclear reactor designs. However, since the driving forces of passive systems are weak, they are more vulnerable to associated uncertainties and there may be a non-zero probability for the system to deviate from the intended behavior and leads to functional failure. Methods for quantification of the functional failure include Monte-Carlo simulation of the system uncertainties using a validated mechanistic code. Generally, the mechanistic codes used for complex system modeling are computationally expensive and Monte- Carlo simulation for estimating small failure probabilities requires more time and often become prohibitive. In this respect, recently, functional reliability methodologies including advanced simulation techniques such as subset simulation, Markov chain Monte-Carlo, importance sampling, and response conditioning method are reported in open literature. Unlike in the case of direct Monte Carlo simulation, for the probability estimates obtained using these advanced simulations, analytical formulas are not available to estimate standard error and confidence interval. In this paper, the estimation of standard error and confidence interval of functional reliability estimates using computationally efficient re-sampling methods based on bootstrap technique are described. Numerical application of these methods, to quantify the variability of functional reliability estimates, is also explained.

This study compared fixed-effects (FE) and random-effects (RE) models in meta-analysis for synthesizing multivariate effect sizes under the framework of structural equation modeling. Monte Carlo simulations were conducted to examine the performance characteristics of the two models under different data conditions. The results indicated that, for the homogeneous case, there was little difference between the FE model and the RE model applications. But the FE model had better performance in standard error estimation when number of studies is not large and the sample size of primary studies is small. Furthermore, under the heterogeneous case, FE model exhibited biased estimates of population parameters and extreme levels of inflated Type I error in testing the effect size estimates. However, RE model maintained unbiased estimates of the population parameters, and controlled Type I error well under various data conditions investigated. These findings provided empirical evidence that it is likely that RE model application in a meta-analysis would be preferred when the number of primary studies and the sample sizes in the primary studies are reasonably large, and FE model could be favored for situations with smaller numbers of studies and uniformly small sample sizes of primary studies.

This article investigates empirically the determinants of central banks’ reserve holdings for a large panel data set of developing and transition countries covering the period from 1975 to 2003. It estimates both a static and a dynamic relationship and applies estimators for homogeneous and heterogeneous panel data. Thereby, it examines the extent to which conclusions of panel data studies on the determinants of international reserve holdings are robust to the inclusion of dynamics as well as to the consideration of heterogeneity across countries. The results show that the neglect of dynamics and heterogeneity in country behaviour may lead to misleading inferences. Independently of the chosen estimation method, the findings suggest that trade openness and external debt are robust determinants of the level of reserves. Central banks take precautionary measures against the downside of the increasing international economic integration.

In time series econometric theory, the sign of the parameter may be pre-assigned, that is the parameter may be ordered or restricted. Estimation of this restricted parameter is then a vital problem. If we know the parameters are restricted by some constraints, it is reasonable to expect that we should be able to do better by incorporating such additional information than by ignoring them. The paper concerned with estimating and testing restricted hypotheses in Panel data regression model. The aim of the paper: constructing a modified LM test statistic to test the joint effect of heteroscedasticity and serial correlation in a random effect error component model, where the hypotheses are restricted. Monte Carlo results show that the tests have good size and power under various forms of heteroscedasticity and serial correlation. Keywords: Panel Data Model, heteroscedasticity, serial correlation, unconstraint and constraint based LM test

During 2007, the Singapore Economic Review invited submissions of research papers for consideration to be collected in a Special Issue on: The Theory and Practice of the Econometric Analysis of Panel Data. More in particular, papers were solicited advancing the understanding of the accuracy and adequacy of econometric inference obtained from panel data analysis, or producing such inference relating to economic or general social issues by analyzing panel data preferably (but not necessarily) on South-East Asia at the country, sub-regional, or regional level. From the submitted papers, a selection was made covering many of the divergent aspects of advanced panel data analysis. These papers were thoroughly refereed and this is the resulting special issue. It contains contributions with applications addressing issues in macro, micro, and financial economics and some focus also on the further development and understanding of the techniques of panel data analysis. Three of the eight papers analyze data on South-East Asia. The majority of the articles in this issue concern the analysis of standard panel data, constituting repeated observations in time on a cross-section of subjects. For some of these studies, the time-series sample size is relatively large or about equal in size to the cross-section sample, whereas others focus on the typical micro panel in which the number of time-series observations is very small and the cross-section sample size is relatively large. Mostly, the available panel data sets are unbalanced, meaning that not all cross-section units have been observed over exactly the same time period. In two papers, the panel nature of the analyzed data is less standard. They concern the series of bids during a large number of auctions, and the individual members of a large number of households. It seems fair to say that this collection of papers demonstrates abundantly how ubiquitous and diverse panel data are, how challenging and rewarding their

Many panel data sets encountered in macroeconomics, international economics, regional science, and finance are characterized by cross-sectional or “spatial” dependence. Standard techniques that fail to account for this dependence will result in inconsistently estimated standard errors. In this paper we present conditions under which a simple extension of common nonparametric covariance matrix estimation techniques yields standard error estimates that are robust to very general forms of spatial and temporal dependence as the time dimension becomes large. We illustrate the relevance of this approach using Monte Carlo simulations and a number of empirical examples.

Deep generative models (DGMs) present a promising avenue for generating realistic, synthetic data to augment existing health care datasets. However, exactly how the completeness of the original dataset affects the quality of the generated synthetic data is unclear. In this paper, we investigate the effect of data completeness on samples generated by the most common DGM paradigms. We create both cross-sectional and panel datasets with varying missingness and subset rates and train generative adversarial networks, variational autoencoders, and autoregressive models (Transformers) on these datasets. We then compare the distributions of generated data with original training data to measure similarity. We find that increased incompleteness is directly correlated with increased dissimilarity between original and generated samples produced through DGMs. Care must be taken when using DGMs to generate synthetic data as data completeness issues can affect the quality of generated data in both panel and cross-sectional datasets.

Tourism is one of the major drivers of the Greek economy. The contribution of tourism to the Greek economy has proved especially relevant during the period of the credit and euro crises with a high budgetary and balance of payment deficits. From that perspective this study examines the impact of the socio-economic and geographical determinants of foreign tourism demand in Greece. For the empirical analysis a panel dataset of 31 countries is used over the period 2001-2010. The panel data estimation indicates that distance and trade have more explanatory power than relative prices and other determinants such as transport infrastructure. Income is statistically significant in 3 out of the 8 specifications. Also political stability seems to play an important role in tourism demand. The results are mixed for the competitive prices between Greece and its main tourism competitors. An interesting finding is that the Olympic Games of 2004 seem to have had a negative impact on international tourist arrivals in Greece in that year.

This manuscript examines the influence of macroeconomic and bank‐specific factors on credit quality in Palestine over the last decade. For this purpose, empirical tests are conducted using panel dataset of the fixed and random effects estimates form the period of 2007 to 2018. The results of fixed effects show ample evidence of significant impact from interest, profitability and credit supply to credit default when financial crisis in included in the panel data analysis. As result, interest and credit supply positively impact non‐performing loans (NPLs) with statistical significance, while profitability has significant negative affiliation with NPLs. It also found that Palestinian commercial banks are able to cushion their NPLs during and after the global crisis. The novelty of this research provides a good knowledge in credit quality and risk control. Therefore, it can help in understanding the underlying causes of credit risk in this country and empower the commercial banks to sustain their competitive environment. Hence, it could be of considerable use to the monetary authorities to control credit default and protect Palestinian banks from financial distress.