Panel Stationarity Test with Structural Breaks*

In this paper, we extend the heterogeneous panel data stationarity test of Hadri [Econometrics Journal, Vol. 3 (2000) pp. 148–161] to the cases where breaks are taken into account. Four models with different patterns of breaks under the null hypothesis are specified. Two of the models have been already proposed by Carrion‐i‐Silvestre et al. [Econometrics Journal, Vol. 8 (2005) pp. 159–175]. The moments of the statistics corresponding to the four models are derived in closed form via characteristic functions. We also provide the exact moments of a modified statistic that do not asymptotically depend on the location of the break point under the null hypothesis. The cases where the break point is unknown are also considered. For the model with breaks in the level and no time trend and for the model with breaks in the level and in the time trend, Carrion‐i‐Silvestre et al. [Econometrics Journal, Vol. 8 (2005) pp. 159–175] showed that the number of breaks and their positions may be allowed to differ across individuals for cases with known and unknown breaks. Their results can easily be extended to the proposed modified statistic. The asymptotic distributions of all the statistics proposed are derived under the null hypothesis and are shown to be normally distributed. We show by simulations that our suggested tests have in general good performance in finite samples except the modified test. In an empirical application to the consumer prices of 22 OECD countries during the period from 1953 to 2003, we found evidence of stationarity once a structural break and cross‐sectional dependence are accommodated.     

Finite Sample Correction Factors for Panel Cointegration Tests*

In this paper we present finite T mean and variance correction factors and corresponding response surface regressions for the panel cointegration tests presented in Pedroni (1999, 2004) , Westerlund (2005) , Larsson et al. (2001) and Breitung (2005) . For the single equation tests, we consider up to 12 regressors and for the system tests vector autoregression dimensions up to 12 variables. All commonly used specifications for the deterministic components are considered. The sample sizes considered are T ∈ {10,20,30,40,50,60,70,80,90,100,200,500}.     

Testing for Multicointegration in Panel Data with Common Factors*

This paper addresses the concept of multicointegration in a panel data framework and builds upon the panel data cointegration procedures developed in Pedroni [Econometric Theory (2004), Vol. 20, pp. 597–625]. When individuals are either cross‐section independent, or cross‐section dependence can be removed by cross‐section demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes. The paper also deals with the issue of cross‐section dependence using approximate common‐factor models. Finite sample performance is investigated through Monte Carlo simulations. Finally, we illustrate the use of the procedure investigating an inventories, sales and production relationship for a panel of US industries.     

Unobserved Heterogeneity or Measurement Errors? Testing for Correlated Effects with Measurement Errors *

This paper addresses the problem of endogenous regressors due to the presence of unobserved heterogeneity, when this is correlated with the regressors, and caused by regressors’ measurement errors. A simple two‐stage testing procedure is proposed for the identification of the underlying cause of correlation between regressors and the error term. The statistical performance of the resulting sequential test is assessed using simulated data.     

Testing for Error Correction in Panel Data*

This paper proposes new error correction‐based cointegration tests for panel data. The limiting distributions of the tests are derived and critical values provided. Our simulation results suggest that the tests have good small‐sample properties with small size distortions and high power relative to other popular residual‐based panel cointegration tests. In our empirical application, we present evidence suggesting that international healthcare expenditures and GDP are cointegrated once the possibility of an invalid common factor restriction has been accounted for.     

Parental Divorce and Students’ Performance: Evidence from Longitudinal Data*

In this article, we analysed data from the National Education Longitudinal Study to investigate whether experiencing parental divorce during adolescence had an adverse impact on students’ performance on standardized tests. To account for the potential endogeneity of parental divorce we employed double and triple difference models that rely on observing teenagers from intact and divorced backgrounds before and after the divorce occurs. We found that parental divorce does not negatively affect teenagers’ cognitive skills. Our results also suggest that cross‐sectional estimates overstate the detrimental effect of parental divorce.     

Correlated risks vs contagion in stochastic transition models

This paper studies the problem of disentangling risk correlation and contagion in a set of individual binary processes. The two admissible values correspond to bad and good risk states of an individual. The risk correlation is captured by introducing a dynamic frailty, whereas the contagion passes through the effect of the lagged number of individuals in the bad risk state. We study carefully the dynamic properties of the joint process. Then, we focus on the limiting case of large populations (portfolios). The difficulty to identify risk correlation and contagion in finite samples is illustrated by means of Monte-Carlo simulations.     

Testing the Political Replacement Effect: A Panel Data Analysis*

This article tests for the existence of the political replacement effect, as suggested by Acemoglu and Robinson: [American Political Science Review, Vol. 100, pp. 115–131]. They argue that the implementation of market‐oriented reform is crucially driven by the political calculus of incumbent governments: they implement economic policy change if such a choice is not expected to reduce their chances to retain power. This implies a non‐monotonic relationship between the level of political competition and the extent of economic reform. We test this hypothesis using data for 102 countries over the period 1980 to 2005. Our results strongly support the theory.     

Diagnostic Tests of Cross‐section Independence for Limited Dependent Variable Panel Data Models*

This article considers the problem of testing for cross‐section independence in limited dependent variable panel data models. It derives a Lagrangian multiplier (LM) test and shows that in terms of generalized residuals of Gourieroux et al. (1987) it reduces to the LM test of Breusch and Pagan (1980) . Because of the tendency of the LM test to over‐reject in panels with large N (cross‐section dimension), we also consider the application of the cross‐section dependence test (CD) proposed by Pesaran (2004) . In Monte Carlo experiments it emerges that for most combinations of N and T the CD test is correctly sized, whereas the validity of the LM test requires T (time series dimension) to be quite large relative to N. We illustrate the cross‐sectional independence tests with an application to a probit panel data model of roll‐call votes in the US Congress and find that the votes display a significant degree of cross‐section dependence.     

Testing for Panel Cointegration with Multiple Structural Breaks*

This paper proposes a Lagrange multiplier (LM) test for the null hypothesis of cointegration that allows for the possibility of multiple structural breaks in both the level and trend of a cointegrated panel regression. The test is general enough to allow for endogenous regressors, serial correlation and an unknown number of breaks that may be located at different dates for different individuals. We derive the limiting distribution of the test and conduct a small Monte Carlo study to investigate its finite sample properties. In our empirical application to the solvency of the current account, we find evidence of cointegration between saving and investment once a level break is accommodated.     

The Impact of Training on Productivity and Wages: Evidence from British Panel Data*

It is standard in the literature on training to use wages as a sufficient statistic for productivity. This paper examines the effects of work‐related training on direct measures of productivity. Using a new panel of British industries 1983–96 and a variety of estimation techniques we find that work‐related training is associated with significantly higher productivity. A 1% point increase in training is associated with an increase in value added per hour of about 0.6% and an increase in hourly wages of about 0.3%. We also show evidence using individual‐level data sets that is suggestive of training externalities.     

Panel LM Unit‐root Tests with Level Shifts*

This paper proposes a new panel unit‐root test based on the Lagrangian multiplier (LM) principle. We show that the asymptotic distribution of the new panel LM test is not affected by the presence of structural shifts. This result holds under a mild condition that N/T→k, where k is any finite constant. Our simulation study shows that the panel LM unit‐root test is not only robust to the presence of structural shifts, but is more powerful than the popular Im, Pesaran and Shin (IPS) test. We apply our new test to the purchasing power parity (PPP) hypothesis and find strong evidence for PPP.     

Truncated Product Methods for Panel Unit Root Tests*

This paper proposes two new panel unit root tests based on Zaykin et al. (2002) ’s truncated product method. The first one assumes constant correlation between P‐values and the second one uses sieve bootstrap to allow for general forms of cross‐section dependence in the panel units. Monte Carlo simulation shows that both tests have reasonably good size and are powerful in cases of some very large P‐values. The proposed tests are applied to a panel of real GDP and inflation density forecasts, resulting in evidence that professional forecasters may not update their forecast precision in an optimal Bayesian way.     

Cross‐sectional Dependency and Size Distortion in a Small‐sample Homogeneous Panel Data Unit Root Test*

In this paper, we investigate the effects of cross‐sectional disturbance correlation in a homogeneous panel data unit root test. As reported by other authors, the unit root test has incorrect size in the presence of cross‐sectional correlation. We suggest that a previously known estimator can be used to reduce the size distortions. We supply response surface estimates for critical values and study the size characteristics of the proposed test. We find that the suggested estimator performs well in small‐sample homogeneous panel data unit root tests. The reduction in size distortion comes at a small cost of lower power against a stationary alternative.     

Panel unit root tests in the presence of a multifactor error structure

This paper extends the cross-sectionally augmented panel unit root test (CIPS$CIPS$) proposed by Pesaran (2007) to the case of a multifactor error structure, and proposes a new panel unit root test based on a simple average of cross-sectionally augmented Sargan–Bhargava statistics (CSB$CSB$). The basic idea is to exploit information regarding the m$m$ unobserved factors that are shared by k$k$ observed time series in addition to the series under consideration. Initially, we develop the tests assuming that m⁰$m^0$, the true number of factors, is known and show that the limit distribution of the tests does not depend on any nuisance parameters, so long as k≥m⁰−1$k\ge m^0-1$. Small sample properties of the tests are investigated by Monte Carlo experiments and are shown to be satisfactory. Particularly, the proposed CIPS$CIPS$ and CSB$CSB$ tests have the correct size for all   combinations of the cross section (N$N$) and time series (T$T$) dimensions considered. The power of both tests rises with N$N$ and T$T$, although the CSB$CSB$ test performs better than the CIPS$CIPS$ test for smaller sample sizes. The various testing procedures are illustrated with empirical applications to real interest rates and real equity prices across countries.     

Testing for Seasonal Unit Roots in Monthly Panels of Time Series*

We consider the problem of testing for seasonal unit roots in monthly panel data. To this aim, we generalize the quarterly cross‐sectionally augmented Hylleberg–Engle–Granger–Yoo (CHEGY) test to the monthly case. This parametric test is contrasted with a new non‐parametric test, which is the panel counterpart to the univariate record unit–root seasonal (RURS) test that relies on counting extrema in time series. All methods are applied to an empirical data set on tourism in Austrian provinces. The power properties of the tests are evaluated in simulation experiments that are tuned to the tourism data.     

Further Evidence on the Statistical Properties of Real GNP*

The well‐known lack of power of unit‐root tests has often been attributed to the short length of macroeconomic variables and also to data‐generating processes (DGPs) departing from the I(1)–I(0) models. This paper shows that by using long spans of annual real gross national product (GNP) and GNP per capita (133 years), high power can be achieved, leading to the rejection of both the unit‐root and the trend‐stationary hypothesis. More flexible representations are then considered, namely, processes containing structural breaks (SB) and fractional orders of integration (FI). Economic justification for the presence of these features in GNP is provided. It is shown that both FI and SB formulations are in general preferred to the autoregressive integrated moving average (ARIMA) [I(1) or I(0)] formulations. As a novelty in this literature, new techniques are applied to discriminate between FI and SB. It turns out that the FI specification is preferred, implying that GNP and GNP per capita are non‐stationary, highly persistent but mean‐reverting series. Finally, it is shown that the results are robust when breaks in the deterministic component are allowed for in the FI model. Some macroeconomic implications of these findings are also discussed.     

A Panel CUSUM Test of the Null of Cointegration*

This paper proposes a simple residual‐based panel CUSUM test of the null hypothesis of cointegration. The test has a limiting normal distribution that is free of nuisance parameters, it is robust to heteroskedasticity and it allows for mixtures of cointegrated and spurious alternatives. Our Monte Carlo results suggest that the test has small‐size distortions and reasonable power. In our empirical application to international R&D spillovers, we present evidence suggesting that total factor productivity is heterogeneously cointegrated with foreign and domestic R&D capital stocks.     

Disproving Causal Relationships Using Observational Data*

Economic theory is replete with causal hypotheses that are scarcely tested because economists are generally constrained to work with observational data. We describe a method for testing a hypothesis that one observed random variable causes another. Contingent on a sufficiently strong correspondence between the two variables, an appropriately related third variable can be employed for the test. The logic of the procedure naturally suggests strong and weak grounds for rejecting the causal hypothesis. Monte Carlo results suggest that weakly grounded rejections are unreliable for small samples, but reasonably reliable for large samples. Strongly grounded rejections are highly reliable, even for small samples.     

Estimating and Forecasting with a Dynamic Spatial Panel Data Model*

This study focuses on the estimation and predictive performance of several estimators for the dynamic and autoregressive spatial lag panel data model with spatially correlated disturbances. In the spirit of Arellano and Bond (1991) and Mutl (2006) , a dynamic spatial generalized method of moments (GMM) estimator is proposed based on Kapoor, Kelejian and Prucha (2007) for the spatial autoregressive (SAR) error model. The main idea is to mix non‐spatial and spatial instruments to obtain consistent estimates of the parameters. Then, a linear predictor of this spatial dynamic model is derived. Using Monte Carlo simulations, we compare the performance of the GMM spatial estimator to that of spatial and non‐spatial estimators and illustrate our approach with an application to new economic geography.