Takashi Yamagata

A bias-adjusted LM test of error cross-section independence

This paper proposes a bias-adjusted version of Breusch and Pagan (1980) Lagrange multiplier (LM) test statistic of error cross-section independence, in the case of panel models with strictly exogenous regressors and normal errors. The exact mean and variance of the test indicator of the LM test statistic are provided for the purpose of the bias-adjustments. It is shown that the centring of the LM statistic is correct for fixed T and N. Importantly, the proposed bias-adjusted LM test is consistent even when the Pesarans (2004) CD test is inconsistent. Also an alternative bias-adjusted LM test, which is consistent under local error cross-section dependence of any fixed order p, is proposed. The finite sample behaviour of the proposed tests is investigated and compared to that of the LM and CD tests. It is shown that the bias-adjusted LM tests successfully control the size, maintaining satisfactory power in panel with exogenous regressors and normal errors. However, it is also shown that the bias-adjusted LM test is not as robust as the CD test to non-normal errors andsor in the presence of weakly exogenous regressors. Copyright Royal Economic Society 2007

A Spatio-Temporal Model of House Prices in the US

The purpose of this paper is to apply recent advances in the econometrics of panel data to a problem that has a clear spatial dimension. We model the dynamic adjustment of real house prices using data at the level of US States. In the last decade, in most OECD countries there has been a significant rise in real house prices. This attracted the attention of many international organisations and central banks. In this paper we consider interactions between housing markets by examining the extent to which real house prices at the State level are driven by fundamentals such as real income, as well as by common shocks, and determine the speed of adjustment of house prices to macroeconomic and local disturbances. We take explicit account of both cross sectional dependence and heterogeneity. This allows us to find a cointegrating relationship between house prices and incomes and to identify a small role for real interest rates. Using this model we then examine the role of spatial factors, in particular the effect of contiguous states by use of a weighting matrix. We are able to identify a significant spatial effect, even after controlling for State specific real incomes, and allowing for a number of unobserved common factors.

Pairwise Tests of Purchasing Power Parity

Given nominal exchange rates and price data on N + 1 countries indexed by i = 0,1,2,…, N, the standard procedure for testing purchasing power parity (PPP) is to apply unit root or stationarity tests to N real exchange rates all measured relative to a base country, 0, often taken to be the U.S. Such a procedure is sensitive to the choice of base country, ignores the information in all the other cross-rates and is subject to a high degree of cross-section dependence which has adverse effects on estimation and inference. In this article, we conduct a variety of unit root tests on all possible N(N + 1)/2 real rates between pairs of the N + 1 countries and estimate the proportion of the pairs that are stationary. This proportion can be consistently estimated even in the presence of cross-section dependence. We estimate this proportion using quarterly data on the real exchange rate for 50 countries over the period 1957–2001. The main substantive conclusion is that to reject the null of no adjustment to PPP requires sufficiently large disequilibria to move the real rate out of the band of inaction set by trade costs. In such cases, one can reject the null of no adjustment to PPP up to 90% of the time as compared to around 40% in the whole sample using a linear alternative and almost 60% using a nonlinear alternative.

Testing CAPM with a Large Number of Assets

This paper is concerned with testing the time series implications of the capital asset pricing model (CAPM) due to Sharpe (1964) and Lintner (1965), when the number of securities, N, is large relative to the time dimension, T, of the return series. In the case of cross-sectionally correlated errors, using a threshold estimator of the average squares of pair-wise error correlations a test is proposed and is shown to be valid even if N is much larger than T. Monte Carlo evidence show that the proposed test works well in small samples. The test is then applied to all securities in the S&P 500 index with 60 months of return data at the end of each month over the period September 1989-September 2011. Statistically significant evidence against Sharpe-Lintner CAPM is found mainly during the recent financial crisis. Furthermore, a strong negative correlation is found between a twelve-month moving average p-values of the test and the returns of long/short equity strategies relative to the return on S&P 500 over the period December 2006 to September 2011, suggesting that abnormal profits are earned during episodes of market inefficiencies.

The Asymptotic Distribution of the F-Test Statistic for Individual Effects

(the number of cross-sections) and T is fixed (the number of time periods). Three theoretical results emerge: (i) the standard F-test procedure will still deliver asymptotically valid inferences; (ii) under (pure) local random effects, the F-test and random effects test procedures have identical asymptotic power; (iii) under local fixed, or random effects which are correlated with the regressors, the F-test will have higher asymptotic power than the random effects test. Copyright Royal Economic Society 2006

On Testing Sample Selection Bias Under the Multicollinearity Problem

ABSTRACT This paper reviews and extends the literature on the finite sample behavior of tests for sample selection bias. Monte Carlo results show that, when the “multicollinearity problem” identified by Nawata (1993) is severe, (i) the t-test based on the Heckman–Greene variance estimator can be unreliable, (ii) the Likelihood Ratio test remains powerful, and (iii) nonnormality can be interpreted as severe sample selection bias by Maximum Likelihood methods, leading to negative Wald statistics. We also confirm previous findings (Leung and Yu, 1996) that the standard regression-based t-test (Heckman, 1979) and the asymptotically efficient Lagrange Multiplier test (Melino, 1982), are robust to nonnormality but have very little power.

Pairwise Tests of Purchasing Power Parity Using Aggregate and Disaggregate Price Measures

In this paper we adopt a new approach to testing for purchasing power parity, PPP, that is robust to base country effects, cross-section dependence, and aggregation. We test for PPP applying a pairwise approach to the disaggregated data set recently analysed by Imbs, Mumtaz, Ravan and Rey (2005, QJE). We consider a variety of tests applied to all 66 possible pairs of real exchange rate among the 12 countries and estimate the proportion of the pairs that are stationary, for the aggregates and each of the 19 commodity groups. To deal with small sample problems, we use a factor augmented sieve bootstrap approach and present bootstrap pairwise estimates of the proportions that are stationary. The bootstrapped rejection frequencies at 26%-49% based on unit root tests suggest some evidence in favour of the PPP in the case of the disaggregate data as compared to 6%-14% based on aggregate price series.

A Heteroskedasticity-Robust F-Test Statistic for Individual Effects

We derive the asymptotic distribution of the standard F-test statistic for fixed effects, in static linear panel data models, under both non-normality and heteroskedasticity of the error terms, when the cross-section dimension is large but the time series dimension is fixed. It is shown that a simple linear transformation of the F-test statistic yields asymptotically valid inferences and under local fixed (or correlated) individual effects, this heteroskedasticity-robust F-test enjoys higher asymptotic power than a suitably robustified Random Effects test. Wild bootstrap versions of these tests are considered which, in a Monte Carlo study, provide more reliable inference in finite samples.