Benoit Perron

Bootstrapping factor-augmented regression models

This paper proposes and theoretically justifies bootstrap methods for regressions where some of the regressors are factors estimated from a large panel of data. We derive our results under the assumption that T/N→c, where 0≤c<∞ (N and T are the cross-sectional and the time series dimensions, respectively), thus allowing for the possibility that the factor estimation error enters the limiting distribution of the OLS estimator as an asymptotic bias term (as was recently discussed by Ludvigson and Ng (2011)). We consider general residual-based bootstrap methods and provide a set of high-level conditions on the bootstrap residuals and on the idiosyncratic errors such that the bootstrap distribution of a rotated OLS estimator is consistent. We subsequently verify these conditions for a simple wild bootstrap residual-based procedure.

Asymptotic Local Power of Pooled T-Ratio Tests for Unit Roots in Panels with Fixed Effects

. This latter test is equivalent to the well-known pooled t test proposed by Levin et al. (2002, Journal of Econometrics 108, 1--24), and its power depends only on the mean of the local-to-unity parameters. This implies that it has the same power against homogeneous and heterogeneous alternatives with the same mean autoregressive parameter. We then compare these tests to a panel version of the Sargan-Bhargava (1983, Econometrica 51, 153--74) statistic for a unit root and the common point-optimal test of Moon et al. (2007, Journal of Econometrics 141, 416--51). Monte Carlo simulations confirm the usefulness of our local-to-unity framework. Copyright Royal Economic Society 2008

Efficient Estimation of the Seemingly Unrelated Regression Cointegration Model and Testing for Purchasing Power Parity

Abstract This paper studies the efficient estimation of seemingly unrelated linear models with integrated regressors and stationary errors. We consider two cases. The first one has no common regressor among the equations. In this case, we show that by adding leads and lags of the first differences of the regressors and estimating this augmented dynamic regression model by generalized least squares using the long-run covariance matrix, we obtain an efficient estimator of the cointegrating vector that has a limiting mixed normal distribution. In the second case we consider, there is a common regressor to all equations, and we discuss efficient minimum distance estimation in this context. Simulation results suggests that our new estimator compares favorably with others already proposed in the literature. We apply these new estimators to the testing of the proportionality and symmetry conditions implied by purchasing power parity (PPP) among the G-7 countries. The tests based on the efficient estimates easily reject the joint hypotheses of proportionality and symmetry for all countries with either the United States or Germany as numeraire. Based on individual tests, our results suggest that Canada and Germany are the most likely countries for which the proportionality condition holds, and that Italy and Japan for the symmetry condition relative to the United States.

The Shape of the Risk Premium: Evidence from a Semiparametric Generalized Autoregressive Conditional Heteroscedasticity Model

We examine the relationship between the risk premium on the Center for Research on Security Prices (CRSP) value-weighted index total return and its conditional variance. We propose a new semiparametric model in which the conditional variance process is parametric and the conditional mean is an arbitrary function of the conditional variance. For monthly CRSP value-weighted excess returns, the relationship between the two moments that we uncover is nonlinear and nonmonotonic.

ON THE BREITUNG TEST FOR PANEL UNIT ROOTS AND LOCAL ASYMPTOTIC POWER

This note analyzes the local asymptotic power properties of a test proposed by Breitung (2000, in B. Baltagi (ed.), Nonstationary Panels, Panel Cointegration, and Dynamic Panels). We demonstrate that the Breitung test, like many other tests (including point optimal tests) for panel unit roots in the presence of incidental trends, has nontrivial power in neighborhoods that shrink toward the null hypothesis at the rate of n−1/4T−1 where n and T are the cross-section and time-series dimensions, respectively. This rate is slower than the n−1/2T−1 rate claimed by Breitung. Simulation evidence documents the usefulness of the asymptotic approximations given here.The authors thank Paolo Paruolo and a referee for comments on an earlier version of the paper. Phillips acknowledges partial support from a Kelly Fellowship and the NSF under grant SES 04-142254. Perron acknowledges financial support from FQRSC, SSHRC, and MITACS.

An Empirical Analysis of Nonstationarity in Panels of ExchangeRates and Interest Rates with Factors

This paper studies nonstationarities in panels of exchange rates and interest rates. For this, we survey developments in the analysis of nonstationary panels with cross-sectional dependence modeled as a factor model. We focus on panel unit root tests and on inference on the nonstationary factors. Our results suggest that PPP does not hold for our panel of 17 exchange rates due to the presence of nonstationary factors. The dominant factor has a very strong European flavor. Moreover, we find a single nonstationary factor in a panel of Canadian and U.S. interest rates of different maturities and risk. Since some of the idiosyncratic components are stationary, these series are cointegrated. The dominant factor has a level interpretation as in the term structure literature.

Semi-Parametric Weak Instrument Regressions with an Application to the Risk-return Trade-off

We extend the local-to-zero analysis of models with weak instruments to models with estimated instruments and regressors and with higher-order dependence between instruments and disturbances. This framework is applicable to linear models with expectation variables that are estimated nonparametrically, such as the risk-return tradeoff in finance and the effect of inflation uncertainty on real economic activity. Our simulation evidence suggests that Lagrange multiplier confidence intervals have better coverage in these models. We apply these methods to excess returns on the S&P 500 index, yen-dollar spot returns, and excess holding yields between 6-month and 3-month Treasury bills.

Bootstrap Prediction Intervals for Factor Models

We propose bootstrap prediction intervals for an observation h periods into the future and its conditional mean. We assume that these forecasts are made using a set of factors extracted from a large panel of variables. Because we treat these factors as latent, our forecasts depend both on estimated factors and estimated regression coefficients. Under regularity conditions, asymptotic intervals have been shown to be valid under Gaussianity of the innovations. The bootstrap allows us to relax this assumption and to construct valid prediction intervals under more general conditions. Moreover, even under Gaussianity, the bootstrap leads to more accurate intervals in cases where the cross-sectional dimension is relatively small as it reduces the bias of the ordinary least-squares (OLS) estimator.

Bootstrap Inference in Regressions with Estimated Factors and Serial Correlation

This paper considers bootstrap inference in a factor-augmented regression context where the errors could potentially be serially correlated. This generalizes results in Goncalves and Perron (2013) and makes the bootstrap applicable to forecasting contexts where the forecast horizon is greater than one. We propose and justify two residual-based approaches, a block wild bootstrap (BWB) and a dependent wild bootstrap (DWB). Our simulations document improvement in coverage rates of confidence intervals for the coefficients when using BWB or DWB relative to both asymptotic theory and the wild bootstrap when serial correlation is present in the regression errors.

Point‐Optimal Panel Unit Root Tests with Serially Correlated Errors

Generalizations of the point‐optimal panel unit root tests of Moon, Perron and Phillips (MPP) are developed to cover cases of serially correlated errors. The resulting statistics involve two modifications relative to those of MPP: (a) the error variance is replaced by the long‐run variance; (b) centring of the statistic is adjusted to correct for second‐order bias effects induced by the correlation between the error and lagged dependent variable.