"Panel Data Measures for Price Discovery", Econometric Reviews , Published online: 30 January 2021. (with Joakim Westerlund and Paresh Narayan)
This paper considers disaggregated price data that are observed not only for multiple markets over extended periods of time, but also for a large number of assets. The previous literature has argued that in such data rich environments, which arise frequently in applied work, the analysis of price discovery can be made more precise by accounting for the panel structure of the data. Moreover, since the individual assets are not that interesting anyways, little is lost by taking the overall panel perspective. These arguments are, however, mainly based on empirical observations, and there is little in terms of econometric support. The purpose of the present study is to fill this gap in the literature. This is done by offering a full-blown econometric analysis of panel analogs of the information share and permanent--transitory measures of price discovery, which are the workhorses of the time series literature. Both measures are shown to be consistent and they support standard normal inference, which is in contrast to the time series case, where such inference is only possible for the permanent-transitory measure.
Dynamic panel data regression models with fixed effects to account for unobserved heterogeneity are standard econometric tools. It is not until recently, however, that the problems involved when fitting such regressions to leverage data have been investigated. The main problem is that models of leverage are extremely noisy, much more so than what can be accommodated using fixed effects. The present article can be seen as a reaction to this. The purpose is to consider a more general interactive effects model in which there are multiple time effects, each with their own firm-specific sensitivities. Our empirical results suggest that proper accounting for the interactive effects and the bias that they cause leads to a marked increase in the estimated speed of adjustment to target leverage.
"On the Robustness of the Pooled CCE Estimator", Journal of Econometrics, Volume 220, Issue 2, February 2021, Pages 325-348. (with Arturas Juodis and Joakim Westerlund)
Among the existing estimators of factor-augmented regressions, the CCE approach is the most popular. A major reason for this popularity is the simplicity and good small-sample performance of the approach, making it very attractive from an empirical point of view. The main drawback is that most of the available asymptotic theory is based on quite restrictive assumptions, such as that the common factor component should be independent of the regressors. The present paper can be seen as a reaction to this. The purpose is to study the asymptotic properties of the pooled CCE estimator under more realistic conditions. In particular, the common factor component may be correlated with the regressors, and the true number of common factors, r, can be larger than the number of estimated factors, which in CCE is given by k+1, where k is the number of regressors. The main conclusion is that while the estimator is generally consistent, asymptotic normality can sometimes fail when r > k+1.
"Forecasting Using Cross-Section Average-Augmented Time Series Regressions", The Econometrics Journal, Published online: 12 October 2020. (with Joakim Westerlund)
There is a large and growing body of literature concerned with forecasting time series variables by the use of factor-augmented regression models. The workhorse of this literature is a two-step approach in which the factors are first estimated by applying the principal components method to a large panel of variables, and the forecast regression is then estimated, conditional on the first-step factor estimates. Another stream of research that has attracted much attention is concerned with the use of cross-section averages as common factor estimates in interactive effects panel regression models. The main justification for this second development is the simplicity and good performance of the cross-section averages when compared with estimated principal component factors. In view of this, it is quite surprising that no one has yet considered the use of cross-section averages for forecasting. Indeed, given the purpose to forecast the conditional mean, the use of the cross-sectional average to estimate the factors is only natural. The present paper can be seen as a reaction to this. The purpose is to investigate the asymptotic and small-sample properties of forecasts based on cross-section average–augmented regressions. In contrast to most existing studies, the investigation is carried out while allowing the number of factors to be unknown.
"CCE Estimation of Factor-Augmented Regression Models with More Factors than Observables", Journal of Applied Econometrics, Volume 34, Issue 2, March 2019, Pages 268-284. (with Joakim Westerlund and Jean-Pierre Urbain)
This paper considers estimation of factor‐augmented panel data regression models. One of the most popular approaches towards this end is the common correlated effects (CCE) estimator of Pesaran (Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica, 2006, 74, 967–1012, 2006). For the pooled version of this estimator to be consistent, either the number of observables must be larger than the number of unobserved common factors, or the factor loadings must be distributed independently of each other. This is a problem in the typical application involving only a small number of regressors and/or correlated loadings. The current paper proposes a simple extension to the CCE procedure by which both requirements can be relaxed. The CCE approach is based on taking the cross‐section average of the observables as an estimator of the common factors. The idea put forth in the current paper is to consider not only the average but also other cross‐section combinations. Asymptotic properties of the resulting combination‐augmented CCE (C3E) estimator are provided and tested in small samples using both simulated and real data.
"Econometric Analysis of Panel Data Models with Multifactor Error Structures", Annual Review of Economics, Volume 11, 2019, Pages 495-522. (with Franz Palm and Jean-Pierre Urbain)
Economic panel data often exhibit cross-sectional dependence, even after conditioning on appropriate explanatory variables. Two approaches to model cross-sectional dependence in economic panel data are often used: the spatial dependence approach, which explains cross-sectional dependence in terms of distance among units and the residual multi-factor approach, which explains cross-sectional dependence by common factors that affect individuals to a different extent. This paper reviews the theory on estimation and statistical inference for stationary and non-stationary panel data with cross-sectional dependence, in particular for models with a multifactor error structure. Tests and diagnostics for testing for unit roots, slope homogeneity, cointegration and for the number of factors are provided. Finally, we discuss issues such as estimating common factors, dealing with parameter plethora in practice, testing for structural stability and non-linearity and ways to deal with model and parameter uncertainty. Finally, we address issues related to the use of these economic panel models.
"Islamic Spot and Index Futures Markets: Where is the Price Discovery?", Pacific-Basin Finance Journal, Volume 52, December 2018, Pages 123-133. (with Paresh Narayan, Dinh Bach Phan and Joakim Westerlund)
This paper examines the source of price discovery for Islamic stocks. We pair a large number of Islamic stocks to country-specific futures and estimate price discovery using a vector error correction model. The results obtained using data for 19 countries suggest that for most countries (63% of the sample) price discovery is dominated by the spot market. We show that for there countries, a mean-variance investor makes annualized average profit of 4.91% compared to an average buy-and-hold profit of 2.97% per annum.
"On the Role of the Rank Condition in CCE Estimation of Factor-Augmented Panel Regressions ", Journal of Econometrics, Volume 197, Issue 1, March 2017, Pages 60-64. (with Simon Reese and Joakim Westerlund)
A popular approach to factor-augmented panel regressions is the common correlated effects (CCE) estimator of Pesaran (Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica (74), 967–1012, 2006). This paper points to a problem with the CCE approach that appears in the empirically relevant case when the number of factors is strictly less than the number of observables used in their estimation. Specifically, the use of too many observables causes the second moment matrix of the estimated factors to become asymptotically singular, an issue that has not yet been appropriately accounted for. The purpose of the present paper is to fill this gap in the literature.
"Testing for Predictability in Panels with General Predictors", Journal of Applied Econometrics, Volume 32, Issue 3, April/May 2017, Pages 554-574. ( with Joakim Westerlund and Paresh Narayan)
The difficulty of predicting returns has recently motivated researchers to start looking for tests that are either robust or more powerful. Unfortunately, the way that these tests work typically involves trading robustness for power or vice versa. The current paper takes this as its starting point to develop a new panel-based approach to predictability that is both robust and powerful. Specifically, while the panel route to increased power is not new, the way in which the cross-section variation is exploited to achieve also robustness with respect to the predictor is. The result is two new tests that enable asymptotically standard normal and chi-squared inference across a wide range of empirical relevant scenarios in which the predictor may be stationary, unit root non-stationary, or anything in between. The cross-section dependence of the predictor is also not restricted, and can be weak, strong, or indeed anything in between. What is more, this generality comes at no cost in terms of test construction. The new tests are therefore very user-friendly.
"On the Estimation and Testing of Predictive Panel Regressions", Journal of International Financial Markets, Institutions and Money, Volume 45, November 2016, Pages 115-125. (with Joakim Westerlund and Paresh Narayan)
Hjalmarsson (Predicting Global Stock Returns, Journal of Financial and Quantitative Analysis 45, 49-80, 2010) considers an OLS-based estimator of predictive panel regressions that is claimed to be mixed normal under very general conditions. In a recent paper, Westerlund et al. (2016) show that while consistent, the estimator is generally not mixed normal, which invalidates standard normal and chi-squared inference. The purpose of the present paper is to study the consequences of this theoretical result in small samples, which is done using both simulated and real data.