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.     

Sources of the great moderation: A time-series analysis of GDP subsectors

Recent work finds evidence that the volatility of the U.S. economy fell dramatically around the first quarter of 1984. We trace the timing of this so-called “Great Moderation” across many subsectors of the economy in order to better understand its root cause. We find that the interest rate sensitive sectors generally experience a much earlier volatility decline than other large sectors of the economy. The changes in Federal Reserve stabilization policies that occurred during the early 1980s support the view that an improved monetary policy played an important role in stabilizing real economic activity. We find only mild evidence that “good luck” was important and little evidence to support the claim that improved inventory management was important.     

Adaptive consistent unit-root tests based on autoregressive threshold model

This paper proposes SupWald tests from a threshold autoregressive model computed with an adaptive set of thresholds. Simple examples of adaptive threshold sets are given. A second contribution of the paper is a general asymptotic null limit theory when the threshold variable is a level variable. We obtain a pivotal null limiting distribution under some simple conditions for bounded or asymptotically unbounded thresholds. Our general approach is flexible enough to allow a choice of the auxiliary threshold model or of the threshold set involved in the test specifically designed for nonlinear stationary alternatives relevant for macroeconomic and financial topics involving arbitrage in presence of transaction costs. A Monte-Carlo study and an application to the interest rates spread for French, German, New-Zealander and US post-1980 monthly data illustrate the ability of the adaptive SupWald tests to reject unit-root when the ADF does not.     

First difference maximum likelihood and dynamic panel estimation

First difference maximum likelihood (FDML) seems an attractive estimation methodology in dynamic panel data modeling because differencing eliminates fixed effects and, in the case of a unit root, differencing transforms the data to stationarity, thereby addressing both incidental parameter problems and the possible effects of nonstationarity. This paper draws attention to certain pathologies that arise in the use of FDML that have gone unnoticed in the literature and that affect both finite sample performance and asymptotics. FDML uses the Gaussian likelihood function for first differenced data and parameter estimation is based on the whole domain over which the log-likelihood is defined. However, extending the domain of the likelihood beyond the stationary region has certain consequences that have a major effect on finite sample and asymptotic performance. First, the extended likelihood is not the true likelihood even in the Gaussian case and it has a finite upper bound of definition. Second, it is often bimodal, and one of its peaks can be so peculiar that numerical maximization of the extended likelihood frequently fails to locate the global maximum. As a result of these pathologies, the FDML estimator is a restricted estimator, numerical implementation is not straightforward and asymptotics are hard to derive in cases where the peculiarity occurs with non-negligible probabilities. The peculiarities in the likelihood are found to be particularly marked in time series with a unit root. In this case, the asymptotic distribution of the FDMLE has bounded support and its density is infinite at the upper bound when the time series sample size T→∞$T\to \infty$. As the panel width n→∞$n\to \infty$ the pathology is removed and the limit theory is normal. This result applies even for T$T$ fixed and we present an expression for the asymptotic distribution which does not depend on the time dimension. We also show how this limit theory depends on the form of the extended likelihood.     

The VIX,the variance premium and stock market volatility

We decompose the squared VIX index, derived from US S&P500 options prices, into the conditional variance of stock returns and the equity variance premium. We evaluate a plethora of state-of-the-art volatility forecasting models to produce an accurate measure of the conditional variance. We then examine the predictive power of the VIX and its two components for stock market returns, economic activity and financial instability. The variance premium predicts stock returns while the conditional stock market variance predicts economic activity and has a relatively higher predictive power for financial instability than does the variance premium.     

Distribution-free bounds for serial correlation coefficients in heteroskedastic symmetric time series

We consider the problem of testing whether the observations _X1,…,_Xn$X_1,\dots ,X_n$ of a time series are independent with unspecified (possibly nonidentical) distributions symmetric about a common known median. Various bounds on the distributions of serial correlation coefficients are proposed: exponential bounds, Eaton-type bounds, Chebyshev bounds and Berry–Esséen–Zolotarev bounds. The bounds are exact in finite samples, distribution-free and easy to compute. The performance of the bounds is evaluated and compared with traditional serial dependence tests in a simulation experiment. The procedures proposed are applied to U.S. data on interest rates (commercial paper rate).     

Specification tests of parametric dynamic conditional quantiles

This article proposes omnibus specification tests of parametric dynamic quantile models. In contrast to the existing procedures, we allow for a flexible specification, where a possible continuum of quantiles is simultaneously specified under fairly weak conditions on the serial dependence in the underlying data-generating process. Since the null limit distribution of tests is not pivotal, we propose a subsampling approximation of the asymptotic critical values. A Monte Carlo study shows that the asymptotic results provide good approximations for small sample sizes. Finally, an application suggests that our methodology is a powerful alternative to standard backtesting procedures in evaluating market risk.