Many unit root tests have distorted sizes when the root of the error process is close to the unit circle. This paper analyses the properties of the Phillips-Perron tests and some of their variants in the problematic parameter space. We use local asymptotic analyses to explain why the Phillips-Perron tests suffer from severe size distortions regardless of the choice of the spectral density estimator but that the modified statistics show dramatic improvements in size when used in conjunction with a particular formulation an autoregressive spectral density estimator. We explain why kernel based spectral density estimators aggravate the size problem in the Phillips-Perron tests and yield no size improvement to the modified statistics. The local asymptotic power of the modified statistics are also evaluated. These modified statistics are recommended as being useful in empirical work since they are free of the size problems which have plagued many unit root tests, and they retain respectable power.

This paper studies dynamic identification of parameters of a dynamic stochastic general equilibrium model from the first and second moments of the data. Classical results for dynamic simultaneous equations do not apply because the state space solution of the model does not constitute a standard reduced form. Full rank of the Jacobian matrix of derivatives of the solution parameters with respect to the parameters of interest is necessary but not sufficient for identification. We use restrictions implied by observational equivalence to obtain two sets of rank and order conditions: one for stochastically singular models and another for nonsingular models. Measurement errors, mean, long-run, and a priori restrictions can be accommodated. An example is considered to illustrate the results.

We consider the situation when there is a large number of series, N, each with T observations, and each series has some predictive ability for some variable of interest. A methodology of growing interest is first to estimate common factors from the panel of data by the method of principal components and then to augment an otherwise standard regression with the estimated factors. In this paper, we show that the least squares estimates obtained from these factor-augmented regressions are consistent and asymptotically normal if . The conditional mean predicted by the estimated factors is consistent and asymptotically normal. Except when T/N goes to zero, inference should take into account the effect of “estimated regressors” on the estimated conditional mean. We present analytical formulas for prediction intervals that are valid regardless of the magnitude of N/T and that can also be used when the factors are nonstationary.

This paper develops a new methodology that makes use of the factor structure of large dimensional panels to understand the nature of nonstationarity in the data. We refer to it as PANIC-Panel Analysis of Nonstationarity in Idiosyncratic and Common components. PANIC can detect whether the nonstationarity in a series is pervasive, or variable-specific, or both. It can determine the number of independent stochastic trends driving the common factors. PANIC also permits valid pooling of individual statistics and thus panel tests can be constructed. A distinctive feature of PANIC is that it tests the unobserved components of the data instead of the observed series. The key to PANIC is consistent estimation of the space spanned by the unobserved common factors and the idiosyncratic errors without knowing a priori whether these are stationary or integrated processes. We provide a rigorous theory for estimation and inference and show that the tests have good finite sample properties. Copyright The Econometric Society 2004.

It is widely known that when there are errors with a moving-average root close to −1, a high order augmented autoregression is necessary for unit root tests to have good size, but that information criteria such as the AIC and the BIC tend to select a truncation lag (k) that is very small. We consider a class of Modified Information Criteria (MIC) with a penalty factor that is sample dependent. It takes into account the fact that the bias in the sum of the autoregressive coefficients is highly dependent on k and adapts to the type of deterministic components present. We use a local asymptotic framework in which the moving-average root is local to −1 to document how the MIC performs better in selecting appropriate values of k. In Monte-Carlo experiments, the MIC is found to yield huge size improvements to the DFGLS and the feasible point optimal PT test developed in Elliott, Rothenberg, and Stock (1996). We also extend the M tests developed in Perron and Ng (1996) to allow for GLS detrending of the data. The MIC along with GLS detrended data yield a set of tests with desirable size and power properties.

This paper provides evidence that the two leading principal components in a panel of 23 commodity convenience yields have statistically and quantitatively important predictive power for inflation even after controlling for unemployment gap and oil prices. The results hold up in out-of-sample forecasts, across forecast horizons, and across G7 countries. The convenience yields also explain commodity prices and can be seen as informational variables about future economic conditions as conveyed by the futures markets. A bootstrap procedure for conducting inference when the principal components are used as regressors is also proposed.

Many continuous-time term structure of interest rate models assume a factor structure where the drift and volatility functions are affine functions of the state-variable process. These models involve very specific parametric choices of factors and functional specifications of the drift and volatility. Moreover, under the affine term structure restrictions not all factors necessarily affect interest rates at all maturities simultaneously. This class of so-called affine models covers a wide variety of existing empirical as well as theoretical models in the literature. In this paper we take a very agnostic approach to the specification of these diffusion functions and test implications of the affine term structure restrictions. We do not test a specific model among the class of affine models per se. Instead, the affine term structure restrictions we test are based on the derivatives of the responses of interest rates to the factors. We also test how many and which factors affect a particular rate. These tests are conducted within a framework which models interest rates as functions of “fundamental” factors, and the responses of interest rates to these factors are estimated with nonparametric methods. We consider two sets of factors, one based on key macroeconomic variables, and one based on interest rate spreads. In general, despite their common use we find that the empirical evidence does not support the restrictions imposed by affine models. Besides testing the affine structure restrictions we also uncover a set of fundamental factors which appear remarkably robust in explaining interest rate dynamics at the long and short maturities we consider.

Serena Ng, Huntley Schaller, The Risky Spread, Investment, and Monetary Policy Transmission: Evidence on the Role of Asymmetric Information, The Review of Economics and Statistics, Vol. 78, No. 3 (Aug., 1996), pp. 375-383

This paper provides a survey of business cycle facts, updated to take account of recent data. Emphasis is given to the Great Recession, which was unlike most other postwar recessions in the United States in being driven by deleveraging and financial market factors. We document how recessions with financial market origins are different from those driven by supply or monetary policy shocks. This helps explain why economic models and predictors that work well at some times do poorly at other times. We discuss challenges for forecasters and empirical researchers in light of the updated business cycle facts.

Relative prices are nonstationary and standard root-T inference is invalid for demand systems. But demand systems are nonlinear functions of relative prices, and standard methods for dealing with nonstationarity in linear models cannot be used. Demand system residuals are also frequently found to be highly persistent, further complicating estimation and inference. We propose a variant of the translog demand system, the NTLOG, and an associated estimator that can be applied in the presence of nonstationary prices with possibly nonstationary errors. The errors in the NTLOG can be interpreted as random utility parameters. The estimates have classical root-T limiting distributions. We also propose an explanation for the observed nonstationarity of aggregate demand errors, based on aggregation of consumers with heterogeneous preferences in a slowly changing population. Estimates using U.S. data are provided.