This paper presents a new approach to estimation and inference in panel data models with a multifactor error structure where the unobserved common factors are (possibly) correlated with exogenously given individual-specific regressors, and the factor loadings differ over the cross section units. The basic idea behind the proposed estimation procedure is to filter the individual-specific regressors by means of (weighted) cross-section aggregates such that asymptotically as the cross-section dimension ( N) tends to infinity the differential effects of unobserved common factors are eliminated. The estimation procedure has the advantage that it can be computed by OLS applied to an auxiliary regression where the observed regressors are augmented by (weighted) cross sectional averages of the dependent variable and the individual specific regressors. Two different but related problems are addressed: one that concerns the coefficients of the individual-specific regressors, and the other that focusses on the mean of the individual coefficients assumed random. In both cases appropriate estimators, referred to as common correlated effects (CCE) estimators, are proposed and their asymptotic distribution as N →∞, with T (the time-series dimension) fixed or as N and T →∞(jointly) are derived under different regularity conditions. One important feature of the proposed CCE mean group (CCEMG) estimator is its invariance to the (unknown but fixed) number of unobserved common factors as N and T →∞(jointly). The small sample properties of the various pooled estimators are investigated by Monte Carlo experiments that confirm the theoretical derivations and show that the pooled estimators have generally satisfactory small sample properties even for relatively small values of N and T.

Least squares bias in autoregression and dynamic panel regression is shown to be exacerbated in case of cross section dependence. The bias is substantial and is shown to have serious effects in applications like HAC estimation and dynamic half-life response estimation. To address the bias problem, this paper develops a panel approach to median unbiased estimation that takes into account cross section dependence. The new estimators given here considerably reduce the effects of bias and gain precision from estimating cross section error correlation. The paper also develops an asymptotic theory for tests of coefficient homogeneity under cross section dependence, and proposes a modiÞed Hausman test to test for the presence of homogeneous unit roots. An orthogonalization procedure is developed to remove cross section dependence and permit the use of conventional and meta unit root tests with panel data. Some simulations investigating the Þnite sample performance of the estimation and test procedures are reported.

Abstract: The paper investigates the common dynamic properties of business cycle fluctuations across countries, regions, and the world. We employ a Bayesian dynamic latent factor model to estimate common components in the main macroeconomic aggregates (output, consumption and investment) in a sixty-country sample covering seven regions of the world. In particular, we simultaneously estimate (i) a dynamic factor common to all aggregates, regions, and countries (the world factor); (ii) a set of 7 regional dynamic factors common across aggregates within a region; (iii) 60 country factors to capture dynamic comovement across aggregates within each country; and (iv) a component for each aggregate that captures idiosyncratic dynamics. We decompose the volatility in each aggregate into the fraction due to the world, region, country, and idiosyncratic components. The results indicate that the world factor is an important source of volatility for aggregates in most countries, providing evidence for a world business cycle. We find that the region-specific factor plays only a minor role in explaining fluctuations in economic activity. While the world and regional factors together account for a larger share of fluctuations in output than in consumption, the country-specific and idiosyncratic components play much larger roles in explaining investment dynamics. We also explore how the three aggregates in each country relate to the world, region and country factors, and document similarities and differences across regions, countries and aggregates. We link the empirical results to the economic structures of the countries in the sample.

Factors estimated from large macroeconomic panels are being used in an increasing number of applications. However, little is known about how the size and composition of the data affect the factor estimates. In this paper, we question whether it is possible to use more series to extract the factors and that yet the resulting factors are less useful for forecasting, and the answer is yes. Such a problem tends to arise when the idiosyncratic errors are cross-correlated. It can also arise if forecasting power is provided by a factor that is dominant in a small dataset but is a dominated factor in a larger dataset. In a real time forecasting exercise, we find that factors extracted from as few as 40 pre-screened series often yield satisfactory or even better results than using all 147 series. Our simulation analysis is unique in that special attention is paid to cross-correlated idiosyncratic errors, and we also allow the factors to have weak loadings on groups of series. It thus allows us to better understand the properties of the principal components estimator in empirical applications.

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Most empirical analyses of monetary policy have been confined to frameworks in which the Federal Reserve is implicitly assumed to exploit only a limited amount of information, despite the fact that the Fed actively monitors literally thousands of economic time series. This article explores the feasibility of incorporating richer information sets into the analysis, both positive and normative, of Fed policymaking. We employ a factor-model approach, developed by Stock and Watson (1999a,b), that permits the systematic information in large data sets to be summarized by relatively few estimated factors. With this framework, we reconfirm Stock and Watson’s result that the use of large data sets can improve forecast accuracy, and we show that this result does not seem to depend on the use of finally revised (as opposed to “real-time”) data. We estimate policy reaction functions for the Fed that take into account its data-rich environment and provide a test of the hypothesis that Fed actions are explained solely by its forecasts of inflation and real activity. Finally, we explore the possibility of developing an “expert system ” that could aggregate diverse information and provide benchmark policy settings. *Prepared for a conference on “Monetary Policy Under Incomplete Information”,

This paper introduces the concepts of time-specific weak and strong cross section dependence. A double-indexed process is said to be cross sectionally weakly dependent at a given point in time, t, if its weighted average along the cross section dimension (N) converges to its expectation in quadratic mean, as N is increased without bounds for all weights that satisfy certain ‘granularity’ conditions. Relationship with the notions of weak and strong common factors is investigated and an application to the estimation of panel data models with an infinite number of weak factors and a finite number of strong factors is also considered. The paper concludes with a set of Monte Carlo experiments where the small sample properties of estimators based on principal components and CCE estimators are investigated and compared under various assumptions on the nature of the unobserved common effects.

This paper proposes a new forecasting method which makes use of information from a large panel of time series. As in Forni, Hallin, Lippi and Reichlin (2000), and in Stock and Watson (2002a,b), the method is based on a dynamic factor model. We argue that our method improves upon a standard principal component predictor in that, first, it fully exploits all the dynamic covariance structure of the panel and, second, it weights the variables according to their estimated signal-to-noise ratio. We provide asymptotic results for our optimal forecast estimator and show that in finite samples our forecast outperforms the standard principal components predictor.

This paper develops a new methodology that makes use of the factor structure of large dimensional panels to understand the nature of non-stationarity in the data. We refer to it as PANIC – a ‘Panel Analysis of Non-stationarity in Idiosyncratic and Common components’. PANIC consists of univariate and panel tests with a number of novel features. It can detect whether the nonstationarity is pervasive, or variable-specific, or both. It tests the components of the data instead of the observed series. Inference is therefore more accurate when the components have different orders of integration. PANIC also permits the construction of valid panel tests even when cross-section correlation invalidates pooling of statistics constructed using the observed data. The key to PANIC is consistent estimation of the components even when the regressions are individually spurious. We provide a rigorous theory for estimation and inference. In Monte Carlo simulations, the tests have very good size and power. PANIC is applied to a panel of inflation series.

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