This paper considers regression models for cross-section data that exhibit crosssection dependence due to common shocks, such as macroeconomic shocks. The paper analyzes the properties of least squares (LS) estimators in this context. The results of the paper allow for any form of cross-section dependence and heterogeneity across population units. The probability limits of the LS estimators are determined, and necessary and sufficient conditions are given for consistency. The asymptotic distributions of the estimators are found to be mixed normal after recentering and scaling. The t� Wald, and F statistics are found to have asymptotic standard normal, χ2,andscaledχ2 distributions, respectively, under the null hypothesis when the conditions required for consistency of the parameter under test hold. However, the absolute values of t, Wald, and F statistics are found to diverge to infinity under the null hypothesis when these conditions fail. Confidence intervals exhibit similarly dichotomous behavior. Hence, common shocks are found to be innocuous in some circumstances, but quite problematic in others. Models with factor structures for errors and regressors are considered. Using the general results, conditions are determined under which consistency of the LS estimators holds and fails in models with factor structures. The results are extended to cover heterogeneous and functional factor structures in which common factors have different impacts on different population units.

This paper proposes a standardized version of Swamy’s test of slope homogeneity for panel data models where the cross section dimension (N) could be large relative to the time series dimension (T). The proposed test, denoted by ˜ ∆, exploits the cross section dispersion of individual slopes weighted by their relative precision. In the case of models with strictly exogenous regressors, but with non-normally distributed errors, the test is shown to have a standard normal distribution as (N, T) j → ∞ such that √ N/T 2 → 0. When the errors are normally distributed, a mean-variance bias adjusted version of the test is shown to be normally distributed irrespective of the relative expansion rates of N and T. The test is also applied to stationary dynamic models, and shown to be valid asymptotically so long as N/T → κ, as (N, T) j → ∞, where 0 ≤ κ < ∞. Using Monte Carlo experiments, it is shown that the test has the correct size and satisfactory power in panels with strictly exogenous regressors for various combinations of N and T. Similar results are also obtained for dynamic panels, but only if the autoregressive coefficient is not too close to unity and so long as T ≥ N.

We start by discussing some general weaknesses and limitations of the econometric approach. A template from sociology is used to formulate six laws that characterize mainstream activities of econometrics and the scientific limits of those activities. Next, we discuss some proximity theorems that quantify by means of explicit bounds how close we can get to the generating mechanism of the data and the optimal forecasts of next period observations using a finite number of observations. The magnitude of the bound depends on the characteristics of the model and the trajectory of the observed data. The results show that trends are more elusive to model than stationary processes in the sense that the proximity bounds are larger. By contrast, the bounds are of smaller order for models that are unidentified or nearly unidentified, so that lack or near lack of identification may not be as fatal to the use of a model in practice as some recent results on inference suggest. Finally, we look at one possible future of econometrics that involves the use of advanced econometric methods interactively by way of a web browser. With these methods users may access a suite of econometric methods and data sets online. They may also upload data to remote servers and by simple web browser selections initiate the implementation of advanced econometric software algorithms, returning the results online and by file and graphics downloads.

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This paper considers estimation of slope coe ¢ cients in large panel data models where even after conditioning on common observed e¤ects the cross section units might remain dependently distributed. This could arise when the cross section units are subject to unobserved common e¤ects and/or if there are spill over e¤ects due to spatial or other forms of local dependencies. Initially it focuses on a regression model where the idiosyncratic errors are spatially dependent and possibly serially correlated, and derives the asymptotic distributions of the (generalized) …xed e¤ects and the mean group estimators under homogeneous and heterogeneous slope coe ¢ cients. Semiparametric and non-parametric estimation of the variances of these estimators is considered. The paper then focuses on a panel data model with a multifactor error structure and spatial correlation. It is established that, under this framework, the Common Correlated E¤ects (CCE) estimator, recently advanced by Pesaran (2006), continues to provide estimates of the slope coe ¢ cient that are consistent and asymptotically normal. Small sample properties of the CCE estimator under various patterns of cross section dependence, including spatial forms, are investigated by Monte Carlo experiments. Results show that the CCE approach works well in the presence of weak and/or strong cross sectionally correlated errors.

This paper re-examines the panel unit root tests proposed by Chang (2002). She establishes asymptotic independence of the t-statistics when integrable functions of lagged dependent variable are used as instruments even if the original series are cross sectionally dependent. From this rather remarkable result she claims that her non-linear instrumental variable (NIV) panel unit root test is valid under general error cross correlations for any N (the cross section dimension) as T (the time dimension of the panel) tends to infinity. We show that her claim is valid only if N ln T / √ T → 0, as N and T → ∞, and this condition is unlikely to hold in practice, unless N is very small. The favourable simulation results reported by Chang are largely due to her particular choice of the error correlation matrix, which results in weak cross section dependence. Also, the asymptotic independence property of the t-statistics disappears when Chang’s modified instruments are used. Using a common factor model with a sizeable degree of cross section correlations, we are able to show that Chang’s NIV panel unit root test suffers from gross size distortions, even when N is small relative to T (for example N =5, T =100). JEL Classification: C12, C15, C22, C23. Key Words: Non-linear Instrumental Variable (NIV) Panel unit root tests, Cross-section dependence, Finite sample properties. We would like to thank Michael Binder, George Kapetanios, and Junsoo Lee for helpful discussions and Mutita Akusuwan for computing the results reported in Table 5 of this paper. We are also grateful to Yoosoon Chang for providing us with her Gauss program. 1 1

In this paper we investigate a ‘global’ production function for agriculture, using FAO data for 128 countries from 1961-2002. Our review of the empirical literature in this field highlights that existing cross-country studies largely neglect variable time-series properties, parameter heterogeneity and the potential for heterogeneous Total Factor Productivity (TFP) processes across countries. We motivate the case for technology heterogeneity in agricultural production and present statistical tests indicating nonstationarity and cross-section dependence in the data. Our empirical approach deals with these difficulties by adopting the Pesaran (2006) Common Correlated Effects estimators, which we extend by using alternative weight-matrices to model the nature of the cross-section dependence. We furthermore investigate returns to scale of production and production dynamics. Our results support the specification of a common factor model in intercountry production analysis, highlight the rejection of constant returns to scale in pooled models as an artefact of empirical misspecification and suggest that agro-climatic environment, rather than neighbourhood or distance, drives similarity in TFP evolution across countries. The latter finding provides a possible explanation for the observed failure of technology transfer from advanced countries of the temperate ‘North’ to arid and/or equatorial developing countries of the ‘South’.

... empirics literature has used increasingly sophisticated methods to select relevant growth determinants in estimating cross-section growth regressions. The vast majority of empirical approaches however limit cross-country heterogeneity in production technology to the specification of Total Factor Productivity, the ‘measure of our ignorance’ (Abramowitz, 1956). The central theme of this survey is an investigation of this choice of specification against the background of pertinent data properties when the units of observations are countries or regions and the time-series dimension of the data becomes substantial. We present two general empirical frameworks for cross-country productivity analysis and demonstrate that they encompass the approaches in the growth empirics literature of the past two decades. We then develop our central argument, that cross-country heterogeneity in the impact of observables and unobservables on output is important for reliable empirical analysis. This idea is developed against the background of the pertinent time-series and cross-section properties of macro panel data.

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This paper provides a review of the literature on unit roots and cointegration in panels where the time dimension (T), and the cross section dimension (N) are relatively large. It distinguishes between the first generation tests developed on the assumption of the cross section independence, and the second generation tests that allow, in a variety of forms and degrees, the dependence that might prevail across the different units in the panel. In the analysis of cointegration the hypothesis testing and estimation problems are further complicated by the possibility of cross section cointegration which could arise if the unit roots in the different cross section units are due to common random walk components.