This paper considers estimation and inference in panel vector autoregressions (PVARs) where (i) the individual effects are either random or fixed, (ii) the time-series properties of the model variables are unknown a priori and may feature unit roots and cointegrating relations, and (iii) the time dimension of the panel is short and its cross-sectional dimension is large. Generalized Method of Moments (GMM) and Quasi Maximum Likelihood (QML) estimators are obtained andthencomparedintermsoftheirasymptoticandfinite sample properties. It is shown that GMM estimators based only on standard orthogonality conditions break down if the underlying time series contain unit roots. Extended GMM estimators making use of further moment conditions are not subject to this problem. However, their finite sample performance is shown to deteriorate as a ratio of cross-section to time-series variation is increased, while the performance of the fixed effects QML estimator is invariant to this ratio. The QML estimators also tend to outperform the various GMM estimators in finite sample. Overall, our findings favor the use of the fixed effects QML estimator, given that it does not impose any restrictions on the distribution generating the individual effects. The paper also shows how the fixed effects QML

Currently, evidence on the ‘resource curse ’ yields a conundrum. While there is much crosssection evidence to support the curse hypothesis, time series analyses using vector autoregressive (VAR) models have found that commodity booms raise the growth of commodity exporters. This paper adopts panel cointegration methodology to explore longer term effects than permitted using VARs. We find strong evidence of a resource curse. Commodity booms have positive short-term effects on output, but adverse long-term effects. The long-term effects are confined to “high-rent”, non-agricultural commodities. We also find that the resource curse is avoided by countries with sufficiently good institutions. We test the channels of the resource curse proposed in the literature and find that a substantial part of it is explained by high public and private consumption, low or inefficient total investment, and an overvalued exchange rate. Our results fully account for the cross-section results in the seminal

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 …rst 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 di¤erent 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 di¤erent cross section units are due to common random walk components.

In the vehicle routing problem with time windows a number of identical vehicles must be routed to and from a depot to cover a given set of customers, each of whom has a specified time interval indicating when they are available for service. Each customer also has a known demand, and a vehicle may only serve the customers on a route if the total demand does not exceed the capacity of the vehicle. The most effective solution method proposed to date for this problem is due to Kohl, Desrosiers, Madsen, Solomon, and Soumis. Their algorithm uses a cutting-plane approach followed by a branchand -bound search with column generation, where the columns of the LP relaxation represent routes of individual vehicles. We describe a new implementation of their method, using Karger's randomized minimum-cut algorithm to generate cutting planes. The standard benchmark in this area is a set of 87 problem instances generated in 1984 by M. Solomon; making using of parallel processing in both the cutting-pla...

A common …nding in the empirical literature on the validity of purchasing power parity (PPP) is that it holds when tested for in panel data, but not in univariate (i.e. country speci…c) analysis. The usual explanation for this mismatch is that panel tests for unit roots and cointegration are more powerful than their univariate counterparts. In this paper we suggest an alternative explanation for the mismatch. More generally, we warn against the use of panel methods for testing for unit roots in macroeconomic time series. Existing panel methods assume that cross-unit cointegrating or long-run relationships, that tie the units of the panel together, are not present. However, using empirical examples on PPP for a panel of OECD countries, we show that this assumption is very likely to be violated. Simulations of the properties of panel unit root tests in the presence of long-run cross-unit relationships are then presented to demonstrate the serious cost of assuming away such relationships. The empirical size of the tests is substantially higher than the nominal level, so that the null hypothesis of a unit root is rejected very often, even if correct.

The European Economy Group (EEG) was formed in 1998 within the framework

... 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.

An IV approach, using as instruments nonlinear transformations of the lagged levels, is explored to test for unit roots in panels with general dependency and heterogeneity across cross-sectional units. We allow not only for the cross-sectional dependencies of innovations, but also for the presence of cointegration across crosssectional levels. Unbalanced panels and panels with di¤ering individual shortrun dynamics and cross-sectionally related dynamics are also permitted. Panels with such cross-sectional dependencies and heterogeneities appear to be quite commonly observed in practical applications. Yet none of the currently available tests can be used to test for unit roots in such general panels. We also more carefully formulate the unit root hypothesis in panels. In particular, using order statistics we make it possible to test for and against the presence of unit roots in some of the individual units for a given panel. The individual IV t-ratios, which are the bases of our tests, are asymptotically normally distributed and cross-sectionally independent. Therefore, the critical values of the order statistics as well as the usual averaged statistic can be easily obtained from simple elementary probability computations. We show via a set of simulations that our tests work well, while other existing tests fail to perform properly. As an illustration, our tests are applied to some of the data sets that were used in earlier studies.

As a unified discipline, econometrics is still relatively young and has been transforming and expanding very rapidly over the past few decades. Major advances have taken place in the analysis of cross sectional data by means of semi-parametric and non-parametric techniques. Heterogeneity of economic relations across individuals, firms and industries is increasingly acknowledged and attempts have been made to take them into account either by integrating out their effects or by modeling the sources of heterogeneity when suitable panel data exists. The counterfactual considerations that underlie policy analysis and treat-ment evaluation have been given a more satisfactory foundation. New time series econometric techniques have been developed and employed extensively in the areas of macroeconometrics and finance. Non-linear econometric techniques are used increasingly in the analysis of cross section and time series observations. Applications of Bayesian techniques to econometric problems have been given new impetus largely thanks to advances in computer power and computational techniques. The use of Bayesian techniques have in turn provided the investigators with a unifying framework where the tasks of forecasting, decision making, model evaluation and learning can be considered as parts of the same interactive and iterative process; thus paving the way for establishing the foundation of “real time econometrics”. This paper attempts to provide an overview of some of these developments.

We propose new tests for panel cointegration by extending the panel unit root tests of Choi [2001] and Maddala and Wu [1999] to the panel cointegration case. The tests are flexible, intuitively appealing and relatively easy to compute. We investigate the finite sample behavior in a simulation study. Several variants of the tests compare favorably in terms of both size and power with other widely used panel cointegration tests.