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393
Lag length selection and the construction of unit root tests with good size and power
 Econometrica
, 2001
"... It is widely known that when there are errors with a movingaverage 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 conside ..."
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Cited by 534 (14 self)
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It is widely known that when there are errors with a movingaverage 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 movingaverage root is local to −1 to document how the MIC performs better in selecting appropriate values of k. In montecarlo experiments, the MIC is found to yield huge size improvements to the DF GLS 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.
Testing for Common Trends
 Journal of the American Statistical Association
, 1988
"... Cointegrated multiple time series share at least one common trend. Two tests are developed for the number of common stochastic trends (i.e., for the order of cointegration) in a multiple time series with and without drift. Both tests involve the roots of the ordinary least squares coefficient matrix ..."
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Cited by 455 (7 self)
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Cointegrated multiple time series share at least one common trend. Two tests are developed for the number of common stochastic trends (i.e., for the order of cointegration) in a multiple time series with and without drift. Both tests involve the roots of the ordinary least squares coefficient matrix obtained by regressing the series onto its first lag. Critical values for the tests are tabulated, and their power is examined in a Monte Carlo study. Economic time series are often modeled as having a unit root in their autoregressive representation, or (equivalently) as containing a stochastic trend. But both casual observation and economic theory suggesthat many series might contain the same stochastic trendso that they are cointegrated. If each of n series is integrated of order 1 but can be jointly characterized by k < n stochastic trends, then the vecto representation of these series has k unit roots and n k distinct stationary linear combinations. Our proposed tests can be viewed alternatively as tests of the number of common trends, linearly independent cointegrating vectors, or autoregressive unit roots of the vector process. Both of the proposed tests are asymptotically similar. The firstest (qf) is developed under the assumption that certain components of the process have a finiteorder vector autoregressive (VAR) representation, and the nuisance parameters are handled by estimating this VAR. The second test (q,) entails computing the eigenvalues of a corrected sample firstorder autocorrelation matrix, where the correction is essentially a sum of the autocovariance matrices. Previous researchers have found that U.S. postwar interest rates, taken individually, appear to be integrated of order 1. In addition, the theory of the term structure implies that yields on similar assets of different maturities will be cointegrated. Applying these tests to postwar U.S. data on the federal funds rate and the three and twelvemonth treasury bill rates providesupport for this prediction: The three interest rates appear to be cointegrated.
Empirics for Economic Growth and Convergence
 European Economic Review, Vol
, 1996
"... important in reshaping this article. X. SalaiMartin has generously donated insight and time to try and make me understand. He need not, however, agree with all my statements below. All calculations were performed using the econometrics shell tsrf. Nontechnical Summary The convergence hypothesist ..."
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Cited by 195 (4 self)
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important in reshaping this article. X. SalaiMartin has generously donated insight and time to try and make me understand. He need not, however, agree with all my statements below. All calculations were performed using the econometrics shell tsrf. Nontechnical Summary The convergence hypothesisthat poor economies might \catch up" has generated a huge empirical literature: this paper critically reviews some of the earlier key ndings, clari es their implications, and relates them to more recent results. Particular attention is devoted to interpreting convergence empirics. The paper argues that relating them to growth theories, as usually done, gives but one interpretation to convergence dynamics; it does not exhaust their importance. Instead, if we relate convergence to the dynamics of income distributions, it broadens the issues on which such empirics can shed light; it connects with policy concerns on persistent or growing inequality, regional coreperiphery stagnation, and tendencies for ongoing capital ows across developed and developing countries. The main ndings are: (1) The muchheralded uniform 2 % rate of convergence could arise for reasons unrelated to the dynamics of economic growth. (2) Usual empirical analysescrosssection (conditional) convergence regressions, time series modelling, panel data analysiscan be misleading for understanding convergence; a model of polarization in economic growth clari es those di culties. (3) The data, more revealingly modelled, show persistence and immobility across countries: some evidence supports Baumol's idea of \convergence clubs"; some evidence shows the poor getting poorer, and the rich richer, with the middle class vanishing. (4) Convergence, unambiguous up to sampling error, is observed across US states. Empirics for Economic Growth and Convergence by
Dynamic Panel Estimation and Homogeneity Testing under CrossSection Dependence, Cowles Foundation Discussion Paper n.1362
, 2002
"... 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 halflife response estimation. To address the bias problem, t ..."
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Cited by 165 (8 self)
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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 halflife 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.
Discounting the Distant Future: How Much Do Uncertain Rates Increase Valuations?
 Journal of Environmental Economics and Management
, 2000
"... Costs and benefits in the distant futuresuch as those associated with global warming, longlived infrastructure, hazardous and radioactive waste, and biodiversityoften have little value today when measured with conventional discount rates. We demonstrate that when the future path of this conve ..."
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Cited by 96 (5 self)
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Costs and benefits in the distant futuresuch as those associated with global warming, longlived infrastructure, hazardous and radioactive waste, and biodiversityoften have little value today when measured with conventional discount rates. We demonstrate that when the future path of this conventional rate is uncertain and persistent (i.e., highly correlated over time), the distant future should be discounted at lower rates than suggested by the current rate. We then use two centuries of data on U.S. interest rates to quantify this effect. Using both random walk and meanreverting models (which are indistinguishable based on historical data), we compute the certaintyequivalent ratethat is, the single discount rate that summarizes the effect of uncertainty and measures the appropriate forward rate of discount in the future. Using the random walk model, which we consider more compelling, we find that the certaintyequivalent rate falls from 3% now to 2% after 100 years, to 1% af...
Longrun purchasing power parity during the recent float, Working paper 215
, 1990
"... This paper examines the relevance of longrun purchasing power parity (PPP). which allows for measurement errors. during the recent floating exchange rate period. Previous empirical studies generally fail to find support for longrun PPP over this period. In this paper the cointegration property of ..."
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Cited by 70 (4 self)
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This paper examines the relevance of longrun purchasing power parity (PPP). which allows for measurement errors. during the recent floating exchange rate period. Previous empirical studies generally fail to find support for longrun PPP over this period. In this paper the cointegration property of exchange rates and prices is examined using a maximum likelihood procedure, and we find significant evidence favorable to longrun PPP. Further tests for symmetry and proportionality indicate that these two conditions are not generally consistent with the data. The results support the hypothesis of longrun PPP with measurement errors in prices. 1.
Nonlinear IV unit root tests in panels with crosssectional dependency
 Journal of Econometrics
, 2002
"... We propose a unit root test for panels with crosssectional dependency. We allow general dependency structure among the innovations that generate data for each of the crosssectional units. Each unit may have di®erent sample size, and therefore unbalanced panels are also permitted in our framework. ..."
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Cited by 66 (6 self)
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We propose a unit root test for panels with crosssectional dependency. We allow general dependency structure among the innovations that generate data for each of the crosssectional units. Each unit may have di®erent sample size, and therefore unbalanced panels are also permitted in our framework. Yet, the test is asymptotically normal, and does not require any tabulation of the critical values. Our test is based on nonlinear IV estimation of the usual ADF type regression for each crosssectional unit, using as instruments nonlinear transformations of the lagged levels. The actual test statistic is simply de¯ned as a standardized sum of individual IV tratios. We show in the paper that such a standardized sum of individual IV tratios has limit normal distribution as long as the panels have large individual time series observations and are asymptotically balanced in a very weak sense. We may have the number of crosssectional units arbitrarily small or large. In particular, the usual sequential asymptotics, upon which most of the available asymptotic theories for panel unit root models heavily rely, are not required. Finite sample performance of our test is examined via a set of simulations, and compared to those of other commonly used panel unit root tests. Our test generally performs better than the existing tests in terms of both ¯nite sample sizes and powers. We apply our nonlinear IV method to test for the purchasing power parity hypothesis in panels.