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376
Statistical Analysis of Cointegrated Vectors
 Journal of Economic Dynamics and Control
, 1988
"... We consider a nonstationary vector autoregressive process which is integrated of order 1, and generated by i.i.d. Gaussian errors. We then derive the maximum likelihood estimator of the space of cointegration vectors and the likelihood ratio test of the hypothesis that it has a given number of dimen ..."
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Cited by 2576 (12 self)
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We consider a nonstationary vector autoregressive process which is integrated of order 1, and generated by i.i.d. Gaussian errors. We then derive the maximum likelihood estimator of the space of cointegration vectors and the likelihood ratio test of the hypothesis that it has a given number of dimensions. Further we test linear hypotheses about the cointegration vectors. The asymptotic distribution of these test statistics are found and the first is described by a natural multivariate version of the usual test for unit root in an autoregressive process, and the other is a x2 test. 1.
A Simple Estimator of Cointegrating Vectors in Higher Order Cointegrated Systems
 ECONOMETRICA
, 1993
"... Efficient estimators of cointegrating vectors are presented for systems involving deterministic components and variables of differing, higher orders of integration. The estimators are computed using GLS or OLS, and Wald Statistics constructed from these estimators have asymptotic x2 distributions. T ..."
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Cited by 507 (3 self)
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Efficient estimators of cointegrating vectors are presented for systems involving deterministic components and variables of differing, higher orders of integration. The estimators are computed using GLS or OLS, and Wald Statistics constructed from these estimators have asymptotic x2 distributions. These and previously proposed estimators of cointegrating vectors are used to study longrun U.S. money (Ml) demand. Ml demand is found to be stable over 19001989; the 95 % confidence intervals for the income elasticity and interest rate semielasticity are (.88,1.06) and (.13,.08), respectively. Estimates based on the postwar data alone, however, are unstable, with variances which indicate substantial sampling uncertainty.
Stochastic Trends and Economic Fluctuations
 American Economic Review
, 1991
"... Are business cycles mainly the result of permanent shocks to productivity? This paper uses a longrun restriction implied by a large class of realbusinesscycle modelsidentifying permanent productivity shocks as shocks to the common stochastic trend in output, consumption, and investmentto provid ..."
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Cited by 246 (6 self)
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Are business cycles mainly the result of permanent shocks to productivity? This paper uses a longrun restriction implied by a large class of realbusinesscycle modelsidentifying permanent productivity shocks as shocks to the common stochastic trend in output, consumption, and investmentto provide new evidence on this question. Econometric tests indicate that this commonstochastictrend / cointegration implication is consistent with postwar U.S. data. However, in systems with nominal variables, the estimates of this common stochastic trend indicate that permanent productivity shocks typically explain less than half of the businesscycle variability in output, consumption, and investment. (JEL E32, C32) A central, surprising, and controversial result of some current research on real business cycles is the claim that a common stochastic trendthe cumulative effect of permanent shocks to productivityunderlies the bulk of economic fluctuations. If confirmed, this finding would imply that many other forces have been relatively unimportant over historical business cycles, including the monetary and fiscal policy shocks stressed in traditional macroeconomic analysis. This paper shows that the hypothesis of a common stochastic productivity trend has a set of econometric implications that allows us to test for its presence, measure its importance, and extract estimates of its realized value. Applying these procedures to consumption, investment, and output for the postwar United States, we find results that both support and contradict this claim in the realbusinesscycle literature. The U.S. data are consis
Error Bands for Impulse Responses
 Econometrica
, 1999
"... We show how correctly to extend known methods for generating error bands in reduced form VAR’s to overidentified models. We argue that the conventional pointwise bands common in the literature should be supplemented with measures of shape uncertainty, and we show how to generate such measures. We fo ..."
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Cited by 172 (5 self)
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We show how correctly to extend known methods for generating error bands in reduced form VAR’s to overidentified models. We argue that the conventional pointwise bands common in the literature should be supplemented with measures of shape uncertainty, and we show how to generate such measures. We focus on bands that characterize the shape of the likelihood. Such bands are not classical confidence regions. We explain that classical confidence regions mix information about parameter location with information about model fit, and hence can be misleading as summaries of the implications of the data for the location of parameters. Because classical confidence regions also present conceptual and computational problems in multivariate time series models, we suggest that likelihoodbased bands, rather than approximate confidence bands based on asymptotic theory, be standard in reporting results for this type of model. 1 I.
Variable trends in economic time series
 J. Econom. Perspectives
, 1988
"... T he two most striking historical features of aggregate output are its sustained long run growth and its recurrent fluctuations around this growth path. Real per capita GNP, consumption and investment in the United States during the postwar era are plotted in Figure 1. Both growth and deviations fro ..."
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Cited by 103 (2 self)
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T he two most striking historical features of aggregate output are its sustained long run growth and its recurrent fluctuations around this growth path. Real per capita GNP, consumption and investment in the United States during the postwar era are plotted in Figure 1. Both growth and deviations from the growth trendoften referred to as "business cycles"are apparent in each series. Over horizons of a few years, these shorter cyclical swings can be pronounced; for example, the 1953, 1957 and 1974 recessions are evident as substantial temporary declines in aggregate activity. These cyclical fluctuations are, however, dwarfed in magnitude by the secular expansion of output. But just as there are cyclical swings in output, so too are there variations in the growth trend: growth in GNP in the 1960s was much stronger than it was in the 1950s. Thus, changes in long run patterns of growth are an important feature of postwar aggregate economic activity. In this article we discuss the implications of changing trends in macroeconomic data from two perspectives. The first perspective is that of a macroeconomist reassessing the conventional dichotomy between growth and stabilization policies. As an
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...
A price target for U.S. monetary policy? Lessons from the experience with money growth targets
 Brookings Papers on Economic Activity
, 1996
"... SOMETIMES IT IS hard to leave well enough alone. During the first half of the 1980s U.S. monetary policy was the central actor at work in reducing the American economy's ongoing rate of price inflation from low double digits to low single digitsand, moreover, doing so at a real cost that was a ..."
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Cited by 91 (14 self)
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SOMETIMES IT IS hard to leave well enough alone. During the first half of the 1980s U.S. monetary policy was the central actor at work in reducing the American economy's ongoing rate of price inflation from low double digits to low single digitsand, moreover, doing so at a real cost that was at most consistent with existing estimates of the cost of disinflation, if not a little better. In the first half of the 1990s inflation slowed further, again at a real cost well within the range of standard "sacrifice ratio " calculations. For well over a year, as of the time of writing, unemployment has been at or below the conventional 6 percent estimate of the "nonaccelerating inflation " rate of unemployment, while inflation itself, after allowance for the upward bias in the current consumer price index (as recently evaluated by the advisory commission established by the Senate Finance Committee), is within 1 percentage point of zero. Yet despite this impressive track record of success over a period now spanning a decade and a half, there is still no end to calls for fundamental reform of the way in which the Federal Reserve System goes about making monetary policy. For practical purposes the cutting edge of this urge to redesign the U.S. monetary policymaking framework is a bill, currently pending before the U.S. Senate, that would formally establish the target of price We are grateful to Jeff Amato and Dmitry Dubasov for research assistance; to Mark Gertler, James Tobin, and numerous other colleagues for helpful discussions; and to the
Measuring monetary policy with VAR models: An evaluation
 European Economic Review
, 1998
"... This paper evaluates VAR models designed to analyse the monetary policy transmission mechanism in the United States by considering three issues: specification, identification, and the effect of the omission of the longterm interest rate. Specification analysis suggests that only VAR models estimate ..."
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Cited by 83 (2 self)
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This paper evaluates VAR models designed to analyse the monetary policy transmission mechanism in the United States by considering three issues: specification, identification, and the effect of the omission of the longterm interest rate. Specification analysis suggests that only VAR models estimated on a single monetary regime feature parameters stability and do not show signs of misspecification. The identification analysis shows that VARbased monetary policy shocks and policy disturbances identified from alternative sources are not highly correlated but yield similar descriptions of the monetary transmission mechanism. Lastly, the inclusion of the longterm interest rate in a benchmark VAR delivers a more precise estimation of the structural parameters capturing behaviour in the market for reserves and shows that contemporaneous fluctuations in longterm interest rates are an important determinant of the monetary authority’s
Testing for cointegration when some of the cointegrating vectors are prespecified, Econometric Theory
, 1995
"... Many economic models imply that ratios, simple differences, or "spreads " of variables are I(O). In these models, cointegrating vectors are composed of l's, O's, and l's and contain no unknown parameters. In this paper, we develop tests for cointegration that can be applied ..."
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Cited by 75 (1 self)
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Many economic models imply that ratios, simple differences, or "spreads " of variables are I(O). In these models, cointegrating vectors are composed of l's, O's, and l's and contain no unknown parameters. In this paper, we develop tests for cointegration that can be applied when some of the cointegrating vectors are prespecified under the null or under the alternative hypotheses. These tests are constructed in a vector error correction model and are motivated as Wald tests from a Gaussian version of the model. When all of the cointegrating vectors are prespecified under the alternative, the tests correspond to the standard Wald tests for the inclusion of error correction terms in the VAR. Modifications of this basic test are developed when a subset of the cointegrating vectors contain unknown parameters. The asymptotic null distributions of the statistics are derived, critical values are determined, and the local power properties of the test are studied. Finally, the test is applied to data on foreign exchange future and spot prices to test the stability of the forwardspot premium. 1.
The Monetary Transmission Mechanism in the Euro Area: More Evidence from the VAR Analysis
, 2001
"... Nontechnical summary 5 1 ..."