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100
A Simple Estimator of Cointegrating Vectors in Higher Order Cointegrated Systems," Econometrica 61
, 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 237 (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.
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 208 (5 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.
Inference in Linear Time Series Models with Some Unit Roots," Econometrica
, 1990
"... This paper considers estimation and hypothesis testing in linear time series models when some or all of the variables have unit roots. Our motivating example is a vector autoregression with some unit roots in the companion matrix, which might include polynomials in time as regressors. In the general ..."
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Cited by 158 (6 self)
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This paper considers estimation and hypothesis testing in linear time series models when some or all of the variables have unit roots. Our motivating example is a vector autoregression with some unit roots in the companion matrix, which might include polynomials in time as regressors. In the general formulation, the variable might be integrated or cointegrated of arbitrary orders, and might have drifts as well. We show that parameters that can be written as coefficients on mean zero, nonintegrated regressors have jointly normal asymptotic distributions, converging at the rate T'/2. In general, the other coefficients (including the coefficients on polynomials in time) will have nonnormal asymptotic distributions. The results provide a formal characterization of which t or F testssuch as Granger causality testswill be asymptotically valid, and which will have nonstandard limiting distributions.
Consumption, Aggregate Wealth, and Expected Stock Returns
 THE JOURNAL OF FINANCE • VOL. LVI, NO. 3 • JUNE 2001
, 2001
"... This paper studies the role of fluctuations in the aggregate consumption–wealth ratio for predicting stock returns. Using U.S. quarterly stock market data, we find that these fluctuations in the consumption–wealth ratio are strong predictors of both real stock returns and excess returns over a Treas ..."
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Cited by 150 (18 self)
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This paper studies the role of fluctuations in the aggregate consumption–wealth ratio for predicting stock returns. Using U.S. quarterly stock market data, we find that these fluctuations in the consumption–wealth ratio are strong predictors of both real stock returns and excess returns over a Treasury bill rate. We also find that this variable is a better forecaster of future returns at short and intermediate horizons than is the dividend yield, the dividend payout ratio, and several other popular forecasting variables. Why should the consumption–wealth ratio forecast asset returns? We show that a wide class of optimal models of consumer behavior imply that the log consumption–aggregate wealth ~human capital plus asset holdings! ratio summarizes expected returns on aggregate wealth, or the market portfolio. Although this ratio is not observable, we provide assumptions under which its important predictive components for future asset returns may be expressed in terms of observable variables, namely in terms of consumption, asset holdings and labor income. The framework implies that these variables are cointegrated, and
Resurrecting the (C)CAPM: A CrossSectional Test When Risk Premia Are TimeVarying
 Journal of Political Economy
, 2001
"... This paper explores the ability of conditional versions of the CAPM and the consumption CAPM—jointly the (C)CAPM—to explain the cross section of average stock returns. Central to our approach is the use of the log consumption–wealth ratio as a conditioning variable. We demonstrate that such conditio ..."
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Cited by 139 (5 self)
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This paper explores the ability of conditional versions of the CAPM and the consumption CAPM—jointly the (C)CAPM—to explain the cross section of average stock returns. Central to our approach is the use of the log consumption–wealth ratio as a conditioning variable. We demonstrate that such conditional models perform far better than unconditional specifications and about as well as the FamaFrench threefactor model on portfolios sorted by size and booktomarket characteristics. The conditional consumption CAPM can account for the difference in returns between lowbooktomarket and highbooktomarket portfolios and exhibits little evidence of residual size or booktomarket effects. We are grateful to Eugene Fama and Kenneth French for graciously providing the
An autoregressive distributed lag modelling approach to cointegration analysis
 Cambridge University
, 1999
"... This paper examines the use of autoregressive distributed lag (ARDL) models for the analysis of longrun relations when the underlying variables are I(1). It shows that after appropriate augmentation of the order of the ARDL model, the OLS estimators of the shortrun parameters are p Tconsistent wi ..."
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Cited by 80 (3 self)
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This paper examines the use of autoregressive distributed lag (ARDL) models for the analysis of longrun relations when the underlying variables are I(1). It shows that after appropriate augmentation of the order of the ARDL model, the OLS estimators of the shortrun parameters are p Tconsistent with the asymptotically singular covariance matrix, and the ARDLbased estimators of the longrun coe¢cients are superconsistent, and valid inferences on the longrun parameters can be made using standard normal asymptotic theory. The paper also examines the relationship between the ARDL procedure and the fully modi…ed OLS approach of Phillips and Hansen to estimation of cointegrating relations, and compares the small sample performance of these two approaches via Monte Carlo experiments. These results provide strong evidence in favour of a rehabilitation of the traditional ARDL approach to time series econometric modelling. The ARDL approach has the additional advantage of yielding consistent estimates of the longrun coe¢cients that are asymptotically normal irrespective of whether the underlying regressors are I(1) or I(0).
2007), “Evidence of a Shift in the ShortRun Price Elasticity of Gasoline Demand,” forthcoming: Energy Journal
"... Understanding the sensitivity of gasoline demand to changes in prices and income has important implications for policies related to climate change, optimal taxation and national security, to name only a few. While the shortrun price and income elasticities of gasoline demand in the United States ha ..."
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Cited by 68 (12 self)
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Understanding the sensitivity of gasoline demand to changes in prices and income has important implications for policies related to climate change, optimal taxation and national security, to name only a few. While the shortrun price and income elasticities of gasoline demand in the United States have been studied extensively, the vast majority of these studies focus on consumer behavior in the 1970s and 1980s. There are a number of reasons to believe that current demand elasticities differ from these previous periods, as transportation analysts have hypothesized that behavioral and structural factors over the past several decades have changed the responsiveness of U.S. consumers to changes in gasoline prices. In this paper, we compare the price and income elasticities of gasoline demand in two periods of similarly high prices from
Understanding Trend and Cycle in Asset Values: Reevaluating the Wealth Effect on Consumption
 American Economic Review
, 2004
"... Both textbook economics and common sense teach us that the value of household wealth should be related to consumer spending. Early academic work by Franco Modigliani (1971) suggested that a dollar increase in wealth (holding � xed labor income) leads to an increase in consumer spending of about � ve ..."
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Cited by 61 (4 self)
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Both textbook economics and common sense teach us that the value of household wealth should be related to consumer spending. Early academic work by Franco Modigliani (1971) suggested that a dollar increase in wealth (holding � xed labor income) leads to an increase in consumer spending of about � ve cents. Since then, the socalled “wealth effect ” on consumption has increasingly crept into both mainstream and policy discussions of the macroeconomy. 1 Today, it is commonly presumed that signi �cant movements in wealth will be associated with movements in consumer spending, either contemporaneously or subsequently. Quantitative estimates of roughly the magnitude reported by Modigliani are routinely cited in
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 51 (1 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
NarrowBand Analysis Of Nonstationary Processes
, 1999
"... The behaviour of averaged periodograms and crossperiodograms of a broad class of nonstationary processes is studied. The processes include nonstationary ones that are fractional of any order, as well as asymptotically stationary fractional ones, and the crossperiodogram can involve two nonstationa ..."
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Cited by 37 (11 self)
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The behaviour of averaged periodograms and crossperiodograms of a broad class of nonstationary processes is studied. The processes include nonstationary ones that are fractional of any order, as well as asymptotically stationary fractional ones, and the crossperiodogram can involve two nonstationary processes of possibly di#erent orders, or a nonstationary and an asymptotically stationary one. The averaging takes place either over the whole frequency band, or on one that degenerates slowly to zero frequency as sample size increases. In some cases it is found to make no asymptotic di#erence, and in particular we indicate how the behaviour of the mean and variance changes across the twodimensional space of integration orders. The results employ only localtozero assumptions on the spectra of the underlying weakly stationary sequences. It is shown how the results can be readily applied in case of fractional cointegration with unknown integration orders. 1 1. INTRODUCTION In the analy...