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Full-Text Articles in Economics
Vector Autoregression And Causality: A Theoretical Overview And Simulation Study, Hiro Y. Toda, Peter C.B. Phillips
Vector Autoregression And Causality: A Theoretical Overview And Simulation Study, Hiro Y. Toda, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper provides a theoretical overview of Wald tests for Granger causality in levels vector autoregressions (VAR’s) and Johansen-type error correction models (ECM’s). for VAR models the results for inference are not encouraging. The limit theory typically involves nonstandard distributions and nuisance parameters, and there is no sound statistical basis for testing causality in such a framework. Granger causality tests in ECM’s also suffer from nuisance parameter dependencies asymptotically and nonstandard limit theory. But, in spite of these difficulties Johansen-type ECM’s do offer a sound basis for empirical testing of the rank of the cointegration space and the rank of …
Vector Autoregression And Causality, Hiro Y. Toda, Peter C.B. Phillips
Vector Autoregression And Causality, Hiro Y. Toda, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper develops a complete limit theory for Wald tests of Granger causality in levels vector autoregression (VAR’s) and Johansen-type error correction models (ECM’s) allowing for the presence of stochastic trends and cointegration. Earlier work by Sims, Stock and Watson (1990) on trivariate VAR systems is extended to the general case, thereby formally characterizing the circumstances when these Wald tests are asymptotically valid as chi-square criteria. Our results for inference from unrestricted levels VAR are not encouraging.
An Improved Heteroskedasticity And Autocorrelation Consistent Covariance Matrix Estimator, Donald W.K. Andrews, Christopher J. Monahan
An Improved Heteroskedasticity And Autocorrelation Consistent Covariance Matrix Estimator, Donald W.K. Andrews, Christopher J. Monahan
Cowles Foundation Discussion Papers
This paper considers a new class of heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators. The estimators considered are prewhitened kernel estimators with vetor autoregressions employed in the prewhitening stage. The paper establishes consistency, rate of convergence, and asymptotic truncated mean squared error (MSE) results for the estimators when a fixed or automatic bandwidth procedure is employed. Conditions are obtained under which prewhitening improves asymptotic truncated MSE. Monte Carlo results show that prewhitening is very effective in reducing bias, improving confidence interval coverage probabilities, and rescuing over-rejection of t -statistics constructed using kernel-HAC estimators. On the other hand, prewhitening is …
The Dividend-Price Ratio And Expectations Of Future Dividends And Discount Factors, John Y. Campbell, Robert J. Shiller
The Dividend-Price Ratio And Expectations Of Future Dividends And Discount Factors, John Y. Campbell, Robert J. Shiller
Cowles Foundation Discussion Papers
A linearization of a rational expectations present value model for corporate stock prices produces a simple relation between the log dividend-price ratio and mathematical expectations of future log real dividend changes and future real discount rates. This relation can be tested using vector autoregressive methods. Three versions of the linearized model, differing in the measure of discount rates, are tested for United States time series 1981-1986: versions using real interest rate data. The results yield a metric to judge the relative importance of real dividend growth, measured real discount rates and unexplained factors in determining the dividend-price ratio.
Weak Convergence To The Matrix Stochastic Integral Bdb, Peter C.B. Phillips
Weak Convergence To The Matrix Stochastic Integral Bdb, Peter C.B. Phillips
Cowles Foundation Discussion Papers
The asymptotic theory of regression with integrated processes of the ARIMA type frequently involves weak convergence to stochastic integrals of the form ∫ 0 1 WdW , where W ( r ) is standard Brownian motion. In multiple regressions and vector autoregressions with vector ARIMA processes the theory involves weak convergence to matrix stochastic integrals of the form ∫ 0 1 BdB ’, where B ( r ) is vector Brownian motion with non scalar covariance matrix. This paper studies the weak convergence of sample covariance matrices to ∫ 0 1 BdB ’ under quite general conditions. The theory is …