Hypothesis Testing for the Long‐Run Coefficients β

Abstract Grant and Lebo (2016) and Keele et al. (2016) clarify the conditions under which the popular general error correction model (GECM) can be used and interpreted easily: In a bivariate GECM the data must be integrated in order to rely on the error correction coefficient, $\alpha _1^\ast$ , to test cointegration and measure the rate of error correction between a single exogenous x and a dependent variable, y. Here we demonstrate that even if the data are all integrated, the test on $\alpha _1^\ast$ is misunderstood when there is more than a single independent variable. The null hypothesis is that there is no cointegration between y and any x but the correct alternative hypothesis is that y is cointegrated with at least one—but not necessarily more than one—of the x's. A significant $\alpha _1^\ast$ can occur when some I(1) regressors are not cointegrated and the equation is not balanced. Thus, the correct limiting distributions of the right-hand-side long-run coefficients may be unknown. We use simulations to demonstrate the problem and then discuss implications for applied examples.

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Hypothesis Testing with Near-Unit Roots: The Case of Long-Run Purchasing-Power Parity

10.20955/r.75.37-48 ◽

1993 ◽

Vol 75 (4) ◽

Cited By ~ 1

Author(s):

Michael J. Dueker

Keyword(s):

Hypothesis Testing ◽

Purchasing Power Parity ◽

Unit Roots ◽

Purchasing Power ◽

Power Parity ◽

Long Run

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Comovements Between Diffusion Processes

Econometric Theory ◽

10.1017/s0266466600006113 ◽

1997 ◽

Vol 13 (5) ◽

pp. 646-666 ◽

Cited By ~ 5

Author(s):

Valentina Corradi

Keyword(s):

Hypothesis Testing ◽

Error Correction ◽

Linear Combination ◽

Diffusion Processes ◽

Sampling Schemes ◽

Long Run ◽

Linear Diffusions

The aim of this paper is to characterize and analyze long-run comovements among diffusion processes. Broadly speaking, if X = (X1,,X2,;t ≥ 0) is a nonergodic diffusion in R2, but there exists a linear combination, say, γ′X, that is instead ergodic in R, then we say there exists a linear stochastic comovement between the components of X. Linear diffusions exhibiting stochastic comovements admit an error correction representation. Estimation of γ and hypothesis testing, under different sampling schemes, are considered.

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