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An essay on unit root tests and measurement error
After the publication of Nelson and Plosser's (1982) influential paper, it has been a general accepted view that real output and prices are nonstationary. This view, however, is being seriously challenged. The apparent line of attack is applied econometricians frequently assume macroeconomic time series are free of measurement error. This is an assumption that, almost surely, does not hold in practice. ^ In this dissertation, the influence of measurement error upon unit root tests is explored. Then, the behavior of the normalized bias and t-ratio statistics used to test the unit root is examined (1 )with asymptotic theory and (2) via computer simulations. I find that the presence of measurement error is highly distorting to the limiting distributions derived in Dickey-Fuller (1979). Specifically, the new limiting distributions of the t-ratio and normalized bias statistics are on the left-hand-side of the original “measurement error-free” Dickey-Fuller distributions. Furthermore, the new limiting distributions are not free of nuisance parameters. Therefore, inferences based on the Dickey-Fuller tests will be highly misleading. ^ Two nuisance parameters enter the new limiting distributions: (1) the variance of measurement error and (2) the variance of the disturbances that drive the underlying stochastic process. Both variances are not directly observable and estimating them is a complicated matter. However, this technical difficulty can be resolved through the method of identification and the estimators of the variances can be constructed. Relying on the proposed variance estimators, modified test statistics, whose limiting distributions are independent of nuisance parameters, are proposed. ^ Using Monte Carlo experiments and response surfaces, sets of accurate critical values of the modified test statistics are estimated. My Monte Carlo experiments show that the modified normalized bias tests have better size properties than the modified t-ratio tests. In addition, the modified normalized bias tests have very good size properties even if the errors follow an MA(1) process with an MA coefficient of moderate size. The modified normalized bias tests are used to test for unit roots in the growth rate of GNP and the CPI. Using the new tests, I find that the growth rate of these macroeconomic time series is nonstationary. ^
Ng, YongKad, "An essay on unit root tests and measurement error" (2004). ETD collection for University of Nebraska - Lincoln. AAI3137862.