02873cam a22002657 4500001000600000003000500006005001700011008004100028100002100069245015400090260006600244490005100310500001500361520147500376530006101851538007201912538003601984690019602020690017002216700002002386710004202406830008602448856003702534856003602571t0122NBER20170430165117.0170430s1992 mau||||fs|||| 000 0 eng d1 aElliott, Graham.10aInference in Time Series Regression When the Order of Integration of a Regressor is Unknownh[electronic resource] /cGraham Elliott, James H. Stock. aCambridge, Mass.bNational Bureau of Economic Researchc1992.1 aNBER technical working paper seriesvno. t0122 aJune 1992.3 aIt is well known that the distribution of statistics testing restrictions on the coefficients in time series regressions can depend on the order of integration of the regressors. In practice the order of integration is rarely blown. This paper examines two conventional approaches to this problem, finds them unsatisfactory, and proposes a new procedure. The two conventional approaches- simply to ignore unit root problems or to use unit root pretests to determine the critical values for second-stage inference - both often induce substantial size distortions. In the case of unit root pretests, this arises because type I and II pretest errors produce incorrect second-stage critical values and because, in many empirically plausible situations, the first stage test (the unit root test) and the second stage test (the exclusion restriction test) are dependent. Monte Carlo simulations reveal size distortions even if the regressor is stationary but has a large autoregressive root, a case that might arise for example in a regression of excess stock returns against the dividend yield. In the proposed alternative procedure, the second-stage test is conditional on a first-stage "unit root" statistic developed in Stock (1992); the second-stage critical values vary continuously with the value of the first-stage statistic. The procedure is shown to have the correct size asymptotically and to have good local asymptotic power against Granger-causality alternatives. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aC32 - Time-Series Models • Dynamic Quantile Regressions • Dynamic Treatment Effect Models • Diffusion Processes • State Space Models2Journal of Economic Literature class. 7aC22 - Time-Series Models • Dynamic Quantile Regressions • Dynamic Treatment Effect Models • Diffusion Processes2Journal of Economic Literature class.1 aStock, James H.2 aNational Bureau of Economic Research. 0aTechnical Working Paper Series (National Bureau of Economic Research)vno. t0122.4 uhttp://www.nber.org/papers/t012241uhttp://dx.doi.org/10.3386/t0122