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Partially Identified Econometric Models, Peter C.B. Phillips
Partially Identified Econometric Models, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper studies a class of models where full identification is not necessarily assumed. We term such models partially identified. It is argued that partially identified systems are of practical importance since empirical investigators frequently proceed under conditions that are best described as apparent identification. One objective of the paper is to explore the properties of conventional statistical procedures in the context of identification failure. Our analysis concentrates on two major types of partially identified model: the classic simultaneous equations model under rank condition failures; and time series spurious regressions. Both types serve to illustrate the extensions that are needed …
Asymptotic Properties Of Residual Based Tests For Cointegration, Peter C.B. Phillips, Sam Ouliaris
Asymptotic Properties Of Residual Based Tests For Cointegration, Peter C.B. Phillips, Sam Ouliaris
Cowles Foundation Discussion Papers
This paper develops an asymptotic theory for residual based tests for cointegration. These tests involve procedures that are designed to detect the presence of a unit root in the residuals of (cointegrating) regressions among the levels of economic time series. Attention is given to the augmented Dickey-Fuller (ADF) test that is recommended by Engle-Granger (1987) and the Z(a) and Z(t) unit root tests recently proposed by Phillips (1987). TWo new tests are also introduced, one of which is invariant to the normalization of the cointegrating regression. All of these tests are shown to be asymptotically similar and simple representations of …