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Extra info for Economic Modelling at the Bank of France: Financial Deregulation and Economic Development in France (Routledge New International Studies in Economic Modelling)

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Table D2 in Johansen and Juselius (1990) presents critical values which allow for such a misspecification: a second relation is then rejected too. But the number of relations under H2* depends on the lags: k=2 leads to no relation at all, even at 10 per cent, while to k=4 yields one relation. This suggests that this relation may not be reliable. Asset shares, relative returns and inflation The three-variate VAR is estimated with k=3, for both hypotheses about the trend. Less than two cointegrating relations are rejected under H2 or H2*, with both Valmax and Trace tests.

Two cointegrating vectors therefore should exist, they would span the same space as the one spanned by the pair of components (3, 4). 48 Both components 3 and 4 apparently have non-zero coefficients for income. Without income, two components are also required to reach 88 per cent of the total variance (70 per cent plus 18 per cent). There seems to be only one cointegration relation in the vector (NRSX, RRET, INFL). We have also estimated the correlations between the residuals of an univariate AR(4): Xt=Σ(i=1…4)DiLjXt+εt (10) where the Ds are diagonal matrices.

In any case, one has to perform a system analysis, instead of one based on a single equation. Complementary tests of linear restrictions on the four-variate model We now present some tests within the four-variate VAR, in order to show that the singleequation estimates can be related to the long-run static equilibrium of the VAR (Johansen, 1992). The tests are first aimed at including both EGY cointegrating vectors in the model: the connection between inflation and returns, and the asset demand equation.

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