Sims's finding that nominal money stock is strictly exogenous in a distributed-lag regression of nominal income on nominal money stock is not inconsistent with the appearance and real income and nominal interest rates as strictly exogenous regressors in the quarterly money-demand equations estimated in real form. This strict exogeneity of real income and interest rates in real money-demand equations is due to the restriction implied by estimation in the real form, and these implicit restrictions seem to conflict with the sample information.
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Yash P. Mehra (1978) studied this question.
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