Tests of Variance Bounds Implied by Cagan's Hyperinflation Model
在卡甘恶性通胀货币需求模型下，推导并检验理性预期下实际和名义货币余额及通胀率的方差界，使用1921-1923年德国恶性通胀数据，比较两种预期生成机制。
Within the context of a demand for money model during a hyperinflation which Cagan [1956] made famous, this paper examines the implied variability of the underlying variables when expectations are formed rationally 'a la Muth [1961]. The measure of variability adopted in the paper is the variance, and the focus is on the derivation and testing of the implied variability of both the expectations and the realizations of real and nominal money balances and inflation rates. Empirical evidence is provided for the case of the German hyperinflation of 1921-1923. Specifically, two sets of variance bound tests are analyzed. The first set (Model 1) investigates the implied variance bounds on the rationally expected growth rates of the underlying variables, and the second set (Model 2) explores the bounds on the observed outcomes of the levels of these variables. For the purpose of empirical implementation, since the expectation variables in Model 1 are unobservable, they have to be inferred from the available data by invoking additional specifications not required by Model 2. Two expectations generating mechanisms are employed in the paper. One requires conditioning expectations on the past historical values of the underlying variables. The second alternative specification involves the assumption of an efficient foreign exchange market. To the extent that the expected cost of holding domestic money is the expected change in the exchange rate, as has been observed by Frenkel [1977, 1979] to be the case, the forward premium on foreign exchange can be used to infer inflationary expectations. The present paper may be motivated along several lines. Since its inception, Cagan's demand for money model during a hyperinflation has played an important role in studies of hyperinflations, but the empirical results are not uniform.2