Analyzing Indeterminacies in a Real Business Cycle Model with Money
指出Farmer(1997)的货币真实商业周期模型存在数学错误，修正后模型不再产生实体经济的不确定性，而是呈现标准鞍点均衡，价格水平因利率控制而不确定。
In the paper Money in a Real Business Cycle Model (1997) Roger Farmer develops a general equilibrium rational expectations macroeconomic model of business cycles. The model differs from basic real business cycle models in the inclusion of money in the utility function and features an authority, who simultaneously conducts monetary (fixed interest rate) and fiscal (zero government debt) policies. The key feature of the model is the claim that there is a possibility of the existence of multiple stationary equilibria in the real sector of the economy. Its author argues that this is the main reason why the model produces dynamics different from those of other models and that these dynamics are much closer to what is seen in the data. Farmer calibrates his model with standard parameter values for utility and production functions and sets the interest rate to 1 percent and velocity to 6 (which corresponds to M1 as a measure of money). With these settings he declares that this parametrization will produce a real indeterminacy. Given the indeterminacy, one of the equilibria is chosen to be consistent with the variance covariance matrix of errors from a VAR(2) fitted to U.S. data on GDP, interest rate, real balances, and money growth. With this choice the model produces impulse response functions which seem quite close to the data (seven out of sixteen of them lie within two standard errors bounds of those estimates from data). A closer look at the derivation of his equations reveals several mathematical errors. Correcting them shows that Farmer's calibration does not produce indeterminacy in the real sector. Instead, the corrected model's results turn out to be quite standard: the price level is indeterminate because of interest rate control while the real economy exhibits a saddle point equilibrium. Indeed, the corrected system can be reduced to a system of three variablesl (output Wt), interest rate (It) and produc-