Optimal Policy Response with Control Parameter and Intercept Covariance

Parameter uncertainty and the interaction between the uncertain parameters are important aspects of economic policy. In this work, I develop an analytical one-state variable, one-control variable model with two uncertain parameters (the control parameter and the intercept) and a nonzero covariance. I characterize the effect of changes in each of the covariance components on the optimal expected control variable. I found that the nature of the optimal policy maker's response depends on the specific changing component of the covariance, the sign of the correlation coefficient and the sign of the optimal expected control variable when the covariance is zero. I obtain the conditions under which the effect of the covariance is considerable. This work complements previous studies by providing a complete set of cases and conditions for an aggressive or cautionary optimal policy maker's response to changes in each covariance component. Finally, the importance of the analytical results is shown for the regulation of a stock pollutant leading to global warming