انتخاب بهینه ابزار سیاست پولی تحت شتاب و شوک های مالی

This paper, in the spirit of Poole [Poole, William, 1970. The Optimal Choice of Monetary Policy Instruments in a Simple Macro Model. Quarterly Journal of Economics, 84, 192–216.], studies how differently monetary and fiscal shocks influence the appropriate choice of the monetary policy regime. Velocity shocks are introduced by embedding a stochastic cash-in-advance constraint within the New Keynesian framework. In addition to optimal policy under discretion, three classic rules, interest rate targeting, monetary targeting, and the Taylor rule are ranked under both fiscal and velocity shocks. The non-stationarity of prices under the Taylor rule makes it inferior to the other rules under which prices are stationary. Monetary targeting, by stabilizing aggregate demand under fiscal shocks, outperforms interest rate targeting, while the latter provides a better insulation against velocity shocks. Monetary targeting (under fiscal shocks) and interest rate targeting (under velocity shocks) even outperform the optimal policy under discretion for sufficiently high intertemporal elasticities of consumption substitution.

How does the nature of shock influence the choice of a monetary policy instrument? Poole (1970), using a stochastic IS-LM model in a closed economy setting with reduction in variability of aggregate output as the yardstick, showed that shocks indeed mattered for the choice of an appropriate monetary policy instrument. The basic conclusion was that a fixed monetary aggregate better stabilizes output by allowing offsetting interest rate movements under demand (IS) shocks, whereas a fixed interest rate insulates the real side of the economy by letting the money supply adjust to the shocks originating in the money market. This paper revisits the Poole's instrument problem in a closed economy that faces nominal rigidities in the form of Calvo style staggered price adjustment. Within this setting, we study an economy that experiences demand (government expenditure) and monetary (velocity) shocks.2 For each shock, we welfare-rank three simple rules, namely, interest rate targeting, monetary targeting, and the Taylor rule, by comparing them with the optimal policy under discretion. The welfare metric, expressed in terms of the output gap (defined as the difference between the actual and the efficient level of output) and inflation is obtained as a quadratic approximation of the household's utility. Our results identify interest rate targeting as the best rule under velocity shocks, whereas monetary targeting performs best under fiscal shocks. The performance of these rules vis-à-vis discretion however crucially depends on the intertemporal elasticity of consumption substitution. Specifically, for high (low) elasticities we find that interest rate rule under velocity shocks and monetary targeting under fiscal shocks perform better (worse) than discretion. A key feature of our model is the introduction of a stochastic cash-in-advance constraint within the New Keynesian framework of Clarida, Galí, and Gertler (1999). The standard model as exemplified in Clarida, Galí, and Gertler (1999) is a money-in-the-utility function (MIUF) model with preferences separable in consumption and real balances. Changes in money therefore play a limited role in determining the dynamics of real variables. We follow Alvarez, Lucas, and Weber (2000), and introduce velocity shocks as fluctuations in the fraction of current income that households can utilize for current purchases. The cash-in-advance constraint implicitly taxes labor at a rate that fluctuates endogenously with nominal interest rates and shocks to the velocity of money. As a result, nominal interest rates as well as shocks to velocity now appear in the Phillips curve. Thus, complete price stability is not optimal under velocity shocks (akin to exogenous cost-push shocks). Additionally, the interest rate term in the Phillips curve, by raising the cost of stabilizing inflation in terms of output gap (i.e., the cost push effect), endogenously generates an inflation/output gap trade-off. Consequently, complete price stability is never optimal. Fiscal shocks, as in Ravenna and Walsh (2006), are introduced by assuming that the government spends a stochastic fraction of domestic output. Under our assumption, the more the economy produces the more the government spends (i.e., wastes). The output produced under a competitive equilibrium therefore differs from its efficient level that a planner will choose. Once this distortion is accounted for, as in Ravenna and Walsh (2006), fiscal shock not only affects the IS curve but also appears as a cost-push shock in the Phillips curve. An inflation-output gap trade-off emerges and once again complete price stability is not optimal. Our work is closely related to Gali (2003) who uses the standard MIUF framework with Calvo style staggered price and compares the optimal policy with the above three rules in a closed economy, but considers only productivity and fiscal shocks. Gali abstracts from the distortionary effects of fiscal shocks, which are modelled as exogenous shocks to government expenditure. This assumption renders complete price stability to be optimal in his framework. Gali's framework therefore does not involve any conflict between stabilizing inflation and the output gap.3 Then, as a result of the emphasis on price stability, the Taylor rule welfare ranks as the best rule for fiscal shocks. By contrast, monetary targeting, outperforms the Taylor rule in our model due the inclusion of the distortionary effect of fiscal shocks. Collard and Dellas (2005) carry out a similar exercise in a closed economy MIUF setup with Calvo style staggered prices where they compare interest rate targeting with monetary targeting for productivity, fiscal, and money demand shocks. Their paper however focusses only on the simple rules and does not compare them with the optimal policy. Contrary to the popular notion, they find that monetary targeting outperforms interest rate targeting for money demand shocks (modelled as preference shocks). The key to this result, is the non-separabilty of consumption, leisure, and real balances in the utility function. While there is greater stability of output and inflation under interest rate-targeting, it is still welfare dominated by monetary targeting due to the strong negative covariance between consumption and leisure under the latter. By contrast we find that an interest rate peg not only better stabilizes output and inflation but also outperforms a monetary targeting regime from a welfare perspective. Our results differ because we introduce money demand shocks through a stochastic cash-in-advance constraint. This allows us to abstract from the money's direct role in the utility function: a feature that is in line with the contemporary literature on optimal monetary policy. Furthermore, the separability of consumption and leisure in the utility function in our model not only facilitates a simple, sharp, and insightful presentation of optimal policies, but also allows us to compare it with simple ad hoc rules in a straightforward manner.4 Importantly, we find that for that for low values of intertemporal elasticity of consumption substitution discretionary policy outperforms the simple rules in the case of both fiscal and velocity shocks. However the money rule in the case of fiscal shocks and the interest rate rule in the case of velocity shocks outperform discretionary policy for high elasticities.

This paper, in the spirit of Poole (1970), examines the role of shocks for the optimal choice of monetary policy instruments within a New-Keynesian framework. Money is explicitly modeled through a cash-in-advance constraint with velocity shocks. We welfare rank interest rate targeting, monetary targeting, and the Taylor rule under supply monetary (velocity) and demand (fiscal) shocks. The equilibrium dynamics as well as welfare under each rule is contrasted against optimal policy under discretion. Our ranking are: interest rate targeting under velocity shocks and monetary targeting under fiscal shocks. Further, discretionary policy outperforms the simple rules for low values of elasticity of intertemporal substitution. However the money rule in the case of fiscal shocks and the interest rate rule in the case of velocity shocks outperform discretionary policy for high elasticities. To sum up, under velocity shocks, an interest rate targeting effectively insulates the real side of the economy by letting money supply adjust with the shock. Monetary targeting on the other hand generates excessive nominal income volatility and, as a result, output and price volatility. The Taylor rule due to its non-stationarity of prices generates a higher inflation and output variability relative to an interest rate peg. Further, we find that for high values of the intertemporal elasticity of substitution an interest rate peg outperforms even policy under discretion. Under fiscal shocks, monetary targeting, by fixing the nominal income, effectively stabilizes aggregate demand. An interest rate peg on the other hand leads to excessive output volatility while the Taylor rule with its non-stationary prices generates too much inflation variability. Analogous to the case under velocity shocks we find that for high values of the intertemporal elasticity of substitution a monetary targeting regime outperforms policy under discretion. The results thus validate Poole's prescription of fixing interest rates when monetary shocks are predominant, and fixing money supply when demand shocks are predominant