Removing the Hazard of Fedwire Daylight

analysis of the transactions demand formoney. The commodity-demand elasticity withrespect to the real interest rate, b , , was set tounity because, of all (equally arbitrary) values,unity is the most straightforward choice. (Econo-metric evidence currently available does notprovide direct knowledge of this elasticity.) Therelative sizes of the disturbances give consider-able scope to demand-side influences on outputand employment, and allow for a relativelyunstable money-demand function.In the basic simulation, firms were assumed tochoose employment to equate the marginal prod-uct of labor with the real wages, so 4 = 1. In asecond simulation, 4 was set equal to one-third,in order to see whether the results of the basicsimulation were robust with respect to thisparameter.Five different policy rules were simulated,with their response coefficients chosen so as totarget ( 1 ) money, ( 2 ) output, ( 3 ) the price level,( 4 ) nominal income, or (5) optimal employ-ment. The last of these is, of course, the onlyoptimal policy by the criterion employed, but itis instructive to compare results of other poten-tial targets.The policy rules' response coefficients, q andthe p i ,are displayed in table 1. The final-formsolution for the money supply is determined byboth these coefficients and the solution for thenominal interest rate (because of the qR, term inthe money supply rule), and is shown in table 2 Loss due toPolicy Criterion shocks to:MoneyOutputPrice Level Nominal Income Optimal Productivity2.8614.991.800.380.19Goods demand6.913.041.962.472.35Money demand4.520.241.280.660.76 TOTAL LOSS14.2918.275.043.513.30 SOURCE: Author's calculations. for each of the five alternative policies. In theimmediate period of impact, the monetaryauthority's response to a shock is equal to q , itsinterest rate response coefficient, times theresponse of the interest rate to the shock. Forexample, under a policy of stabilizing output, themoney supply is increased 1.06 for each one-point change in the interest rate. A productivityshock in period t reduces the interest rate by-0.10 (not shown in tables) under this policy rule,so the response of money at time t to a produc-tivity shock in period t is 1.06 times -0.10, orabout -0.11.Only after one period has passed can themonetary authority observe all three shocksindependently and tailor its response to eachone separately. For example, the output-stabiliz-ing policy contracts the money supply by 2.17 attime t for a one-unit innovation to productivityin the previous period, E . This responsereflects two channels: first, an indirect channelinvolving the change in the interest rate, -0.19,times the response coefficient q = 1.06, or about-0.20. To this is added the direct response coef-ficient on t 1 productivity, p1 = -1.97. Together,these add to -2.17, the total contraction of themoney supply required to prevent period-t out-put from responding to period t 1 productivityinnovations. A similar calculation involving directand indirect effects finds that the output-stabilizing policy contracts the money supply attime t by 1.81 in response to a unit productivityinnovation in period t 2.Aside from the constant-money policy, the pol-icies considered are identical in their money-supply responses to goods demand or moneydemand shocks, once these shocks are observed.In this model, all the activist targets are essentiallyequivalent in terms of the implied response ofthe money supply to these demand-side shocks.The main difference among the active money-supply policies lies in the response of money toproductivity shocks. The output-stabilizing poli-cy's response is too restrictive; it contractsmoney at time t by 2.17 after a unit productivityinnovation in period t 1, contrasting with anoptimal increase of 1.33. The price-stabilizationrule responds too expansively; it expands themoney supply by 3.41. The nominal incometarget's response is to expand the money supplyby 1.25, very close to optimal. These differencesamong alternative active policies in theirresponse to productivity shocks account for therelative rankings of their efficiency.Ekpected welfare losses under alternative pol-icies, shown in table 3, are the sum of the meansquared deviations of group one and group twoemployment levels from optimal employmentlevels. Given the information constraint theauthority faces, it can reduce this loss measure to3.30 using the optimal policy. Most of this loss,2.35, is attributable to goods-demand shocksoccurring in the current period; a small fractionis attributable to productivity shocks occurring inthe current period. Distortions due to shocks inperiod t 1 can be completely eliminated bypolicy responses, while distortions due to t 2or earlier shocks are eliminated by wage recon-tracting by both groups of firms.The nominal income targeting policy is closeto optimal; its welfare loss is 3.51, only slightlyhigher than for the optimal policy. The output-stabilizing policy is far worse, with a totalexpected loss of 18.27, most of which is due toproductivity shocks. The constant-money policyis not much better than the output-stabilizingpolicy; it generates substantial employment dis-tortions in the face of goods-demand andmoney-demand shocks, which the activist poli-cies make active efforts to prevent. Finally, theprice-stabilization policy results in somewhatgreater losses than the nominal income policy,but results in much smaller losses than the out-put or money targeting policies.