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Vol. 25, No. 2 ECONOMIC REVIEW 1989 Quarter 2 Removing the Hazard ot Fedwire Daylight 2 Overdrafts b y E.J. S te ve n s Capital Subsidies and the Infrastructure Crisis: Evidence from the Local Mass-Transit Industry 11 b y Brian A . C rom w e ll Employment Distortions Under Sticky Wages and Monetary Policies to Minimize Them by J a m e s G. H oehn FEDERAL RESERVE BANK OF CLEVELAND 22 r a r r r M I C R E V I E W 1989 Quarter 2 Vol. 2 5 . No. 2 Removing the Hazard 2 of Fedwire Daylight Overdrafts Economic Review is published quarterly b y the Research b y E.J. S te ve n s D e p a rtm e n t o f the Federal R eserve B an k of C leve lan d. Review Free Federal Reserve daylight overdrafts misallocate resources. One reason is Cop ie s o f the the moral hazard of fully insuring a paying bank’s access to whatever volume available through our Public of daylight overdraft credit it needs. This paper contrasts the effects of three A ffa irs and B an k Relations recent proposals for pricing daylight overdrafts and demonstrates that reduc D e p a rtm e n t, 2 1 6 / 5 7 9 -2 1 5 7 . are ing moral hazard depends on how, rather than on how much, pricing affects daylight overdrafts. If payment practices and modes of bank financing were unresponsive to pricing, it would suggest that the moral hazard of Federal Reserve daylight overdrafts has been an insidious force behind the rapid C oordin ating Ec o n o m is t: Randall W . Eb erts growth of interbank lending and securities-market trading in recent decades. Ed ito rs : W illia m G . M u rm a n n Robin Ratliff Capital Subsidies and 11 the Infrastructure Crisis: Evidence from the Local Mass-Transit Industry D e s ig n : M ich ae l G a lk a T y p e s e ttin g : L iz H a n n a Op in ion s s ta te d in Review by Brian A. C ro m w e ll Economic are th o s e of the a u th ors an d not necessarily those o f the Federal R e s e rve Public investment and maintenance decisions are potentially distorted by B a n k of C le ve la n d or o f the budget procedures, political pressures, and capital subsidies. Empirical evi B oard of G o ve rn o rs o f th e F e d dence from two recent studies of the mass-transit industry is summarized eral R e s e rve S y s te m . and suggests that federal capital subsidies have important effects on infra structure decisions of local governments. M aterial m a y be reprinted pro vid e d th a t th e source is credited. Employment Distortions Under Sticky Wages 2 2 and Monetary Policies to Minimize Them b y J a m e s G. H oehn Sticky nominal wages can result in distortion of employment levels as demand for goods and labor productivity change. This article shows that employment distortions can be minimized by a monetary policy that allows some price deflation when productivity improves. Policies that target nominal income or the price level result in smaller distortions than do policies that target output or money. Ple as e send copies of reprinted m aterial to the editor. I S S N 0 0 13 -0 2 8 1 Rem oving the H a za rd of Fedw ire Daylight Overdrafts by E.J. Stevens E .J . Stevens is an assistant vice president and economist at the Fed eral Reserve Bank of Cleveland. The author thanks John Carlson, Charles Carlstrom, Randall Eberts, and Wil liam Gavin for their useful comments on earlier drafts of this paper. Introduction The 12 Federal Reserve District Banks extend about $115 billion of credit within a few hours on an average business day, only to take it back again before the close of business. This huge sum reflects banks’ daylight overdrafts of their deposit accounts at Federal Reserve Banks when making large-dollar-value payments to other banks using Federal Reserve wire transfer systems. 1 If all goes well, subsequent receipts from other banks extinguish the daylight overdrafts before the end of the day. Daylight overdrafts via Fedwire are not allo cated by any market process and are free, a result of the order in which a bank’s payments and receipts occur. The same might seem to be true of checks presented and deposits made to any checking account during a day, but there is a ■ crucial distinction: a Fedwire payment is irrevo cable upon receipt, while a check is only a pro visional payment. Therefore, the Federal Reserve is the party at risk if a daylight overdraft is not repaid by the end of a day. Free daylight overdrafts are costly. O f course, the Federal Reserve faces no financing or resource costs in issuing daylight credit because it has the power to create money; failure of a bank to elimi nate its daylight overdraft by the end of a day would simply add to Federal Reserve assets (claims on a bank) and liabilities (bank reserve deposits) . 2 The costs arise from resource misallocations. One source of these inefficiencies, and the focus of this paper, is the “moral hazard” involved in providing free daylight overdrafts. 3 Fedwire fully insures a payor bank’s access to whatever volume of daylight overdraft credit it needs to make payments that are immediately available 1 These systems include Fedwire, for transfer of resen/e balances from one bank to another, and the securities wire, for transfer of book-entry U .S . government securities from one bank to another in return for reserve balances. ■ 2 The term Fedwire will be used here to refer to both systems. A third system, ing the value of the asset, causing a charge against Federal Reserve income C H IP S (Clearing House Interbank Payment System ), is operated by the private that would reduce Treasury receipts. Failure to repay might result from a bank’s insolvency, perhaps impair New York Clearing House Association; credit extended among participants in this system adds another $45 billion of interbank daylight credit on an ■ 3 average day. resource misallocations resulting from this moral hazard. Stevens (1988) provides a discussion of the probable nature of some and irrevocable. The result is a form of insurance that removes any incentive for payee banks to monitor or manage credit risk in receiving pay ments that payor banks fund with daylight credit. Suggestions have been made to price Fedwire daylight overdrafts in an effort to control them. Market sources of funding would replace some or all Fedwire daylight overdrafts in making pay ments and would require compensation based on credit risk. Market discipline would then pro vide the now-missing incentive for payor banks to attend to risk, thereby avoiding moral hazard. This paper suggests that economizing need not bring about the market discipline that would elimi nate moral hazard. The first section provides a brief review of Fedwire daylight overdraft history, Federal Reserve payment system risk policy, and the problem of moral hazard. The second part shows how differences among three recently pro posed daylight overdraft pricing mechanisms can influence the extent of daylight overdraft reduc tion and, more important, the way in which banks reduce daylight overdrafts. The final part argues that reducing Fedwire moral hazard does not but on banks reduce depend on daylight overdrafts, and that this should be a cri terion for choosing among pricing proposals. how much, how I. Fedwire Daylight Overdrafts and Moral Hazard A bank goes into daylight overdraft when it has made more payments from its account at a Fed eral Reserve Bank by some point during a day than can be covered by its opening reservedeposit balance plus payments received by that point in the day. A common example is that of a bank dependent on continuous overnight federal funds borrowing. Operational conve nience leads it to return the borrowed funds each morning, before borrowing replacement funds in the afternoon. The midday period is spent in overdraft, funded by the Federal Reserve. As recently as 30 years ago, the U.S. largedollar-value payments system was for the most part a cash-in-advance system. Irrevocable Fed wire payments were riskless both to payees and to the Federal Reserve because they were drawn against positive balances. Since then, Federal Reserve daylight risk exposure has mushroomed, associated with the telecommunications revolu tion in the payments mechanism, the prolifera tion of new financial instruments, and the explo sion of trading volumes in worldwide money and capital markets. A simple comparison illustrates the extent of the change. In 1947, reserve-deposit balances represented 700 percent of (seven times) the value of daily debits (Fedwire, checks, etc.) to member-bank reserve accounts. That is, the aver age bank could make all of its own and its cus tomers’ payments for seven successive business days without ever receiving a single offsetting payment, and without exhausting its initial reserve-deposit balance. By 1983, balances were a minuscule 4 percent of daily debits. The aver age bank could meet demands for payment for only 2 0 minutes of a single eight-hour business day before it would have to receive some offset ting payments, or go into overdraft. 4 Initially, the evolution from a cash-in-advance system toward automatic daylight credit seems to have gone undetected, but confronting the grow ing daylight credit risk problem became unavoid able in the late 1970s under the pressures of technological change and a demand for sameday net settlement service by potentially compet ing private large-dollar-value payment networks. Originally, starting in 1918, telegraph, telephone, or mail messages to the Federal Reserve were the only mechanisms for transferring ownership of reserve-deposit balances between banks with same-day finality. Related devices were official checks, offering only next-day finality, and inter bank messages that simply instructed a bank to use Fedwire to transfer funds. Introducing computer-to-computer telecom munications technology for payments by Fed wire and by the Clearing House Interbank Pay ment System (CHIPS), and for interbank message systems, suggested a new possibility in the 1970s. Private payment networks like CHIPS and the then-proposed CashWire network each would be capable of clearing payment messages among its own participants continuously during the day before presenting a single balanced set of net debit and credit positions to the Fed in time to achieve same-day final settlement. Compared to the next-day systems prevalent then, this would offer the advantage of reducing costly overnight float financing of banks in net debit position by those in net credit position. In addition, it would shorten the length of time during which overnight float exposed banks to credit risk. Operating details of telecommunica tion devices, accounting-system modifications, backup facilities, and daily time schedules were laid out quickly, but the enterprise foundered on ■ 4 Reduced reserve requirements represent only a small portion of this change. To have maintained the 1947 reserve deposits/debits ratio with the 1983 volume of debits would have involved reserve deposits equal to an impossible two-and-a-third times the total assets of all commercial banks. the “unpostable debit”—what to do if one of the participants had insufficient funds in its reserve account to cover its private network net debit at settlement hour. Some found the unpostable debit an opera tional inconvenience to be ignored: from an operations perspective, it was no problem as long as the accounting system accepted negative numbers. After all, a Federal Reserve Bank did not check to see whether a bank had sufficient funds to cover a Fedwire transfer. Why should a net settlement message be treated any differently? Others found it troubling to design a system in which the central bank automatically would guar antee a private network settlement by accepting an unpostable debit as an offset to irrevocable credits. That issue is not fully resolved even today, but two developments did force some action with respect to daylight overdrafts. 5 One development was the increasing inci dence of overdrafts of reserve accounts and adoption of the current Federal Reserve overnight overdraft policy.6 High inter est rates, escalating wire-transfer traffic, and de clining reserve requirements were making reserve-deposit accounts a less and less effective buffer stock in banks’ daily reserve-balance man agement. With no formal overnight overdraft pol icy other than Regulation D (that banks maintain an average required balance over a one- or twoweek reserve maintenance period), concern was mounting that banks might abuse the Federal Reserve by running overnight overdrafts when especially profitable opportunities arose. Developing an overnight overdraft policy led to more widespread realization within the Fed eral Reserve that daylight overdrafts were a fact of life. Not only was there no mechanism in place to prevent daylight overdrafts, but neither was there a way to know how widespread the practice was. The second development was a carefully constructed survey of the incidence of daylight overdrafts. This provided the factual foundation for debating and developing the overnight initial Federal Reserve payment system risk (PSR) policy: guidelines for determining limits on day light overdraft positions; continued recording of daylight overdraft positions (in addition to a real time mechanism to control daylight overdrafts at problem banks and special institutions); and a stated intention to ratchet-down limits over time. Pricing daylight overdrafts now is being sug gested as a next step for this policy. The problem with free Fedwire daylight over drafts is moral hazard. The term refers to the hazard an insurer faces as a result of the elimina tion of incentives for an insured party to avoid a risk precisely because any losses arising from that risk are covered by insurance. Fire, life, and casualty insurers protect against moral hazard in a variety of ways. For example, coinsurance in the form of deductibles or copayments gives the insured a stake in preventing loss; inspection and requirements to remove risks give the insurer the ability to manage risk. Fedwire does have some similar protections. The payor bank’s net worth is at stake if it is unable to repay its credit, constituting a form of coinsurance. Regulation, supervision, and exam ination of banks guard against imprudent bank ing practices, now extended to include payment practices. However, initial limits on daylight overdraft exposure deliberately have been set high, and do not yet apply to overdrafts from book-entry securities transfers. As a result, Fed wire moral hazard is real, particularly in the short run between bank examinations. Payee banks have no reason to limit payments received during a day, regardless of the volume of daylight overdrafts per dollar of net worth of the payor bank, because the Federal Reserve is at risk. Payor banks face no external disincentives that would raise the cost of daylight overdraft credit as the volume they use increases and as their credit quality falls. Federal Reserve protec tions against moral hazard are not yet very strong. II. Avoiding Daylight Overdrafts ■5 Adjustments The most recent effort to resolve the unpostable debit issue is that of the New York Clearing House Association, which has adopted a requirement that C H IP S members participate in a loss-sharing arrangement. It also has proposed federal legislation apparently intended to give legal priority to net work payment claims over all others if a network member becomes insolvent. See American Banker, ■ 6 April 7 ,1 9 8 9 , pp. 1 and 16. Overnight overdrafts are subject to a penalty of the larger of $50, or the larger of 10 percent or a rate 2 percentage points above the federal funds rate prevailing on the day the overdraft is incurred. The penalty charge is in addi tion to the cost of making up the reserve-deposit deficiency for reserverequirement purposes, Any bank could eliminate daylight overdrafts by holding more overnight reserve deposit balances, by borrowing balances for a few moments or hours during the day, or by modifying its own or its customers’ payment practices to prevent a negative balance. Such adjustments might be costly, of course, but would be worthwhile if they cost less per dollar than a daylight overdraft. A cost-minimizing bank might acquire excess reserves in the federal funds market. After meet ing its temporary daylight need to cover pay ments, the bank would then have these extra funds available to hold, or to loan out overnight, if it could. The marginal cost of preventing a day light overdraft would be the difference between the cost of borrowing and the return on lending. A private daylight loan market does not now operate, but such a market would provide a second possibility for avoiding Federal Reserve daylight overdrafts. 7 Daylight loans could redis tribute existing reserve balances from banks hav ing them and not needing them during the day for payment purposes, but only overnight for reserve-requirement purposes, to banks not hav ing them and needing them during the day, but not overnight. Free Federal Reserve daylight credit preempts such a market now, but if day light overdrafts were to become costly, and timely delivery were assured, borrowing in a daylight loan market might become an inexpen sive way for a bank to prevent overdrawing its reserve account during a day, with repayment before close of business. Finally, a bank could alter the amounts of debits and credits to its account, or their sequence dur ing the day. It might do this by lengthening the maturity of its liabilities, or by adopting a con tinuing contract for federal funds borrowing, with daily renegotiation of the rate but no daily repayment and re-receipt of funds. Or, pairs of institutional customers operating in securities markets might be induced to net their transac tions obligations during a day, producing a single net obligation for daily payment, again reducing debits that might now precede credits. Or, groups of banks might join in private payment networks, substituting daylight credit on the pri vate networks for Federal Reserve daylight over drafts. Only net settlement of end-of-day posi tions would need to be accomplished through Federal Reserve accounts.8 Modifying payment practices in these ways would involve some costs, too, such as paying higher rates on longer-term liabilities, or receiving lower prices or revenues for payment services when institutional customers engage in obliga tion netting, or sharing the cost of a private pay ment network. Some tactics would be more expensive than others, so the marginal cost of preventing daylight overdrafts in reserve accounts by modifying payment practices would increase with the volume of overdrafts avoided. In equilibrium, cost-minimizing banks would adopt the unique combination of adjustment mechanisms having marginal costs equal to or less than the marginal cost of a daylight over draft. Pricing daylight overdrafts would lead banks to adjust from today’s zero marginal cost to something higher. Throe Proposals to Price Daylight Overdrafts Three specific pricing proposals that have been receiving attention are evaluated in this section.9 One would treat each daylight overdraft as an automatic overnight discount-window loan, booked at a penalty rate. A second would require a bank to hold additional balances at a Federal Reserve Bank in proportion to its day light overdrafts. A third would simply impose a slight fee per dollar of daylight overdraft. The penalty rate proposal comes from Wayne Angell, member of the Board of Governors of the Federal Reserve System. A bank would be required to borrow the amount of any daylight overdraft as a collateralized loan from its Federal Reserve Bank discount window at an above-market penalty rate, but the Federal Reserve Bank would pay an explicit (belowmarket) rate of return on excess reserves. 10 The combination of the two features means that, under normal circumstances, no bank would run a daylight overdraft intentionally and pay the penalty discount rate, because the maximum alternative cost would be only the interest-rate spread between the cost of financing extra excess reserves, perhaps the federal funds rate, and the earnings rate on excess reserves. The same spread would become the cost of borrowing daylight funds in the likely event that a private daylight loan market developed. Banks Penalty Rate ■ 9 These proposals are described in VanHoose (1988), the Angell proposal of a penalty rate; Hamdani and Wenninger (1988), supplemental balances; and ■ 7 Simmons (1987) contains an extensive discussion of daylight funds market possibilities. ■ 8 Humphrey (1987) and Board of Governors of the Federal Reserve Sys tem, Large-Dollar Payments System Advisory Group (1988) contain detailed Board of Governors of the Federal Reserve System , Large-Dollar Payments System Advisory Group (1988), fees. ■ 10 Penalty-rate borrowing would differ from an overnight overdraft in that a bank would be required to post eligible collateral for the loan associated with explanations of a number of these potential modifications of payment a daylight overdraft, but would not involve the cost of making up a reserve- practices. deposit deficiency for reserve-requirement purposes. would never pay more than this spread for a day light loan because they could always borrow re serves in the federal funds market and lend at the overnight rate; lenders would never charge less than this spread because they could always sell their reserves at the federal funds rate, of course forgoing the rate earned on excess reserves. Note, however, that excess reserves and a day light loan market would be relevant only to the extent that daylight overdrafts were not elimi nated by modifications in payment practices that were less costly than the rate spread. 11 The supplemental balance proposal has been described by the staff of the Federal Reserve Bank of New York. A bank would be required to hold a special interestbearing deposit (the supplemental balance) in a current period equal to some fraction (the sup plemental balance ratio) of prior-period daylight overdrafts of its combined reserve and supple mental deposit accounts. The maximum cost of a dollar’s daylight overdraft today would be the supplemental balance ratio multiplied by the expected next-period spread between the cost of financing a dollar’s supplemental balance and the rate earned on the supplemental balance. With both this rate spread and the ratio adminis tratively fixed, the maximum cost of a daylight overdraft would be a simple constant amount per dollar of daylight overdraft. The cost would set an upper limit on the mar ket rate for daylight loans. And, as in the penalty rate case, supplemental balances and daylight lending would emerge only to the extent that less-expensive modifications in payment practices failed to eliminate daylight overdrafts. Banks would not use ordinary non-interestbearing excess reserves to avoid daylight over drafts, because the cost of financing them at the federal funds rate normally would be greater than the supplemental balance ratio times the rate spread. Unlike the penalty rate proposal, the supplemental balance approach would not Supplemental Balances ■ 11 necessarily eliminate all daylight overdrafts. Only at a very low earnings rate on supplemental bal ances (perhaps even a negative rate) would it be certain that banks would find payment-system modifications (or excess reserves) a cheaper way to avoid daylight overdrafts. The fee proposal has been suggested by the Federal Reserve System’s Large-Dollar Pay ments System Advisory Group. It would simply have the Federal Reserve impose a fee for Fed wire overdrafts in excess of a base amount estab lished for each bank. The maximum cost to a bank of a dollar’s daylight overdraft would be that fee. Extra excess reserves would not be used in this case unless the fee were set than the federal funds rate. A limited daylight loan market could develop, redistributing the required re serves of banks whose need for daylight balances was less than their need for required reserve balances. And, of course, neither daylight over drafts nor daylight loans might be necessary if sufficient modifications in payment practices were forthcoming at a marginal cost less than the fee. In brief summary, then, each of the three pric ing proposals might be capable of eliminating Fed eral Reserve daylight overdrafts entirely through inexpensive modifications in payment practices. However, if modifying payment practices and redistributing required reserves through a day light loan market were not sufficiently respon sive to price, the outcome of pricing would differ substantially among the three proposals: . The penalty rate regime would eliminate remaining daylight overdrafts by expand ed holdings of excess reserves and their redistribution in a daylight loan market. . The supplemental balance regime would eliminate of the remaining daylight overdrafts by expanded holdings of reserves in the form of supplemental bal ances and their redistribution in a daylight loan market. • The fee regime would eliminate of the remaining daylight overdrafts, unless the fee became a penalty rate. Fees higher all some none Note also that the penalty rate proposal contains the seeds of a prob lem for monetary policy. Extra demand for excess reserves would be matched, III. Pricing and on average, by extra supply through open market operations, maintaining a Moral Hazard policy-desired level of the federal funds rate, on average. However, the varia bility of the federal funds rate around the average rate might increase, reflect ing variations in payment needs for balances within a day, or pertiaps day-today, unrelated to reserve requirements and monetary growth. A bulge in payment needs that drove up the daylight loan rate during a day would drive up the federal funds rate by the same amount, because the overnight earnings rate on excess reserves is administratively fixed. No creditor would lend fed eral funds during the day for less than the sum of the daylight loan rate and the overnight rate. A s long as policymakers value the federal funds rate as a tool or information variable, adopting the penalty rate proposal might involve some risk of less-precise policy implementation. Each of the three pricing proposals could reduce daylight overdrafts, but to what extent would they reduce moral hazard? None of the proposals would directly relate price to a bank’s credit quality or to the volume of its daylight overdrafts. Nor would any of them introduce the kind of actuarial relation between price and risk expo sure needed to establish an insurance fund. Reduced moral hazard would have to come as a by-product of pricing, in some form of en hanced market discipline. This could not be administered by payee banks on Fedwire, for they remain free of any risk in receiving payments. Results, therefore, could come only from the behavior of other creditors, or from eliminating payments requiring daylight funding. Investigat ing the adjustment mechanisms banks could use in response to pricing, however, reveals an uncertain basis for expecting market discipline to flourish. Excsss Reserves Both the penalty rate and the supplemental balance proposals could create a need to finance extra holdings of interest-bearing reserve bal ances. In both proposals, the earnings rate on those balances would be uniform across all banks, but the rate paid in the market to finance the extra balances might vary with the credit quality of a payor bank. If so, then the marginal cost of avoiding or funding a daylight overdraft would vary with the credit quality of the borrowing bank, injecting market discipline into payments. O f course, moral hazard in the current depositinsurance systems tends to dampen the role of credit quality in pricing both deposits and de posit insurance, and in pricing any kind of financ ing for a bank considered “too big to let fail.” However, to the extent that a bank’s marginal cost of funds can vary with credit quality, moral hazard would be diminished relative to the cur rent arrangement of free daylight overdrafts. Daylight Loans Similar assertions are made about the market discipline of a daylight loan market: if pricing induced banks needing daylight funds to borrow them from banks having surplus daylight funds, risk premiums would emerge in daylight loan rates, as market scrutiny sorted borrowers by credit quality. ■ 12 Another strand of thinking about daylight overdrafts would add a third qualification, also relevant to excess reserves: the “event risk” problem. Credi tors might not have a w ay to assure themselves that the debtor would not borrow additional sums, an event raising the riskiness of their loans after-thefact. If this were the case, early credit would be underpriced and risk premi ums too low. This is a problem for any creditor, and gives rise to restrictive covenants in lending agreements. To be a serious qualification in the daylight loan case, however, would require a demonstration both that the second quali fication does not hold, so that private lenders actually are at risk, and that covenants in standard daylight loan agreements combined with innovations in electronics network monitoring, such as already exist in C H IP S , could not deal with the problem. A n elaborate treatment of the underpricing/overlending case can be found in Gelfand and Lindsey (1989). This argument needs two qualifications. 12 One is that neither the supplemental balance nor, more especially, the fee proposal provides much basis for an extensive daylight loan market. Bal ances available for daylight lending would be limited to those of banks whose need for pay ment balances was less than their required, or required plus supplemental, reserve balances. This suggests only a limited stock of reserve deposits available for market allocation of day light loans to replace free daylight overdrafts, at least relative to the penalty rate proposal. The second qualification recognizes the tooeasy presumption that daylight lenders actually would be at risk. The presumption rests on an apparent analogy between unsecured overnight interbank loans in the federal funds market and the envisioned unsecured intraday interbank loans in a daylight loan market. Whatever the similarity between overnight and intraday lend ing, it does not extend readily to risk of loss. Federal funds loans are risky even though their dominant maturity is only one day. While deposit insurance and the “too big to let fail” maxim may minimize risk, it is still possible for a bank to be closed, resulting in at least a delay in repay ment, if not partial or complete loss of interest and principal to its federal funds market creditors. Even with assurance that a loan is for only one day, banks routinely impose limits on their lend ing to individual banks as a matter of credit pol icy, and risk premiums sometimes are required. Daylight loans would seem to be much closer to a riskless opportunity. Under what circum stances could a borrower fail to repay? One is if regulatory authorities closed the bank a day, rather than following the precedent of clos ing banks only after close of business. Closing a bank in the midst of a day’s business would seem exceedingly awkward in a financial and legal environment where the timing of competing claims arriving by different means (over the counter, mail, messenger, telephone, day-ahead magnetic tape, off-line telecommuni cation, on-line telecommunication) is not readily distinguished. In fact, one by-product of pricing daylight overdrafts could be a standard timetable for posting each off-line activity to the daylight balance monitor, and use of that standard for defining priorities among claimants. Such a m on itor could make intraday closings easier to arrange, but unless all of this were to become well established, authorities are not likely to close a bank during daylight hours. Ruling out unexpected daylight closings means that all lending and borrowing banks would have access to Fedwire, and could make irrevocable repayment of daylight loans if they wished to do during so. Daylight loans could be riskless because, in the normal case, a bank in trouble would in no way be prevented from sending Fedwires to repay daylight loans, even though that were to result in a daylight overdraft. It may seem ludicrous to imagine a bank bor rowing in the daylight loan market in order to avoid a daylight overdraft, but then repaying the loan later the same day by going into daylight overdraft— except as part of a tactic calculated to trigger a discount-window loan or an overnight overdraft. Nonetheless, the point is made— that any bank on the ex post monitor could make irrevocable repayment of a daylight loan during banking hours Daylight loans would carry the risk of nonpayment only if the borrowing bank preferred to default on the loan rather than overdraw its account at a Reserve Bank. Daylight loans are riskless unless there are good reasons to think that any unex pectedly insolvent bank would prefer default in the market to overdraft at the Federal Reserve and potential closing. The inexpensive technology of ex post m oni toring of daylight overdrafts is perfectly adequate for ex post booking of a penalty rate loan, or ex post calculating of a supplemental balance to be held in the future, or ex post billing of a simple fee. The difficulty with the technology is that it leaves unclear who is at risk, or perhaps makes only too clear who is at risk, in interbank daylight lending. As long as interbank daylight lending is riskless, no market discipline emerges from it. The moral hazard of free Federal Reserve daylight overdrafts would remain the moral hazard of private daylight loans. unexpectedly if it wanted to do so. not Payment Practices Modifying payment practices would be expected to reduce moral hazard. For example, as banks replace overnight federal funds with longermaturity financing, their creditors would accept and demand compensation for additional risk. This risk formerly was accepted by the Federal Reserve, when daylight overdrafts provided an automatic means for an unexpectedly insolvent bank to close without having renewed its over night credit. A different example of risk shifting is that of netting the many payments of two customers into a single obligation. This would eliminate moral hazard because self-interest of the parties in the netting process would demand risk eval uation and compensation and would impose limits on any credit-risk exposure they might assume with respect to one another. As a third example, pricing would encourage the migration of payments from Fedwire to pri vate networks. Moral hazard would diminish as payments shifted to private systems because, with prerequisite credit limits and loss-sharing agreements in place among participants, banks would be expected to ration and/or price net work credit on the basis of credit quality. How Much Good Would Pricing Do? One thing certain is that none of the proposals would enlist the self-interest of payee banks directly in monitoring the credit quality of payor banks. As long as Fedwire provides irrevocable ownership of good funds upon receipt, payee banks do not extend credit in the Fedwire pay ment process, are not at risk, and have no incen tive to monitor the credit quality of payor banks. Market discipline would have to originate from other pressures on payor banks to manage payment risks. That said, the most crucial unknown factor is the rate at which the marginal cost of modifying payment practices rises as the volume of eliminated daylight overdrafts increases. If this marginal cost rises relatively slowly, so that inexpensive modifications effec tively will eliminate all Fedwire daylight over drafts, then moral hazard should disappear, sup planted by the market discipline of risk-sharing agreements in private payment networks, by net ting agreements among banks’ customers, and by the risk aversion of banks’ creditors (and, perhaps in the future, of banks’ insurers). On the other hand, if this marginal cost rises relatively rapidly, the major burden of rationing daylight overdrafts would have to be borne through the direct mechanism of a pricing scheme. In this event, conjecture becomes somewhat more dependable — at least concern ing the relative strengths of the three proposals. The penalty rate proposal, while eliminating daylight overdrafts altogether, is not likely to be effective in removing moral hazard. Ex post day light overdraft monitoring would leave the Fed eral Reserve bearing the credit risk of an active interbank daylight loan market, redistributing a much enlarged volume of excess reserves. Highquality banks could borrow excess reserves needed to avoid the penalty rate, not only for their own accounts, but also for riskless lending to lower-quality banks, with repayment assured by irrevocable Fedwire transfers. The supplemental balance approach would more successfully tie the cost of daylight funding to perceptions of a bank’s credit quality in the interday markets (via a risk spread paid for sup plemental balances). This seems to be the most effective of the three pricing devices for injecting market discipline into the cost of funding payments. The simple fee proposal offers little protection against moral hazard to the extent that changes in payment practices fail to eliminate daylight overdrafts. Flat-rate pricing of assured access to daylight credit may discourage its use, but pro vides no basis for scrutiny of the credit quality of payor banks, and no risk-based market disincen tive for payor banks to limit daylight funding of payments. 13 The higher the proposed price, the more scope there will be for modifications in payment prac tices to eliminate Fedwire daylight overdrafts. But, in the limit, if sufficient modifications were not forthcoming, a price above the federal funds rate would guarantee elimination of daylight overdrafts, no matter which proposal was adopted, because excess reserves would be the economical way to avoid the price. Charging this high price would transform each proposal into a variant of the penalty rate proposal. However, unless a substantial earnings rate was offered on overnight holdings of excess reserves, daylight overdraft elimination would be quite costly to the banking system. In any case, imposing this net cost on banks and their customers to eliminate daylight overdrafts would not avoid moral hazard to the extent that excess reserves would feed an extensive market in riskless daylight loans. IV. Conclusion Fedwire daylight overdrafts of Federal Reserve deposit accounts create a moral hazard that pric ing might reduce. Pricing could have the desired result to the extent that banks would respond by modifying payment practices, or by bringing payments-related credit needs under more effec tive market discipline based on risk evaluation. Much of Fedwire payment and daylight over draft volume can be traced to unsecured inter bank lending and to settlement of securitiesmarket trading. Rapid growth of these activities has taken place within the nationwide frame- ■ 13 This m ay overstate the case in one w ay. Pricing would operate only on daylight overdrafts in excess of a "free" allowance, determined as a per cent of capital. Price then depends on credit quality, in that capital influences price. Beyond that first step, however, no discipline from the market or from regulatory credit evaluation would discourage additional borrowing. work of free Fedwire daylight overdrafts. There is little basis in actual experience, therefore, for predicting the responsiveness to pricing of either Fedwire daylight overdrafts or the financialmarket activities they reflect. The hope is that modifications in payment practices would be sufficiently responsive to price that there would be no need to test the strength of credit-market discipline; that moral hazard could be eliminated at relatively low cost. The danger is that payment practices would be unresponsive to price and that market discipline would not be engaged because of a large residual element of moral hazard in the form of priced day light overdrafts or riskless daylight loans. If this were to be the actual outcome, it would suggest that, in addition to efficient allocation of finan cial resources, an insidious driving force in the rapid growth of interbank lending and securitiesmarket trading in recent decades has been the moral hazard of Fedwire daylight overdrafts. References Board o f Governors o f the Federal Reserve Sys tem, “A Strategic Plan for Managing Risk in the Payments System,” Report of the Large-Dollar Payments System Advisory Group to the Pay ments System Policy Committee of the Federal Reserve System, Washington, D.C., August 1988. Gelfand, Matthew D. and Lindsey, David E., “The Simple Microanalytics of Payments Sys tem Risk,” Finance and Economics Discussion Series No. 61, Board of Governors of the Fed eral Reserve System, March 1989Hamdani, Kausar and Wenninger, John A., “The Macroeconomics of Supplemental Balances, Appendix C,” Report of the Task Force on Control ling Payments System Risk to the Payments System Policy Committee of the Federal Reserve System, Board of Governors of the Federal Reserve System, August 1988. System, Controlling Risk in the Payments Humphrey, David B., “Payments System Risk, Market Failure, and Public Policy,” in Elinor Harris Solomon, ed., Electronic Funds Trans fers and Payments: The Public Policy Issues, Boston: Kluwer-Nijhoff Publishing, 1987. Simmons, Richard D., “Would Banks Buy Day time Fed Funds?” Fed eral Reserve Bank of Chicago, May/June 1987, 36-43. Economic Perspectives, Stevens, E.J., “Pricing Daylight Overdrafts,” 8816, Federal Reserve Bank of Cleveland, December 1988. Working Paper VanHoose, David, “The Angell Proposal: An Overview,” mimeo, Board of Governors of the Federal Reserve System, June 1988. Capital Subsidies and the Infrastru ctu re C risis: Evidence from the Local M a s s -T ra n s it Industry by Brian A. Cromwell Brian a . Cromwell is an economist at the Federal Reserve Bank of Cleveland. The author would like to thank Paul Bauer, Michael Bell, John Davis, Randall Eberts, Erica Groshen, Jam es Poterba, and William Wheaton for useful suggestions and discus sion. William Lyons and Dottie Nicholas of the Transportation Sys tem Center provided invaluable assistance with the data. Financial support from the National Graduate Fellowship Program and the M IT Center for Transportation Studies is gratefully acknowledged. tions and concluded that “...the quality of Ameri ca’s infrastructure is barely adequate to fulfill current requirements, and insufficient to meet the demand of future economic growth and development. ” 2 Debates and studies of the infrastructure “cri sis” involve a wide range of policy issues related to measuring the costs and benefits of public capital. The issue of what level of infrastructure is optimal involves addressing questions of how to measure the current state of and future needs for public capital, how to measure the impact of infrastructure on productivity and regional growth, and how expenditures on public capital should be weighed against other uses of public monies. Questions of financing involve tradi tional issues of fiscal federalism and public finance, including what level of government should provide infrastructure services, who should pay, and what financing mechanisms raise revenue with the least economic cost. While most studies argue that increased public investment is needed, a more provocative set of Introduction The condition of the public capital stock— perceived by many to be dilapidated and inadequate— has received considerable attention in political, media, and academic circles in recent years. Pat Choate and Susan Walter’s gave striking examples of crumbling infra structure and suggested that enormous increases in infrastructure investment were needed just to maintain the existing levels of services. The media and political attention given this work was high lighted by tragedies such as the 1983 collapse of the Interstate 95 bridge in Connecticut. More sys tematic studies by the Urban Institute and the Congressional Budget Office (1983) catalogued the existing state of public infrastructure and pro jected the need for new public investment. 1 More recently, the National Council of Public Works Improvement (1988) completed a series of studies examining the state of the nation’s public infrastructure, entitled Ruins America in Fragile Founda ■ 1 The Urban Institute project included a series of case studies on munici pal infrastructure. For example, see Humphrey et al. (1979). For a review of infrastructure needs studies, see Peterson et al. (1986). ■ 2 National Council of Public Works Improvement (1988), p. 1. questions focuses on how public infrastructure arrived at its present condition and critiques the decision-making process itself In particular, it is alleged that the structure of infrastructure financ ing mechanisms, combined with political and budgetary pressures, induce public officials to systematically underfund the maintenance of the existing capital stock, leading to excessive dete rioration of public infrastructure. The study of infrastructure maintenance, however, has received little empirical attention due to the lack of data on local maintenance policies and a lack of natu ral experiments with which to evaluate publicsector maintenance. This article reviews questions regarding infra structure policy with a focus on how the costs and benefits of public capital and maintenance deci sions are potentially distorted by budget proce dures, political pressures, and the structure of federal grant policies. I then describe how the local mass-transit industry provides an opportu nity to investigate public-sector investment and maintenance decisions. Empirical evidence from two recent studies of the local mass-transit indus try, Cromwell (1988a, 1988b), is then summar ized. The results suggest the structure of federal grant policies has important effects on infrastruc ture decisions of state and local governments. I. Infrastructure Policy Incentives Budget Processes Leonard (1986) argues that ignoring deprecia tion and deferring maintenance are both power ful forms of hidden spending that are not accounted for by local governments. Failure to reinvest or maintain existing infrastructure is, in effect, to live off an inherited bank account. Cur rent taxpayers spend assets provided to them by previous generations. This spending is obscured, however, by the lack of records and comprehen sive accounting for fixed-asset investments from year to year. Current accounting procedures for capital and maintenance by local governments appear to be inadequate for effective management of public infrastructure.3 The Government Accounting Standards Board, which sets standards for publicsector accounting, requires governments to ■ 3 These arguments were first advanced by Leonard (1986) and are also presented in Blumenfeld (1986) and the National Council of Public Works Improvement (1988). maintain records of fixed assets recorded at his torical cost in a separate account group held apart from operating funds. Recording the value of immovable infrastructure assets— bridges, roads, sewers— is explicitly optional, as is the recording of depreciation. Even if a governmen tal unit does recognize depreciation, it is shown as an offset to the value of assets, not as an oper ating cost as in the private sector. When tight funds result in deferred maintenance, there is no notation in capital records of the decline in asset values from the failure to maintain them, making preventive and routine maintenance an attractive target for budget cuts. In a 1983 survey of city and county officials by the American Planning Association, 29 percent reported having poor information on the current conditions of the city’s or county’s capital stock and 48 percent felt they had weak methods of evaluating the cost-effectiveness of proposed projects. Hatry et al. (1984, 1986) surveyed over 40 public works agencies and found capital investment decisions to be highly decentralized. In general, agency management determined what analysis should be undertaken and deter mined priorities. While most agencies had for mal procedures for rating and ranking potential projects, these rankings were often based prima rily on subjective information. They found few explicit estimates of expected improvement in service levels or expected reductions in future costs from individual proposed projects. Budgeting procedures for maintenance were found to be even more deficient. The agencies surveyed undertook only a small amount of reg ular, systematic examination of capital mainte nance and repair options and did not regularly and systematically examine trade-offs between preventive maintenance activity (such as painting bridges or cleaning sewers) and other major options, such as rehabilitation or reconstruction. The Hatry study found no examples in which a local government considered the costs of deferred maintenance. Several proposals for maintenance evaluation procedures have surfaced in recent years for sev eral common forms of public infrastructure. For example, Archuleta (1986) proposed a program for effective preventive maintenance for water and wastewater facilities. Pavement maintenance management systems promoted by the American Public Works Association (1987) enable managers to monitor road pavement conditions and sched ule needed repairs. Carlson (1986) of the Fed eral Highway Administration proposed a similar systematic maintenance review process for bridges. Implementation of such proposals, however, often requires a crisis atmosphere. The state of Connecticut, for example, instituted a comprehensive bridge inspection and repair program that identified and ranked needed bridge reconstruction following the 1-95 tragedy. There is no obvious general groundswell of pub lic opinion, however, for the reform of infrastruc ture accounting procedures. Maintenance and Visibility Many aspects of the infrastructure problem, par ticularly issues of maintenance and rehabilitation, have low levels of visibility and are not readily apparent to voters and elected officials. The costs of neglected infrastructure accrue over time and are not immediately apparent or measurable. As discussed in Eberts (1988), often they occur in the form of lost productivity and slower regional growth. Even when observed, the long-run benefits of maintenance practices are potentially discounted by elected officials with short time horizons. Cohen and Noll (1984), for example, demonstrate that legislators maximizing the probability of reelection seek to defer such costs. Elected officials may also derive greater utility from new investment than from maintenance. Possible sources of utility from capital projects for public officials include political support and contributions from direct project beneficiaries. Weingast et al. (1981) present a model of legisla tive behavior in which the geographic incidence of benefits and costs systematically biases public decisions toward larger-than-efficient projects. Capital projects give benefits directly to a small group, while their costs are widely distributed. Further political benefits come from being associated with large and visible investment proj ects that do not accrue from the more mundane activities of maintenance. An assistant secretary for Housing and Urban Development asked, “Have you ever seen a politician presiding over a ribbon-cutting for an old sewer line that was repaired?” 4 Such effects further encourage the substitution of investment for maintenance. financing of new capital and the traditional emphasis of federal grant policies on capital subsidies. Local governments often finance new pur chases of capital, as well as major reconstruction and rehabilitation, through borrowing. Ordinary maintenance expenditures, however, are counted as operating expenses and are financed through current funds. This treatment of maintenance stems in part from the wide variance of mainte nance activities. Certain maintenance activities, such as sweeping sidewalks or patching potholes, have immediate short-term benefits and, accord ing to the benefit principle of public finance (those who benefit from public services should pay), should be paid for by the immediate bene ficiaries through current revenues. The benefits of other maintenance activities, such as painting bridges or flushing sewers, accrue over many years. Maintenance of this sort constitutes a form of public investment that according to the benefit principle should be paid over many years through debt-financing. 5 Treating all maintenance activities as current expenses ineligible for debt-financing ignores their investment component and results in under financing when operating budgets are tight. Dur ing periods of budget constraints, officials choose between funding preventive maintenance at the expense of cutting back on other programs, or allowing infrastructure to deteriorate until major reconstruction is needed, which can be funded through debt. As the mayor of Lincoln, Nebraska observed, “In the choice between laying off police and maintaining sewers, the sewers always lose. ” 6 Federal grant policies for public infrastructure further exacerbate the bias against infrastructure maintenance. Under the rationale that local tax payers should pay to operate the facilities pre sented to them, federal grants often heavily sub sidize new construction, but provide no assistance for maintenance or other operating expense. A wide range of federal grant programs pro vide major assistance for infrastructure at the ■ Capital Financing Policies 5 Maintenance is often considered in the operations research and investment literature to be a fixed operating expense. For a standard example, see the optimal equipment replacement model in Jorgenson et al. (1967) and the discussion in Nickell (1978). For good reviews of models of preventive The political and budgetary bias against infra structure maintenance is reinforced by two common features of capital financing: debt- maintenance, see Pierskall and Voelker (1976) and Sherif and Smith (1981). The treatment of maintenance as a form of investment is shown in Bitros (1976). This approach is used in models of housing stock maintenance, in which maintenance expenditures have important effects on rental income and sale price. See Vorst (1987), Arnott et al. (1983), and Sweeney (1974) for examples of such models. ■ 4 Newsweek, August 2 ,1 9 8 2 . Also cited in Leonard (1986). ■ 6 Newsweek, op. cit. state and local level. In 1988, $25 billion in fed eral grants accounted for 2 6 percent of state and local capital spending. This included $13-7 bil lion granted by the Federal Highway Administra tion (FHWA) for the construction and rehabilita tion of highways; $2 . 6 billion from the Environmental Protection Agency for pollution control and abatement; $2.4 billion in capital financing for mass transit administered by the Urban Mass Transit Administration (UMTA); and $3.1 billion granted through the Community Development Block Grant program .7 While the structure of grants varies from pro gram to program, most provide capital assistance at a high matching rate, with the state and local government required to meet the matching share. The FWHA provides financing for comple tion, rehabilitation, and reconstruction of the interstate highway system at a 90 percent match ing rate. Discretionary grants from UMTA for major rail and subway systems provide funds up to a 75 percent matching rate. Formula grants from UMTA pay 80 percent of the cost of regular transit vehicle replacement. No corresponding subsidies, however, are provided for mainte nance. These subsidies distort the relative prices facing local governments for new investment versus maintenance of existing infrastructure. Even if the federal matching rate is not specified in formula, the expectation of federal aid poten tially induces local officials to substitute away from maintenance. The empirical work we now turn to attempts to identify such substitution. ever, I examine the impact of capital subsidies on investment and maintenance decisions of local governments, using data on the maintenance policies of both publicly and privately owned local mass-transit providers. While not address ing all issues of infrastructure maintenance, these studies suggest that the structure of federal grants has significant effects on the infrastructure decisions of state and local governments. The data used were collected under the Sec tion 15 Reporting System administered by the Urban Mass Transportation Administration (UMTA). Section 15 data for fiscal year (FY) 1979 through FY1985 are available for 435 transit sys tems. The data set contains extensive informa tion on vehicle fleets as well as expenditures and labor hours for vehicle maintenance, provid ing a consistent measure of public capital and maintenance efforts not previously seen. These data provide an unusually detailed panel of local governments’ physical assets. Vehicle inventories for each system are broken down by model, year of manufacture, and mileage. Data are also available for certain privately owned and operated systems. Their inclusion in the Section 15 data results from contracting with a public recipient of Section 9 funds to provide transit services. As these contracts often provide for the leasing of public vehicles, care was taken to examine maintenance and scrappage decisions only on vehicles owned outright by private operators. Federal Transit Policies II. Local Mass Transit: A Natural Experiment on Subsidies and Infrastructure As discussed in the previous section, several elements of public accounting, political and bud get processes, and capital financing potentially lead to underfunding of infrastructure mainte nance and result in excessive deterioration of public capital. Empirical research on the relative importance of these issues, however, has been limited by a dearth of data on capital assets and maintenance, and by a lack of obvious natural experiments with which to evaluate public-sector maintenance practices. In two recent studies, Cromwell (1988a) and Cromwell (1988b), how- ■ 7 See U .S . Office of Management and Budget (1989). For further discus sion of federal grants-in-aid, see Delmar and Menendez (1986). The federal government finances a major part of local public mass transportation. The principal federal grant program for entities that only oper ate bus lines (the focus of these studies) is the Section 9 formula grant program that distributes funds to urbanized areas for use in transit operat ing and capital expenditures. The Section 9 capi tal funds are principally used for vehicle replace ment and pay up to 80 percent of the cost of a new vehicle. As funds are adequate for normal vehicle replacement, this matching rate represents an enormous marginal subsidy for new capital. Vehicle maintenance, however, is counted as an operating expense and is ineligible for the capital subsidy. Due to a desire by UMTA to wean local entities away from operating assis tance, the Surface Transportation Act of 1982 capped the level of funds available for operating assistance for FY1983 and beyond to some 90 percent of the FY1982 level, or to 50 percent of a property’s operating deficit, whichever was T A B L E III. Empirical Evidence on Subsidies and Transit Capital 1 Used Transit Vehicle Prices in 1 9 8 7 and 1988 Evidence from Used-Bus Prices Year of Manufacture Average Price Public 1961-65 1966-70 1971-75 1976-80 Private 1961-65 1966-70 1971-75 1976-80 $ 301 841 1,648 Max. Price Min. Price $ $ 8,863 1 ,0 0 0 3,500 6 ,0 0 0 17,000 $3,500 6,590 7,500 18,000 10 0 400 250 3,300 Number < Observatic 255 163 239 8 — — 11 — — 11 — — — 9 1 SOURCE: Telephone survey by author. lower. The overwhelming majority of publictransit properties are constrained by the cap and receive no operating assistance on the margin. Federal control over maintenance principally consists of setting an upper limit for deteriora tion of federally purchased equipment. UMTA requires local transit properties to operate buses purchased with federal funds for at least 1 2 years or 500,000 miles.8 Failure to do so results in a penalty in federal assistance for new capital pur chases. This 12-year limit, however, is below the potential operating life of 15 to 20 years for standard bus models when properly maintained. The structure of the UMTA grants results in a large distortion in the relative price of mainte nance versus new investment for buses over 1 2 years old. If the capital and maintenance deci sions of local government are sensitive to the structure of subsidies, we would expect the fol lowing results. First, publicly owned buses should depreciate quickly, with little physical or financial value left after 12 years. Second, we would expect higher average levels of mainte nance in the private sector compared to the pub lic sector. Finally, in the public sector we would expect low levels of scrappage before the 1 3 year point, a marked shift in scrappage at year 13, then high levels of scrappage thereafter. A similar pattern for privately owned vehicles is unlikely, as they are not subject to such a discon tinuity in the price of new equipment.9 Evidence from used-bus prices supports the thesis that public equipment depreciates rapidly. The used-bus market is highly fragmented and ad hoc in nature. The disposition of equipment is not re ported in the Section 15 data, and no central data source of used-bus prices or sales exists. UMTA officials report, however, that the used transit bus market is depressed. The supply of public vehi cles over 1 2 years old far exceeds demand— and vehicles are most commonly sold for scrap. Depressed prices, however, are also consistent with systematic undermaintenance of equipment. To confirm this, I collected transaction prices for some 645 transit vehicles sold in 1987 and 1988 by contacting all properties that solicited bids for used vehicles during this period . 10 The results of this survey are shown in table 1. Prices for publicly owned vehicles manufactured before 1971 ranged from $100 to $3,500, with an ■9 Previous studies on transit subsidies have used detailed engineering data from specific transit systems to simulate the effects of capital bias in the subsidy structure on scrappage dates. Tye (1969) used data from the Cleve land and Chicago transit systems to simulate the effect of subsidies in the late 1960s that paid for new capital at a 66.6 percent rate, but which provided no assistance for operating expenses. He calculated that the subsidy would lead a cost-minimizing transit firm to replace buses at half the efficient age. For average levels of utilization, this implied scrappage at 8 to 10 years versus an efficient 1 7 to 20 years, with the resulting waste of resources equaling 2 7 per cent of the subsidy. Similarly, Armour (1980) used data from Seattle Metro and calculated that the 80 percent federal capital subsidy reduced the optimal scrappage point from 20.5 to 26 years to 8.5 to 10 years. Frankena (1987) is the paper closest in spirit to the empirical work pre sented here. Using probit estimation with 1961 to 1983 data on scrappage of Canadian buses, this study shows that scrappage increases with age, and that significantly higher average scrappage rates followed the imposition of a capital-biased subsidy program in 1972. He finds no significant change, how ever, in the scrappage rate when the capital subsidies take effect at age 15 (the critical point in the Canadian subsidy program). In general, the hazardmodel estimators used here dominate the probit approach. They allow for vari ation in the underlying hazard rate over time, and control for bias introduced by vehicles dropping out of the sample when scrapped. The results, as will be seen, show a significant impact on scrappage when subsidies take effect. ■ 10 bids in Used-bus prices were obtained by contacting all agencies soliciting Passenger Transport between January 1987 and June 1988. Typically, less than 10 bids were received per auction with a mean of five bids reported by properties that would provide this information. Those bidding included Caribbean nations, church groups, charter-bus operators, people planning to make recreational vehicles, and farmers in need of storage space. If the vehi cles were purchased with federal funds, U M T A collected 80 percent of the proceeds with an allowance made for administrative expenses. The costs of soliciting bids or holding an auction, however, often were reported to exceed ■8 See U M T A (June 1985). the remaining local share. T A B L E 2 Vehicle Maintenance Expenses and Labor Hours1 Private Public Expenses per mile ($ 1 .0 0 ) 0.77 ( 0 .1 2 ) 0.53 ( 0 .0 2 ) Labor hours per 1 , 0 0 0 miles 37.8 (3.6) 29.3 (1.4) Percent of fleet > 1 2 years old 38.4 2 2 .0 Percent mileage on vehicles > 1 2 years old 26.7 1 1 .2 Number of observations 22 10 0 a. 1984 cross-section sample means (standard errors). SOURCE: Author’s calculations. average price of $511. Even vehicles reported to be well-maintained typically did not sell for over $3,000. Prices for vehicles manufactured between 1971 and 1975 ranged from $250 for scrapped vehicles to $6 , 0 0 0 for well-maintained vehicles. Prices for newer vehicles manufactured between 1976 and 1980 averaged $8,863. I was also able to obtain used-vehicle prices for a much smaller sample of privately owned vehicles. These prices, also shown in table 1, suggest that the private vehicles are in better condition and command a higher price, with prices averaging from $3,500 to $7,500 for vehi cles manufactured before 1976. Other private companies, however, reported selling their vehi cles for scrap at the depressed prices similar to those received by public agencies. The extremely low prices on used buses sug gest that maintenance practices can lead to rapid deterioration of equipment in the public sector. It is important, however, to distinguish between variations in maintenance and depreciation attrib utable to unavoidable operating conditions, and variations due to capital grant policies or bureau cratic behavior that are potential sources of gov ernment inefficiency. The empirical work that fol lows attempts to identity these separate effects. Evidence on Maintenance The impact of the capital grant structure on aver age levels of maintenance is examined in Cromwell (1988a). My initial empirical work examines a cross-section of Section 15 data for FY1984 from 122 transit properties. The sample consists of single-mode bus operators— properties that provide only fixed-route bus ser vice as opposed to rail or demand-response service— that operated at least five revenue vehi cles. Table 2 reports sample means for mainte nance expenses and maintenance employees, scaled by annual vehicle miles. In general, the average levels of both expenses and labor hours follow the predicted patterns. The private sys tems, on average, spend 45 percent more on maintenance per mile and devote 29 percent more labor hours to maintenance than do the public systems. The average age of vehicles in private systems is substantially higher than that for public fleets, with 38.4 percent of the private fleets being more than 1 2 years old compared to 2 2 . 0 percent of the public fleets. The distribution of vehicles weighted by miles is similar, with 26.7 and 11.2 percent of the mileage being run on vehicles older than 1 2 years for the private and public systems, respectively. The older fleet in the pri vate systems is consistent with privately owned capital deteriorating slower than publicly owned capital as a result of greater maintenance efforts. The means shown in table 2, while consistent with the predicted results regarding the private versus public operators, do not control for sys tematic differences due to wages, operating condi tions, and fleet composition. For example, many of the private systems operate in the New York metropolitan area, which is noted for its harsh operating conditions. To examine the public/ private differential more systematically, I use pooled time-series cross-section regression anal ysis on a sample of systems between 1 9 8 2 and 1985. Independent variables include maintenance wage rates, operating conditions, fleet composi tion, fleet age, and a dummy variable for opera tion in the New York area. The results show that, controlling for wages, operating conditions, and fleet composition, privately owned transit com panies devote some 14 to 17 percent more labor hours to maintenance than do publicly owned and managed transit companies. The analysis then uses this public/private differential, along with cross-state variation in grant policies, to measure the elasticity of maintenance with respect to cap ital subsidies. The point estimates suggest an elasticity of -0 .1 6 , meaning that a 1 0 percent increase in the subsidy rate for transit capital reduces vehicle maintenance by 1 . 6 percent. The estimates are statistically significant and suggest that average maintenance levels are higher in the private sector. They do not neces sarily demonstrate, however, that public capital deteriorates at a faster rate than privately owned F I G U R E capital. The higher levels of maintenance labor hours could be attributed to less capital-intensive maintenance practices. Furthermore, an implicit assumption that maintenance is qualitatively sim ilar between the two sectors could be false. If one sector fixes equipment upon failure, as opposed to conducting preventive maintenance, differences in overall maintenance levels could result. The companion analysis in Cromwell ( 1 9 8 8 b), however, directly examines the scrap page and retirement rates of private versus pub lic equipment to determine whether the higher maintenance in the private sector is reflected in longer equipment life. Scrappage Rate Public Vehicles Percent Evidence on Scrappage Vehicle Age (years) SOURCE: Author’s calculations. F I G U R E Scrappage Rate Private Vehicles Percent 2 Cromwell (1988b) examines the impact of sub sidies on equipment life by tracking vehicles in the UMTA data set from 1982 through 1985. Scrappage decisions were observed for 15,829 vehicles, including 1,005 privately owned vehi cles from 11 privately owned companies. Vehi cles that changed from active to inactive status or that were dropped from the fleets between report years were counted as scrapped. The results pro vide strong evidence that federal grant policies have a direct impact on local scrappage decisions. The probability of scrappage for public and private vehicles of different ages (or empirical hazard) can be estimated directly from the observed scrappage rates and is plotted, with 95 percent confidence intervals, in figures 1 and 2 . 11 The estimates in general suggest the importance of federal grant policies for public-sector scrap page. The hazard for public vehicles averages under 4 percent for years prior to age 13, then jumps to over 1 1 percent at age 1 3 , decreases slightly at age 14, then rises steadily to 37 per cent by age 19. Standard errors calculated for these estimates suggest that the hazards for pub lic vehicles are measured with much precision and that the shift at the 1 3 -year point is statisti cally significant. ■ 11 The empirical scrappage rate presented here is also known as the Kaplan-Meier (1958) hazard estimator, which directly estimates the hazard function from the sample of vehicles. For each time /, the number of failures D(t) (that is, the number of vehicles scrapped) is divided by the total number of vehicles at risk at the start of time t, R(t). Censored spells (that is, vehicles that are not observed to be scrapped) are included in the risk set previous to their censor time and are dropped thereafter. This treatment of censoring Vehicle Age (years) SOURCE: Author’s calculations. yields a consistent estimate of the true hazard at each time t as long as the censoring mechanism and vehicle age are independent of each other. The standard errors were estimated following a suggestion in Kalbfleisch and Prentice (1980). F I G U R E Scrappage Rate Private vs. Public Vehicles Percent Vehicle Age (years) SOURCE: Author’s calculations. Percent 3 The private-vehicle hazards are estimated with less precision and exhibit more volatility, but in general show a rise in scrappage from near 0 for the 1 -to 6 -year period to an average 5 percent for the 7- to 10-year period to 9 percent at the 13-year point. Due to only one scrappage out of 143 in the age- 1 2 risk set, however, the esti mated hazard at year 1 2 is quite low, and a shift appears to occur at the 1 3 -year point— contrary to the predicted pattern. This shift can be attrib uted, however, to the smallness of the sample size and, given the estimated hazards in the sur rounding years, the pattern of estimated hazards for private vehicles appears to be markedly dif ferent from the public sector. These empirical hazard rates do not account for heterogeneity across transit systems in prices of maintenance and operating conditions. Given the large number of private vehicles operating in the New York metropolitan area, for example, adverse operating conditions might have a major impact on observed private-sector scrappage. To account for this heterogeneity, I employed a haz ard estimator that allows for nonparametric esti mation of the baseline scrappage rate, while per mitting estimation of the impact of operating conditions, wage rates, and other explanatory var iables. 12 The resulting baseline hazards are shown in figure 3. The impact of the grant structure on public-sector scrappage is readily apparent. While the private-sector baseline remains under 5 percent until year 16, and then rises steadily through year 2 0 , the public-sector baseline takes a distinct and significant jump at the 1 3 -year point from 1 percent to over 8 percent, twice that of the private sector. Scrappage then rises to over 14 percent for 15- and 16 -year-old vehicles and remains above the private sector until year 19. The distinct difference in scrappage rates can be attributed to the availability of federal grants. An alternative approach to examining public and private scrappage is to look at the survivor functions for the two sectors. The survivor func tion is defined as the percentage of vehicles of a given vintage that survive to a given age, as shown in figure 4. The functions further empha size the difference between public and private ■ 12 The baseline hazard estimates shown here are estimated using the semiparametric hazard estimator shown in M eyer (1988) and first developed in Vehicle Age (years) Prentice and Gloeckler (1978). This estimator allows for control of explanatory variables without imposing a specific structural form on the underlying baseline SOURCE: Author’s calculations. hazard. Cromwell (1988b) also presents estimates using the fully parametric estimator which imposes the commonly used Weibull baseline as shown in Lancaster (1979) and Katz (1986). scrappage policies. They track closely through year 1 2 , then diverge as public scrappage sharply increases. Again, this shift in the survivor func tion at the 1 3 -year point can be attributed to the sudden availability of federal subsidies. By age 1 6 , only 47 percent of the public vehicles sur vive, compared to 73 percent for private vehicles. At age 20, 45 percent of private vehicles are still estimated to be in operation, versus 2 0 percent for the public sector. The consistently lower survival rate of publicly owned vehicles after the availability of federal funds is direct evidence that federal capital grants reduce equipment life in the local public sector. It suggests that federal grant policies that subsidize the purchase of new capital, but that ignore the maintenance of existing capital, result in the increased deterioration of public infra structure. The magnitude of savings for the tran sit industry from a shift in policies, however, may be small if increased maintenance expenses offset reduced vehicle expenditures. In a simula tion of vehicle replacement reported in Crom well (1988b), this is the case. In spite of increased deterioration of public capital, the net efficiency losses of the federal subsidies appear to be low. There may be unobserved costs, how ever, in terms of quality of service that result from lower maintenance levels and increased deterioration of equipment. IV. Conclusion Several aspects of public accounting, political and budgetary procedures, and capital financing potentially lead local governments to systemati cally underfund the maintenance of public infra structure. The resulting excessive deterioration of public capital has been advanced as a possible source of the “infrastructure crisis” of recent years. This article summarizes the results of two stud ies of one aspect of infrastructure maintenance: the impact of large federal capital subsidies for new investment with no corresponding subsi dies for maintenance. Using data from the local mass-transit industries, the empirical results sug gest federal subsidies for new transit vehicles lower maintenance levels and increase scrap page rates in public transit systems. The extremely low resale value of used vehicles further suggests excessive deterioration. In the case of local mass transit, however, the net cost of the distortion appears to be small. The results suggest that increased purchases of vehicles are offset by lower maintenance costs. While the efficiency losses of the transit subsi dies for new vehicles appear to be small, they still show that local governments respond signifi cantly to incentives in the price of maintenance versus new investment introduced by federal subsidies. Given the several other biases against infrastructure maintenance discussed in section I, this suggests that federal policies should focus more on the maintenance and upkeep of facili ties purchased with federal funds. Possible pro posals to support maintenance include reducing the distortion in the relative price of mainte nance versus new investment facing local author ities through direct federal subsidies of impor tant maintenance activities or through a reduction in the federal subsidy rate for capital projects. Adoption of preventive maintenance programs developed by public works experts could also be a requirement of receiving federal aid. Leonard suggests the development of a maintenance schedule at the time of acquisition of a new capital facility. The financial require ments for maintenance would be a formal liabil ity recorded on a jurisdiction’s financial state ment. Reforms in this direction would help ensure that existing capital is better preserved and that large projected investments in new infrastructure are not wasted. Finally, future research in this area could include analysis on how the incentive effects described here for the local mass-transit industry apply to other forms of infrastructure. Using the standard optimal equipment replacement model in Cromwell (1988b), one would expect that the elasticity of optimal equipment life with respect to capital subsidies is larger for capital goods with shorter useful equipment lives, and larger for capital goods whose acquisition costs are large relative to maintenance costs. It would be interesting to examine the difference in magni tude of the distorting effects of federal subsidies for infrastructure with these characteristics. Furthermore, the distorting effects of capital subsidies are likely to be more severe when the deterioration of infrastructure is less visible— as in the case of sewers, water mains, or the under sides of bridges. Less visibility reduces the ability of voters or federal bureaucrats to monitor the condition of local infrastructure. Such monitor ing potentially acts as a check on the incentives to undermaintain that are introduced by capital subsidies. References American Public Works Association, “Good Practices in Public Works,” prepared for the National Council on Public Works Improve ment, August 1987. Archuleta, E., “Standardized Inventory and Con ditions Indexes for Water and Wastewater Facilities,” June 1986. APWA Reporter, Armour, R., “An Economic Analysis of Transit Bus Replacement,” 1980, 41-54. 6, Transit Journal, Amott, R., Davidson, R., and Pines, D., “Housing Quality, Maintenance, and Rehabilitation,” 1983, 467-94. Review of Economic Studies, 50, Bitros, G., “A Statistical Theory of Expenditures in Capital Maintenance and Repairs,” October 1976, 917-36. 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Carlson, E., “Put Your Bridge Money Where It’s Needed,” June 1986. APWA Reporter, America in Ruins: Beyond the Public Works Pork Barrel, Choate, Pat and Walter, Susan, Washington, D.C.: Council of State Planning Agencies, 1981. Cohen, L. and Noll, R., “The Electoral Connec tion to Intertemporal Policy Evaluation by a Legislator,” Stanford University, Center for Economic Policy Research, Publication No. 36, 1984. Public Works Infrastructure: Policy Considerations for the 1980s, Washington, D.C., 1983. Congressional Budget Office, Cromwell, Brian, (1988a) “The Impact of Fed eral Grants on Capital Maintenance in the Local Public Sector,” 8812, Federal Reserve Bank of Cleveland, November Working Paper 19 8 8 . ------ , Neary, Kevin, and Allen, Joan, “The Capital Investment and Maintenance Decision Process in the Public Sector,” prepared for the National Council on Public Works Improve ment, Washington D.C.: The Urban Institute, October 1986. Humphrey, Nancy, Peterson, G., and Wilson, Peter, Washington, D.C.: The Urban Institute, 1979. Plant, The Future of Cleveland’s Capital Jorgenson, Dale, McCall, John J., and Radnor, Roy, Chicago: Rand McNally, 1967. Optimal Replacement Policy, The Statisti cal Analysis of Failure Time Data, New York: Kalbfleisch, J. and Prentice, Ross L., John Wiley & Sons, Inc., 1980. Kaplan, E.L. and Meier, Paul, “Nonparametric Estimation from Incomplete Observations,” Journal of the American Statistical Associa tion, 1958, 53, 457-81. Katz, Lawrence, “Layoffs, Recall and the Dura tion of Unemployment,” No. 1825, January 1986. National Bureau of Economic Research Working Paper Lancaster, Tony, “Econometric Methods for the Duration of Unemployment,” July 1979, 939-56. Econometrica, 47, Checks Unbalanced: The Quiet Side of Public Spending, New York: Leonard, Herman B., Basic Books, Inc., 1986. Meyer, Bruce, “Semiparametric Estimation of Hazard Models,” mimeo, Northwestern Uni versity, 1 9 8 8 . 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Biometrics, 34, Sherif, Y. and Smith, M., “Optimal Maintenance Models for Systems Subject to Failure—A Review,” 1981 47-74. terly, Naval Research Logistics Quar ,32, Sweeney, J., “A Commodity Hierarchy Model of the Rental Housing Market,” 1974, 288-323. Urban Economics, 1, Journal oj Tye, William B., “The Economic Costs of the Urban Mass Transportation Capital Grant Pro gram,” Ph.D. thesis, Department of Econom ics, Harvard University, Cambridge, Mass., October 1969. Special Analysis D, Budget of the United States Government, Fiscal Year 1990, Washington, U.S. Office of Management and Budget, D.C.: U.S. Government Printing Office, January 1989. Urban Mass Transportation Administration, U.S. Department of Transportation, National Urban Mass Transportation Statistics, Section 15 Annual Report, Washington, D.C.: U.S. Government Printing Office, various years. Urban Mass Transportation Administration, U.S. Department of Transportation, Circular 9030. 1, June 1985. Urban Mass Transportation Administration, U.S. Department of Transportation, August 1986. A Directory of Urban Public Transportation Service, Vorst, A., “Optimal Housing Maintenance under Uncertainty,” March 1987, 209-27. Journal of Urban Economics, 21, Weingast, Barry R., Shepsle, Kenneth H., and Johnson, Christopher, “The Political Econ omy of Benefits and Costs,” August 1981, 642-64. cal Economy, Journal of Politi 89, Em ploym en t Distortions Under S tic ky W ages and M on e tary Policies to M in im ize Them by James G. Hoehn Jam es G. Hoehn is an economist at the Federal Reserve Bank of Cleve land. The author would like to thank Charles Carlstrom, Brian Cromwell, Randall Eberts, William Gavin, Anil Kashyap, and John Roberts for help ful discussions and comments on drafts of this paper. Introduction A major problem that monetary authorities must address is that contracts are made in nominal terms. During the contract interval, the terms may become inappropriate and cause misalloca tions if one of the parties has discretion over activity levels. The prototype case emphasized by macroecon omists is that of the labor contract, which may run for three years, during which the nominal wage is stuck, despite changes in the marginal productivity and disutility of labor caused by var ious events. Employers have some discretion over employment levels and can improve profits by adjusting employment in response to changes in the state of the economy. The profit-maximizing employment level will not, generally, be the same as the socially optimal level because the wage is stuck and does not perfectly reflect changes in the disutility of labor. An optimal monetary policy has the effect of tending to make the real wage match the marginal disutility of work in various states of the economy. This article explores how the money supply can be manipulated by the Federal Reserve to keep the real wage close to the marginal disutility of work in various states of the economy, and there by minimize social welfare losses associated with the employment distortions arising from sticky wages. The primary contribution of the analysis is to provide a social welfare metric defined in terms of the outcomes of an IS-LM Phillips Curve model. Simulations are run to compare the social loss under various monetary policies, including the one that is optimal in the model, as well as policies that target money, output, nominal income, and the price level. The simulations are not intended to encompass all possible struc tures of the economy, but instead are meant to suggest how various policies might compare under the assumptions of the model in meeting the social goal of labor-market efficiency. I. Employment Distortion Under Nominal Wage Contracts According to the basic neoclassical theory of wage determination, wages tend to be set at a level that reflects both productivity and disutility of work. If the nominal wage is set in advance, it will tend to be set at a level equal to the expected marginal revenue product of labor and the marginal disutility of work. Then, the real wage will be expected, on average, to clear the labor market, and employment will be at optimal levels (leaving aside issues related to monopoly power or other such sources of externalities, which are not essentially monetary problems because there is little the monetary authorities can do to ameliorate them). Once the nominal wage is set, unanticipated events can render that wage incorrect and cause misallocation. For example, if the demand for commodities rises beyond what was expected at the time contracts were signed, and if monetary policy keeps the money supply constant, the price level will rise, lowering the real wage under contracts. This reduction in the real wage will tend to cause an expansion of employment by profit-maximizing firms. In an extreme case of period-by-period profit-maximization, the expansion of employment would carry to the point at which the marginal product of labor falls to the lower real wage. This expansion of employment is socially inappropriate because the additional employment produces less value of output than the disutility of work it incurs. To take another example of how predeter mined wages can result in inefficiency, consider an autonomous cyclical labor productivity improvement. Further assume, for illustration, that as output supply increases, the price level is kept from falling by monetary expansion. The profit-maximizing firms expand employment in order to take advantage of the higher productivity, but will not face increasing unit labor costs if the contract calls for employees to supply all the labor the firm wants at a predetermined wage. Employ ment will overexpand because firms are not required to consider the rising disutility of work. Ideally, real wages should be regulated by pol icy so that they match the marginal disutility of work. In the case of an autonomous cyclical labor productivity shock, real wages should rise to keep pace with the rise in the disutility’ of work associated with higher employment. A monetary policy that tended to allow the price level to fall when autonomous increases in labor productivity occur could help real wages match the marginal disutility of work. Then, the employment level would still rise with productivity improvements, but not excessively so. One policy that tends to set up a negative relation between labor produc tivity shocks and the price level is a nominal income, or GNP, target. In simulations with a model, GNP targets are close to optimal in that people’s time tends to be allocated between labor and leisure in an appropriate way. II. A Simulation Model The simulation model combines the notion of sticky wages and the IS-LM demand apparatus with autonomous labor productivity shocks. Elsewhere, I have shown that a simpler (constant-velocity) version of the model can account for stylized facts, such as the natural-rate hypothesis and the mild procyclicity of real wages and productivity (see Hoehn [1988]), so long as forward-looking expectations guide nominal wage contractors. The IS-LM apparatus for representing intuitions about demand is pre ferred here over simple velocity equations, because the effects of monetary policy can be offset or enhanced by changes in velocity, and because IS-LM allows assessment of the informa tion policymakers can obtain from observations on the nominal interest rate. The model has three shocks: to money demand, to commodity demand, and to the marginal labor productivity schedule. These features provide a model con sistent with the stylized facts and containing util itarian welfare criteria for policy Relative to the standard macroeconomic m od els involving wage stickiness, four changes are offered to make a useful policy model. (i) Expectations of inflation and productivity are forward-looking (Muthian rational). (ii) Labor productivity is subject to autono mous cyclical variations (as well as to variations induced by shifts in commodity and labor demand). (iii) Employment is determined not strictly by demand, but is also influenced by supply. (iv) The information content of the interest rate is used by goods demanders and the central bank. To incorporate these features, the following model is offered. Supply Sector Following Fischer (1977), represent multiyear nominal wage bargaining with two-period stag gered, or overlapping, contracts. The model economy is composed of two groups of firms, identical in all respects, except for the date at which currently effective labor contracts were signed. Firms having signed wage contracts at the end of last period 1 ) are referred to as group one firms, while those that signed wage con tracts at the end of the period before last are referred to as group two firms. The groups are competitive in that they take the commodity price as given, and contract with workers to pay them their expected marginal revenue product. (t - (t-2 ) Economywide aggregates are simulated by tak ing the average of the two groups’ firms. The main difference between the determina tion of wages in the model here and that of other sticky-wage models is that contract wages here adjust completely and efficiently to informa tion available at the time of wage bargains. In some other models, such as that of Taylor (1979), wages can take longer than a contract interval to respond completely to events, and are subject to random variations conceived of as wage-setting errors. Taylor’s model can be justi fied as more realistic. However, the model used here is more consistent with microeconomic theory about the determination of wages and is consistent with the natural-rate hypothesis: the average level of employment is invariant with respect to the money supply rule. As in most sticky-wage models, variations in employment are those for a representative worker. Implicitly, employment variations are variations in hours worked among workers who each have jobs in all states of the economy. The model falls short of accounting for unemployment. The determination of employment and wages reflects both Keynesian and neoclassical ele ments. Hall (1980) and Barro (1977) have sought to reconcile the fact of sticky wages with the neoclassical theory of employment determi nation by arguing that sticky wages need not have any misallocational effects. Efficient con tracts, which could be implemented in the absence of transactions or enforcement costs, would involve optimal employment determina tion as productivity varied, so that sticky wages would have no allocational effects. Here, it is supposed that there are constraints on optimal contracts that prevent workers and firms from effecting optimal contracts. However, the tradi tional Keynesian assumption that employment is strictly demand-determined is softened. Instead, the employment reflects both the optimal level (the employment level associated with the inter section of demand and notional supply curves) and the demand for labor at prevailing prices and wages. This is simulated by an equation for employment that makes it a weighted average of both the optimal level and the notional demand. The weight attached to the demand can be con ceived of as the degree to which sticky wages have misallocational effects or, alternatively, the degree to which the problems of ideal contract enforcement are effective constraints. In order to derive this employment equation, first the notional labor demand is developed, then the notional labor supply is formulated, and then they are put together. Finally, the employ ment equation, in conjunction with the produc tion function and stochastic assumptions about productivity disturbances, implies a supply func tion, or Phillips Curve: a semireduced form equation for output supply as a function of the state of technology and unexpected inflation. Notional Labor Demand A firm’s production function is (1) Yit = UtN yit , 0 < < 1, 7 i= 1,2, Yit t, Nit U i where is the output of a firm in group in period is the labor input of a firm in group and is a global productivity shock. The marginal product of labor is i, Vty ( N „ y ^ ^ \ (2) «= 1,2. In logarithmic form, output is (3 ) y it = ut + y n it, i= 1 ,2 , u, n where the lowercase letters and are natu ral logarithms of their uppercase counterparts. The (log of the) marginal product of labor is (4) dY'. In i —aNjt — ) = ut + ln ( y ) - ( l- y ) n it, i= 1 ,2. i The notional demand for labor by firm in period d i t, is given by the condition that the real wage equals the marginal product of labor: t, n (5) ( wit- p t ) = ut + In ( y ) - ( \ - y ) n d it, i= 1 ,2, or (5 0 nf p, ) + ut+ In ( =— -— 1- 7 7 )], where wjt is the (log of the) wage received by group firms’ workers in period and is the (log of the) price level. i t, p Notional Labor Supply The notional supply of labor to a firm is condi tioned on the real wage rate: 1 (6 ) n% = 0 O+ jS j> /31(w it- p t ), , i = , . 0 1 2 Determination of Contract Wage Aggregate Commodity Supply If the labor market cleared each period, fully reflecting the taste and technology conditions underlying notional labor supply and demand, These elements are sufficient to specify the supply sector of the economy, under the assumption that labor input partly reflects the demand, and partly reflects the optimal level: n 1t= n it ’ t^ien employment level at firm i in period t would be (11) n it = <f>nft + (l-</>)«* . n*it = [p0+ (3xln (y)\M 0+ (3XM0 ut (7) where M0 = [1+0 ^1-y)] - 1 , n with * denoting the market-clearing employ ment level. If wages were not sticky, but varied to clear the market, they would be w*t = p,+ [In ( (8 ) 7 ) - (1 -y)f30\ M0 + M0ur The contractual wage rate is the expectation of the rate that would clear the labor market. The con tract wage for group is found by taking the expec tation of ( 8 ) conditioned on information available in period when the contract was signed. i The parameter </> represents the degree to which sticky wages cause misallocations, or employ ment distortions. Using (3), (5'), (7), (9), (10), and (11), it can be shown that the (log of the) output of group one is ( 12) y \ t= y A+ M 2et + M\P\t t~\ + A/]P j W /, _ 2 + G-^pf- Et _\pt }, where A = [J30+ J31In ( )]M0 1M0 M,: = + 7 t-i, 7 wit = Et i p t + [In ( + M0E,_i ut , (9) 7 ) - (1 -7 ) ^ 0 ] Mq Et i ut= p xu, _j + t t , 0 < p < l , e ~ N ( 0, cje2) M0 ) A/0( l- 4 > ) 7 1 1 - 7 - 7 and the output of group two is 03 ) y2,= 7 ^ + M2et + M2plet_ 1 + 1 M^p]ut_2 + Gx (pt - Et_2 p t ). Total output for the economy is taken as the average of and 2t: y Xt (14) 1 /8 1 t-i ut ■ 7 7 1 - where is the operator that conditions ran dom variables on realizations at and earlier. Note that, in this formulation, the nominal wage will generally be different in each of the two periods subject to the contract. Finally, let be a first-order autoregressive process, (1 0 ) ( 1 1 y y t= y A + M 2et+ + Mxp]ut_2 + Gq ^ (pt E^jpt^), i =1 The notional labor supply schedule could be derived from the primitive where utility function: c 0+ c , Yt - c 2Nct\ c, > 0, c 2 > 0, c 3 > 1, 2 (1 M. - + 0 7 M0 2 (l-7) 3 and the budget constraint: 7 M0) Yr (W ,IP ,)N r The first-order condition on N = is: Taking the natural logarithm and rearranging it, one obtains the labor supply function: n t = In wt -Pi7 [ c , / c 2 c 3 ] + ------------ ^— which is the same as equation (6) of the text for = 1/(c 3- 7 0 2(1 - 7 ) c 1 ( ^ / P , ) = c 2c 3 A /f3 ‘ 1). - ■ / } Q= In [c , Ic 2c 3] 1). (Thanks to Charles Carlstrom for this argument.) and Equation (14) provides a characterization of the supply sector of the economy. It shows that output depends on productivity variations and on unanticipated inflation, both with coefficients that depend uniquely on the elasticity of output with respect to labor input, y, the elasticity of notional labor supply, ,, and the degree of misallocation, <£. Higher values increase the responsiveness of output to productivity varia tions; the responsiveness of output to unantici pated inflation is proportional to </>. fi (31 Demand Sector The demand sector of the model is a variant of the familiar IS-LM apparatus, introduced in Hoehn (1987). The main innovation is that goods demanders are allowed to update their inflation expectations in light of the current nominal interest rate and to revise their assess ments of the real interest rate accordingly. Much complexity in solutions results from this innova tion. The innovation is necessary if the authori ty’s use of the information in the interest rate is to be studied without making the implausible assumption that the authorities know more (specifically, the current interest rate) than do other people. The innovation ensures that any influence monetary policy has over real variables does not arise from superior information.2 The commodity demand function, or IS curve, yf= b0 - bl[Rt- ( E \_ xp t+!-/>,)] + x t , bx> , (15) 0 xt= p2x t_ j + A,, < p 2< , k ~ N (0 ,o 2 K) (16) 0 1 where E t - \ Pt+ i = E [pt + | n j , 1 Clt = S observable state of economy at time t and = state vector (given a specific identity in the next section). The nominal interest rate, t , is measured as the natural logarithm of unity plus the coupon rate of return. The future price ■ 2 R The effect of allowing goods demanders to extract information about inflation from the nominal interest rate was analyzed extensively in Hoehn (1987). It can reverse the usual effects of money supply or demand shocks on the price level and output during the temporary period before shocks become fully known to all. For example, output and prices m ay temporarily rise in response to an increase in money demand. But such cases arise only in cases of extreme policies, such as crude attempts to smooth interest rates by expanding money greatly in response to a rise in the interest rate, or where structural parameters or relative variances of shocks take on extreme values. E)_ xp t+x expectation, , is conditioned on the observed state of the economy, t , an informa tion set that includes the current economywide interest rate, , and the lagged state vector, j . j can differ from + x be cause people use the current nominal interest rate to update their inflation expectations. is a stochastic demand shock. The money-demand function is conventional: St_ E +t_ Cl Rt Et_ xp t xt (17) m dt -p '= a0 - a xRt+ a 2y t + vt , (18) vt= p$)t_ x+ t\t i 0 < p 3< 1 , r)~ N (0 ,o 2), vt where is the log of the quantity of money and is a first-order autoregressive random disturbance. vt Policy Sector Given the model, a policy rule that is adequate for the policy targets and criteria to be consi dered, is (19) mf= qRt + n0 + iixut_ x + ^2^1- 1 + ^ 3 Xt - 1 + ^ 4 E [ - 2 Ut _ j • Harberger Welfare Metric The loss function measures a representative indi vidual’s frustration in obtaining an optimal alloca tion of time between labor and leisure, as pro ductivity and demand conditions change. The method, due to Harberger (1971), of measuring individual frustrations uses the labor supply and demand curves, assuming that they accurately reflect preferences and thereby show how workers and firms would want to adjust output and employment in response to changing pro ductive opportunities. Equilibrium between notional supply and demand is then supposed to be optimal. Equilibrium values of output and employment in this log-linear model are a strict log-linear function of , as shown in equation (7). The welfare loss is taken as proportional to the square of the deviation of the actual from the optimal employment level. This welfare-loss metric is proportional to the area of the familiar Harberger welfare-loss triangles, as shown in the figure of the next section. In the model with two staggered contracting firm groups, an approximate measure of the expected Harberger welfare loss over the span of a contract is ut F I G U R E Optional Employment Equates the Marginal Product of Labor With the Marginal Disutility of Work treatment of the simpler case in which the authorities know the full state and can change the money supply continuously to keep employ ment for both groups of firms at the ideal level. Readers interested in the final-form solution and the optimal policy rule in the full model may find them available in Hoehn (1989). The optimal employment level for each group, , is determined by the intersection of the marginal product of labor schedule, , and the labor supply or marginal disutility of work schedule, s, as shown in the figure. This employment level will be chosen by firms only if the real wage is equal to ( (This state ment holds true for any degree of misallocation, , except zero, in which case nominal wage stickiness cannot create employment distortion. The case illustrated here is the simple case of pure demand-determination of employment, </> = 1. O f course, the size of employment distor tions will be smaller if <^> is a fraction.) The optimal employment level and the real wage that will induce firms to choose the optimal employment level vary with autono mous labor productivity shocks. For example, a cyclical improvement in labor productivity raises the optimal employment level and the asso ciated real wage. The figure illustrates this with a shift in the marginal product of labor schedule from to , which raises the optimal employment level to This optimal level will be chosen by firms if the real wage rises to ( The productivity shock case reveals the suboptimality of a price-stabilization policy. Because nominal wages are fixed during the contract interval, stable prices imply that the real wage would remain at the initial level of ( Firms would choose the employment level j, at which the marginal product equals the unchanged real wage. The expansion of employment from * to is an excessive response to the improvement in productivity, because the marginal disutility of work exceeds the marginal product of labor for employment levels above The Harberger welfare loss tri angle is BAD. To prevent firms from overexpansion, the monetary authorities should allow the price level to fall by enough to raise the real wage to ( . Somewhat ironically, this policy will involve an expansion in the money supply. If the money stock were unchanged, the price level would fall too much as output rose. For exam ple, if the velocity of money were constant and the quantity of money were constant, then a productivity improvement would raise the mar ginal product of labor and— via deflation— raise n*0 Marginal 3roduct 3f labor MPL0 n w/p)*0 . Marginal disutility 3f work <p *eal wage Employment SOURCE: Author’s calculations. (20) E (n Xt- n*Xt)2 + E (n 2t- n*2t)2, Expected Welfare Loss = njt where the are actual employment levels and the are the market-clearing employment levels of equation (7). This measure is the sum of the variances of employment from optimal for each of the two periods of any contracting firm, during which it will first be a group-one firm, and then a group-two firm. n*it MPL0 MPL x u /p )\ . w/p)*0 . n n III. How Policy Can Minimize Employment Distortions To understand how a well-chosen policy rule can improve welfare, it is useful to examine the nature of the money-supply responses to various shocks that would fully prevent employment dis tortions. Such a degree of success is not possible in reality because of policymaker uncertainty about shocks. In the model simulations, it is assumed that the authorities know the structure of the economy, the current interest rate, and the lagged state of the economy; the authorities do not have full information about current shocks. This complicates analysis, motivating a heuristic n\. n\ u /p )\ nx □ (u /p ) the real wage by the same amount, to j, leaving the profit-maximizing level of employ ment at . The labor market is then at point in the figure, with welfare loss triangle EFA. The optimal policy response to the productivity shock is to expand the money supply enough to moderate the deflation, so that real wages rise to ( , but no further. The shift from point to point in response to the productivity improvement will always be obtained under a nominal income target, because that shift lowers the price level and raises the output level by the same proportion, leaving their product unchanged. In the simula tions with the IS-LM demand apparatus, the velocity of money falls with favorable productiv ity shocks. Consequently, the nominal income target will necessarily require increases in money to obtain point . If the increase in money is not forthcoming, as under a constant-money pol icy, the price level will fall more than one-forone with the productivity improvement, and the profit-maximizing employment level falls below . The welfare loss resulting from sticky wages under a productivity shift is greater under a con stant money policy than under the nominal income target, once velocity changes are accounted for. The optimal policy response to a commoditydemand or money-demand shock is easier to understand than the optimal response to a pro ductivity shock. In the model as specified, such shocks do not alter either the marginal product of labor schedule or the marginal disutility of work. Consequently, the optimal level of employment is unchanged. The optimal policy will attempt to prevent the employment level from changing with demand and money shocks. Employment can be insulated from distortions arising from such shocks by a policy that stabi lizes the price level. A stable price level prevents the real wage from changing, preventing firms from desiring a change in employment. Money supply should be decreased with increased commodity demand by an amount adequate to prevent inflation. Money supply should be increased one-for-one with increases in the money-demand function. A policy of output stabilization is unambigu ously worse than a policy of price stabilization. Both of these policies give an appropriate response to commodity-demand and moneydemand shocks, but the distortion concurrent with a productivity shock is unambiguously larger under the output stabilization policy. As soon as a single-minded output-stabilizing authority observes a productivity improvement, it will deflate the price level by reducing the F n*Q iv/p)\ E F n*0 F money supply The result is deflation sufficient to drive the real wage above ( , and employment declines below , say to The ability of the authority to stabilize output in this example is limited because recontracting firms can offset the real-wage effects of excessive deflation by lowering nominal wages. As soon as one of the groups recontracts, it will reduce wages to aim at an increased employment level, driving the authorities to further reduce employment in the second group via yet more deflation. The second group cannot protect itself against the negative employment distortions by recontracting for lower nominal wages until one more period passes and the old contract expires. The second group’s employment must be reduced, if output is to be stabilized, by enough to offset not only the economywide increase in productivity, but must also offset the increase in employment at the recontracting firms, who will rationally anticipate deflation and reduce wages to allow employment to increase to the optimal employment level. Because the loss function is the sum of squared group employment distor tions, the concentration of the employment dis tortion in the second group of firms leads to a sizeable welfare loss. u /p )x n*Q n- . IV. A Numerical Simulation In order to illustrate how various policy rules influence employment distortions arising from sticky wages, a simulation can be conducted with particular numerical values for structural parameters. The values chosen for this simula tion were the following: (2 1 ) /?1= 1/ 2 = 7 ax = a2 = 2 cj“ = 1 ct“ 1 / 2 2 /3 = 2 0 = bx = 1 1 a^= 5 p,= 4/5, i- , , . 1 2 3 The elasticity of labor supply with respect to the cyclical variations in the real wage was set at one-half, an arbitrary but plausible value. The elasticity of output with respect to labor input, 7 , was set at the midpoint of its permissible range, also arbitrary but plausible. The value assigned to the money demand elasticity with respect to the nominal interest rate, , implies, for example, that an increase in the rate from 5 to 6 percent would, for given levels of income and prices, lower real money demand by approximately 1.9 percent. The money-demand elasticity with respect to output, , was set at somewhat less than unity, as suggested by ax a2 T A B L E 1 Alternative Policy Rules ( 0 = 1 ) Policy Criterion Parameter2 q Mi Money Output Price Level Nominal Income Optimal 0.0 0.0 0.0 0.0 0.0 +1.06 -1.97 -2.44 +0.80 -0.05 +3.35 -1.56 +0.80 -0.84 +0.62 +0.48 +2.06 -1.98 +0.80 b a. The m oney supply rule is m( - qR{ + /Uj u( _ j + n2 x t - l + g oods supply, and m oney demand. b ^3 vt - 1 + ^4 ^ t - 2 ut - V where u, x, and v are disturbances to g ood s demand, b. The policy parameter ^4 is irrelevant to the criterion. In simulations, SOURCE: Author’s calculations. T A B L E +1.73 -2.10 +0.80 -0.04 ^4 is set to zero. 2 Response of Money to Innovations ( 0 = 1 ) Policy Criterion_________________________________ Innovation Money Output Price Level -0 . 1 1 -2.17 -1.81 +3.41 +2.05 +1.25 +0.98 +1.33 +1.06 +0.25 -1 . 6 0 -1.28 -0.01 - 1.60 -1.28 +0.15 - 1.60 -1.28 +0.12 - 1.60 -1.28 +0.31 +0.80 +0.64 -0 . 0 2 +0.80 +0.64 +0.19 +0.80 +0.64 +0.15 +0.80 +0.64 Productivity t t- 1 t-2 0 .0 0.0 0 .0 + 0.01 Nominal Income - 0.06 Optimal - 0.06 Goods Demand t tt-2 0.0 1 0 .0 0 .0 Money Demand t tt-2 0 .0 1 0 .0 0 .0 SOURCE: Author’s calculations. abstract analysis of the transactions demand for money. The commodity-demand elasticity with respect to the real interest rate, , was set to unity because, of all (equally arbitrary) values, unity is the most straightforward choice. (Econo metric evidence currently available does not provide direct knowledge of this elasticity.) The relative sizes of the disturbances give consider able scope to demand-side influences on output and employment, and allow for a relatively unstable money-demand function. In the basic simulation, firms were assumed to choose employment to equate the marginal prod uct of labor with the real wages, so </> = 1. In a second simulation, </> was set equal to one-third, in order to see whether the results of the basic bx simulation were robust with respect to this parameter. Five different policy rules were simulated, with their response coefficients chosen so as to target ( 1 ) money, ( 2 ) output, ( 3 ) the price level, (4) nominal income, or (5) optimal employ ment. The last of these is, of course, the only optimal policy by the criterion employed, but it is instructive to compare results of other poten tial targets. The policy rules’ response coefficients, and the '■, are displayed in table 1. The final-form solution for the money supply is determined by both these coefficients and the solution for the nominal interest rate (because of the term in the money supply rule), and is shown in table 2 q n qRt T A B L E 3 Welfare Losses Under Alternative Policies ( 0 = 1 ) Loss due to shocks to: ______________________________________ Policy Criterion Money Productivity7 Goods demand Money demand Output Price Level 6.91 4.52 14.99 3.04 0.24 1.80 1.96 1.28 14.29 18.27 5.04 2 .8 6 TOTAL LOSS Nominal Income Optimal 0 .6 6 0.19 2.35 0.76 3.51 3.30 0 .3 8 2.47 SOURCE: Author’s calculations. for each of the five alternative policies. In the immediate period of impact, the monetary authority’s response to a shock is equal to , its interest rate response coefficient, times the response of the interest rate to the shock. For example, under a policy of stabilizing output, the money supply is increased 1 . 0 6 for each onepoint change in the interest rate. A productivity shock in period reduces the interest rate by -0 . 1 0 (not shown in tables) under this policy rule, so the response of money at time M o a produc tivity shock in period is 1 . 0 6 times -0 .1 0 , or about -0 .1 1 . Only after one period has passed can the monetary authority observe all three shocks independently and tailor its response to each one separately. For example, the output-stabilizing policy contracts the money supply by 2.17 at time for a one-unit innovation to productivity in the previous period, This response reflects two channels: first, an indirect channel involving the change in the interest rate, -0.19, times the response coefficient = 1.06, or about -0.20. To this is added the direct response coef ficient on 1 productivity, = -1.97. Together, these add to -2.17, the total contraction of the money supply required to prevent period out put from responding to period - 1 productivity innovations. A similar calculation involving direct and indirect effects finds that the outputstabilizing policy contracts the money supply at time by 1.81 in response to a unit productivity innovation in period Aside from the constant-money policy, the pol icies considered are identical in their moneysupply responses to goods demand or money demand shocks, once these shocks are observed. In this model, all the activist targets are essentially equivalent in terms of the implied response of the money supply to these demand-side shocks. The main difference among the active moneysupply policies lies in the response of money to q t t t et_ x . q t- n] t t t-2 . -t productivity shocks. The output-stabilizing poli cy’s response is too restrictive; it contracts money at time by 2.17 after a unit productivity innovation in period 1 , contrasting with an optimal increase of 1.33. The price-stabilization rule responds too expansively; it expands the money supply by 3-41. The nominal income target’s response is to expand the money supply by 1.25, very close to optimal. These differences among alternative active policies in their response to productivity shocks account for the relative rankings of their efficiency. Expected welfare losses under alternative pol icies, shown in table 3 , are the sum of the mean squared deviations of group one and group two employment levels from optimal employment levels. Given the information constraint the authority faces, it can reduce this loss measure to 3.30 using the optimal policy. Most of this loss, 2.35, is attributable to goods-demand shocks occurring in the current period; a small fraction is attributable to productivity shocks occurring in the current period. Distortions due to shocks in period can be completely eliminated by policy responses, while distortions due to or earlier shocks are eliminated by wage recon tracting by both groups of firms. The nominal income targeting policy is close to optimal; its welfare loss is 3-51, only slightly higher than for the optimal policy. The outputstabilizing policy is far worse, with a total expected loss of 18.27, most of which is due to productivity shocks. The constant-money policy is not much better than the output-stabilizing policy; it generates substantial employment dis tortions in the face of goods-demand and money-demand shocks, which the activist poli cies make active efforts to prevent. Finally, the price-stabilization policy results in somewhat greater losses than the nominal income policy, but results in much smaller losses than the out put or money targeting policies. t t-l t- t-2 Response of (nzt - n*2 t) to Innovations ( 0 = 1) Policy Criterion Innovation Money Output Price Level Nominal Income Optimal -0.28 -1.64 -0.34 -3-84 -0.28 +1.28 0.0 -0.32 -0.42 0.0 -0.30 +0.70 0.0 +0.78 +0.76 0.0 0.0 0.36 0.0 -0.26 -0.28 Productivity t tt-2 1 0.0 0.0 0.0 0.0 Goods Demand t tt - +0.70 +1.58 1 +0.88 0.0 0.0 2 0.0 0.0 0.0 0.0 Money Demand t tt- - 0.38 - -0.80 0.0 1 2 0.16 0.0 0.0 - 0.0 0.0 0.0 0.0 0.0 SOURCE: Author’s calculations. T A B L E 5 Welfare Losses Under Alternative Policies With 0 = 1 / 3 Loss due to shocks to: ______________________________________ Policy Criterion Output Money Price Level Productivity Goods demand Money demand 0.51 1.37 0.83 0 .6 0 TOTAL LOSS 2.72 Nominal Income Optimal 0.05 0.54 0.04 0.54 0.14 0.44 0.32 0 .2 2 0 .2 2 1.78 0.98 0.80 0.79 1.03 0 .2 1 SOURCE: Author’s calculations. The deviations of employment from optimal for the two groups can be read from table 4. The table lists the deviations for the second group; the deviations for the first group, ( \,), are the same as for the second group for period ? shocks, but recontracting by this group makes the period - t employment distortion equal to zero for t 1 or earlier shocks. A one-unit inno vation in productivity at time t raises the optimal employment level for both groups by 0.40 in time Given that the effect of an innovation on the marginal productivity schedule decays at the rate = .8 , optimal employment increases by 0 . 3 2 and by about 0.26 in response to unit pro ductivity innovations in periods t - 1 and t - 2 . The gross suboptimality of the output- nxt - n - t. px stabilizing policy reflects the employment distor tion in the second, nonrecontracting, group, in response to a productivity innovation in period Because policy responds by contracting the money supply, generating deflation and an excessive rise in the real wage for the nonrecon tracting group, employment for that group falls by 3 52, in sharp contrast with the increase of 0.32 in optimal employment. The distortion is then -3.84. In order to keep output fixed, the authorities must reduce employment in the second group, and this reduction must be enough to offset both the economywide produc tivity improvement and the rise in employment by 0 . 3 2 in the first, recontracting, group. The GNP targeting policy is very close to t-1 . T A B L E 6 Relation Between Money and Output Under Alternative Policies (0=1) Policy Criterion Covariation due to shocks to-. Productivity Goods demand Money demand CORRELATION Money 0 .0 0 .0 0 .0 Output Price Level Nominal Income Optimal -1.51 +0 . 2 2 -1.95 +8.76 -0 . 0 1 +0 . 0 2 +3 . 1 0 +0 . 1 2 -0 . 1 2 +3.48 +0.09 -0 . 1 1 -0.30 +0.59 +0.30 +0.34 SOURCE: Author’s calculations. optimal. It handles money-demand and commodity-demand variations appropriately, and generates a mild and nearly optimal deflation in response to productivity improvements. The degree of closeness to optimality depends on various parameters, but is not, it appears, sensi tive to the degree to which sticky wages cause misallocations, 0 , at least at the chosen values of the other structural parameters. Table 5 shows the welfare losses in the model for </> = 1 / 3 . The output targeting policy is generally the worse in terms of employment distortion (except when 0 = 1 / 3 , when the constantmoney policy is worse). The output targeting policy generates the greatest losses when pro ductivity shocks occur. Output targets handle commodity- and money-demand shocks, how ever, in an appropriate manner. The price-stabilization policy results in over employment when a productivity improvement occurs. The policy is too stimulative; it does not provide for the deflation required to raise the real wage in line with marginal productivity at the new optimal employment level. In the case of commodity- and money-demand shocks, however, a policy of price stabilization provides essentially the same optimal response as does the nominal and real GNP targets. The constant-money policy accrues losses in the case of all kinds of shocks. The loss attend ing productivity shocks is less than in the case of the output target, but the money-targeting policy fails to respond appropriately to commodity- or money-demand shocks. In the simulation, the constant-money policy results in less employ ment distortion than the output-stabilizing pol icy, unless the degree of misallocation is small, such as 0 = 1 / 3 . V. Conclusion A monetary policy that seeks to aid wage con tractors in avoiding employment distortions due to sticky wages will attempt to keep the real wage equal to the marginal disutility of labor in all states of the economy. Such a policy will require money supply expansion when cyclical improvements in labor productivity occur. To the extent that productivity variations are an important factor in the business cycle, the optimal money supply rule will involve a posi tive correlation between money and output. (See table 6 .) Hence, the belief, common among economists, that sticky-wage models argue for a countercyclical or output-stabilizing policy is not necessarily correct, once productivity shocks are taken account of. In simulations, it was found that a nominal income target might be reasonably close to the optimal policy. This result is useful because the Federal Reserve may not be able to predict and target optimal employment levels because of uncertainty about the structural parameters and shock variances needed in a welfare analysis, yet can probably predict and target nominal income using its models and judgmental forecasters. After all, the main objective of macroeconomet ric models has been the prediction and potential control of national income. The analysis of this paper tends to give additional justification to proposals for nominal income targeting, includ ing those by Meade (1978), Tobin (1980), Hall (1983), Gordon (1985), and McCallum (1987). The relative near-optimality of a nominal income target might not be robust to all con ceivable values of the labor market parameters, 7 and however. For example, if the marginal product of labor curve declines steeply ( 7 close to zero), and/or if the notional labor supply curve is nearly horizontal ( / very large), then a price target will do as well or better than a nom inal income target. More precisely, if [l + /3j(l - 7 )] _ 1 is close to unity, then a nominal income target will be close to optimal, but if is close to zero, then a price level target will be close to optimal.3 In the simula tion, 7 = 1/2 and = 1/2, so .8 , which is rather close to unity. In order to adequately con firm the relative efficiency of a nominal income target relative to a price target, econometric evi dence and a sensitivity analysis are needed to rule out small values of In general, the optimal policy response to a productivity improvement will be one that is less stimulative than that implied by a price target and more stim ulative than that implied by a nominal income target. If the specification of the model were modi fied to allow for costs of changing commodity prices ( “menu costs”), or to allow for some degree of commodity price stickiness, then a price-targeting policy might yet be better than a nominal income target. Many other elements of more detailed macroeconometric models have unknown implications for the welfare analysis. Much more research along these lines is needed for an adequate welfare analysis of monetary pol icy toward the business cycle. M0= Exogenous Variables e \ u innovation to the productivity disturbance, innovation to the commodity-demand dis turbance, x innovation to the money-demand distur bance, 77 v M0 /3{ M0 = State Vector = r?,, M0 . Glossary of Variables and Parameters Endogenous Variables y y\ y2 p R m w w* n n\ n2* n ■3 output output of group 1 firms output of group 2 firms price level nominal interest rate money stock wage rate market-clearing wage rate employment employment of group 1 firms employment of group 2 firms optimal employment level Bean (1983) apparently was the first to note this. u t -1 ’ E t - 2 u t -1 ’ ’ X t -1 >E t - 2 X t -1 > v,_x , Et_2vt_l } Information Set, or Observed State ^ ’ ^t -1 ’ E t - 2 v t-\ E t -2 -1 ’ X t -1 ’ E l - 2 X t -1 ’ ^7-1 ’ ) Parameters All nonpolicy parameters are nonnegative. <2 , = elasticity of money demand with respect to interest rate = ( (1 + ) = elasticity of money demand with respect to output = elasticity of aggregate demand with respect to real interest rate j3j = elasticity of notional labor supply with respect to real wage 7 = elasticity of output with respect to labor input coefficient of money-supply response to interest rate = coefficients of money-supply response to lagged state variables (see equation 19 of the text) cb din M/P ) /din R bx q- Hi at = 2 ax = av = variance of productivity innovation variance of commodity-demand innovation variance of money-demand innovation References Barro, Robert J., “Long-Term Contracts, Sticky Prices and Monetary Policy,” July 1977, 305-16. Journal of Mone 3, tary Economics, Bean, Charles R , “Targeting Nominal Income: An Appraisal,” December 1983, 93, Economic Journal, 806-19. Fischer, Stanley, “Long-Term Contracts, Rational Expectations, and the Optimal Money Supply Rule,” February 1977, 191-205. Journal of Political Economy, 85, Gordon, Robert J., “The Conduct of Domestic Monetary Policy,” in Albert Ando, Hidekazu Eguchi, Roger Farmer, and Yoshio Suzuki, eds., Cam bridge, Mass.: The MIT Press, 1985, 45-81. Monetary’Policy in Our Times, Hall, Robert, “Employment Fluctuations and Wage Rigidity.” Washington, D.C.: The Brook ings Institution, 1980. Brookings Papers on Eco nomic Activity, ________ , “Macroeconomic Policy under Struc tural Change,” Federal Reserve Bank of Kansas City, 1983, 102-3. Policy, Industrial Change and Public Harberger, Arthur C., “Three Basic Postulates for Applied Welfare Economics: An Interpretive Essay,” Journal o f Economic Literature, Sep tember 1971, 785-97. 9, Hoehn, James G., “Monetary Policy Under Rational Expectations With Multiperiod Wage Stickiness and an Economy-Wide Credit Market,” 8716, Federal Reserve Bank of Cleveland, December 1987. Working Paper ________, “Procyclical Real Wages Under Nominal-Wage Contracts with Productivity Variations,” Federal Reserve Bank of Cleveland, 1988 Quarter 4, 11-23. Economic Review, 24, ________, “A Welfare Analysis of Monetary Policy with Nominal Wage Contracts and Demand and Productivity Shocks,” Federal Reserve Bank of Cleveland, unpublished working paper, available from the Bank on request (1989). McCallum, Bennett T., “The Case for Rules in the Conduct of Monetary Policy,” 1987, 415-29. shaftliches Archiv, 123, Weltwirt- Meade, J.E., “The Meaning of Internal Balance,” September 1978, 423-35. Economic Journal, 88, Taylor, John B., “Staggered Wage Setting in a Macro Model,” May 1979, 108-13. American Economic Review: Papers and Proceedings, Tobin, James, “Stabilization Policy Ten Years After.” Washington, D.C: The Brookings Institution, 1980, 19-72. Brookings Papers on Economic Activity, 1, Recent Developments in Macroeconomics Conference Proceedings Offered T h e p a p e rs in th is s p e c ia l is s u e o f th e Credit, and B anking Jo u rn a l o f Money, w e re p re s e n te d a n d d is c u s s e d a t a c o n fe re n c e o n “ R e c e n t D e v e lo p m e n t s in M a c r o e c o n o m ic s ” h e ld a t t h e F e d e r a l R e s e r v e B a n k o f C le v e la n d . T h is c o n fe r e n c e w a s o r g a n ize d to d is c u s s th e p ra c tic a l a s p e c ts o f re c e n t d e v e lo p m e n ts in m a c ro e c o n o m ic re s e a rc h a n d t o d is c u s s th e re le v a n c e o f th e s e d e v e lo p m e n ts fo r e c o n o m ic p o lic y . Uses Contents ■ Identification of Current Issues ■ Classroom Assignments ■ Literature Review ■ Recent Developments in Macroeconomics: A Very Quick Refresher Course ■ Postwar Developments in Business Cycle Theory: A Moderately Classical Perspective N. Gregory Mankiw Comment by Herbert Stein Comment by Edmund Phelps Bennett T. McCallum Comment by Lawrence Summers Comment by Peter K. Clark ■ Some Recent Developments in Labor Economics and Their Implications for Macroeconomics ■ On the Roles of International Financial Markets and Their Rele vance for Economic Policy Lawrence F. Katz Comment by Robert Topel Comment by Thomas Kniesner Alan C. Stockman Comment by Patrick Kehoe Comment by J. David Germany F o r a lim ited tim e , yo u m a y order a c o p y of th e co nference p ro cee d ings a t the reduced price of $ 5 .0 0 (re g u la rly $ 1 0 .0 0 ) . C o n sid e r bu lk ■ What Microeconomics Teaches Us About the Dynamic Macro Effects of Fiscal Policy Laurence J. 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