The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
Working Paper Series Liquidity Effects and Transactions Technologies WP 93-01 Michael Dotsey Federal Reserve Bank of Richmond Peter Ireland Federal Reserve Bank of Richmond This paper can be downloaded without charge from: http://www.richmondfed.org/publications/ This is a preprint of an article published in The Journal of Money, Credit, and Banking, v. 27, iss. 4, pp. 1441-58, copyright 1995 by the Ohio State University Press. All rights reserved. Reprinted with permission. Working Paper 93-1 LIQUIDITY EFFECTS AND TRANSACTIONS TECHNOLOGIES Michael Dotsey* and Peter Ire1 and* Research Department Federal Reserve Bank of Richmond February 1993 *We would like to thank Mary Finn, Robert King, Kevin Reffett, Alan Stockman, and seminar participants at Duke and Virginia Tech for helpful suggestions. We would also like to thank Stephen Stanley for research assistance. The views expressed here are solely those of the authors and do not necessarily represent those of the Federal Reserve Bank of Richmond or the Federal Reserve System. 1. Introduction Recently there has been renewed interest in using general equilibrium models to understand the effects of monetary policy on interest rates and real economic activity. This research effort has involved the search for models that will account for the liquidity effects--the decrease in short-term interest rates and the increase in output and employment-that are associated with expansionary monetary policy. liquidity effects have been isolated by Cochrane (1989), Christian0 and Eichenbaum (1991b), Empirically, Strongin (1991), and Gordon and Leeper (1992). More informally, financial market participants usually interpret Federal Reserve engineered rises in short-term nominal interest rates as a tightening of monetary policy. The theoretical impetus for this literature is found in Lucas (1990). No two papers use the exact same specification, but a common feature of the literature is the presence of cash-in-advance (CIA) constraints that limit the amount of money available for use in loan or securities markets.' Each change in specification involves various assumptions about financial structure that place infinite transactions costs on flows of funds across segmented markets. differences Most frequently, the in specification are motivated by the emphasis of the particular model: whether it is primarily concerned with asset pricing or with generating business cycles. In fact, the assumption of infinite transactions costs across markets is most reasonable when applied to understanding the behavior of 'For various examples see Fuerst (1992), Christian0 (1991), Christian0 and Eichenbaum (1991b, 1992), Coleman, Gilles, and Labadie (1992), Schlagenhauf and Wrase (1992). -2asset prices on a daily or weekly basis. To study the effects of monetary policy at business cycle frequencies, however, assumptions of infinite transactions costs are less innocuous. In this paper we consider the effects of relaxing these extreme assumptions in the monetary business cycle model of Christian0 and Eichenbaum (1991b).2 generalizing portfolios We do this by their CIA constraints, allowing agents to rearrange their at a finite cost after observing the monetary disturbance. Given the quarterly periodicity of the model, it seems realistic that agents have access to such a transactions technology. Our ultimate goal is to study the interaction between the magnitude of the transactions costs and the presence of liquidity effects on a quarterly basis. The CIA constraints in Christian0 and Eichenbaum's model give rise to one of the model's principal implications, that "a disproportionately large share of monetary injections is absorbed by firms to finance variable inputs" (Christian0 and Eichenbaum 1992, p.352). In the absence of detailed flow-of-funds data with which to test this implication, our generalized illuminates an alternative, Specifically, version of the Christiano-Eichenbaum but closely related, model implication. our transactions technology gives rise to a spread between loan and deposit rates that varies systematically with the size of the monetary shock. In essence, our framework reveals that prices (i.e., interest rates), rather than quantities (i.e., flows of funds), can be used to assess the empirical relevance of the Christiano-Eichenbaum fact, we find that specifications model. In for transactions costs that allow the 2We choose the Christiano-Eichenbaum model as a starting point because it is the most developed and successful in this class of models. - 5 - model to match the behavior of key interest rate spreads either remove or greatly dampen the liquidity effects that are present in Christian0 and Eichenbaum's original work. The next section briefly reviews Christian0 and Eichenbaum's model. Section 3 generalizes this model, as suggested above, by allowing agents more flexibility to adjust their financial portfolios in response to monetary disturbances. parameterization Section 4 describes the solution and of our generalized model, while section 5 presents the results and section 6 concludes. 2. The Christiano-Eichenbaum Model Here we briefly sketch out the main features of the Christian0 and Eichenbaum model. justification Each period is broken into two parts--the being that production requires a sustained flow of labor input and that open market operations occur in the midst of ongoing productive activity. The division of the period into two parts is a tractable way of representing such an environment. During the first part of the period, following the realization of the technology shock but prior to the realization of the monetary shock, households allocate their portfolios between a transactions medium and the liability of a financial intermediary. part- of-period labor effort. They also decide on their first- To finance their wage bill, firms decide how much to borrow from intermediaries at a first-part-of-period interest rate. They also decide how much to invest. nominal In this model, -4payments to labor are subject to a cash-in-advance constraint while investment is a credit good. In the middle of the period, a monetary disturbance the form of a lump-sum transfer to intermediaries. then make their second-part-of-period occurs in Households and firms labor decisions, with firms borrowing their wage payments from intermediaries at a second-part-of-period rate. interest Households make their consumption decisions subject to a cash-in- advance constraint that involves not only their initial holdings of the medium of exchange but their current period wage receipts as well. The liquidity effect arises because the lump sum transfer affects the quantity of loanable funds. decisions, It is augmented by the fact that certain production namely initial labor hours, are state variables from the perspective of second-part-of-period of the economic environment a. decisions. A more formal description follows. u t 1 The firm's oroblem The firm's problem is to maxim ize E f /3t" CrtqFt~fl~ where F, P t+1 t=o is the flow of nominal profits, u,,,,,is the representative marginal utility of consumption at time ttl, time ttl, and the information set @ disturbances dated t-l agent's Pt+, is the price level at includes all variables and and earlier as well as the first-part-of-period rate Wit, the first-part-of-period wage loan rate Rlt, the capital stock Kt+,, -5the technology shock z,, and the first-part-of-period The firm performs this maximization subject to (1) F,= Pt[fW,,z,H,)-K,+,l - R,,N,, - (2) z, = exp(/.W8,) (3) 0, = (hp (4) W&t 5 Nl, (5) W&t s N,, (6) Kt+, = I, t (l-6)K, (7) H, = [(1/2)Hlt1'Pt (l/2)H2t1'P]P + I&, hours worked H,,. R&t + w2t-ww + (N,t-W2tH2t) + f& where f(K,,z,H,) describes output as a function of capital, labor, and the technology shock, N,, and NZt are the amounts of funds borrowed to finance wage payments, and H, gives the effective amount of labor, which depends on both first and second-part-of-period second-part-of-period hours. Thus, the marginal product of labor depends on H,,. The technology innovation cot is normally distributed with mean zero and standard deviation ug. Based on 0: (i.e., prior to the monetary disturbance X,) the firm chooses H,,, Nit, and Kt+,. After observing X, and all other variables -6dated t and earlier, the firm chooses H,, and N,,. Thus, the information set 0: contains all variables dated t and earlier. b. The intermediary's problem The financial intermediary accepts deposits B, from households and makes loans N,, and NZt to firms. It also receives a lump sum transfer of X, dollars halfway through the period. subject to (8) D, = (9) N,, w-4 + N2t t + s Bt R2tN2t + - R;B, t (B,tX,-N,,-N2J xt by choosing N,, and B, based on the information set @ information contained in Cl:. In equilibrium, and N,, based on intermediaries also face a zero profit condition with respect to funds received from households (10) R:‘B, = R,,N,, + R2tU$,-X,) - The deposit rate Rt is determined after the realization of the monetary shock. C. The household's oroblem - 7 The household maximizes discounted expected lifetime utility E '& flt[u(Ct,J,)I&], where C, is consumption and J, is leisure, subject to (11) 3, = 1 - L,, - L,, (12) P,C, 5 M, (13) I$+, I R:B, + D, + F, + (Mt-Bt+W,tL,t+W2tL2t-PtCt) - Bt + WItLIt + W2tL2t where L,, is first-part-of-period labor supply, L,, is second-part-of-period labor supply, and M, is money holdings. The household chooses L,, and B, based on information in n: (i.e., before seeing the contemporaneous money shock). Recall that Rt does not belong to f$. In the second part of the period, L,,, C,, and M,,, are chosen. d. Eauilibrium The model is closed with a description of the money supply process; it is governed by (14) x, = (X,/M,) = (Mt+,-Mt)/“‘t (15) x, = u-PJX + Ppt-1 + E,t -8where the monetary innovation E,, is normally distributed with mean zero and standard deviation CJ,. An equilibrium for this economy can now be defined as a set of prices and quantities such that (i) firms, households, and intermediaries are all optimizing and (ii) markets clear. Market clearing in the loan, labor, and goods markets is implied by the conditions (16) N,, t N,, = (17) Ljt = Hjt W C, + Kt+, = B, t X, j=1,2 f(K,,z,H,) t (14)K,. With this economic environment, Christian0 and Eichenbaum (1991b) are able to generate liquidity effects, although these effects lack the required persistence. Given their interpretation of the period length as one quarter, it seems natural to question the complete inability of economic agents to alter their portfolios in response to economic disturbances. Modern financial markets certainly offer a multitude of ways for easily and quickly transferring funds.3 In the next section, therefore, we investigate the effects of embedding a costly transactions technology into this model. 3The lack of significant welfare costs due to inflation in many of these models is used as a justification for ignoring transaction technologies. We do not find this argument persuasive since it may still be in an agent's interest to exercise portfolio rearrangement. This decision depends on marginal conditions not overall welfare considerations. -93. Transactions Costs Model Our transactions technology allows agents to deposit or withdraw additional funds after observing the monetary disturbance. requires us to distinguish between first-part-of-period are made costlessly, and second-part-of-period This deposits Bit, which deposits Bzt, which require the use of a costly transactions technology. As in the Christian0 and Eichenbaum model, the household divides its money holdings M, between savings deposits B,, and cash M,-B,,. The initial deposits earn Rt, injection. a rate that is determined after the monetary Upon observing X,, the household can transfer funds between its savings account and cash. The dollar value of this transfer, Btt, earns Rd2t; its value can be positive (a deposit) or negative (a withdrawal). In order to make a transfer, the household must expend an amount of time given by T,(S,d,/M,),where T, is convex, continuously differentiable, satisfies T,(O)=O. and Note that transactions costs are specified here as functions of the fraction of the total money supply that is moved. In this sense, these resource costs are invariant to changes in the nominal unit of account. One interpretation of the convex transactions cost function T, in our representative over heterogeneous agent model is that it is obtained by aggregating agents , each of whom faces a different fixed cost of - 10 performing cash management proximities to a bank). activities (induced, perhaps, by different Agents with the lowest fixed cost are the first to adjust their deposits when interest rates change, while those with the highest costs require substantial interest rate movements before engaging in cash management. In the aggregate, total cash management costs are smooth and convex. Intermediaries their portfolio. also incur transactions costs when altering Following the realization of X,, there will be a change in the demand for loans, and intermediaries can respond by altering their supply of savings accounts, f3.Jt.This can be done at a cost T,(B,s,/M,), where T, is also convex, continuously differentiable, T,(O)=O. Specifically, and satisfies intermediaries must hire T,(B:JM,) units of labor at a wage rate of W,, in order to alter the level of intermediation. the household's cost function T,, the representative intermediary's function T, can be interpreted as an aggregate over heterogenous institutions, Like cost financial each of which faces a different fixed cost of altering its portfolio. Incorporating these changes into the Christian0 and Eichenbaum model requires the following modifications. equations (8’ In the intermediary's problem, (8) and (9) are replaced with 1 Dt = R,,N,, + R&t - R-h t - R,d,B,s, + (B,, + B;t + xt - N,, - N2t - w,,T,(B,s,/M,)) - 11 - Pa’> N,, 5 B,, Equation (8') takes into account the effect of the wage payments W,,T,(B,S,/M,) Equations (9a') and (9b') reflect the balance on dividends. The zero-profit condition for the sheet constraints on loans. intermediary's first-part-of-period (lo’) deposit activity becomes B,,Rld, = N,,R,, + (B,,$,)R,,. For the household, equations (ll)-(13) become (11’) J, = 1 - L,, - L,, - L,, - T,(B;&) (12’) P&t I Nt - B,,- s,d, + W,,L,, + M2tL2t + J+‘3tL3t (13’) N,+, I R:‘,B,, + U’f, + &s,d, - B,, - + Dt + Ft Bit + W,, + W2, + M&t - Ptct) l - 12 The household now has two additional uses of its time, the labor L,, supplied to intermediaries part-of-period and the cost T,(B$M,) of performing second- transactions. An equilibrium for the economy is defined, as before, as a set of prices and quantities such that (i) firms, households, and intermediaries conditions (16’) are optimizing and (ii) markets clear. are now given by equations The market clearing (17), (18), and N,,+ N2t+ W,,T&,/NJ = B,,+ Bzt+ Xt (19) L3t= TJB,,/f$) (20) BZdt = Bzst = B,, Equation (16') implies equilibrium for labor market clearing. for second-part-of-period 4. in loan markets. Equation (19) provides Equation (20) is the market clearing condition deposits. Solution and Parameterization a. Solution For the transactions costs economy, the first order conditions of the firm, intermediary, and household as well as the market clearing - 13 conditions form a system of 19 nonlinear equations in 19 unknowns that completely describes the behavior of equilibrium prices and quantities. The 19 equations can be reduced to a 5-equation system as outlined in the appendix. Fourteen of the equations are used to obtain expressions for the 14 unknowns R2t* C,, Nit, N2t, H2t, Lit, L2t, L3t, P,, W2t, W,,, R,d,, R,d,, Rltl and When these expressions are substituted into the remaining 5 equations, we are able to solve for Bit, B2t, Hit, Kt+,, and W,,. These 5 equations are depicted by (21)-(25) where for ease of exposition we have refrained from substituting out R,:, +=Pt - +&+,P,+, t+1 Ujt - Unto 1 n: t F t 1 n: t+2 1 = 0 1 - !!!+p, 1 0; = 0 t+1 , R,d,, 1 = 0 Rlt, and R2t: - 14 - +(R,,d2J I 0; t+1 where fkt ’ u,, and Ujt = 0, 1 are the marginal utilities of consumption 51, ' and fH$ and leisure and are the marginal products of capital, first-part-of- period labor, and second-part-of-period labor. Equation (21) is the firm's first order condition for capital. It reveals that the firm balances the benefits from (i) paying an extra dollar in dividends at time t and (ii) using the extra dollar to buy capital at time t, thereby producing and selling additional output in period ttl, and using the proceeds to pay a higher dividend in period ttl. Equation (22) describes the household's first-part-of-period labor supply. It indicates that the household equates the marginal utility of an extra unit of leisure to the marginal utility of an extra unit of real wages. Equations (23) and (24) are the first order conditions for the household's deposit decisions. They show that in each sub-period, the household balances the utility cost of lower consumption against the utility gain from higher consumption on second-part-of-period in period t in period ttl. The return deposits is adjusted to take into account the - 15 marginal transactions costs T,/cB2,/M,). Finally, equation (25) describes how the intermediary acts so as to equalize its expected rate of return on first-part-of-period and second-part-of-period loans. It is not possible to obtain exact solutions to the system (21)-(25). Thus, we follow Christian0 and Eichenbaum (1991b) numerical methods to construct an approximate solution. in using The five-equation system is linearized and solved by the method of undetermined coefficients described by Christian0 (1991) and Christian0 and Eichenbaum (1991a). To apply numerical methods, preferences and technologies are specialized to No<$<l, ##O $4 =o = K;(ztHt)'-=t (l-S)K, f(K,,z,H,) TJB2,/M) = a,(B2,/MJ2 T&,/M) = a,W2,/MJ2. The functional forms for U and f are exactly those used by Christian0 and Eichenbaum (1991b). The quadratic functional form for T, and T, is a - 16 simple one that satisfies the requirements that costs are convex with Ti(O)=O for i=H and i=B. b. Parameterization We use the same parameter values to describe tastes, technology, (1991b) and the money supply process that Christian0 and Eichenbaum choose by comparing the model's steady figures from the US time series data. state These values are fl=(l.03)-".25,$=O, y=O.761, a=0.346, 6=0.0212, /~=0.0041, 8=1, p=10/9, x=0.0119, pX=0.81, implications to p,=O.9857, ae=0.01369, and a,=0.0041. The critical parameters for our results are those of the transactions technologies. The intermediary's first order condition for its optimal supply of second-part-of-period (26) Rzt$T/(s2,,flt) t = 2q,R~t~(B2t,Nt) t deposits is = Rzt - R,d,. This first order condition links the intermediary's transactions parameter a, to the behavior of the loan-deposit In our model, second-part-of-period interest rate spread. deposits are the intermediary's marginal source of funds from the non-financial Similarly, second-part-of-period funds from the financial sector. cost sector. loans are the firm's marginal source of Natural analogs to the deposit rate R$ and the loan rate R,, in the US economy, therefore, are the rate on small - 17 time deposits (which consist mostly of small CD's) and the commerical paper rate. Since the monetary shock sXt is distributed symmetrically about zero and since the quadratic transactions costs function is symmetric about zero, equation (26) indicates that the loan-deposit rate spread will be approximately zero on average in the model. This contrasts with the US data, where the commerical paper rate-small CD rate has been positive on average since CD rates were deregulated in 1984. Thus, it is not possible to choose the parameter a, to match the average interest rate spread from the data.4 It is possible, however, to choose a, to match the standard deviation of the spread, equal to 0.000838, that is in US quarterly data, 1984:1-1992:3. This is the approach that we take. Ideally, the household's transactions cost parameter a, could be chosen based on the household's first order condition for Btt, given above by equation (24). (27) 2a+(B,,,NJ t = flE In fact, equation (24) implies that +- R2”t 1 Q: t+1 which is t+l 1 - 1, 4The positive average spread found in the data could be matched by the model simply by assuming that the intermediary faces constant marginal costs associated with making loans or accepting deposits. Adding this assumption to the model would not change its implications for the presence or absence of liquidity effects, and we would still require the standard deviation of the loan-deposit spread to parameterize the cost function 1,. - 18 which shows how the presence of transactions costs alters the standard consumption-based asset-pricing Euler equation. Again, the symmetry of the of E,, and the function T, imply that the left-hand-side distribution (27) will be approximately zero on average in the model economy. of Hence a" cannot be chosen to match the sample average of jI(C,/C,+,)(P,/P,+,)R$-1 the US data, which is negative using quaterly figures from 1984:l 1992:3. from through Moreover, since the standard deviation of the conditional expectation on the right-hand-side of (27) cannot be easily estimated using US data, a" cannot be chosen to match a sample standard deviation either. Thus, in the absence of observable data with which to choose a", it is simply assumed that the household's transactions multiple of the intermediary's costs, so that a,=Xa,. reduces the problem of parameterizing costs are some This strategy transactions costs to one of choosing a value for a, to match the standard deviation of the commerical papersmall CD rate spread found in the US data, for any given value of X. Below, we present results for a wide range of values for the free paramter A. 5. Results Insight into the complicated mechanism by which monetary surprises affect real activity in the model can be gained by examining Table 1, which describes the contemporaneous unanticipated (a,=a,=O). response of our economy to an doubling of the money supply when transactions costs are zero With zero transactions costs, the economy is similar to more - 19 conventional cash-in-advance models in which there are no liquidity effects. Column 2 shows results for the case where there is no serial correlation in monetary disturbances, so that pX=O. Agents deposit roughly 89 percent of their money holdings in a savings account, and banks lend half of that amount out in first-part-of period loans. disturbance, If there was no the other half of savings would be lent out in the second- part-of period, and each half of the period would look identical. With a permanent doubling of the money supply half way through the period, agents exactly offset the real effects of additional money through cash management. In order for real quantities to remain unchanged in the new equilibrium, second-part-of-period prices. wages must double, as must With the same steady state real wage, hours worked do not change. To meet their second-part-of-period funds as in the steady state. have 1.43 to lend. wage bill, firms require twice as much In particular, they need 0.89. But banks A transfer by consumers of 0.56 from savings to transaction accounts allows the loan market to clear at the steady state nominal interest rate and preserves the steady state equilibrium. In the presence of serial correlation in money growth, firms reduce their demand for labor in response to an inflation tax (column 3). Output falls and nominal interest rates rise as in a standard cash-inadvance model. With no transactions costs, agents fully offset the liquidity effects, and only the inflation tax effects are left. Offsetting liquidity effects requires more than a one-for-one movement in savings deposits since firms require smaller second-part-of-period the case of white noise monetary disturbances. loans than in - 20 If transactions costs are infinite (as they are in the original Christiano-Eichenbaum the monetary shock. an equilibrium model), on the other hand, consumers cannot react to In this case, a doubling of the price level cannot be since the loan market no longer clears at the steady state nominal interest rate. more labor. Interest rates must fall, inducing firms to demand Real wages and output increase in equilibrium. Figure 1 shows the effect of a one standard deviation positive shock to the money supply on the nominal interest rate and hours worked in the original Christiano-Eichenbaum (1991b) model. The impulse response functions are computed by starting the economy in its nonstochastic state and tracing out the model's response to a monetary t=10 .5 steady injection at The graphs show that, indeed, the Christiano-Eichenbaum model gives rise to liquidity effects associated with the policy shock: the nominal interest rate falls and hours worked increases in response to a monetary easing. The liquidity effect does not persist, however. the money supply process displays positive serial correlation, injection raises inflationary expectations Thus, for t211, advance models: Because the surprise in periods following the shock. the model displays the usual effects found in cash-inthe interest rate increases and hours worked declines. Eventually, the effects of the shock die out and the economy returns to its steady state. Figure 2 shows the impulse response functions for economies in which, for a given value of A, a, is chosen so that the standard deviation of the loan-deposit rate spread in the model matches the standard deviation 'The interest rate in figures 1 and 2 is (Rzt)': the second-part-ofperiod deposit rate, expressed in annualized terms. Hours worked are expressed as a fraction of steady state hours worked. - 21 of the commerical paper-small CD rate spread in the US data. With X held fixed, the standard deviation of R,,-R,d,is strictly increasing as a function of a,; the interest rate spread becomes increasingly variable as the intermediary's costs increase. Thus, for each value of A, there is a unique value of a, that allows the model to match the standard deviation of the spread from the data. For any fixed value of a,, the standard deviation of the spread in the model is strictly decreasing as a function of A; the spread becomes more variable as the household's costs decrease. Thus, the value of a, that allows the model to match the data increases as X becomes larger. For X=1, a,=0.03; for X=3, a,=0.04; for X=5, a,=0.09; and for X=7, a,=0.45. Note that these figures imply that as X increases, so do the total transactions costs of intermediaries and households combined. For the first two cases, in which the household's transactions costs are 1 or 3 times the magnitude of the intermediary's costs, figure 2 reveals that the added financial flexibility that our model offers leads to the complete elimination of the dominant liquidity effect seen in figure 1. In response to a surprise monetary injection, the interest rate rises and hours worked fall, both reflecting the effects of higher expected inflation. For the third case, in which the household's costs are 5 times those of the intermediary, the liquidity effect returns. Relative to the benchmark case shown in figure 1, however, the decline in interest rates and the increase in hours worked is significantly dampened by the cash management efforts of intermediaries and households. Only for the final - 22 case, where household costs are 7 times those of the intermediary, are the liquidity effects similar in magnitude to those in figure 1. In order to offset the effects of monetary shocks in our model, agents must transfer money across markets in spite of transactions For each of the four parameterizations summarizes the contemporaneous costs. shown in figure 2, table 2 response of the example economy to a one standard deviation positive money shock. For comparison, the table also includes figures for the economy with no transactions costs (a,=a,=O) and the original Christiano-Eichenbaum (ag=aH=~). economy with infinite transactions Column 3 of the table shows that the contemporaneous costs response of the interest rate to the surprise monetary injection is positive in the economy with no transactions costs and in the economies with X=1 and X=3, where the liquidity effects are dominated by the expected inflation effects. The liquidity effects return in the remaining examples and are largest, of course, in the original Christiano-Eichenbaum model. Columns 4 and 5 of table 2 report the size of the transfer B,, as a ratio of the total money supply and the money shock, respectively. Since the money shock is positive, households wish to withdraw funds from their savings accounts after the shock; hence BZt is negative. transactions With no costs, the model reverts to a standard cash-in-advance model and agents actually over compensate for the shock, so that B2,/cXt<-1. They do this in an effort to smooth consumption, which requires additional transaction balances to offset lower second-part-of-period wage payments. Wage payments fall because firms hire less labor in the face of the inflation tax. As transaction costs increase, agents transfer a smaller fraction of the monetary innovation from their savings balances. Transfers - 23 are precluded altogether in the original Christiano-Eichenbaum model, so B2,=0 in this case. Column 6 of table 2 shows the household's marginal time cost -TH’(B2,//Yt) of cash management following the surprise injection, expressed in minutes per quarter year.6 It is assumed, following Christian0 (1991), that the model's time endowment of 1 unit per period represents 1460 hours per quarter in real time. representative These figures indicate that with X=1, the household would have to spend an additional 17.5 minutes to withdraw an additional unit of money following its optimal response to the monetary shock. With X=3, the household would require an additional 50 minutes per quarter to withdraw an extra unit of money. With X=5, the marginal cost is 91 minutes per quarter, and with X=7, the marginal cost is 123 minutes per quarter. With a disaggregated interpretation of the transactions cost functions, the results for X=1 imply that only agents who face a fixed time cost of less than 17.5 minutes per quarter will engage in cash management after the money shock. With this parameterization, most of the agents do adjust their portfolios in response to the shock, since most of the open market operation is offset. parameterization Introspection indicates that this implies quite low transactions costs. On the other hand, when X=7 the marginal household requires over two hours per quarter to adjust its portfolio. %ince TH’(B2,/M,) additional deposit, Almost no households find it worthwhile to transfer is the household's marginal cost of making an -T/(B,,/M,) additional withdrawal. is its marginal cost of making an - 24 funds between accounts in this case. Table 2 suggests, therefore, that liquidity effects continue to dominate in our generalized Christiano-Eichenbaum cash management transactions model only when the household's marginal costs of are very large. With small or moderate marginal costs, the liquidity effect is either eliminated or significantly 6. version of the dampened. Conclusion In this paper we have experimented with relaxing the extreme restrictions imposed by CIA constraints on flows of funds across markets. These constraints may be appropriate in models where the period length is interpreted as one day or one week, but at the quarterly horizon agents are likely to have access to a more flexible transactions Introducing such a transactions technology technology. into the model of liquidity effects developed by Christian0 and Eichenbaum (1993b) reveals that this model has a implication not previously considered literature: it predicts that the spread between interest rates on loans and deposits should be systematically supply. in the related to shocks to the nominal money When the transaction technologies are parameterized so that the model matches the behavior of interest rate spreads in the US data, the ability of the Christiano-Eichenbaum substantially reduced. model to explain liquidity effects is Only when marginal transactions costs are quite high does the model continue to predict that the interest rate will fall and hours worked will rise in response to a surprise monetary For reasonable parameterizations, injection. the liquidity effects vanish completely. - 25 We believe that our results cast doubt on the usefulness of this class of models for studying liquidity effects at business cycle Research efforts should return to the more careful frequencies. methodology of building financial structure from microfoundations alternatively, or, be directed toward extending other classes of models that can also generate negative correlations between nominal interest rates and money. Fuhrer and Moore (1992), for instance, alter the Phelps-Taylor contracting model by specifying staggered contracts that are negotiated in real rather than nominal terms. In this setting they can generate inflationary persistence that is consistent with the data as well as generate liquidity effects. The model in Goodfriend (1987), which has no nominal rigidities, can also produce correlations consistent with liquidity effects. In that model, purposeful behavior by the Fed can set up negative correlations between the federal funds rate and money. If the Fed wishes to reduce inflation, it can do so by reducing the future money supply. Due to anticipated inflation effects, the nominal interest rate would then fall, increasing the demand for money. If the Fed were also concerned with price level surprises, it could supply money today in order to prevent price level movements. The outcome is a negative correlation between interest rates and money. Of course, this mechanism is not what is thought of as a liquidity effect, but the example shows how Fed behavior rather than the presence of financial rigidities can be largely responsible for any negative correlations between money and nominal interest rates that can be found in the data. - 26 FIGURE 1 Interest Rate 1.025s 1.024.. 1.0151 : : 1234567 : : : : : : 6 : 9 : : IO II : 12 : : : I3 14 I5 Time Period Hours : I6 : 17 : I6 : : 22 : 23 : : : : I9 20 21 22 23 I9 : 20 : 21 : 24 : 25 Worked 1.0025 1.0020~- 1.0015- 1.00I0-1.0005.- 1.0000 -- 0.9995*- 0.999OJ : 1 : 2 : 3 : 4 : 5 : 6 : 7 : 6 : 9 : : IO I1 : : : I2 I3 I4 Time Period : I5 : 16 : I7 : i6 : : 24 : 25 J - 27 FIGURE 2 Interest Rate Legend 1.065.. 1.060-- - lambda - 1 --. lambda - 3 . . ’ lambda - 5 - - 7 lambda 1.0701.065.. 1.060-f 1.0601: : : :::::: :::::: :: ::::: ::: :: : 1 2 3 4 5 6 7 6 9 10111213 1415161716 19202122232425 Tlme Period Hours : Worked 1.003 Legend 1.002 - lambda - --m lambda - 3 . . . lambda - 5 - - 7 1.001 1.000 0.999 0.996 0.997 1 2 3 4 5 6 7 6 9 10111213 1415 16 I7 I6 19202122232425 Time Period lambda 1 - 28 TABLE 1 Response of the Economy to a Doubling of the Money Supply When Transaction Costs are Zero Nonstochastic 81 B2 .886 0 Steady State Doubling Money(P,=O) Doubling Money(P,=.W ,886 .886 -.557 -1.063 Hl .109 .109 .109 H2 .109 .109 .050 Wl 4.070 4.070 4.070 w2 4.070 8.140 7.573 1.325 2.650 3.574 3.071 3.071 2.119 P 4/P C Rl R2 .754 .754 .560 1.007 1.007 1.007 1.007 1.007 1.707 Notes: The table presents equilibrium prices and quantities for the economy with zero transactions costs (a =a"=O), which is similar to a basic cash-inadvance model. Column 1 describes the nonstochastic steady state. Columns 2 and 3 describe the economy after an unanticipated doubling of the money supply with px=O and px=0.81. - 29 TABLE 2 Cash Management Response to a One Standard Deviation Monetary Shock (&,=0.00410) 0 0 0.799 -0.00435 -1.06 0 1 0.03 0.399 -0.00333 -0.821 17.5 3 0.04 0.0339 -0.00239 -0.583 50.3 5 0.09 -0.447 -0.00115 -0.282 91.0 7 0.45 -0.808 -0.000224 -0.0545 123.4 (0 co -0.895 0 0 aD Notes: The table describes each example economy's contemporaneous response to a positive, one-standard deviation monetary shock. The parameters X and aa describe the household and intermediary's transactions technologies as indicated in the text. The example with X=0 and a,=0 is similar to a basic cash-in-advance model; the example with X=~0 and a,=a is equivalent to the original Christiano-Eichenbaum model. AR2t is the percentage change in the z;;;;erly loan rate, expressed as a fraction of the monetary . B,,/M, and B Jcxt are second-part-of-period deposits, expressed as a frac z Ion of the total money supply and the monetary shock. -TH/(B2,//Yt) is the household's marginal transactions costs following the shock, expressed in minutes per quarter. - 30 References Christiano, Lawrence J. "Modeling the Liquidity Effect of a Money Shock.' Federal Reserve Bank of Minneapolis Ouarterlv Review 15 (Winter 1991) : 3-34. Christiano, Lawrence J. and Martin Eichenbaum. 'Technical Appendix for Liquidity Effects, Monetary Policy, and the Business Cycle." Working Paper 478. Minneapolis: Federal Reserve Bank of Minneapolis, Research Department, May 1991a. "Liquidity Effects, Monetary Policy and the Business Cycle.' Manuscript. Minneapolis: Federal Reserve Bank of Minneapolis, Research Department, June 1991b. 'Liquidity Effects and the Monetary Transmission Mechanism." American Economic Review 82 (May 1992): 346-53. Cochrane, John H. "The Return of the Liquidity Effect: A Study of the Short-Run Relation Between Money Growth and Interest Rates.' Journal of Business and Economic Statistics 7 (January 1989): 75-83. Coleman, W.J., C. Gilles, and P. Labadie. "Discount Window Borrowing and Liquidity." Manuscript. Washington: Board of Governors of the Federal Reserve System, 1992. Fuerst, Timothy S. "Liquidity, Loanable Funds, and Real Activity." Journal of Monetarv Economics 29 (February 1992): 3-24. Fuhrer, Jeff and George Moore. "Inflation Persistence.' Manuscript. Washington: Board of Governors of the Federal Reserve System, March 1992. Goodfriend, Marvin. 'Interest Rate Smoothing and Price Level TrendStationarity." Journal of Monetarv Economics 19 (1987): 335-48. Gordon, David B. and Eric M. Leeper. "The Dynamic Impacts of Monetary Policy: An Exercise in Tentative Identification.' Manuscript. Atlanta: Federal Reserve Bank of Atlanta, Research Department, November 1992. Lucas, Robert E., Jr. 'Liquidity and Interest Rates." Journal of Economic Theory 50 (April 1990): 237-64. Schlagenhauf, Don E. and Jeffrey M. Wrase. 'Liquidity and Real Activity in Three Monetary Models." Discussion Paper 68. Minneapolis: Federal Reserve Bank of Minneapolis, Institute for Empirical Macroconomics, July 1992. - 31 Strongin, Steven. "The Identification of Monetary Policy Disturbances: Explaining the Liquidity Puzzle." Manuscript. Chicago: Federal Reserve Bank of Chicago, Research Department, December 1991. Appendix: Derivation of Equilibrium Conditions This appendix shows that the behavior of equilibrium prices and quantities is completely described by equations (21)-(25). Let uCt, uJt, be as defined in the text. The firm's first order fkt’ fHt, andfHt i 2 conditions for K t+1' H and H2t are given by it' U (A.11 -Pt P E -f P - E P :R; kt+l t+l =o t+2 t+1 (A.21 1 f3U ct+2 ct+l : R' (WItRlt-PtfH t) = t 1 0 I (A.31 W R - P f 2t 2t t lf2t = 0. The household's first order conditions for Lit, L2,, Lst, Bit, and Btt are U (A.41 -w E ct 1t P t UJt :R: 1 =o U ct (A.51 U Jt -w =o 2t p t U ct (A.61 UJt -w =o 3t p t U (A.71 BU ct ct+1 E RZt pt - pt+l r U (A.81 E u JtT;I (B2tRrlt ct BU ) ct+1 + Mt - pt+l A2 The intermediary's first order conditions for Nit and Bit are (A.91 (Rlt-R2t) : n1 t E W (A.101 Rzt + T;IB2/Mt) Rzt ; 1 = - 0 Rzt = 0. t Note that the market clearing condition Blt=BIt=Bzthas been substituted into both (A.81 and (A.lO). Other equilibrium conditions in the costly household transactions model include the household's cash-in-advance constraint (A.111 P C = t t Mt - Blt - B2t + wltLlt + W2tL2t + W3tL3t and the firm's cash-in-advance constraints, (A.121 Nit = WitHit (A.131 Nzt = W2tH2t, all of which will hold with equality as indicated so long as net nominal interest rates are positive, the market clearing conditions (A.141 N1t + N2t (A.151 ct + Kt+l (A.161 L it = H it (A.171 L (A.181 L3t = Tg(Bzt/MtI, 2t + W3tTB(B2t/Mt) = = Bit + B2t + xt K;(z~H$'-~ + (l-8)Kt = f(Kt,Hlt,H2t.zt) = H 2t and the zero-profit condition (A.191 R" B it it = RltNlt + R2t(BIt-NIt). Equations (A.l)-(A.191 represent 19 nonlinear equations in the 19 unknowns B 1t' B2,s Ct, Nit, N2,, Hit, Hz,, Lit, L2,, L3t, Kt+l, Pt, Wit, W2,, W3,, Rzt, Rzt, Rlt, and Rzt. A3 Equations (A.5) and (A.6) imply that W2t=W3t,which can be used to eliminate WJt from the system, Equation (A.lO), which implies that = Rlt Rzt - W R 2 zt M T;(B2/Mt), t can be used to eliminate Rzt from the system. Equation (A.19) implies that Rzt = where o ultRlt+ (~-o~~)R~~, which can be used to eliminate Ryt from the system. lt=Nlt'Blt' Equations (A.16)-(A.18) can be used to eliminate Lit, L2,, and L3t: L L 1t = Hlt 2t = L H2t 3t = TB(B2/Mt). Equations (A.2) and (A.3) can be used to eliminate RIt and Rzt: E R it (u .t+l'Pt+l )PtfHlt : R: = R 2t = PtfH 1 2 P2t. Equation (A.5) implies that w2t = u Jt P/u t ct' which can be used to eliminate W2t, while equations (A.12) and (A.13) can be used to eliminate Nit and Nzt. We have used the 11 equations (A.2), (A.3), (A.5), (A.6). (A.lO), (A.12), (A.13), and (A.16)-(A.19), to eliminate the 11 unknowns R W2t' W3t, Rlt, Nits N2,, Lit, L2,, L3ta and Rtt. 1t' R2,, Substituting these results into the remaining equations yields a system of 8 equations in the 8 uI&oms Bit, B2,, Ct, Hit, Hz,, Kt+l, Pt. and Wit: A4 U (A.11 SU ct+1 -Pt E D ct+2 -f - P kt+l t+l P = : R: 0 J U (A.41 E UJt - w ct = 0 it p t U SU ct pt U ct -Pt+l u E (A.7') ct+1 - f Jt 3; H2t 1 =o (A.8') r U E I ct -+ UJtT;(B2tf13t) (A.9'1 - P Mt pt PtT;(B2/Mt) '%t+l uct f& 2 t+1 E [ +fHIt-;frr2t] Mt : $ 1 32; -qt ] = 1 =o Cl Mt + xt (A.ll') Pt = ct U (A.14') (A.15') H 2t Ct = - -? UP [WItHlt-BIt-B2t-Xtl - Ts(B2/Mt) Jt t = f(Kt,Hlt,H2t.zt)- Kt+l. Equations (A.11'1, (A.14'), and (A.15') can now be used to eliminate the variables Pt, H2t, and Ct from the system. Substituting these variables out of (A.1). (A.41, (A.7'1, (A.8'1, and (A.9') reduces the 8equation system to a five equation system in the unknowns Bit, B2,, Hit, A5 K t+1' and W it' Equations (21)-(25) in the text express these 5 equations in their original forms (A.11, (A.41, (A.71, (A.81, and (A.9). The 5equation system can be linearized and solved by the undetermined coefficient method outlined by Christian0 (1991) and Christian0 and Eichenbaum (1991a).
@FedFRASER