This article attempts to narrow the gap between

Transcription

1 Evan F. Koenig Senior Eonomist and Poliy Advisor Rethinking the IS in IS LM: Adapting Keynesian Tools to Non-Keynesian Eonomies Part 1 This artile attempts to narrow the gap between two maroeonomi paradigms by showing that, in modified form, a graphial tool taken from one of these paradigms an be used to analyze models drawn from the other. The two paradigms are the Keynesian and real-business-yle approahes to maroeonomis. The graphial tool is the IS LM diagram. The IS LM diagram was originally developed by Hiks (1937) as a graphial representation of ideas put forth by Keynes in his General Theory. Not surprisingly, given its origins, the IS LM diagram has ome to be assoiated with traditional Keynesian maroeonomi analysis analysis that treats household expetations as either irrelevant or exogenously determined and in whih pries fail, in the near term, to lear the markets for goods and for labor. Not all Keynesians are omfortable with the assumption that households are myopi. Nevertheless, the IS LM diagram remains the graphial framework of hoie among those who treat sluggish prie adjustment seriously. 1 Expetations have usually been inorporated into textbook IS LM analysis in only the most rudimentary way. Given its pedigree, the IS LM diagram would seem ill-suited to analyzing an eonomy like that desribed by Barro (1990), in whih pries adjust instantaneously to lear all markets, households are forward-looking, and maroeonomi flutuations are due solely to shoks to tastes, tehnology, and government purhases. The point of this artile, however, is that household myopia is not an essential omponent of the IS LM framework. One this myopia is eliminated, the IS LM framework beomes flexible enough to enompass a simple Barro-style real-business-yle model as a speial ase. Furthermore, in working through the modified IS LM model, one gains an appreiation for whih of the traditional Keynesian results flow from the assumed myopia of households, as opposed to sluggish prie adjustment. No attempt is made here to pass judgment on the relative merits of alternative models; nor does this artile attempt to develop new theoretial insights. The models examined are simple, omparable to those typially inluded in popular undergraduate textbooks. A more intelletually satisfying reoniliation of the Keynesian and realbusiness-yle paradigms would move away from the assumption maintained throughout this artile that households and firms are prie takers. Until researh in this diretion makes further progress, any devie that provides ommon ground for maroeonomists and poliymakers with differing perspetives provides a valuable servie. Overview The artile begins with a review of how a simple market-learing eonomy responds to poliy and tehnology shoks. Then, under the assumption that people omprehend the long-run impliations of suh shoks, the short-run responses of Stephen P. A. Brown, Zsolt Besi, and Mark A. Wynne offered valuable omments and suggestions. The views expressed are not neessarily those of the Federal Reserve Bank of Dallas or the Federal Reserve System. 1 Examples of intermediate-level texts that rely heavily on the IS LM model are Mankiw (1992), Hall and Taylor (1988), Dornbush and Fisher (1987), and Gordon (1987). Eonomi Review Third Quarter

2 the eonomy to urrent and antiipated future hanges in the money supply, government purhases, and tehnology are determined. The shortrun analysis has two parts. The first part is a thought experiment in whih the dollar prie of output is held fixed at an arbitrary level and output and employment are sales-determined. It is in this thought experiment that variants of the traditional IS and LM urves play an important role in determining the level of output. While the LM urve is fairly standard, the IS urve, beause it reflets the savings deisions of households, depends heavily on expetations about the future. The final step in the analysis is to determine what, in fat, the short-run equilibrium prie level will be. Depending on the speed of prie adjustment, results either are idential to those obtained from Barro s real-business-yle model or are reminisent of those obtained from Keynesian models. The essential features of the expetationsaugmented IS LM approah an be presented in a setting that abstrats from apital investment. In models without investment, ausality runs entirely from the future to the present: the urrent ations of private deisionmakers depend on expeted future eonomi onditions, while future eonomi onditions are independent of people s urrent ations. This one-way ausality onsiderably simplifies the analysis of poliy and tehnology shoks. Aordingly, I defer disussion of maroeonomi models with investment to Part 2 of the artile, whih will be published in a subsequent issue of this Review. Long-run equilibrium In real-business-yle models, the eonomy is assumed always to be in a full-information, marketlearing equilibrium. This setion reviews how a typial real-business-yle eonomy responds to tehnology and poliy shoks. Similar, but more detailed, analyses have been presented by Barro (1990) and Barro and King (1984). Later in the artile, we allow for the possibility that sluggish prie adjustment or imperfet information may delay the eonomy s response to urrent shoks. Aordingly, for our purposes, it is both onvenient and aurate to all the full-information, marketlearing equilibrium long-run equilibrium. Briefly, the analysis of this setion shows 34 that an inrease in government purhases raises long-run equilibrium output and employment while reduing long-run equilibrium onsumption and the real wage. An adverse tehnology shok redues long-run equilibrium output, the long-run equilibrium real wage, and long-run equilibrium onsumption. Its effet on long-run equilibrium employment is ambiguous. The real interest rate is determined by the requirement that aggregate saving equal zero. Monetary poliy determines the long-run equilibrium prie level. The representative household. The representative household is endowed with a ertain quantity of time, L. The household divides this time between market and nonmarket ativities (between labor and leisure ). Earnings from market ativities are used to purhase output from firms ( onsumption ). To maximize its total satisfation, the household will alloate its time so as to equate the rate at whih it is willing to trade leisure for onsumption to the rate at whih leisure and onsumption trade for one another in the marketplae. Thus, (1) MRS l = w, where MRS l denotes the household s willingness to exhange leisure for onsumption (its marginal rate of substitution between leisure and onsumption) and where w denotes the real wage rate. It is usual to assume that both leisure and onsumption are normal goods, meaning that as the household s wealth inreases (holding the real wage onstant), the household hooses more of both. In equation 1, assuming normality is equivalent to assuming that the marginal rate of substitution is a dereasing funtion of leisure and an inreasing funtion of onsumption. Graphially, in a plot with leisure on the horizontal axis and onsumption on the vertial axis, the real wage is the negative of the slope of the household s budget line, while the marginal rate of substitution is the negative of the slope of the household s indifferene urve map. Equation 1 says that the household selets the point on its budget line that is tangent to one of its indifferene urves. See Figure 1. The representative firm. The representative firm hires labor from the representative household and produes output, whih is sold either to households or to the government. The firm finds it profitable

3 Figure 1 The Representative Household The representative household hooses l units of leisure and units of onsumption. Figure 2 The Representative Firm The representative firm hires n units of labor and produes y units of output. Output Slope = w Slope = w y L l Leisure n Labor to hire labor up to the point where the output produed by an additional unit of labor equals the real wage. Thus, (2) MP n = w, where MP n denotes the marginal produt of labor. It is usual to assume that labor is subjet to the law of diminishing marginal returns: in equation 2, the marginal produt of labor is a dereasing funtion of the hours of work purhased by the firm. Graphially, equation 2 says that the firm will operate at that point on its prodution funtion where the slope of its prodution funtion equals the real wage. See Figure 2. 2 The government. The government purhases output from firms, finaning its spending with lumpsum (that is, nondistortionary) taxes. For simpliity, hanges in government purhases will be assumed to have no effet on household preferenes for private onsumption and leisure and to have no effet on the prodution tehnology. As a pratial matter, these simplifying assumptions mean that flutuations in government purhases are probably best interpreted as the ounterpart to threatoffsetting hanges in real-world military spending. Equilibrium. Figure 1 depits the optimum of the representative household in a plot of onsumption against leisure. Figure 2 depits the optimum of the representative firm in a plot of output against labor. Leisure and labor are related to one another by the equation (3) n = L l, where n and l denote hours of work and of leisure, respetively. Output and onsumption are related to one another by the equation (4) y = + g, where y,, and g denote output, onsumption, and government purhases, respetively. Equations 3 and 4 allow one to transfer Figure 2 into the same spae as Figure 1. This transfer is aomplished by taking the mirror image of Figure 2 and shifting the resultant graph downward by the amount g. See Figure 3. Finally, Figure 4 ombines Figures 1 and 3 to depit the overall long-run equilibrium of the eonomy. In the figure, the 2 This and all subsequent figures assume that labor is essential to prodution. Eonomi Review Third Quarter

4 Figure 3 The Leisure Opportunity Set of the Representative Household equilibrium levels of leisure and onsumption are l e and e, respetively, and the equilibrium real wage is w e. Comparative statis. An inrease in government purhases redues the amount of output available for onsumption at any given quantity of leisure. In Figure 4, the effet of an inrease in government purhases is to shift the leisure onsumption opportunity lous downward by the amount of the inrease in g. Beause leisure and onsumption are normal goods, the representative household will hoose to absorb the impat of the downward shift in its opportunity lous by utting bak on both leisure and onsumption, rather than on onsumption alone. As shown in Figure 5, the new equilibrium of the eonomy is below and to the left of the original equilibrium. Beause the new equilibrium lies to the left of the original equilibrium, it orresponds to a point that is farther out along the prodution funtion. Thus, output is higher and the real wage is lower than before. The intuition underlying these results is that households, feeling poorer, are more willing to work than before. The resultant rightward shift in the labor supply shedule drives down the equilibrium real wage, making it profitable for firms to inrease hours of work and expand prodution. An adverse tehnology shok, whih might 36 y g Slope = w l L x n Leisure be due, for example, to a deterioration in the weather, an be modeled as a onstant-perentage redution in the amount of output produed at any given quantity of labor. In Figure 4, the leisure onsumption opportunity lous rotates downward, falling more (in absolute terms) at low levels of leisure than at high levels of leisure. The representative household is unambiguously worse off than before, and the redution in its wealth tends to indue delines in both leisure and onsumption (muh as in Figure 5). On the other hand, the new opportunity lous is flatter than the old. The flattening of the opportunity lous redues the marginal reward for working, so it provides households with an inentive to substitute leisure for onsumption. The net effet of these wealth and substitution effets is negative for onsumption but ambiguous for leisure. The deline in onsumption is aompanied by an equal deline in output. The real wage falls, refleting both households inreased supply of labor (due to the wealth effet) and firms inreased hesitany to demand labor (due to labor s lower marginal produtivity). See Figure 6. The interest rate. In a full-information, marketlearing eonomy without apital investment, the real interest rate plays a largely passive role. As we have seen, the equilibrium levels of onsumption, output, and hours an be found, in eah period, without bringing the interest rate into the analysis Figure 4 Long-Run Equilibrium e g e Slope = w e l e L Leisure

5 Figure 5 Effets of Inreased Government Purhases An inrease in government purhases lowers equilibrium leisure and onsumption. Figure 6 Effets of an Adverse Tehnology Shok An adverse tehnology shok lowers equilibrium onsumption and has an ambiguous effet on equilibrium leisure. e e e e g e l e l e L Leisure l e l e L Leisure at all. It will, nevertheless, be useful later to have an expression for the equilibrium real return on bonds. 3 We an obtain suh an expression from the representative household s optimality onditions. Although aggregate saving must be zero in equilibrium, eah individual household feels free to borrow and lend. The representative household will want to adjust its borrowing and lending until the rate at whih it is willing to trade urrent onsumption for future onsumption mathes the rate at whih urrent onsumption trades for future onsumption in the marketplae. Thus, (5) MRS = r, where MRS denotes the amount of future onsumption ( ) that the household requires as ompensation for a one-unit redution in urrent onsumption and where r denotes the (gross) rate of return on bonds (equal to 1 plus the real interest rate). Turning equation 5 around and substituting into it equilibrium levels of urrent onsumption and future onsumption, eah determined as in Figure 4, yields the real return on bonds that is onsistent with zero desired aggregate saving. Beause urrent onsumption and future onsumption are normal goods, the marginal rate of substitution between urrent onsumption and future onsumption is negatively related to urrent onsumption and positively related to expeted future onsumption. Hene, the equilibrium real rate of return rises in response to shoks that inrease expeted future onsumption relative to urrent onsumption. Intuitively, when they expet the future to be bright in omparison to the present, households are tempted to borrow against their future prosperity. In an eonomy without investment opportunities, the real interest rate must rise to hoke off this inipient borrowing. When they expet the future to be dark in omparison to the present, households are tempted to save for the oming rainy day. The real interest rate must fall until the desire to save is eliminated. 3 Note that in an eonomy with idential households and no apital investment, government bonds are the only seurities traded in equilibrium. Eonomi Review Third Quarter

6 Money and pries. There is no single, generally aepted way of modeling the demand for money. 4 Here, we assume that the representative household makes trade-offs between real money balanes and onsumption in muh the same way it makes trade-offs between leisure and onsumption. We assume, in partiular, that the demand for real money balanes is determined by the equation (6) MRS m = (R 1)/R, where MRS m denotes the additional urrent onsumption that the household demands in ompensation for a one-unit redution in end-of-urrentperiod real money balanes and where R denotes the gross nominal return on bonds. (Thus, R equals 1 plus the nominal interest rate.) Intuitively, MRS m is the rate at whih the household is willing to trade money (m) for onsumption, while (R 1)/R is the opportunity ost of holding money, measured in units of urrent onsumption Most undergraduate maro textbooks assume that the demand for money is an ad ho funtion of gross inome. Real money balanes are also sometimes modeled as an argument of the prodution funtion, as an argument of the household utility funtion, or as a onstraint on urrent household spending (the ash in advane approah). 5 By transferring $1 from ash into bonds, the household raises its purhasing power in the next period by $(R 1), whih has a urrent purhasing power of $(R 1)/R. See Barro (1990, 96 98). The Baumol Tobin money demand model is obtained in the speial ase in whih the household utility funtion takes the form u(,m) = ln() + ln[2m/ (2m + γ/p)] = ln(c), where γ/p is the real transation ost assoiated with eah exhange of interest-bearing assets for money and where C [2m/(2m + γ/p)] is onsumption net of transation osts. 6 Both onsumption and money balanes are assumed to be additively separable from leisure in the household utility funtion, so that the marginal rate of substitution between real balanes and onsumption is independent of leisure. 7 By assuming that prodution adjusts to math hanges in sales, I avoid having to deal with the possibility that households might be rationed in the output market. Whether suh rationing is of pratial signifiane is ontroversial. For an attempt to analyze an eonomy in whih suh rationing ours, see Neary and Stiglitz (1983). Assuming that onsumption and money balanes are both normal goods, equation 6 implies that the demand for money is an inreasing funtion of onsumption and a dereasing funtion of the nominal return on bonds. 6 The nominal rate of return on bonds is related to the real rate of return and inflation by the identity (7) R = rπ, where π denotes the ratio of the future prie level to the urrent prie level. Hene, equation 6 an be rewritten as (6 ) MRS m = 1 P/(rP ), where P and P denote the urrent prie level and next period s prie level, respetively. Suppose that equation 6 is satisfied in the urrent and all future periods. Then a simultaneous doubling of the urrent and all future nominal money supplies and of the urrent and all future prie levels leaves equation 6 unaltered. In general, the only effet of a one-and-for-all surprise hange in the level of the nominal money supply is to ause a proportionate hange in the prie level. The equilibrium values of real variables are entirely unaffeted. A short-run thought experiment There is onsiderable debate among eonomists about whether pries atually adjust suffiiently, in the short run, to keep the eonomy in full-information, market-learing equilibrium. It is worthwhile, therefore, to adopt an analytial framework that allows prie adjustment to be less than immediate. Even if one is personally onvined that market imperfetions are of negligible importane, a framework that does not impose market learing has the advantage of keeping hannels of ommuniation open to those holding ontrary views. Aordingly, this setion attempts to answer a What if question: What would happen to output and interest rates, in response to poliy and tehnology shoks, if the prie level were to remain fixed in the short run, with output and employment adjusting to math the level of sales? 7 The twist on traditional IS LM analysis here is that

7 people s expetations of future eonomi onditions are aknowledged to be an important determinant of their urrent behavior, and people are assumed to omprehend fully the impliations of eah shok for the future ourse of the eonomy. For example, people reognize that a sustained inrease in government purhases will eventually redue the amount of output available for private onsumption. Consequently, the announement of a defense buildup may have an adverse impat on urrent household demand and, hene, on urrent output and employment. We will assume that the short run in our thought experiment the interval over whih the prie level is held fixed and output and employment are sales-determined lasts only one period. 8 Next period, all markets are expeted to lear, with equilibrium determined as in Figure 4. The IS and LM urves. We adopt the standard Keynesian assumption that the markets for money and bonds must ontinue to lear, even if the markets for output and employment do not. The requirement that the demand for money equal the supply of money yields the LM shedule. The requirement that the supply of bonds equal the demand for bonds or, equivalently, that investment equal savings yields the IS shedule. Here, the demand for money is determined by equation 6. Beause the urrent prie level is held fixed in our thought experiment, the monetary authority ontrols the short-run real money supply through its hoie of the short-run nominal money supply. Thus, for a given short-run nominal money supply and long-run prie level target, equation 6 defines an upward-sloping LM shedule. 9 The LM shedule shifts to the right in response to inreases in the short-run nominal money supply and in response to inreases in the monetary authority s pereived long-run prie level target. The only unonventional feature of the LM shedule is that it is a relationship between onsumption and the real rate of return on bonds rather than between inome and the real rate of return on bonds. The ondition that investment equals savings, in the urrent model, redues to the requirement that equation 5 be satisfied. Reall that the marginal rate of substitution between urrent onsumption and future onsumption, whih appears on the lefthand side of equation 5, is a dereasing funtion of urrent onsumption and an inreasing funtion of expeted future onsumption. Consequently, for any given level of expeted future onsumption, equation 5 defines a negative relationship between urrent onsumption and the real return on bonds. It is this negative relationship that takes the plae of the traditional IS urve. 10 Unlike the traditional IS urve, the IS urve defined by equation 5 depends expliitly on expetations of the future. Intuitively, households want to smooth onsumption through time. If expeted future onsumption rises, households desire more onsumption today as well. Thus, with urrent onsumption plotted on the horizontal axis and the real return on bonds on the vertial axis, inreases in expeted future onsumption shift the expetations-augmented IS shedule to the right. Indeed, when MRS depends only on the ratio of future onsumption to urrent onsumption (that is, when household preferenes are homotheti), the rightward shift in the augmented IS shedule is exatly proportionate to the inrease in expeted future onsumption. The stronger is the desire to smooth onsumption, the steeper is the IS urve. It is important to note that the optimality onditions from whih the expetations-augmented IS and LM urves are derived are not ad ho additions to the full-information, market-learing 8 See Koenig (1987) for an analysis of the ase in whih the short run lasts several periods. 9 I have hosen to assume that the monetary authority targets the long-run prie level beause ritis of Keynesian eonomi models have often advoated just suh a poliy. (See, for example, Barro 1986.) One ould assume equally well that the monetary authority holds the long-run money supply fixed, that the monetary authority fixes money growth between the two periods, or that the monetary authority targets the rate of inflation between the two periods. Results differ, somewhat, depending on the long-run poliy rule adopted (though the basi methodology outlined here arries through). 10 As defined here, the expetations-augmented IS urve is a relationship between onsumption and the interest rate, rather than between inome and the interest rate. Given the manner in whih I have hosen to model the demand for money, plotting the expetations-augmented IS and LM urves in onsumption interest rate spae seems natural. For further disussion, see the Appendix. Eonomi Review Third Quarter

8 eonomy we analyzed earlier. In that eonomy, equations 5 and 6 played ritial roles in determining the real return on bonds and the equilibrium prie path. Now, with the urrent-period prie level held exogenously fixed, these same equations determine the urrent-period levels of onsumption, output, and employment. Comparative statis. Figure 7 plots the expetations-augmented IS and LM urves defined by equations 5 and 6 and illustrates the effets of an inrease in the urrent-period money supply. As in traditional IS LM analysis, onsumption (and, so, output) rises and the real interest rate falls, eliminating what would otherwise be an exess supply of money. 11 Similar results are obtained if it beomes known that the monetary authority has adopted a higher long-run prie level target. An inrease in urrent-period government purhases has no impat on either the IS or the LM urve and, hene, has no impat on onsumption or interest rates. With onsumption unhanged, output must rise by the full amount of the inrease in government purhases. These results will seem strange to those used to textbook Keynesian analysis, and they merit explanation. First, given that interest rates fail to rise, why is there no multiplier effet in the model developed here? That is, why does onsumption remain onstant, rather than inrease, as aggregate inome expands? In the standard textbook IS LM model, households are assumed to ignore the future tax Figure 7 assumes that household utility is additively separable between onsumption and money balanes. Though not essential to the analysis, this assumption is onvenient and will be retained throughout the remainder of the artile. For empirial evidene on the separability question, see Koenig (1990). For an analysis of the nonseparable ase, see Koenig (1989). 12 That the representative household ares only about the present disounted value of tax payments follows from equation See Mankiw and Summers (1986) for an analysis of fisal poliy in a model in whih the demand for money is a funtion of onsumption, rather than inome, but households are myopi. Figure 7 Impat of an Inreased Money Supply In the short run, for a given prie level, an inrease in the money supply raises onsumption and lowers the real return on bonds. Real return r r liabilities implied by an inrease in government purhases. Consistent with most of the real-businessyle literature, here we have impliitly gone to the opposite extreme and assumed that people are fully ognizant of the tax impliations of hanges in government spending. The absene of a multiplier effet is exatly what one would expet in a model in whih the timing of (lump-sum) taxes is irrelevant, so that any hange in government purhases might just as well be finaned through an inrease in urrent taxes. 12 After all, when a balanedbudget onstraint is imposed on the textbook model, multiplier effets disappear from it too. Seond, interest rates fail to rise in response to inreased government purhases beause the demand for money is a funtion of onsumption rather than inome. 13 If the more onventional textbook speifiation of money demand were adopted, the urrent model would yield the standard result that inreases in government purhases tend to raise interest rates. (See the Appendix.) would then tend to fall somewhat (though by less than the inrease in government purhases) rather than remain onstant. Summarizing, the response of the urrent model to monetary poliy is entirely onventional. The response of the urrent model to near-term LM LM IS

9 hanges in fisal poliy would be muh like that of a onventional IS LM model with a balanedbudget onstraint, were it not for our assumption that the demand for money depends on onsumption rather than on gross inome. This assumption is not essential to the expetations-augmented approah to IS LM analysis. Expetations-augmented IS LM analysis, unlike onventional IS LM analysis, expliitly reognizes that prospetive fisal and tehnology shoks an have every bit as muh near-term impat on the eonomy as realized shoks. The impat of prospetive shoks is transmitted to today s eonomy through hanges in expeted future onsumption, whih proxy for hanges in permanent inome. For example, we saw (in Figure 5) that an inrease in long-run government purhases tends to lower long-run onsumption. Thus, the prospet of a defense buildup will lower expetations of future onsumption and, by equation 5, shift today s IS urve to the left. Today s onsumption and today s interest rates, onsequently, fall at any given urrent prie level (Figure 8 ). Today s output falls, too, if urrent government purhases are unhanged. (See the box titled The Short-Run Impat of a Permanent Defense Cut for a disussion of what happens if urrent purhases and expetations of future purhases hange simultaneously.) Effets qualitatively similar to those displayed in Figure 8 are also observed in response to a prospetive adverse tehnology shok. Closing the short-run model Thus far, our analysis has taken the short-run prie level as given. This assumption is unneessarily restritive, and we now take steps to relax it. Several alternative models of short-run prie determination are onsidered. At one extreme we have the real-business-yle model, whih assumes that the wage rate and prie level adjust instantaneously to lear the labor and output markets. At the other extreme is a model in whih output pries are set in ontrats before omplete information on tehnology and government poliies is available. Between these extremes are models in whih the prie of output is flexible, but labor ontrats prespeify the wage, and models in whih firms adjust their output in partial ignorane of the pries prevailing in other markets. Figure 8 Impat of an Antiipated Inrease in Future Government Purhases In the short run, for a given prie level, an antiipated inrease in future government purhases lowers onsumption and the real return on bonds. Real return r r As in the preeding setion, we find that the tools of traditional Keynesian analysis an be adapted to analyze models in whih people s urrent behavior depends nontrivially on their expetations of the future ourse of the eonomy. In partiular, we an derive well-defined ounterparts to the traditional Keynesian aggregate demand and aggregate supply urves. The intersetion of these two urves determines the shortrun equilibrium prie and quantity of output. The aggregate demand shedule. As a first step in the diretion of relaxing the fixed-prie assumption, onsider what happens to the IS LM intersetion as the urrent prie of output delines. The position of the IS urve depends only on future onsumption, whih is independent of the urrent prie level. For any given urrent nominal supply of money, however, a deline in the urrent prie level raises the real money supply, shifting the LM urve to the right, as in Figure 7. Given our assumption that the monetary authority targets the long-run prie level, this rightward LM shift is not quite the end of the story. A lower urrent prie level raises expeted inflation (or lowers expeted deflation) and, hene, lowers the demand for money at any given real rate of return on IS LM IS Eonomi Review Third Quarter

10 bonds, shifting the LM urve a bit further to the right (or, more aurately, down). 14 Thus, the level of urrent onsumption determined by the intersetion of the IS and LM urves rises as the urrent prie level falls. The negative short-run relationship between onsumption and the prie level is plotted in Figure 9 and labeled AD. Like the so-alled aggregate demand urve of traditional Keynesian analysis, the AD shedule represents output prie ombinations (or, in the present model, onsumption prie ombinations) in whih the demand for money equals the supply of money and, simultaneously, the representative household is ontent with the intertemporal alloation of output. Obviously, any disturbane that shifts the IS LM intersetion to the right for a given prie level will shift the AD shedule to the right by exatly the same amount. Thus, an inrease in the urrent-period nominal money supply, an inrease in the monetary authority s long-run prie target, a ut in long-run government purhases, and positive long-run tehnology shoks will tend to move the AD shedule to the right. Changes in urrent tehnology and urrent government purhases, on the other hand, have no effet on the AD shedule. 15 The aggregate supply shedule: alternative models The real-business-yle model. In the real-businessyle model, pries adjust instantaneously to lear all markets. In the present ontext, equations 1 and 2, whih define the supply of labor and the demand for labor, must both be satisfied even Note that this endogenous response of expeted inflation to hanges in P implies a more elasti aggregate demand urve than does an inflation target. 15 If the demand for money were assumed to be a funtion of inome rather than onsumption, the IS, LM, and AD shedules would be more appropriately plotted with inome on the horizontal axis. Inreases in urrent government purhases would shift the IS shedule and, hene, the AD shedule also to the right, muh as in a traditional Keynesian analysis. Figure 9 Aggregate Demand Curve with Alternative Aggregate Supply Shedules Output prie AS RBC in the short run. Thus, short-run equilibrium levels of onsumption and leisure are determined as in Figure 4. In Figure 9, the ombinations of prie and onsumption onsistent with the learing of the labor market are labeled AS RBC. The urve AS RBC is very muh the ounterpart of the traditional Keynesian aggregate supply shedule, exept that the urve AS RBC represents the total amount of output available to the private setor rather than the total amount of output available to the publi and private setors ombined. That the AS RBC shedule is vertial reflets the fat that the indifferene urves and prodution funtion plotted in Figure 4 are independent of the prie of output. The stiky-prie model. The stiky-prie model assumes that the prie of output is fixed in advane. Usually, this approah also assumes that output adjusts one for one in response to unantiipated hanges in sales. (Presumably, either labor ontrats give employers disretion in setting hours of work or the wage rate adjusts so that employees are ontent with whatever hours are required of them.) Equation 2 may be satisfied ex ante but is not, in general, satisfied ex post. In Figure 9, the assumption that output adjusts one for one in response to hanges in sales at a preset prie is refleted in a horizontal aggregate supply shedule, AS SP. AD AS II AS SP

11 The Short-Run Impat of a Permanent Defense Cut In traditional textbook Keynesian analysis, no distintion is made between permanent hanges and temporary hanges in government purhases. Impliitly, the traditional analysis assumes that it is only the ontemporaneous hange in government purhases that affets the short-run equilibrium of the eonomy. In expetations-augmented IS LM analysis, in ontrast, whether a hange in government purhases is thought to be temporary or thought to be permanent is of onsiderable importane. An analysis of the impat of a permanent ut in defense spending illustrates the point. Reall that hanges in government purhases that are expeted to be transitory have no impat whatsoever on the expetations-augmented IS and LM shedules. In our short-run thought experiment, therefore, onsumption and the real return on bonds are not affeted by short-term defense uts. Output falls one for one with government purhases: a $20 billion ut in defense spending results in a $20 billion deline in gross domesti produt. A prospetive hange in government purhases, however, shifts the expetationsaugmented IS shedule in the same diretion as the resultant prospetive hange in longrun onsumption. A prospetive ut in the defense budget would, therefore, shift the IS shedule to the right. Assuming that preferenes are homotheti in urrent and future onsumption (so that the marginal rate of substitution between urrent and future onsumption depends only on the ratio of urrent to future onsumption) and assuming that urrent onsumption and future onsumption are initially equal, the rightward shift in the IS urve will exatly math the inrease in future onsumption. Beause the LM shedule slopes upward, the atual short-run equilibrium level of onsumption in our thought experiment rises by less than the inrease in future onsumption, whih, in turn, rises by less than the future ut in government spending. If a $20 billion ut in the defense budget raises long-run onsumption by $15 billion, then short-run onsumption might rise by only $5 billion. What, then, is the impat of an immediate, permanent ut in the defense budget? rises in the short run but not as muh as it will rise in the long run. The prospet of a rising onsumption path puts upward near-term pressure on interest rates. Output falls in the short run, by more than it will fall in the long run. In our numerial example, onsumption rises by $5 billion in the short run and by $15 billion in the long run. Output falls by $15 billion in the short run and by $5 billion in the long run. Of ourse, these results assume that the monetary authority holds both the long-run prie level and the urrent money supply fixed. The stiky-wage and imperfet-information models. Stiky-wage and imperfet-information models yield an aggregate supply shedule with an elastiity that lies between the elastiities of the real-businessyle and stiky-prie supply shedules. The stikywage model assumes that money wages are set in advane. If the prie of output rises, unexpetedly, relative to the preset wage, firms find it profitable to expand their prodution and hiring (Fisher 1977; Taylor 1980). Equation 1 may be satisfied ex ante but is not, in general, satisfied ex post. In the imperfet-information model, when a firm sees the prie of its produt rise, the firm is not ertain whether this rise reflets an inrease in the prie of its produt relative to the pries of other goods or, instead, an inrease in the general level of pries. Beause of this onfusion, an unexpeted inrease in the general prie level is Eonomi Review Third Quarter

12 Figure 10 Impat of Monetary Stimulus An inrease in the urrent-period money supply or in the monetary authority s long-run prie level target will shift the aggregate demand shedule to the right. Output prie usually aompanied by some inrease in eah firm s output level. Eah firm believes that its behavior is onsistent with profit maximization but disovers, after the fat, that it was mistaken. 16 In Figure 9, the stiky-wage and imperfetinformation models yield aggregate supply urves like that labeled AS II. Comparative statis. Figure 10 illustrates the prie and output (onsumption) effets of a variety of eonomi shoks. Muh as in the traditional Keynesian model, expansionary monetary poliy as refleted in either an unexpeted inrease in the urrent money supply or an upward revision in the monetary authority s pereived long-run prie level target shifts the aggregate demand shedule to the right. In the real-business-yle E AS RBC E 1 E 3 E 2 AS II AS SP AD AD model, the only effet of this shift is to ause an inrease in the urrent prie level. 17 (The eonomy moves from point E to point E 1.) In the stikyprie model, it is output, rather than the prie level, that inreases. (The eonomy moves from point E to point E 2.) The stiky-wage and imperfet-information models yield inreases in both onsumption and the prie level. (The eonomy moves from point E to a point like E 3.) As shown in Figure 11, an unexpeted inrease in urrent-period government purhases shifts eah aggregate supply urve to the left. (Reall that aggregate supply in the urrent model refers to the amount of output available to the private setor, rather than the amount of output available to the eonomy as a whole.) In the real-businessyle, stiky-wage, and imperfet-information versions of the model, onsumption falls (but by less than the inrease in government spending) and the prie level is driven up. The eonomy moves from E to E 1 in the real-business-yle model and from E to a point like E 3 in the stikywage and imperfet-information models. In the stiky-prie model, output rises by the full amount of the inrease in government spending, leaving onsumption and the prie level unhanged. (The eonomy stays at point E.) Figure 11 Impat of Inreased Government Purhases An inrease in urrent-period government purhases shifts the aggregate supply urve to the left. Output prie AS RBC E 1 AS RBC AS II AS II E 3 E AS SP = AS SP 16 For additional explanation of the imperfet-information model, see Luas (1972), Barro (1990, hap. 19), or Mankiw (1992, hap. 11). 17 Reall that, for simpliity, we are assuming that real money balanes are additively separable from both onsumption and leisure in the household utility funtion. AD 44

13 An adverse urrent-period tehnology shok has onsumption and prie effets very like those assoiated with an inrease in urrent-period government purhases. Prospetive hanges in government purhases and tehnology affet the urrent-period equilibrium of the eonomy by altering households long-run onsumption prospets. The announement of future defense uts or the future implementation of improved tehnology will shift the urrent-period aggregate demand shedule to the right in muh the same way as expansionary monetary poliy. In Figure 10, the eonomy will move from E to E 1, E 2, or a point like E 3, depending on whether markets lear instantaneously, the short-run prie level is fixed, or firms have diffiulty distinguishing general prie level movements from relative prie level movements. Conluding remarks The basi idea underlying IS LM analysis is that supply and demand in the finanial markets determine the eonomy s short-run equilibrium quantities of labor and output in the event that the wage rate and prie level fail to ahieve their full-information, market-learing levels. Traditional Keynesian analysis, in addition, treats household expetations as either exogenous or irrelevant. In this artile, we have seen that it is possible to abandon traditional Keynesian myopia without abandoning the basi IS LM framework. Admittedly, the thought experiment that underlies IS LM analysis seems artifiial in realbusiness-yle models, where pries adjust instantaneously to lear all markets. Even in real-businessyle models, however, the equilibrium onditions used to derive the expetations-augmented IS and LM urves are indispensable. Thus, the money demand equals money supply ondition that defines the LM urve determines the equilibrium prie path in a real-business-yle world, while the intertemporal optimality ondition that defines the expetations-augmented IS urve determines the real interest rate. In brief, real-business-yle models impose instantaneous market learing. Expetations-augmented IS LM analysis is onsistent with instantaneous market learing but allows for the possibility that prie adjustment in the labor and output markets is less than immediate. By analyzing a variety of maroeonomi models within a ommon framework, one obtains insights into how the models relate to one another, failitating disussion. A partiular advantage of the IS LM approah developed here is that, in using it, one gains some appreiation for whih of the traditional Keynesian results flow from the assumed myopia of households and firms, whih flow from sluggish wage and prie adjustment, and whih flow from speial assumptions about the determinants of the demand for money. For example, the impat of monetary poliy in the urrent model is quite traditional, despite forward-looking expetations and despite our use of onsumption rather than inome as the sale variable in the money demand funtion. On the other hand, we found that forward-looking expetations eliminate the short-run multiplier effet usually assoiated with an inrease in urrent government purhases. And whether an inrease in urrent government purhases puts near-term upward pressure on interest rates depends ritially on how one models the demand for money. Finally, the traditional distintion between demand shoks and supply shoks is blurred when household onsumption demand is forwardlooking, rather than myopi. Thus, the expetation of a future shift in aggregate supply the result, perhaps, of an antiipated hange in tehnology affets urrent aggregate demand. Postsript. The analysis presented here is inomplete in that it fails to allow for endogenous hanges in apital investment. This omission is potentially serious. Flutuations in investment were given a prominent plae in Keynes own aount of the business yle. Reently, a study by Fama (1992) has onfirmed that flutuations in investment are an important soure of transitory movements in real-world aggregate output. Aordingly, Part 2 of this artile, to be published in a future issue of the Eonomi Review, extends the expetationsaugmented IS LM framework developed here to an eonomy in whih investment is endogenous. Eonomi Review Third Quarter

14 Appendix Derivation of the Comparative Statis Results This Appendix formally derives many of the omparative statis results presented in the main text, and it larifies the relationship between the model developed in this artile and standard textbook Keynesian models. The basi model Suppose, for analytial onveniene, that the representative household s willingness to trade urrent onsumption for future onsumption and its willingness to trade onsumption for money balanes depend only on the ratios of the quantities of the goods in question, so that, for example, the marginal rate of substitution between urrent onsumption and future onsumption depends only on the ratio of urrent onsumption to future onsumption. 1 Equations 5 and 6 then imply (A.1) = φ( r) and (A.2) m = κ( rp/ P), respetively, where both φ( ) and κ( ) are stritly dereasing. Equation A.1 defines an IS shedule, and equation A.2 defines an LM shedule. Differentiating logarithmially, (A.1 ) dln( ) = dln( ) dln( r) and (A.2 ) dln( ) = dln( M) dln( P) + κ [ dln( r) + dln( P) dln( P)], φ where φ rφ /φ > 0 and κ Rκ /κ > 0 equal, in absolute value, the rate-of-return elastiities of onsumption demand and money demand, respetively. Solving for the perentage hange in onsumption and the perentage hange in the real return on bonds, (A.3) dln( ) = { κdln( ) + φ[ dln( M) dln( P)] + κ φ[ dln( P) dln( P)]} /( κ + φ) and (A.4) dln( r) = { dln( ) [ dln( M) dln( P)] κ [ dln( P) dln( P)]} /( κ + φ). Note that onsumption and the real rate of return are inreasing in expeted future onsumption. If households are forward-looking, we know that expeted future onsumption will be inreasing in expeted future produtivity and dereasing in expeted future government purhases: = (θ,g ), where θ is a positive tehnology-shok variable and where 1 > 0 and 1 < 2 < 0. Inreases in both urrent real money balanes and expeted inflation have a positive effet on urrent onsumption and a negative effet on the real rate of return. Both onsumption and the real rate of return are ompletely independent of 1 This ondition will be satisfied if the household utility funtion is additively separable in its arguments and preferenes are homotheti. Additional realism an be obtained at the expense of some additional omplexity by relaxing the separability onditions. (Continued on the next page) 46

15 Appendix Derivation of the Comparative Statis Results Continued urrent government purhases. Thus far, we have treated the urrent prie level, P, as fixed. If, at the opposite extreme, the wage rate and prie level adjust instantaneously to lear the labor and output markets, urrent onsumption is determined as in Figure 4 that is, = (θ,g). Given and, equation A.1 determines the real rate of return on bonds. Equation A.2 determines the urrent prie level. In general, one might expet the aggregate supply shedule to be neither horizontal nor vertial, so that the hanges in onsumption predited by equation A.3 will be only partially offset by hanges in P. Enompassing traditional IS LM analysis By generalizing equations A.1 and A.2, we an formulate a model that inludes traditional Keynesian IS LM analysis as a speial ase. Suppose, in partiular, that 1 λ (A.5) = [ φ( r)] y and (A.6) m = 1 γ y γ κ( rp/ P), where 0 λ < 1 and 0 γ 1. The parameter λ measures the exess sensitivity of onsumption to urrent inome. 2 The parameter γ will be positive to the extent that the demand for money depends on omponents of inome other than onsumption (Mankiw and Summers 1986). Standard textbook Keynesian analysis assumes that λ is lose to 1 and that γ is equal to 1. Furthermore, expeted future onsumption ( ) is held fixed. 3 Logarithmi differentiation of A.5 and A.6 yields IS and LM urves: λ (A.5 ) dln( ) = [( 1 λ) dln( ) ( 1 λ) φ dln( r) + λα dln( g)]/( 1 λα ). (A.6 ) dln( ) = { dln( M) dln( P) γα dln( g) 2 Campbell and Mankiw (1989) put λ at 0.5, but most empirial studies suggest that a value like 0.1 is loser to the mark. Koenig (1990) tests the Campbell Mankiw speifiation and finds it inferior to an alternative model in whih all households are forward-looking but utility is not separable between onsumption and money balanes. 3 An alternative interpretation of the standard Keynesian model is that λ is equal to zero, but households base their expetations of future onsumption solely on their urrent inomes. g + κ [ dln( r) + dln( P) dln( P)]} /( 1 γ + γα ). In deriving these expressions, use has been made of the fat that d ln(y) = α d ln() + α g d ln(g), where α and α g are the respetive shares of onsumption and government purhases in national inome. Alternatively, one an write (A.5 ) dln( y) = [ α( 1 λ) dln( ) α( 1 λ) φdln( r) + α dln( g)]/( 1 λα ) and (A.6 ) dln( y) = { α[ dln( M) dln( P)] + ( 1 γ) αgdln( g) + α κ [ dln( r) + dln( P) dln( P)]}/( 1 γ + γα ). g (Continued on the next page) g Eonomi Review Third Quarter

16 Appendix Derivation of the Comparative Statis Results Continued In the speial ase in whih γ equals 1, so that the demand for money depends on inome rather than onsumption, the LM equation simplifies to dln( y) = dln( M) dln( P) + [ dln( r) + dln( P) dln( P)]. κ The importane of exess sensitivity in determining the strength of the multiplier effet is lear from equations A.5 and A.5. In equation A.5, inreases in government purhases have a positive impat on onsumption demand (for a given rate of return on bonds) only insofar as λ, whih measures the exess sensitivity of onsumption to urrent inome, is greater than zero. Similarly, it follows from equation A.5 that dy/dg = 1/(1 λα ). Thus, hanges in government purhases have a larger than one-for-one impat on the demand for output only to the extent that λ is greater than zero. The IS and LM equations an be solved for perentage hanges in inome, onsumption, and the real rate of return. The general solutions follow: (A.7) dln( y) = { α ( 1 λ) [ dln( M) dln( P)] + α( 1 λ) φ κ[ dln( P) dln( P)] + αg[( 1 γ)( 1 λ) φ + κ] dln( g) + α ( 1 λ) dln( )}/, φ κ and (A.9) where dln( r) = { ( 1 λα )[ dln( M) dln( P)] ( 1 λα ) κ [ dln( P) dln( P)] + αg[ 1 ( 1 γ)( 1 λ)] dln( g) + (1 γ + γα )( 1 λ) dln( )}/, ( 1 λα ) + ( 1 γ + γα )( 1 λ) > 0. κ Standard textbook results are obtained in the speial ase where γ = 1, λ > 0, and is held fixed (so that d ln( ) = 0). Equations A.7 and A.8 imply that dy/dg = [(1 γ )(1 λ) φ + κ ]/ and d/dg = α [γ (1 λ) φ λ κ ]/, respetively. The importane of γ in determining the extent to whih rowding out redues the stimulatory effets of inreased government purhases an be seen by differentiating these multipliers with respet to γ. One obtains ( A10. ) ( dy/ dg)/ γ = ( d/ dg)/ γ = α ( + )( 1 λ) 2 / 2 < 0. φ κ φ Not surprisingly, the more sensitive is the demand for money to hanges in government purhases (the larger is γ ), the more inreases in suh purhases tend to rowd out private spending. φ (A.8) dln( ) = {( 1 λ) [ dln( M) dln( P)] + ( 1 λ) [ dln( P) dln( P)] α [ γ( 1 λ) λ ] dln( g) g φ φ κ + ( 1 λ) dln( )}/, κ φ κ 48