February 1987

93

Structure and Uses of the MPS Quarterly Econometric Model of the

Flint Brayton and Eileen Mauskopf of the Since 1970, when the first working version was Board's Division of Research and Statistics pre- completed, the Board's Division of Research and pared this article. Statistics has used the model for forecasting, for analyzing the consequences of exogenous eco- In the late 1960s, staff members of the Board of nomic shocks and alternative monetary or fiscal Governors of the System, along policies, and for various research projects. Al- with several university , undertook to though many key elements of the original model build a quarterly model of the U.S. economy. remain intact, considerable effort has been de- Their goal was to develop a model that focused voted over the years to maintaining and improv- more intensively than did existing models on the ing the model. These efforts stem from new channels through which affected insights provided by theoretical and applied eco- the real sectors of the economy. The model has nomic research, from revisions in data, and from generally become known by the abbreviation institutional and technological developments that MPS, which reflects the academic affiliations of have caused the performance of some equations two of its key developers, Franco Modigliani to deteriorate. This article provides a general (Massachusetts Institute of Technology) and Al- description of the current structure and uses of bert Ando (University of Pennsylvania), and the the model.2 organization (Social Science Research Council) through which Federal Reserve support for the 1 project was channeled. SUMMARY OF MODEL STRUCTURE

As of late 1986, the MPS model consists of 334 1. Papers describing early versions of the model and citing equations, of which 128 are stochastic and 206 contributors to the development of the model include Frank are identities. In addition, it has 188 exogenous de Leeuw and Edward Gramlich, "The Federal Reserve- MIT Econometric Model," FEDERAL RESERVE BULLETIN, variables. The theoretical core of the model is vol. 54 (January 1968), pp. 11-40; Frank de Leeuw and based on the behavior of cost-minimizing pro- Edward Gramlich, "The Channels of Monetary Policy: A ducers and utility-maximizing consumers. Further Report on the Federal Reserve-MIT Econometric Model," FEDERAL RESERVE BULLETIN, vol. 55 (June 1969), In the long run, when markets clear and expec- pp. 472-91; Robert H. Rasche and Harold T. Shapiro, "The tations are fulfilled, the model behaves like a F.R.B.-M.I.T. Econometric Model: Its Special Features," neoclassical growth model. The long-run growth , vol. 58 (May 1968, Papers and Proceedings, 1967), pp. 123-49; and Albert Ando and Franco rate of the economy is determined by the rate of Modigliani, "Econometric Evaluation of Stabilization Poli- population growth and the rate of technological cies," American Economic Review, vol. 59 (May 1969, progress, both of which are exogenous to this Papers and Proceedings, 1968), pp. 296-314. Jared Enzler. Associate Director of the Division of Re- model. The level of per capita output depends on search and Statistics, was involved in the model development the capital-output ratio and the characteristics of work, managed the model through much of its first decade of operation, and continues to maintain an active interest in and oversight of model developments. Other current and former Board staff who have worked with the model in its operation- 2. A more detailed description of the model, containing a al phase include Robert Anderson, Douglas Battenberg, complete list of the equations (as of 1985), is presented in Richard Berner, Flint Brayton, Tim Grunwald, William Lee, Flint Brayton and Eileen Mauskopf, "The Federal Reserve Eileen Mauskopf, Stephan Thurman, David Wilcox, Anne Board MPS Quarterly Econometric Model of the U.S. Econ- Williams, and David Wyss. omy, "Economic Modelling, vol. 2 (July 1985), pp. 170-292.

Digitized for FRASER http://fraser.stlouisfed.org/ Federal Reserve Bank of St. Louis February 1987

94 Federal Reserve Bulletin • February 1987

the production function.3 Although an optimal affects real output directly through the contribu- capital-output ratio exists at which the sustain- tion of government spending to aggregate de- able level of per capita is highest, mand and less directly through the impact of there is no guarantee that the actual path to policy on disposable income and investment in- which the model converges is this "golden rule" centives; changes in the supply of money affect path. The capital-output ratio that prevails in the both nominal and real interest rates, and the long run will be affected by , among latter influence investment and consumption. other things. The long-run rate The transition from the short-run responses of will be consistent with nonaccelerating infla- the model to the long-run state after either a tion—which, in the model, depends both on the change in policy or some other disturbance is pace of productivity growth and the ratio of often lengthy. As shown in simulation results unemployment benefits to take-home pay. In the described below, however, after about one year long run, the rate of will equal the wages and prices are sufficiently flexible that the excess of the rate of growth of money over that short-run effects of fiscal and monetary policy on needed to support the growth rate of real activi- begin to be offset by supply responses ty; inflation also will depend on any exogenous reflected in movements in wages, prices, and trend in the ratio of income to money. Money is interest rates. neutral in the long run in the sense that a A crucial issue in building economic models is permanent change in the amount of money in the the appropriate way to model expectations. The economy will cause a proportionate change in use in the MPS model of autoregressive (AR) the price level, leaving all real magnitudes un- expectations contrasts to the approach using changed. A permanent change in the rate of (RE) that has prevailed in growth of money, however, will not be neutral in theoretical macroeconomic analysis during the the long run. The consequent changes in the rate past decade. The rational expectations hypothe- of inflation and the nominal rate of interest will sis is based on the assumption that economic have real effects because the demand for money agents use all available information in forming depends on the nominal rate of interest and expectations. In its strong form (SRE), this hy- because some provisions of the tax code are pothesis requires that expectations appearing in defined with respect to nominal, rather than real, a model be consistent with the forecasts of that magnitudes. model.4 For several reasons, the MPS model has In the short run, the properties of the model not adopted this constraint on modeling expecta- are quite different. Because wages and prices are tions. One is practical: the computational diffi- estimated to adjust slowly, neither labor nor culties in estimating and simulating a large-scale goods markets are continuously in equilibrium. model incorporating SRE are formidable; conse- This disequilibrium reflects the presence of ad- quently, most of the empirical models that have justment costs and the assumption that expecta- incorporated this approach have been small. tions are formed autoregressively (for example, Another reason is our belief that the SRE ap- expected inflation depends on past inflation). proach is extreme. The economy is sufficiently Thus, in the short run, the model has properties complex that economic agents are likely to un- that may be characterized as Keynesian: aggre- gate demand largely determines the level of 4. A weaker definition of rational expectations postulates output, and the unemployment rate of labor (and that expectations are optimal forecasts based on available the utilization rate of capital) may be either information. Costs of acquiring and evaluating information could cause economic agents to make use solely of past below or above the natural rate; fiscal policy observations of a variable in forming their expectations of its future values. In this restricted case, the AR model would be rational, but its parameters need not be constant over time: they could vary with changes in policy rules. The distinction 3. The level of per capita output also depends upon the between strong and weak rational expectations is made by level of technology embodied in the existing capital and P. A. V. B. Swamy, J. R. Barth, and P. A. Tinsley, "The on the relative price of energy. The latter determines the Rational Expectations Approach to Economic Modelling," energy intensity of production. Energy prices are exogenous Journal of Economic Dynamics and Control, vol. 4 (May in the model. 1982), pp. 125-47.

Digitized for FRASER http://fraser.stlouisfed.org/ Federal Reserve Bank of St. Louis February 1987

Structure and Uses of the MPS Quarterly Econometric Model of the United States 95

derstand it only imperfectly. Moreover, once To describe the structure of the model in more sluggish adjustments owing to sources other than detail, we split it into aggregate demand, aggre- expectational lags (such as long-term contracts) gate supply, and financial components, although are introduced into economic behavior, SRE a precise division between the demand and sup- models show characteristics similar to those of ply components of the model does not exist. models with AR expectations: both types of models generate business cycles and permit (ex- pected) policy actions to affect real outcomes.5 Aggregate Demand Nevertheless, the AR expectations approach does have some limitations, and it may not be The categories of aggregate demand specified in well suited for the analysis of issues such as the the model follow the National Income and Prod- consequences of large, well-understood shifts in uct Account (NIPA) disaggregation of gross na- policy, policy changes that are widely anticipat- tional product into consumption, investment, ed before they occur, or policies that would government purchases, and exports and imports. continuously surprise economic agents who were Within each category, further disaggregation has assumed to be using AR expectations. In these been made to ensure that the components mod- cases, we accept Lucas's critique that macroeco- eled are reasonably homogeneous. nomic models not based on rational expectations may fail to predict correctly the response to a Consumption. The key variable in the con- 6 policy action. In general, however, the practical sumption sector (CON) consists of spending on importance of the Lucas critique may not be that nondurable goods and services plus the imputed substantial. Sims argues that policymaking value of services from the stock of consumer should be viewed as a gradually evolving random durables. CON measures consumption of dura- process (and that it is viewed as such by the bles and thus differs from the NIPA measure of 7 public), not as discrete shifts in policy regimes. personal consumption because the latter includes Blanchard and Blinder present evidence that, the purchase of durables rather than their use. even after the major policy changes of the past The modeling of the behavior of CON is based decade, key macroeconomic equations with AR on the life-cycle theory, which maintains that expectations do not show the signs of instability consumers maximize utility over their lifetimes, that should have emerged if the Lucas critique subject to the initial value of their wealth and 8 were important. their expectations regarding nonproperty income and the rate of interest. The rate of interest measures the return to postponing consumption 5. One area of research on sources of adjustment lags unrelated to the formation of expectations is that on nominal to a later period. In the equation, nonproperty contracts. See, for example, Stanley Fisher, "Long-Term income is disaggregated into labor and transfer Contracts, Rational Expectations, and the Optimal Money components because of the different life-cycle Supply Rule," Journal of Political Economy, vol. 85 (Febru- ary 1977), pp. 191-205, and John B. Taylor, "Aggregate characteristics of the two—labor income ceases Dynamics and Staggered Contracts," Journal of Political with whereas transfer income may Economy, vol. 88 (February 1980), pp. 1-23. continue for the remainder of an individual's 6. Robert E. Lucas, Jr., "Econometric Policy Evaluation: A Critique," in Karl Brunner and Allan H. Meltzer, eds., The lifetime. The estimated long-run marginal pro- Phillips Curve and Labor Markets, Carnegie-Rochester Con- pensities to consume (MPC) out of labor and ference Series on Public Policy, vol. 1 (Amsterdam: North transfer income are 0.52 and 0.93 respectively. Holland, 1976), pp. 19-46. Wealth also is disaggregated into two compo- 7. Christopher A. Sims, "Policy Analysis with Economet- ric Models," Brookings Papers on Economic Activity, nents—corporate equities and all other types of 1:1982, pp. 107-52. wealth—with estimated MPCs of 0.05 and 0.09 8. Olivier J. Blanchard, "The Lucas Critique and the respectively. In theory, the nonproperty income Volcker Deflation," American Economic Review, vol. 74 (May 1984, Papers and Proceedings, 1983), pp. 211-15; Alan and wealth MPCs are not simply constants but S. Blinder, "Reaganomics and Growth: The Message in the are functions of the rate of interest. Only in the Models," in Charles R. Hulten and Isabel V. Sawhill, eds., case of the wealth MPCs, however, is this depen- The Legacy of Reaganomics (Urban Institute, 1984), pp. 199-228. dence recognized in the estimated equation, and

Digitized for FRASER http://fraser.stlouisfed.org/ Federal Reserve Bank of St. Louis February 1987

96 Federal Reserve Bulletin • February 1987

it is recognized indirectly through the inclusion sity to consume out of nonproperty income, the of property income—the product of the rate of ratio of consumption to total income (property interest and wealth—as an additional explana- and nonproperty income) falls, and the ratio of tory variable.9 The estimated long-run MPC out to income rises. The effect on the saving of property income is 0.40. ratio is very small given the estimated MPCs: in Because both property income and the market the long run each percentage point change in the value of wealth depend on the rate of interest, real after-tax rate of interest moves the private the model has two channels through which saving ratio in the same direction 0.1 to 0.2 interest rates alfect consumption. The latter percentage point.11 channel—variations in the market value of The consumption sector of the model also wealth—is estimated to be by far the stronger includes equations for the purchase of consumer one, except over very long periods. An increase durables; these purchases are treated as invest- in the rate of interest, for example, quickly ment decisions. Consumer durables are disaggre- reduces the market value of wealth, lowering gated into two components—new automobiles consumption and raising saving. But the higher and other consumer durables—and the equations level of saving then causes wealth to grow more for both are specified in stock-adjustment form rapidly, and thus the effect of wealth gradually with the desired depending on income, the diminishes over time.10 The effects of interest real rate of interest, relative prices, and the rate rates on consumption through the former chan- of depreciation. The desired stock of cars is also nel—variations in property income—occur more a function of the price of gasoline and the fuel gradually because property income reflects the efficiency of cars. average returns on existing assets and thus re- sponds slowly to changes in interest rates. The Investment. Fixed investment is divided into estimated MPC out of property income is posi- four categories: residential structures, produc- tive but less than one, and therefore an increase ers' durable equipment, producers' structures in the rate of interest raises both consumption excluding public utility structures and those used and saving through this channel. However, be- in petroleum drilling and mining, and other non- cause the proportion of the increase in property residential structures. The last category is exoge- income that is consumed is less than the propen- nous. Equations for the other three are based on

11. The exact relation between the saving ratio and the rate of interest is derived in Brayton and Mauskopf, "Federal 9. This formulation is based on the simplifying assumption Reserve Board MPS Quarterly Econometric Model," p. 184. that the wealth MPCs are linear functions of the rate of The private saving measure determined by the equation for interest. Property income is measured as the sum of rental, CON differs from NIPA private saving in the definitions of interest, dividend, and proprietors' income, corporate re- both the consumption and the income measures upon which tained earnings, and imputed income on consumer durables, the measure is based. The definition of consumption for the less an adjustment for losses due to inflation on fixed interest model includes the service flow of the durable stock, mea- assets. sured by the sum of the real interest rate and the depreciation 10. In the life-cycle model, the gradual lessening of the rate times the durable stock. By contrast, the NIPA con- wealth effect reflects the fact that only those cohorts of sumption measure includes the purchase of durables. On consumers subject to unexpected gains or losses on their average, this difference is likely to be small and would, in assets change their consumption plans. As time passes, these fact, be zero if the real rate of interest equaled the real growth cohorts form a smaller and smaller fraction, weighted by rate of the stock of consumer durables. The income measure wealth, of the aggregate population of consumers. From this in the CON equation differs from aggregate business and perspective, the rate at which the wealth effect diminishes household income in the NIPA accounts by including the should be gradual, and the parameter estimates in the CON imputed income on the stock of consumer durables and by equation support this conclusion. Assuming that saving flows excluding the inflation premium in the return on private into (or out of) the same wealth category that is subject to the holdings of government- and foreign-issued . The differ- shock to its market value, the rate at which the initial wealth ence in the income measure is more important than the effect dies out over time equals the corresponding wealth difference in the consumption measure in accounting for the MPC. Thus the induced changes in saving reduce the effect of divergence of the two saving measures. Note that NIPA wealth on consumption about 5 percent per year in the case of private saving equals the sum of personal and business a change in the market value of corporate equities and about 9 saving, and that the saving concept in the model includes percent per year for changes in the value of other forms of business saving because retained earnings are part of the wealth. household income measure.

Digitized for FRASER http://fraser.stlouisfed.org/ Federal Reserve Bank of St. Louis February 1987

Structure and Uses of the MPS Quarterly Econometric Model of the United States 97

the neoclassical approach, in which producers placement capacity. On the other hand, invest- add to the capital stock until its marginal product ment in capital whose existing units can be freely equals its implicit rental price. The implicit rental modified {putty-putty capital) responds more in price, which is often called the cost of capital, is the short run than in the long run to a change in calculated from the purchase price of capital, the the cost of capital. The short-run response is after-tax costs of debt and equity finance, eco- greater because it includes the one-time alter- nomic depreciation, tax depreciation allowances, ation of existing capital as well as the replace- and other tax parameters. ment of depreciating capital. The estimated paths For producers' durable equipment and the of adjustment indicate that producers' durable endogenous component of producers' structures, equipment is more likely to be putty-clay and it is assumed that the production technologies in producers' structures to be putty-putty.12 which each is used are of the constant-elasticity- The principal housing equation explains real of-substitution class. This assumption implies per capita expenditures on nonsubsidized hous- that the long-run response of each capital-output ing exclusive of brokers' commissions. The de- ratio has a constant elasticity with respect to sired stock depends on consumption (serving as changes in the cost of capital. For producers' a proxy for permanent income) and on the ratio structures, the estimated elasticity is about 0.5 of the rental price to the consumption deflator. (in absolute value); therefore, the percentage The rental price is a function of the real after-tax change in the long-run ratio of structures to mortgage rate, of tax parameters, and of the output is one-half the percentage change in the price of new residential construction. The de- inverse of its cost of capital. In the case of sired housing stock also depends on the nominal equipment, the estimated elasticity is not signifi- mortgage rate, which is a proxy for qualification cantly different from one (in absolute value); standards imposed by mortgage lenders based on and, to simplify elements of the supply side of the level of monthly mortgage payments. The the model, an elasticity of one is imposed. The elasticity of the housing stock with respect to the long-run ratio of equipment to output thus moves rental price is not constant, and the adjustment proportionately to the inverse of its cost of pattern of expenditures is consistent with a put- capital. ty-putty response. Brokers' commissions, which The equations for these two categories of are a significant fraction of NIPA housing expen- business fixed investment also indicate differ- ditures, are a function of the value of expendi- ences in the paths of adjustment of the types of tures on new single-family housing and of capital capital to their new, desired levels following a gains on existing homes. The latter is a proxy for change in the cost of capital. Investment in sales of existing houses. producers' durable equipment adjusts only grad- Real inventory investment is divided into four ually to the cost of capital, with the maximum categories: nondurable, retail durable, nonretail response achieved in the long run. By contrast, durable, and farm. The first three are modeled the short-run response of investment in produc- using a stock-adjustment specification in which ers' structures to its cost of capital exceeds the the desired inventory-sales ratios are functions long-run effect. These dynamic response pat- of the real rate of interest and tax parameters. In terns suggest that the two types of capital differ addition, short-run movements in inventories are in the degree to which existing units of capital influenced by the degree to which sales are higher can be modified for use with new quantities of or lower than the level anticipated by firms. The other inputs (labor and energy). On the one hand, unexpected component of sales is likely to cause when the factor proportions embodied in the unintended changes in inventory stocks because of initial design cannot be changed subsequently time lags in the process of producing and distribut- (putty-clay capital), investment occurs only to replace existing production capacity as it wears out, assuming output is constant. A change in the 12. The pattern of estimated response to the cost of capital cost of capital thus modifies only the amount of is not a precise indication of whether or not capital is ex post malleable because the response may also reflect adjustment, investment associated with this stream of re- expectational, and decisionmaking lags.

Digitized for FRASER http://fraser.stlouisfed.org/ Federal Reserve Bank of St. Louis February 1987

98 Federal Reserve Bulletin • February 1987

ing most goods. This buffer-stock element of in- proxies: the exchange rate forward premium, ventory behavior is captured by including the past changes in the exchange rate, and the devi- change in sales in the inventory equations. Farm ation of the real exchange rate from a level that inventories are exogenous. was consistent historically with balance of the current account. Equation estimates indicate Government Purchases. Federal, state, and that expectations of the level of the exchange local government purchases are each divided rate are regressive: a movement of the exchange into three components: employee compensation, rate in one direction generates the expectation construction spending, and other purchases. The that the exchange rate will move in the opposite federal components are exogenous. Behavioral direction. equations explain the three categories of state and local purchases. The principal explanatory variables are the level and growth rate of dispos- Aggregate Supply able income, the fraction of the population that is of school age, the unemployment rate, and the The supply side of the model includes the pro- amount of federal grants-in-aid. duction technology, the specification of firms' production and pricing behavior, and the demand Exports and Imports. Exports and imports are for inputs into the production process—labor, each divided into three general groups: merchan- capital, and energy. Besides treating these facets dise trade, service receipts and payments, and of the model, this section describes wage dynam- factor income flows. The principal behavioral ics and briefly discusses how the model's struc- equations in the merchandise trade group are for ture relates to several supply-side issues. These nonagricultural exports and nonpetroleum im- issues include the interest elasticity of private ports. In each case the key explanatory variables saving, the response of consumption to debt- are the level of GNP—domestic GNP for imports financed tax cuts, and the response of labor and foreign GNP for exports—and the relative supply to changes in marginal tax rates. prices of goods produced domestically and abroad. Agricultural exports are exogenous, and The Behavior of Producers: Factor petroleum imports depend on the difference be- and Prices. The cornerstone of the supply side of tween domestic petroleum demand and supply. the model is the production function. Output of Service exports and imports depend on the ap- the principal sector of the economy—nonfarm propriate GNP measure, the relative prices for business exclusive of services of the housing foreign and domestic goods, and the magnitude stock—is assumed to be produced using labor, of trade flows. Factor-income flows are modeled capital, and energy inputs with a Cobb-Douglas as the product of interest rates and stocks of production function. Thus, for a given level of assets. production, the minimizing of costs by firms In the model, the U.S. exchange rate (defined causes the demand for each input to be inversely as a weighted average of 10 bilateral exchange proportional to its own price relative to the price rates) is determined endogenously by the re- of output. This relation between factor demands quirement that the net capital inflow (outflow) and factor prices is based on the estimated equal the current account deficit (surplus). The parameters in the equation for producers' dura- specification of the capital account includes ble equipment, which is the only type of capital equations for domestic investors' holdings of included in the production function for this sec- foreign assets and foreign investors' holdings of tor.13 As described below, however, the demand domestic assets. The demand for these assets for energy does not appear to be based on the depends mainly on the differential between the short-term interest rate on domestic assets and 13. The role of the stock of producers' structures in the that on foreign assets, adjusted for the expected production process is much less clear than the role of rate of change of the exchange rate. This expect- equipment. Clearly, structures are required for most forms of production to occur, but the degree to which structures ed rate of change is represented by several contribute to output and can be substituted for other input

Digitized for FRASER http://fraser.stlouisfed.org/ Federal Reserve Bank of St. Louis February 1987

Structure and Uses of the MPS Quarterly Econometric Model of the United States 99

simple Cobb-Douglas technology, and research It may be expressed as the product of output and is planned to resolve this inconsistency in the a weighted average of the energy-output ratios structure of the model. on the various vintages in use, where the weights The specification of the supply side is compli- represent the share of output produced by each cated by the empirical observation that produc- vintage. The energy-output ratios for each vin- ers' durable equipment is putty-clay. In design- tage depend on the real price of energy at the ing this type of capital, producers choose time the capital was installed. In the estimated particular amounts of labor and energy to be equation, no attempt is made to use specific used with the capital from the possibilities of- vintage weights. Rather, the aggregate energy- fered by the ex ante Cobb-Douglas production output ratio is made a function of a long distribut- function. Once designed and installed, however, ed lag on the relative price of energy, and the that unit of capital is operable only with those slow estimated response of the aggregate ratio to amounts of labor and energy. Because of this the relative price is consistent with the putty- characteristic, it is important to distinguish be- clay characteristic. However, the estimated tween the determination of the optimal factor long-run real price elasticity of -0.33 is lower intensities on a particular vintage of capital and than expected and casts doubt on the appropri- the specification of the aggregate demands for ateness of the Cobb-Douglas production func- capital, labor, and energy. In general, only the tion. demands for these inputs associated with new Analogous to the aggregate demand for ener- vintages of capital will be responsive to changes gy, the aggregate demand for labor (measured in in factor prices; consequently, the aggregate hours) is the sum of labor required across the input demands will be relatively insensitive to different vintages of capital in use. Because the factor prices in the short run.14 Only in the longer optimal labor intensity of each vintage is mod- run, when the capital stock has been totally eled as a function of the optimal intensities of replaced, will the full (inverse) proportionality capital and energy and the parameters of the ex between factor prices and aggregate factor de- ante production function, aggregate labor de- mands hold. These characteristics were de- mand depends on actual output and the average scribed above for investment in producers' dura- capital-output and energy-output ratios in use. ble equipment. In addition, the ex ante production function The aggregate demand for energy is the sum of assumes a constant rate of labor-augmenting energy required on each vintage of capital in use. technological change; and, therefore, the intensi- ty of the labor input in production falls over time, ceteris paribus. Hours per unit of output also factors (particularly labor and equipment) is difficult to define. For this reason, they are not included in the produc- depend on the level of capacity utilization: an tion function. increase in utilization rates increases labor pro- This specification of production technology and firm be- ductivity as overhead labor is used more effi- havior is for the nonfarm business sector exclusive of the ciently, but it reduces productivity as machines services of the housing stock (the implicit rental value). The other sectors of the economy have much simpler production with higher operating costs (due primarily to relationships: output is proportional to labor input (govern- higher labor requirements) must be brought into ment, household, and institution sectors) and to capital input production. The latter relation between capacity (housing output) and is exogenous (farm) or equal to net factor income (the rest of the economy). The discussion in the utilization and productivity attempts to capture remainder of this section applies only to the nonfarm business indirectly variations over time in the vintages sector exclusive of housing output. actually used. 14. On the one hand, the factor intensities on the current vintage of capital depend, in principle, not only on current Prices are set as a markup over unit labor real factor prices but also on their expected values over the costs.15 The existence of the markup stems from lifetime of the vintage because of the putty-clay characteris- tic. On the other hand, lags in decisionmaking and delivery cause the factor proportions on the current vintage to depend 15. An alternative but equivalent way of specifying prices on lagged real factor prices. The use of lagged factor prices in is as a markup over unit factor costs. In this case, prices the model equations should thus be interpreted as reflecting move proportionately with all factor costs (with the sum of both autoregressive expectations and these other sources of the elasticities of factor costs equal to unity) and inversely lagged adjustment. with the rate of technological progress.

Digitized for FRASER http://fraser.stlouisfed.org/ Federal Reserve Bank of St. Louis February 1987

100 Federal Reserve Bulletin • February 1987

the assumption that firms generally operate as and a natural rate of unemployment exists.17 This oligopolists, setting prices above the level that rate is consistent with the maintenance of a would obtain under perfect competition, but not constant rate of inflation but is independent of so high as to induce additional firms to enter the the actual inflation rate. The economy cannot market. As specified in the equation, the actual deviate permanently from the natural rate with- markup varies positively with the degree of utili- out causing an unbounded acceleration or decel- zation of capital and labor and inversely with the eration of prices. In the model, the natural rate degree of price competition from foreign goods. moves positively with the ratio of unemployment In principle, the putty-clay nature of capital also benefits to wages and negatively with the rate of complicates the specification of price behavior. growth of productivity. With trend productivity Prices should be set such that the revenue stream growth of 1.0 percent and unemployment benefits of the newest vintage of capital equals the mark- at their current level, the natural rate of unem- up times the cost stream, both discounted over ployment is 6.4 percent. the lifetime of the capital. A consequence of this rule for setting prices is that labor productivity of Labor Supply. The specification of labor sup- only the most recent vintage of capital rather ply depends largely on demographic factors, with than labor productivity averaged across all vin- some cyclical influence by the employment rate. tages of capital should affect the price. The Although the responsiveness of the labor supply model's price equation, by contrast, uses aver- to the real after-tax wage rate is a critical element age labor productivity, a use that may be justified in the revival of classical , the equa- in part on the basis of short-run adjustment costs tion for aggregate labor supply does not contain for investment in new capital. such a term. The failure to find empirical support for this hypothesis may stem from (1) offsetting Wage Determination and the Natural Unem- income and substitution effects generated by a ployment Rate. The rate of change in compensa- change in the real wage of primary workers, and tion per hour is explained by an expectations- (2) the behavior of nonprimary workers, who augmented Phillips curve. Each percentage point respond positively to their own real wage but decrease in the unemployment rate is estimated negatively to the real wage of primary workers. to raise the rate of change in hourly compensa- tion in the same quarter by 0.85 percentage point Private Saving. Another tenet of supply-side at an annual rate. The behavior of compensation theory that our empirical work fails to substanti- per hour also depends on the rate of inflation in ate is a large positive response of the saving rate the prices of consumer goods, the change in the to the real after-tax rate of interest. As described minimum wage, the ratio of unemployment bene- above, the consumption equation indicates that, fits to wages, the change in female representation although the response of the saving rate to the in the labor force, and changes in employer real after-tax rate of interest is positive, the effect contributions to social security and unemploy- in the long run is weak. In addition, net foreign 16 ment insurance. saving is estimated to be relatively insensitive to As is well known, when the wage equation is the differential between interest rates on U.S. of the Phillips-curve variety, the coefficient on assets and those on foreign assets. One conse- price change determines the existence of a long- quence of the relative insensitivity to the real run tradeoff between inflation and unemploy- interest rate of both private and net foreign ment. If the coefficient is less than unity, there is saving is that persistent government budget defi- such a long-run tradeoff. If the coefficient is cits—which are a form of dissaving—reduce the unity, as it is estimated to be in the model's equation, the long-run Phillips curve is vertical,

17. The equation imposes a unitary price response, but the coefficient value when freely estimated is not significantly different from this value. The existence of a natural unem- 16. Compensation is inclusive of employee and employer ployment rate also requires that the elasticities of the output social security insurance contributions and of other fringe price with respect to factor prices sum to one. The model's benefits. price equation implicitly has this characteristic.

Digitized for FRASER http://fraser.stlouisfed.org/ Federal Reserve Bank of St. Louis February 1987

Structure and Uses of the MPS Quarterly Econometric Model of the United States 101

amount of wealth in individuals' portfolios allo- Financial Sectors cated to the private capital stock. Thus, in the long run, per capita output is smaller than it The financial sector includes equations for the would otherwise be.18 components of the money stock measures Ml The relation between government debt policy and M2 and for the behavior of bank reserves. A and private saving also hinges on the extent to term-structure equation links the long-term rate which individuals' consumption decisions are of interest to the current and past values of a sensitive to expected future tax liabilities. Under short-term interest rate and the rate of inflation. what has become known as the Ricardian equiva- Another equation equates the expected rate of lence proposition, a shift between tax and deficit return on equity (net of a risk premium) to the (bond) finance of government expenditures has expected rate of return on bonds. no effect on consumption.19 This conclusion is based on the intertemporal budget constraint Ml andM2 Components. Ml is modeled as the faced by the government, which ensures that sum of four components: currency plus travelers short-run changes in the financing mix change checks, demand deposits, Super NOWs, and only the time profile of tax liabilities, not their other checking deposits excluding Super NOWs. present value. This view also requires that con- The specification of each equation is based on sumers are forward-looking and see that changes the inventory-theoretic transactions model. The in the short-run financing mix do not affect their principal explanatory variables are the opportu- own intertemporal budget constraints. nity cost (market rate of interest less any explicit For both empirical and theoretical reasons, the return on the deposit), the price level (with specification of the model's consumption equa- homogeneity of degree one imposed), and real tion is not based on the Ricardian equivalence output or consumption. Except in the case of approach. The specification used has explained currency, the elasticity of deposits with respect past consumption well, even over recent years, to the opportunity cost increases as the opportu- when there has been a marked shift toward nity cost rises, and it approaches zero as the deficit finance. In the Ricardian view, the result- opportunity cost approaches zero. The demand ing increase in aftertax income should have been for currency has a constant elasticity with re- saved. Instead, consumption has increased and spect to the opportunity cost. private saving has remained low, as predicted by At the M2 level, all deposit categories in M2 the model's consumption equation. From a theo- but not in Ml,except overnight RPs and Eurodol- retical perspective, the Ricardian equivalence lars, are aggregated for modeling purposes. The proposition is not valid if such factors as liquidity share of household wealth allocated to this aggre- constraints, finite planning horizons, or uncertain- gate depends on measures of the opportunity ty significantly influence consumer behavior.20 cost as well as on the change in wealth due to personal saving (to reflect a temporary rise in the share of wealth allocated to these more liquid deposits when saving increases).

The Yields on Bonds and Equity. The term- 18. In the long run, government deficits always crowd out structure equation relates the yield on corporate gross output; and, unless the capital-output ratio exceeds that consistent with maximum sustainable net output, deficits bonds to current and lagged values of the com- crowd out net output also. mercial paper rate and the rate of inflation. 19. Robert J. Barro, "Are Government Bonds Net Because the effective duration or maturity of a Wealth?" Journal of Political Economy, vol. 82 (November/ December 1974), pp. 1095-117. coupon bond shortens as interest rates rise, the 20. See Robert B. Barsky, N. Gregory Mankiw, and Ste- length of the distributed lags on both the com- phen R. Zeldes, "Ricardian Consumers with Keynesian Pro- mercial paper and inflation rates is allowed to pensities," American Economic Review, vol. 76 (September 1986), pp. 676-91, and the references cited therein. To the vary with the recent level of the commercial 21 extent that these potential factors affect the sensitivity of paper rate. The lag length is estimated to be consumption to contemporaneous aftertax income, they are consistent with the general specification of the model's con- 21. The duration shortens as the interest rate rises because a sumption equation, which freely estimates this parameter. larger fraction of the present value of all payments on a bond—

Digitized for FRASER http://fraser.stlouisfed.org/ Federal Reserve Bank of St. Louis February 1987

102 Federal Reserve Bulletin • February 1987

shorter the higher are recent values of the short- Ml by purchasing through open market opera- term rate. The real return on equity is calculated tions the fraction of the increase in government as a weighted average of dividends and cash debt that the nongovernment sectors do not wish flow, divided by the market value of equity; most to hold at the base value of the short-term of the weight is on dividends. This real rate is interest rate. As shown in entry 1 in table 1, these equated to the real return on bonds—the corpo- assumptions result in a response of the level of rate bond rate less a long distributed lag on the real GNP that peaks at 3.8 percent after four rate of inflation—plus a constant to reflect a risk years and subsides a bit thereafter. This is a premium. typical multiplier-accelerator pattern: the adjust- ment dynamics of most of the investment equa- tions cause the short-run response to exceed the MODEL PROPERTIES long-run response. The size of the long-run re- sponse depends inversely on the degree to which The previous sections have described key com- increases in income escape from the domestic ponents of the structure of the model. This part spending chain in the form of increases in saving, presents simulations to demonstrate more con- a rise in , and purchases of foreign goods. cretely the properties of the model, particularly The second entry shows the consequence of in the short run. Each case has a base simulation altering the monetary policy assumption to one in which the model is adjusted to replicate the in which Ml is held at its base path. The higher historical path of the economy. Then a second level of activity generated by the change in fiscal simulation, in which the time path of an exoge- policy requires an increase in interest rates to nous variable is altered, is performed. The re- hold money demand equal to the fixed supply. sults presented below are differences between (In the loanable funds market, the rise in interest the second simulation and the base simulation.22 rates is necessary to induce the nongovernment sectors to hold all of the increase in government debt.) Under this monetary policy assumption, Response to a Fiscal Shock the boost to real GNP is considerably damped as the higher level of the interest rate crowds out In this simulation, real federal purchases are some interest-sensitive private spending. The permanently increased by 1 percent of real GNP. peak response is 1.4 percent after two to four All tax rates are held constant. The simulation is quarters. performed four different ways to show the rela- In entry 3, prices are endogenized, but wages tive importance of demand and supply responses are still exogenous.23 Monetary policy is again and the dependence of the outcome on the stance characterized by fixed Ml. In this case, produc- of monetary policy. In the first case, the supply ers are permitted to choose the price at which to side of the model is suppressed by holding supply output although labor is still available at wages, prices, and relative factor proportions at the fixed wage rate. Given these assumptions, their base values to highlight the demand effects the real GNP response is further damped after of the fiscal change; thus the supply of output is the first two years, but only by a little. After the first assumed to move one for one with changes in two quarters, prices rise slightly, reflecting some demand at an unchanged price. Monetary policy upward slope to the supply curve for output. The is characterized by holding the federal funds rate higher price level retards aggregate demand at its base value. From the perspective of the through a shift in the distribution of income loanable funds market, fixing the federal funds toward profits and away from real disposable rate requires the monetary authority to increase income (such a shift reduces demand in the short run but not in the long run when households recognize their gains as shareholders). It retards both the coupon and the repayment of principal—is then due to the nearer-term payments. 22. Because the model is nonlinear, the size of the multiplier depends on the characteristics of the base simulation. Experi- 23. The mix of inputs in the production process also is ments have shown that this dependence on initial conditions allowed to change, but this change is of only small quantitative can be significant. importance over the period being simulated.

Digitized for FRASER http://fraser.stlouisfed.org/ Federal Reserve Bank of St. Louis February 1987

Structure and Uses of the MPS Quarterly Econometric Model of the United States 103

1. Simulated responses to an increase in purchases by the federal government1 Percent, except where noted

Quarter following shock Type of simulation 1 2 4 8 12 16 20

1. Exogenous supply side: federal funds rate fixed Real GNP 1.3 1.7 2.3 3.1 3.7 3.8 3.1

2. Exogenous supply side: Ml fixed Real GNP 1.2 1.4 1.4 1.2 1.1 .8 .4 Federal funds rate (percentage points) 1.02 1.24 1.12 .80 .89 .68 .32

3. Exogenous wages: MI fixed Real GNP 1.3 1.5 1.4 1.2 1.0 .5 .1 GNP deflator 0 0 .1 .3 .4 .5 .5 Federal funds rate (percentage points) .98 1.36 1.30 1.05 1.18 .98 .48

4. Full model: Ml fixed Real GNP 1.3 1.4 1.3 1.0 .2 -.9 -2.0 GNP deflator 0 .1 .3 .9 1.8 2.7 3.0 Federal funds rate (percentage points) 1.00 1.42 1.49 1.67 2.20 2.15 1.31

1. Real federal purchases are increased by 1 percent of the base over the period 1981-85, with the base simulation constructed to value of real gross national product. The responses were calculated replicate historical values. aggregate demand also by further raising interest supply-side response that will cause the long-run rates, given the fixed Ml policy. real output multiplier to be negative: the crowd- In each of these three cases, the more expan- ing out of private investment lowers the private sionary fiscal policy leads to a permanent in- capital stock. This is a very gradual process, crease in output because of the suppression of however, and is not apparent over the five-year one or more elements of the supply side of the period shown in the table. model. In a fourth case, when wages are endo- Comparing entries 2 and 4 indicates the rela- genized and the full model is simulated (with tive importance of the supply side of the model fixed Ml), the picture changes dramatically. The over short periods. Both of these multipliers are stimulative fiscal policy now has only a transi- based on the same monetary policy assumption, tory positive effect on real activity. No longer but entry 2 suppresses the supply side of the can firms boost employment at a fixed wage rate; model whereas entry 4 includes it. The results rather, the increase in employment required to for real GNP are virtually the same for the first produce the initially higher level of output leads quarter and are fairly close after one year, but to higher wages. Higher wages boost prices, then diverge significantly. For the period simu- which in turn put further upward pressure on lated, supply-side influences work primarily wages. The wage-price acceleration (relative to through the wage-price sectors; however, in the the values of wages and prices in the base long run, the effect on potential output of simulation) stops as higher prices push up inter- changes in the private capital stock becomes the est rates and crowd out private spending. Private dominant factor.

spending is fully displaced by the highe1 r level of The response of the model to other exogenous government purchases after about 3 /2 years. The shifts in aggregate demand, such as a shift in the response of output then turns negative because investment function, is similar over a five-year the higher price level is inconsistent with the period to that from a change in government unchanged supply of money. In general, the purchases. Over longer periods, however, the dynamic path to the long-run equilibrium will be responses will not be the same to the extent that characterized by gradually damped oscilla- tions.24 The expansive fiscal policy also sets off a

fixed supply of money, an increase in real activity requires that interest rates rise to hold money demand equal to the un- 24. The model tends to oscillate after a shock, especially if changed supply. The higher interest rates eventually lower monetary policy takes the form of holding a monetary aggregate activity. The scenario is then repeated in reverse. The other, unchanged. There are two basic reasons for the cycling. One is and more important, source of cycling is the specification of the the longer lag between interest rates and real activity compared wage equation in growth-rate form. As a result, the real wage with the lag between interest rates and money demand. With a oscillates in response to a shock.

Digitized for FRASER http://fraser.stlouisfed.org/ Federal Reserve Bank of St. Louis February 1987

104 Federal Reserve Bulletin • February 1987

they have different implications for the private the direct effect of monetary policy on financial capital stock and potential output. markets. The effects on selected financial varia- bles are presented in the top third of the table. An increase in Ml initially depresses the short- Response to a Shock in the Level of Money term interest rate by a disproportionately large amount. The "overshooting" of interest rates Because a principal reason for building the model stems from the small contemporaneous elasticity was to focus on monetary and financial forces, of Ml (relative to its long-run elasticity) with much attention has been paid over the years to respect to the short-term interest rate. Because exploring the channels through which monetary the corporate bond rate is modeled by a distribut- factors affect the real economy. This issue has ed lag on the commercial paper rate—and the long been a subject of controversy at both the dividend-price ratio by a distributed lag on the theoretical and the empirical levels. The role of bond rate—these rates can also overshoot initial- money in the model lies well between the ex- ly. By the end of the fifth year, the effect on the tremes of the monetarist school, on the one commercial paper rate is close to 1 percentage hand, and the view that money is a relatively point; the effect on the bond rate is slightly unimportant factor in business cycles, on the smaller; and the change in the dividend-price other. There is, however, a fundamental differ- ratio is about half the change in the bond rate, ence between the short- and the long-run effects reflecting the historical average of the dividend- of money in the model. Over the short run, an earnings payout ratio. The percentage increase in autonomous change in the money supply signifi- stock market wealth equals the percentage de- cantly affects aggregate demand because of the cline in the dividend-price ratio, and the change estimated importance of the real interest rate and in land prices moves inversely but slowly with of wealth in influencing demand. Nevertheless, the decline in the bond rate. By quarter 20, the the effect on demand occurs solely through percentage increase in land prices is about 70 changes in the interest rate—neither the level nor percent of the long-run change consistent with the rate of growth of money enters the behavioral the decline in the bond rate.26 equations (except, of course, the money demand In panel 2, the changes in interest rates and equations). In the long run, an autonomous wealth after 20 quarters, as reported in the last change in the level of money has no effect on the column of panel 1, are fed through to the equa- real economy and, instead, will determine only tions for the components of demand. By using the level of prices. the long-run changes in interest rates and wealth To isolate some of the factors influencing the (that is, those that appear after 20 quarters) full model response to a permanent change in the rather than the complete path as reported in level of money, the simulations were decom- panel 1, the simulation compresses the period posed into several steps. The results are present- over which these demand responses would ap- ed in table 2. pear. Each component of demand is treated In the first stage, the level of Ml is permanent- separately from all other components, and aggre- ly increased by 1 percent relative to the baseline gate output and income are held fixed to abstract value of Ml. Only interest rates and the interest- from multiplier-accelerator effects on spending. sensitive components of wealth are endogen- Thus the direct effects of changes in interest ized.25 Because prices and output are held fixed, rates and wealth on individual components of changes in the rest of the economy do not feed demand are isolated.27 back to the financial sectors, so we can measure 26. The estimated long-run elasticities of land values with respect to the bond rate are (in absolute value) 0.81 for farmland, 0.73 for household ownership of land, and 1.02 for other noncorporate land. 25. Although market values of housing, consumer durables, 27. The percentage change in land prices that is used for the and bonds (with a maturity in excess of one period) would also simulations reported in panel 2 is the change in land prices in change with interest rates, the model captures changes only in evidence when land prices have fully adjusted to the changes in the capitalized values of the stock market and of land. the bond rate.

Digitized for FRASER http://fraser.stlouisfed.org/ Federal Reserve Bank of St. Louis February 1987

Structure and Uses of the MPS Quarterly Econometric Model of the United States 105

In the model, the principal channel through level of output. The modeling of consumer dura- which money and interest rates affect spending is bles, business fixed investment, housing, and the cost of capital, which is the gross return on inventory investment explicitly recognizes this capital given the rate of return on investor equi- link between the cost of capital and investment ty, the rate at which capital depreciates, the tax spending. rate, the cost of debt, and the rate of inflation. A Panel 2 reveals considerable variation in the reduction in the rate of return on equity or debt— way various kinds of investment respond to a holding fixed the rate of inflation—lowers the decline in the interest rate. Several factors ac- cost of capital and raises the optimal capital- count for this variation. A change in the interest output ratio and the rate of spending at a given rate has a bigger impact on the cost of capital the

2. Simulated responses to an increase in money1

Quarter following shock

1 4 8 12 16 20

1. Ml increased: only interest rates endogenous

Commercial paper rate (basis points) -252 -111 -83 -89 -99 -97 Corporate bond rate (basis points) -81 -76 -51 -59 -88 -94 Dividend-price ratio (basis points) -47 -51 -30 -25 -42 -44 Corporate equity Billions of dollars 149 141 103 130 203 293 Percent 12.2 Noncorporate land Billions of dollars 9 28 47 68 86 104 Percent 4.1

2. Interest rate and wealth changed by long-run effect (as reported in quarter 20 of panel one); aggregate output, income, and prices exogenous Producers' durable equipment Billions of 1982 dollars .7 2.4 4.2 8.4 10.7 13.2 Percent .3 1.0 2.0 3.2 3.6 4.1 Producers' structures Billions of 1982 dollars 0 3.7 5.3 7.4 7.5 6.9 Percent 0 2.4 3.9 5.6 5.1 4.5 Housing investment Billions of 1982 dollars 2.6 10.0 8.6 9.6 7.8 6.3 Percent 1.9 9.1 7.4 6.0 4.6 3.5 Inventory investment Billions of 1982 dollars .5 1.7 1.7 1.1 .8 .7 Consumer purchases of new autos Billions of 1982 dollars 0 .8 1.0 1.0 .9 .8 Percent 0 1.9 1.7 1.4 1.2 1.1 Consumer durables other than autos Billions of 1982 dollars .2 1.7 2.9 3.2 3.1 3.1 Percent .1 .8 1.4 1.4 1.2 1.2 Consumption2 Without consumption price change Billions of 1982 dollars 2.2 8.7 13.1 21.0 25.2 27.9 Percent .1 .4 .6 1.0 1.1 1.2 With consumption price change Billions of 1982 dollars 4.7 14.6 20.0 29.0 33.2 35.8 Percent .2 .7 .9 1.3 1.5 1.5

3. Full-model responses for Ml increase Real GNP Billions of 1982 dollars 11 38 36 17 -24 -61 Percent .3 1.2 1.1 .5 -.7 -1.7 GNP deflator (percent) 0 .1 .6 1.4 2.1 2.4 Commercial paper rate (basis points) -229 -15 53 89 56 1 Corporate bond rate (basis points) -82 -20 34 34 49 41 Unemployment rate (percentage points) -.1 -.4 -.5 -.4 0 .6 Exchange rate (percent) -2.9 -2.4 -2.8 -.3 .1 2.8

1. The level of Ml is permanently increased by 1 percent. The 2. Includes the service flow from the stock of consumer durables responses were calculated over the period 1981-85 with the base but not expenditure on new durables, simulation constructed to replicate historical values.

Digitized for FRASER http://fraser.stlouisfed.org/ Federal Reserve Bank of St. Louis February 1987

106 Federal Reserve Bulletin • February 1987

longer the life of the capital.28 Therefore, housing The second consumption row in panel 2 allows and nonresidential structures are more sensitive for an additional influence of interest rate to interest rate changes than are consumer and changes on consumption spending. The model producers' durables, ceteris paribus. Differences definition of consumption includes the imputed in the estimated elasticity of each type of capital flow of services from the stock of consumer to the cost of capital also matter. The larger durables. Because an element of the price of response of producers' durable equipment to the these services is the (real) interest expense on a cost of capital, compared with that of structures, unit of consumer durables, a decline in the offsets some of the greater sensitivity of the cost interest rate directly lowers the price of con- of capital to interest rates that longer-lived struc- sumption, thus stimulating consumption for a tures have. In addition, because the figures in given level of nominal income.29 As shown in the panel 2 represent the dynamic paths of spending last row, including this effect boosts the con- rather than the steady-state effects, the re- sumption response about 50 percent. sponses reflect differences among the markets Another channel that at one time was impor- for the various capital goods in the time between tant in linking the financial and real sectors of the placing an order and receiving the capital and in model was nonprice in the mort- the speed with which actual changes in interest gage market. However, the causes of credit rates lead to expected changes. Equally impor- rationing—deposit rate ceilings, usury con- tant for the dynamic paths is the ex post possibil- straints on mortgage rates, and the lack of inte- ity for factor substitution. Because of its putty- gration of the mortgage and general capital mar- clay nature, producers' durable equipment ad- kets—have diminished considerably over the justs relatively slowly to the change in interest past decade with the deregulation of both the rates, and the short-run response of investment deposit and the mortgage markets. The structure in this type of capital never exceeds the long-run of the model's housing sector thus assumes that response. By contrast, all other categories of the influence of credit rationing has been negligi- capital show a tendency to overshoot in the short ble since the mid-1970s. run. The full-model response to a permanent in- Another way financial variables affect the real crease in the level of Ml, reported in panel 3, economy is by inducing short-run variations in allows for the feedback from output to prices and household net worth. In the model, the market interest rates and for multiplier-accelerator ef- value of corporate equity is determined by capi- fects on output. Initially, interest rates are low- talizing the dividend stream by the dividend- ered and output is stimulated by the factors price ratio, and the market value of land is described in the first two panels of the table. The determined by capitalizing the expected real out- higher level of output then leads to increases in put of land by the real rate of interest on bonds. prices, and the higher output and higher prices A dollar increase in the value of the stock market together subsequently raise interest rates—de- and the value of land is estimated to increase spite the increase in Ml. Higher interest rates consumption by five cents and nine cents respec- then depress spending relative to the base path, tively. The first consumption row in panel 2 and prices and interest rates will eventually shows the dynamic response of consumption to reverse direction. By quarter 20, the model solu- changes in wealth (consistent with a decline in tion remains far from its steady-state response: the bond rate of a little less than 1 percentage the increase in the price level (2.4 percent) is well point), assuming no change in property income. above the 1 percent that in the long run is By quarter 20, the effects of wealth on consump- tion approximately equal the sum of the effects of the cost of capital on the other categories of demand. 29. One component of the model's measure of nominal property income is not held constant in this case. A decline in consumption prices—given past prices—initially reduces the capital gains households earn on their holdings of government 28. This effect occurs because for longer-lived assets the rate and foreign debt. Because this change in the price level is of interest is a larger fraction and the depreciation rate a smaller permanent, the rate of inflation is ultimately unchanged, so this fraction of the cost of capital. effect does die out.

Digitized for FRASER http://fraser.stlouisfed.org/ Federal Reserve Bank of St. Louis February 1987

Structure and Uses of the MPS Quarterly Econometric Model of the United States 107

consistent with the change in money, and the bles are derived as residuals from autoregressive level of output is 1.7 percent below its long-run equations 32 response of no change. Policy Alternatives

USES OF THE MODEL The model offers a convenient framework for analyzing the effects of alternative monetary and Forecasting fiscal policies or of changes in other exogenous variables. Despite the complexity of the model, The staff of the Federal Reserve Board regularly such simulations often require judgmental adjust- prepares forecasts of the economy, and one ments or adaptations of model equations to cap- element in the forecasts is a projection derived ture fully the important aspects of the issue being from the quarterly model. The model forecast is analyzed. For instance, in simulating the effect of not a purely mechanical projection; rather, it lower energy prices, a judgmental adjustment typically depends on constant adjustments (add has to be made both to the projection of domestic factors) applied to many of the behavioral equa- production of petroleum and to investment in tions. Add factors are introduced for three rea- petroleum drilling rigs because those variables sons: (1) to adjust equations whose post-sample are exogenous to the current structure of the errors have deviated from the estimated error model. characteristics and for which there has been either insufficient time to reestimate the equation Special Uses of the Model or lack of success at respecifying the equation; (2) to reflect shocks to behavior that can be In addition to its use for forecasting and short- identified with events not captured by the struc- run multiplier analysis, the model has served ture of an equation and whose magnitude and other purposes over the years. Often it has been persistence can be roughly predicted; and (3) to simulated to determine the long-run implications incorporate an estimate of an equation's near- of policy changes. A study by Anderson, Ando, term error based on high-frequency data obser- and Enzler, for example, examined the effect of vations. In the last case, a pooled forecast from various fiscal policies on the steady-state values the quarterly model and a monthly short-term of output and the real rate of interest.33 In one set forecasting model are used as aids in generating of simulations reported, the long-term ratio of 30 add factors. The monthly model combines di- net federal debt to nominal GNP was increased rect observations on high-frequency data with a from 0 to 100 percent with the consequence that mix of behavioral and autoregressive equa- the new steady state had a real rate of interest 31 tions. that was higher by 5 percentage points and a As part of the forecasting process, a stochastic level of real GNP that was 5 percent lower. In simulation technique is used to generate confi- another study of fiscal policy, Brayton and Clark dence ranges or probability distributions for the used the model to investigate the longer-run model projection. The approach involves repeat- consequences of the 1981 Economic Recovery edly simulating the model, subjecting each be- Tax Act (ERTA).34 In this case, rather than havioral equation and most exogenous variables to random shocks based on their historical error 32. The stochastic simulation methodology was developed characteristics. The errors for exogenous varia- and implemented by Peter Tinsley, James Berry, Gerhard Fries, Doug Handler, and Arthur Kennickell. It has also been extensively used for the analysis of policy strategies as de- 30. Carol Corrado and Mark Greene, "Reducing Uncertain- scribed in the text. ty in Short-Term Projections: The Linkage of Monthly and 33. Robert Anderson, Albert Ando, and Jared Enzler, "In- Quarterly Models" (Board of Governors of the Federal Reserve teraction between Fiscal and Monetary Policy and the Real System, Division of Research and Statistics, Special Studies Rate of Interest," American Economic Review, vol. 74 (May Section, December 1983). 1984, Papers and Proceedings, 1983), pp. 55-60. 31. Carol Corrado and David Reifschneider, "A Monthly 34. Flint Brayton and Peter B. Clark, The Macroeconomic Forecasting Model of the U.S. Economy" (Board of Governors and Sectoral Effects of the Economic Recovery Tax Act: of the Federal Reserve System, Division of Research and Some Simulation Results, Staff Studies 148 (Board of Gover- Statistics, Special Studies Section, September 1986). nors of the Federal Reserve System, 1985).

Digitized for FRASER http://fraser.stlouisfed.org/ Federal Reserve Bank of St. Louis February 1987

108 Federal Reserve Bulletin • February 1987

simulating the model until it reached an equilibri- Most recently, Anderson and Enzler extended um growth path, they adjusted monetary policy this approach to develop a hierarchical policy to offset the impact of ERTA on real output. reaction function and used stochastic simulation Several results emerged from the study: real to contrast it to the case of Ml targeting.37 This interest rates were significantly higher as a result study also investigated these types of policies in of ERTA; investment was depressed as the in- a forward-looking framework that permits the crease in real interest rates more than offset the policy setting in each period to depend on the stimulus to investment from the acceleration of consequences of the policy as given by determin- depreciation allowances; and the shift from tax istic simulations of the model. to bond finance of federal expenditures, implicit in ERTA, would have led eventually to an unsta- ble budgetary position in which government debt CHANGES TO THE STRUCTURE grew explosively. OF THE MODEL Some other special uses of the model have centered on the analysis of alternative strategies All macroeconomic models are at best approxi- for conducting monetary policy. Two papers by mations to the true structure of the economy. Kalchbrenner and Tinsley in the mid-1970s ap- Exact models cannot be created because of the plied optimal control techniques to this topic.35 complexity of the economy. Moreover, empirical Subsequent studies have used the stochastic methods are limited to estimating behavioral simulation methodology, described above, to an- relations based on available data, however im- alyze a wider range of policy design issues than perfect. Although one hopes to model the impor- can be studied using deterministic simulations tant features of the economy accurately, the (for example, policies that react to shocks) and to passage of time inevitably reveals the failure of evaluate policies on the basis of the degree of parts of a model's structure to explain adequate- control achieved over ultimate targets such as ly economic events. Thus a need to reexamine inflation and unemployment. A series of papers the structure of a model persists. by Tinsley and von zur Muehlen used stochastic The process of reexamination has led over model simulations for three purposes: (1) to rank time to many modifications of the quarterly strategies that focused directly on the ultimate model structure. Among the most important targets with those based on intermediate targets changes was the replacement of the original wage (Ml, M2, nominal GNP, the federal funds rate, equation—which implied a long-run tradeoff be- and the monetary base); (2) to determine whether tween inflation and unemployment—with one in the choice of an intermediate target more closely which no such tradeoff existed.38 The long-run related to the ultimate targets was superior to characteristics of the model's supply side also targeting on variables causally further removed; were altered with the inclusion of the average and (3) to evaluate conditional intermediate tar- capital-output ratio (and, at a later time, the geting in which policy settings were revised in energy-output ratio) in the productivity equa- light of events affecting the ultimate targets.36

Studies Section, November 1983); and P. A. Tinsley and P. von zur Muehlen, "Conditional Intermediate Targetting" 35. J. H. Kalchbrenner and P. A. Tinsley, "On the Use of (Board of Governors of the Federal Reserve System, Divi- Optimal Control in the Design of Monetary Policy," Special sion of Research and Statistics, Special Studies Section, Studies Papers 76 (Board of Governors of the Federal Reserve October 1983). System, Division of Research and Statistics, Special Studies 37. Robert Anderson and Jared Enzler, "Policy Design: Section, July 1975), and J. H. Kalchbrenner and P. A. Tinsley, Policy Rules That Use Forecasts," in R. Dornbush and "On the Use of Feedback Control in the Design of Aggregate S. Fisher, eds., and Finance: Essays in Monetary Policy,"American Economic Review, vol. 66 (May Honor of Franco Modigliani (Cambridge, Mass., and Lon- 1976, Papers and Proceedings, 1975), pp. 349-55. don: M.I.T. Press, forthcoming). 36. P. Tinsley, and P. von zur Muehlen, "A Maximum 38. The original wage equation embodying the long-run Probability Approach to Short-Run Policy, "Journal of tradeoff is described in George de Menil and Jared Enzler, Econometrics, vol. 15 (January 1981), pp. 31—48; P. Tinsley "Prices and Wages in the FR-MIT-Penn Econometric Mod- and P. von zur Muehlen, "The Reliability of Alternative el," in O. Eckstein, ed., The Econometrics of Price Determi- Intermediate Targets (Board of Governors of the Federal nation (Board of Governors of the Federal Reserve System, Reserve System, Division of Research and Statistics, Special 1972), pp. 277-308.

Digitized for FRASER http://fraser.stlouisfed.org/ Federal Reserve Bank of St. Louis February 1987

Structure and Uses of the MPS Quarterly Econometric Model of the United States 109

tion. The foreign sector of the model was elabo- portfolio equations that determine international rated considerably in the mid-1970s in response capital flows have been another source of prob- to the shift from fixed to floating exchange rates lems. These equations do not adequately capture and to the expansion of international trade. As the portfolio shifts and exchange rate movements mentioned above, the structure of the model's that have taken place since the early 1980s. housing sector has changed from one in which Finally, the role of energy in the production credit rationing and the supply of mortgage funds technology will be reexamined, given the incon- played an important role to one in which interest sistency between the estimated price elasticity of rates capture all supply factors. the demand for energy and the use of a Cobb- Work is now planned in several areas to im- Douglas production function. Work in this area is prove the current structure of the model. Recent- likely to affect the labor demand equation, and it ly, considerable effort has been devoted to ex- may have implications for the specification of the plaining the surprisingly strong growth of Ml investment equations. • since 1985. New equations are anticipated for components of Ml and M2 as well as for the own Paulus, "Some Problems of Money Demand," Brookings 39 Papers on Economic Activity, 1:1976, pp. 261-80; Richard D. rates of return on several components. The Porter, Thomas D. Simpson, and Eileen Mauskopf, "Finan- cial Innovation and the Monetary Aggregates,"Brookings Papers on Economic Activity, 1:1979, pp. 213-29; P. A. Tinsley and B. Garrett, with M. E. Friar, "The Measurement 39. This research, which is being undertaken by Richard of Money Demand," Special Studies Papers 133 (Board of Porter, George Moore, David Small, Jong Park, and Dan Governors of the Federal Reserve System, Division of Re- Bagatell, is summarized in Richard D. Porter, Paul A. Spindt, search and Statistics, Special Studies Section, October 1978); and David E. Lindsey, "Econometric Modeling of the De- Thomas D. Simpson and Richard D. Porter, "Some Issues mands for the U.S. Monetary Aggregates: Conventional and Involving the Definition and Interpretation of the Monetary Experimental Approaches" (paper presented at the Pacific Aggregates," in Federal Reserve Bank of Boston, Control- Basin Central Bank Conference on Economic Modeling, ling the Monetary Aggregates III, Conference Series 23 Sydney, Australia, December 1986). Over the years, money (FRBB, October 1980), pp. 161-234; and Flint Brayton, Terry demand has proved to be a difficult area to model, and it has Farr, and Richard Porter, "Alternative Money Demand been the subject of considerable research by members of the Specifications and Recent Growth in Ml" (Board of Gover- Division of Research and Statistics as well as by other nors of the Federal Reserve System, Division of Research researchers. Previous studies of money demand by division and Statistics, Econometric and Computer Applications Sec- economists include Jared Enzler, Lewis Johnson, and John tion, May 1983).

Digitized for FRASER http://fraser.stlouisfed.org/ Federal Reserve Bank of St. Louis