CBO'S METHOD FOR ESTIMATING POTENTIAL OUTPUT October 1995

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CBO'S METHOD FOR ESTIMATINGPOTENTIAL OUTPUTOctober 1995

The Congressional Budget Office's (CBO's) estimate of potential output plays animportant role in its economic forecast. This memorandum describes how CBOestimates and projects potential output. It also compares the estimates of otheragencies and discusses the advantages and disadvantages of alternative methods.Robert Arnold of CBO's Macroeconomic Analysis Division prepared thememorandum under the supervision of Robert Dennis and John Peterson. The manuscript benefited from useful suggestions by Jim Blum, Kim Kowalewski, and DougHamilton. Laurie Brown, John Romley, and Jennifer Wolfson helped produce thefigures. Sherry Snyder edited the memorandum, and Chris Spoor provided editorialassistance.

CONTENTSSUMMARYvINTRODUCTION1POTENTIAL OUTPUT BASEDON A GROWTH MODEL1ESTIMATING HISTORICAL VALUESOF POTENTIAL OUTPUT4The Nonfarm Business Sector 4The Other Sectors 11PROJECTING POTENTIAL OUTPUT13The Nonfarm Business Sector 13The Other Sectors 16The Foreign Sector 16CBO'S ESTIMATE OF POTENTIAL OUTPUT17ADVANTAGES AND DISADVANTAGES OFTHE GROWTH MODEL23

TABLE1.Potential Output and Related Series,Calendar Years 1950-200219FIGURES1.Hours Worked and Potential Hours Worked2.Real GDP and Potential Real GDP183.The GDP Gap and the Change in Inflation214.Comparison of the GDP Gap as Estimated byCBO and Other Forecasters22iv9

SUMMARYEvaluating the state of the economy, gauging inflationary pressures, and projectinglong-term growth require a measure of the economy's productive capacity. Onesuch measure, referred to as potential output, is an estimate of the level of outputconsistent with a stable rate of inflation. Output can exceed its potential level, butonly at the risk of increasing inflation. Similarly, when an economic slowdowndrives output below its potential level, inflation generally recedes.Potential output is an important component in the Congressional BudgetOffice's (CBO's) economic forecast. It plays a role in the long-term projection forreal gross domestic product (GDP) in the forecast for inflation, and it is used tocompute the standardized-employment deficit, which is an important indicator ofthe direction of fiscal policy.Estimating Potential OutputCBO uses the framework of a neoclassical growth model to estimate historicalvalues and project future values of potential output. Growth models use aneoclassical production function, combined with assumptions about the growth ofthe labor force and the rate of saving, to determine how output will grow over thelong term. The primary advantage of using a growth model to estimate and projectpotential output is that it explicitly recognizes the contribution of capital toproduction, unlike some methods of estimating potential output.CBO bases its measure of potential output on real GDP, which comprises fivesectors: nonfarm business, farm, government, nonfarm housing, and householdsand nonprofit institutions. Since different sectors use different methods ofproduction, using a single production function to model overall output would beinappropriate. Also, the necessary data are unavailable for some of the sectors,which prevents the use of a single production function for the whole economy. Forthese reasons, CBO splits real GDP into its components before adjusting each toits potential level.The most important sector in the model is the nonfarm business sector. It isthe largest sector in the economy and the one for which the neoclassical productionfunction is specified. The production function has three inputs: hours worked, thecapital stock, and total factor productivity. To estimate potential output in thenonfarm business sector, the labor input (hours worked) and total factorproductivity are adjusted to their potential levels and then substituted back into theproduction function. Adjusting the capital stock in a similar fashion is notv

necessary because the potential capital stock will be highly correlated with theactual stock of capital.The potential levels of the labor and productivity inputs are calculated witha cyclic-adjustment equation. That equation, which removes the effects of thebusiness cycle, includes the variable to be adjusted as the dependent variable, withthe unemployment gap and several time trends as explanatory variables. Theunemployment gap is the difference, in percentage points, between the unemployment rate and the nonaccelerating inflation rate of unemployment (NAIRU). TheNAIRU provides a benchmark that determines when the economy is at a high rateof resource use. Once the equation has been estimated statistically, it will providean estimate of what the dependent variable would have been over time had theunemployment rate been equal to the NAIRU in every year of that period; that is,it computes the potential level of that variable.The capital input to production is based on the values of the net stock ofprivate capital in the nonfarm business sector, in constant dollars. However, simplyusing the total capital stock would paint a misleading picture of overall capitalaccumulation because doing so would ignore the fact that various types of capitaldiffer in their durability and productivity. Therefore, the capital input in the growthmodel is an index designed to measure the flow of capital services available forproduction. That index accounts for the fact that different types of capital havedifferent levels of productivity.Potential output in each of the sectors other than nonfarm business iscomputed directly, using CBO's cyclic-adjustment equation. This procedure differsslightly from that used for the nonfarm business sector, where the inputs areadjusted to their potential levels and then substituted into the production function.Output in each of the other sectors is adjusted independently, using the sameprocedure. The sole exception is the housing sector. Since output in that sector isnot greatly influenced by the business cycle, potential output in that sector isassumed to equal actual output.Projecting Potential OutputProjecting potential output using the growth model is straightforward: once themodel's exogenous (or independent) variables have been projected, the model canbe solved to compute potential output. The key exogenous variables are the growthof the labor force, the rate of national saving, and the growth of total factorproductivity. With projections of those and other, subsidiary variables, the modelprojects the rate of capital accumulation and, using the production function,potential output.vi

CBO's Estimate of Potential OutputCBO's estimate of potential output provides a useful measure of the capacity of theU.S. economy. Real GDP typically falls below potential GDP during recessionswhereas expansions often drive the level of real GDP above potential. The GDPgap--the difference between output and potential output--does a good job ofpredicting the direction of changes in inflation. When output is below its potentiallevel, then the rate of inflation generally falls; when output is above the level ofpotential, then inflation generally climbs.Advantages and Disadvantages of the Growth ModelThe primary advantage of using the framework of a growth model to estimate andproject potential output is that it explicitly includes capital as a factor ofproduction. Including capital has theoretical appeal; economic theory suggests thatthe ability of a firm or economy to produce will be influenced by the size of itscapital stock, so any measure of potential output should reflect the size of thatstock. Including capital also makes CBO's projections for potential output fullyconsistent with its projection for the federal deficit, allowing CBO to incorporatethe effects of changes in fiscal policy into its medium-term (seven-year) projection.Those changes affect the rate of national saving, which in turn influences the rateof capital accumulation and the growth of potential output.CBO's growth model is also highly disaggregated and thus reveals moreinsights about the economy than would a more aggregated model. Data on thecapital stock indicate that U.S. manufacturers have shifted their investment duringthe past few decades toward equipment (and away from structures) and havededicated a greater proportion of their investment in equipment to computers. Bothof those shifts have directed investment toward more productive types of capital,an effect that would not be captured by a model that included only the total capitalstock.The primary disadvantage of using a model based on a production functionto estimate potential output is that including the capital stock may introducemeasurement error. That problem afflicts many economic variables, but it isparticularly acute for capital. Errors may arise when economic depreciation--thedecline in efficiency resulting from wear and tear or scrappage--is measured andwhen many types of capital goods (that differ in terms of productivity) areaggregated into a single index of capital input.Another limitation of the model is that its projections are quite sensitive tothe assumptions made about total factor productivity and the rate of nationalvii

saving. Even small changes to the projections of those variables, resulting perhapsfrom new information or revised data, can have large effects when compoundedover a 10-year projection horizon. Also, the model is a fairly simple representationof the economy and therefore does not include all possible channels of the influenceof fiscal policy on long-run growth. For example, there is no explicit link betweentax rates and such variables as labor supply, productivity, or saving rates.However, the model does not preclude such effects; if a policy change is largeenough to have an effect on those variables, then the impact could be included inthe projections very easily.viii

INTRODUCTIONAssessing current economic conditions and projecting such variables as growth andinflation require a summary measure of the productive capacity of the economy.That measure, known as potential output, is an estimate of the level of outputattainable when the economy is operating at a high rate of resource use. It is not,however, a ceiling on output that cannot be exceeded. Rather, it is the levelconsistent with a stable rate of inflation: if output rises above potential, thenconstraints on capacity begin to bind and inflationary pressures build; if output fallsbelow potential, then resources are lying idle and inflationary pressures abate.Such fluctuations of output around potential are a regular feature of thebusiness cycle--recessions typically drive output below potential, and expansionsfrequently push output above it. Comparing the growth rates of actual and potentialoutput allows analysts to determine whether the gross domestic product (GDP) gap-the percentage difference between actual and potential output--is shrinking orgrowing.Potential output plays a role in several areas associated with the Congressional Budget Office's (CBO's) economic forecast. In particular, CBO usespotential output to set the level of real gross domestic product in its medium-term(seven-year) projections; it does so by closing the GDP gap that remains at the endof the short-term forecast. CBO also uses the level of potential output to gaugeinflationary pressures. For example, an increase in inflation that occurs when realGDP is below potential (and monetary growth is moderate) can probably beattributed to temporary factors and is unlikely to persist. In addition, potentialoutput is an important input in computing the standardized-employment deficit,which CBO uses to evaluate the stance of fiscal policy and reports regularly as partof its mandate.POTENTIAL OUTPUT BASED ON A GROWTH MODELCBO calculates historical values and projects future values of potential outputusing the framework of a standard neoclassical growth model.1 Growth modelsemploy a neoclassical production function and assumptions the analyst makes aboutgrowth in the labor force and the rate of national saving to determine how outputwill grow over the long term.21.CBO's model is based on one originally developed by researchers at the Brookings Institution to analyze the SocialSecurity trust fund. See Henry J. Aaron, Barry P. Bosworth, and Gary T. Burtless, Can America Afford to Grow Old?(Washington, D.C.: Brookings Institution, 1989) for a description of the original model.2.CBO's method for estimating potential output is similar to the methods used by the International Monetary Fund andthe Organization for Economic Cooperation and Development. See Charles Adams and David Coe, "A SystemsApproach to Estimating the Natural Rate of Unemployment and Potential Output for the United States,"

The crucial advantage of using a growth model to calculate potential outputis that its framework includes the capital stock--a fundamental input to production.Not all methods do; some include only the labor input, and others rely solely on thehistorical behavior of real GDP to estimate potential output. Perhaps moreimportant, CBO's framework models explicitly the factors that determine theaccumulation of capital, so the projection for the capital stock is fully consistent withCBO's projections for private saving and federal deficits. Specifically, a higherprojected rate of saving will lead to faster accumulation of capital and faster growthof potential output. Therefore, lower government deficits, which raise the rate ofnational saving, will speed the growth of the capital stock and potential output inthe model. Conversely, a recession that depresses the private saving rate will alsotemporarily slow the accumulation of capital and the growth in potential output.CBO measures potential output as real gross domestic product adjusted toits potential level.3 GDP comprises the output of five sectors: nonfarm business,government, farm, households and nonprofit institutions, and residential housing,as shown in equation (1). The nonfarm business sector is by far the largest of thefive. In 1994, for example, output in that sector composed 77 percent of real GDP,compared with less than 10 percent for each of the other sectors. The model mustalso include a statistical discrepancy that measures the difference between totalincome and total output, because output is disaggregated by sector on the income,not the product, side of the national income and product accounts (NIPAs). Thestatistical discrepancy would always equal zero if it were possible to measure thecomponents of output and income without error. In addition, GDP plus grossforeign product (the return to domestic residents on factors of production heldabroad minus the return to foreigners on factors of production held in the UnitedStates) equals gross national product, as in equation (2).(1)GDP GDPnfb GDPgovt GDPfarm GDPhhnp GDPhousing statistical discrepancy(2)GNP GDP gross foreign productwhereGDP gross domestic product,GDPnfb gross domestic product in the nonfarm business sector,GDPgovt gross domestic product in the government sector,IMF Staff Papers, vol. 37 (June 1990), pp. 232-293; and Raymond Torres and John P. Martin, "Potential Outputin the Seven Major OECD Countries," OECD Economic Studies, no. 14 (Spring 1990), pp. 127-149.3.CBO currently bases its estimate of potential output on the fixed-weighted, or 1987-dollar, measure of real GDP inthe national income and product accounts. The Bureau of Economic Analysis has announced that it will feature a newmeasure of real GDP--the chain-type annual-weighted index--when it revises the NIPAs in December 1995. CBOwill update its estimate of potential output, basing it on the new measure of real GDP, once the new data have beenreleased.2

GDPfarm gross domestic product in the farm sector,GDPhhnp gross domestic product in the households and nonprofitinstitutions sector,GDPhousing gross domestic product in the housing sector, andGNP gross national product.CBO uses this disaggregated approach to compute potential output for twobasic reasons. First, different sectors have different methods of production; somerely more heavily on their capital stock, others more on their workforce. Using asingle production function to model GDP, which amounts to specifying aproduction method, would therefore be inappropriate. Second, data limitationsprevent the estimation of a single production function for GDP. A complete set ofdata on factor inputs (that is, capital and labor) is available for the nonfarmbusiness sector, but data for many of the other sectors are incomplete. The missingdata affect the way some of the sectors are modeled.Equations (1) and (2) form the basis for estimating potential GDP andpotential GNP. The model computes potential output in each sector and thencomputes potential GDP and GNP as the sum of the individual sectors.(11)(21)GDP* GDP*nfb GDP*govt GDP*farm GDP*hhnp GDPhousing statistical discrepancy*GNP* GDP* gross foreign productwhere (*) denotes the potential values for a series.4 Gross foreign product is notadjusted to potential because it is weakly related to the U.S. business cycle.Output in the residential housing sector does not need to be adjusted topotential because it is largely unaffected by the U.S. business cycle. The Departmentof Commerce measures that output--the flow of housing services--as the sum of allrents paid to the owners of the housing stock, including rent paid to others as wellas an imputed rent on owner-occupied housing.5 Although investment in residentialhousing displays a marked cyclical pattern, the services that flow from the existingstock do not. Therefore, potential output in the housing sector is assumed to equal4.The statistical discrepancy, though marked with an asterisk in equation (11), is not adjusted to potential. However,some of the year-to-year variation in the series is removed using a three-year, centered, moving average. Thatvariation, which arises entirely because of measurement error, is removed to prevent it from affecting the estimateof potential output.5.The sum is adjusted to avoid double-counting payments for intermediate goods and services, such as propertyinsurance, maintenance, and durable goods (appliances). Those adjustments are a small proportion of the total.3

actual output in all time periods, and actual values of housing output are used tocompute potential GDP.Gross foreign product also lacks a strong cyclical component and thereforedoes not need to be adjusted. In the NIPAs, this variable is measured by U.S.receipts of factor income from foreigners minus U.S. payments of factor income toforeigners. Although factor income includes employee compensation, the bulk ofit comes from undistributed corporate profits, interest, and dividend payments-income flows that are only loosely related to the U.S. business cycle. Historicalvalues of potential GNP are computed as the sum of potential GDP and historicalvalues of gross foreign product.ESTIMATING HISTORICAL VALUES OF POTENTIAL OUTPUTEstimates of the historical values of potential output are heavily dependent on theestimate of potential output in the nonfarm business sector. For that sector, CBOuses the growth model's production function, which explains the growth of outputin terms of three factor inputs: labor, capital, and total factor productivity. Thoseinputs are cyclically adjusted (that is, purged of the influence of the business cycle)and then substituted back into the production function, yielding values of potentialoutput. Historical values of potential output in the other sectors are computeddirectly by cyclically adjusting output in each sector.The Nonfarm Business SectorThe heart of the growth model is a neoclassical production function that calculatesGDP in the nonfarm business sector as a function of hours worked (labor), the capitalstock, and total factor productivity in that sector. The production function is(3)log(GDP) 0.7 log(

output allows analysts to determine whether the gross domestic product (GDP) gap--the percentage difference between actual and potential output--is shrinking or growing. Potential output plays a role in several areas associated with the Congres-sional Budget Office's (CBO's) economic forecast. In particular, CBO uses

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