The Performance of Traditional Macroeconomic Models of ... · The Performance of Traditional...

Richard W. Kopcke with Richard S. Brauman

Vice President and Economist, andResearch Associate, respectively, Fed-eral Reserve Bank of Boston.

The Performance ofTraditional MacroeconomicModels of Businesses’Investment Spending

The rate of capital formation by businesses has long been among themost closely watched elements of the national accounts. During thelast decade, this component of investment attracted considerable

interest as capital spending helped support our uncommonly high rate ofeconomic growth. Businesses’ demand for capital goods grew rapidly,accounting for more than its typical share of the demand for output. Notonly did this spending lift the growth of aggregate demand, it alsoincreased our capacity for supplying goods and services, which in turncould allow output to continue growing rapidly in the future.

This article analyzes the performance of conventional models ofinvestment spending by comparing their abilities to describe this spend-ing from 1960 to 1990 as well as their abilities to forecast spending duringthe 1990s. These comparisons test the models and provide standards formeasuring the rate of investment spending. If spending has acceleratedrecently, these models can help define its timing and magnitude, whilesuggesting which macroeconomic forces might be propelling the demandfor capital. The models represent the previous historical relationshipsbetween capital spending and other macroeconomic variables. To thedegree the projections from these models coincide with the course ofinvestment, the motives for that spending may be attributed to familiarforces. To the degree the projections fail to describe spending, the natureof their errors might suggest alternative explanations for the behavior ofthe data.

4 Issue Number 2 – 2001 New England Economic Review

According to this study, capital formation hasbeen relatively low during much of the 1990s. Themodels for producers’ durable equipment and soft-ware suggest that spending fell well below historical norms during the late 1980s and early 1990s, thenrecovered during the remainder of the 1990s. Themodels for nonresidential construction suggest thatspending has remained unusually low since the late1980s. This study finds that the rate of capital forma-

During the last decade, the rate of capital formation attracted

considerable interest as capital spending helped support

our uncommonly high rate of economic growth.

tion displays considerable inertia. Years of high invest-ment tend to follow years of high investment. Morethan previously, this study indicates that the rate ofaggregate capital formation does not depend closelyon the rate of growth of GDP alone or on the cash flowof businesses. Instead, models that describe invest-ment using output and a measure of the cost of capitalperformed better. Nevertheless, recent shifts in thecomposition of the stock of capital goods and in therelative prices of capital goods have undermined theperformance of these models of aggregate investment spending. In many ways, aggregate capital spendingseems to depend more heavily than it has in the paston industries’ unique circumstances and changingtechnologies.

The first section of the article describes the magni-tude and composition of investment in the UnitedStates and discusses some of the issues regarding themeasurement of investment. The second sectiondescribes the six models of investment that are exam-ined in this study. The third section discusses theirabilities to fit the data before 1990 and their abilities toforecast spending after 1990. The concluding sectionobserves that errors of the conventional macroeco-nomic models, the changing composition of capital,and our new methods of measuring the stocks of capi-tal warrant our considering more disaggregateddescriptions of investment spending.

I. The Composition of Investment

Households, governments, and businesses investwhen they set aside a share of their current income inorder to acquire capital assets whose returns promiseto increase their incomes in the future. Often the con-cept of investment emphasizes the purchases of build-ings and equipment. In the national accounts, forinstance, the concept of fixed investment comprisesconstruction spending and purchases of equipmentand software by businesses and governments. But, thiscapital spending constitutes only a portion of invest-ment. The national accounts do not recognize, forexample, households’ purchases of appliances, tools,or other durable goods as investments, because theseaccounts do not attribute any output to these assets.

The measurement of investment becomes morecomprehensive when the concept of output is notlimited to GDP (Nordhaus and Tobin 1972; Eisner1985; Jorgenson and Fraumeni 1989; Kirova andLipsey 1998). From a broad perspective, investmentincludes not only the acquisition of all tangible cap-ital assets but also expenditures for research anddevelopment, education (other than buildings,equipment, and software), environmental improve-ments, law enforcement, and defense. Our recogniz-ing these expenditures as investments, however,entails our recognizing the income that redounds tothe stock of this capital. According to the nationalaccounts, gross private domestic and governmentinvestment accounts for about one-fifth of GDP. InEisner’s total income system of accounts, totalincome exceeded GDP by approximately one-fifth inthe 1980s, and total gross tangible investment,which accounted for about one-third of that income,was approximately twice as great as the grossdomestic investment reported in the nationalaccounts (Eisner 1985, Table B, p. 28). Jorgenson andFraumeni’s full income accounts emphasize theimportance of investment in human capital and ofproduction that is not recorded in market transac-tions, neither of which appears in current account-ing for national income. Their measure of fullincome was about three times GDP in 1984, and fullinvestment, which accounted for almost half of thatincome, was more than seven times gross domesticinvestment as reported in the national accounts(Jorgenson and Fraumeni 1989, Table 5.4, p. 239).Although the accumulation of human capitalthrough education and the growth of the populationaccounted for most of this broad measure of invest-ment, the accumulation of other capital still exceed-

Issue Number 2 – 2001 New England Economic Review 5

ed the national accounts’ measure of investment byalmost 30 percent.

Investment in the National Accounts

Together, gross private domestic fixed invest-ment, government capital spending, expenditures foreducation, and consumers’ purchases of durablegoods account for almost one-third of GDP (Table 1).This share increased by just under 40 percent duringthe past 50 years. At the same time, the compositionof this spending has shifted toward consumers’durable goods and toward the capital assets of busi-nesses, away from government capital spending andresidential construction. Currently, businesses’investment spending, comprising nonresidential con-struction and producers’ purchases of durable equip-ment and software, accounts for approximately one-eighth of GDP. Although businesses’ investmentincreased over the past four decades, it too has shift-ed, favoring equipment and software, whose sharetripled, over nonresidential construction, whoseshare fell by one-quarter.

Gross capital spending of businesses has increasedmore than net investment since the 1960s. In the early1960s, gross investment in equipment and softwarenearly equaled that in nonresidential structures. Now,gross investment in equipment and software is approx-imately three times that of structures. As the stock of capital assets shifted in favor of equipment and soft-ware, which depreciate relatively rapidly, away fromstructures, which depreciate relatively slowly, busi-nesses’ capital budgets had to increase relative to GDP inorder to maintain their existing stock of capital assets.Consequently, the rate of growth of businesses’ stock ofcapital assets has risen little in the last decade comparedto the substantial increase in their gross investmentspending relative to their stock of capital (Figure 1).

One standard for judging the pace of capital for-mation compares the stock of capital assets to thenumber of people who may use that capital or benefitfrom its services (Table 1). From the early 1960s to theearly 1980s, the stock of businesses’ capital assetsincreased 34 percent relative to the labor force. This 1.5percent average annual increase in capital per poten-tial laborer fell to just 0.4 percent from the early 1980sto the late 1990s. From the early 1960s to the early

Table 1

Real Business Fixed Investment, Government’s Capital Spending, and Consumers’ Purchasesof Durable Goods, as a percent of Real GDPa

Years

61–65 66–70 71–75 76–80 81–85 86–90 91–95 96–99

Gross Private Domestic Investment 12.2 12.8 13.4 14.1 14.2 14.2 13.9 17.5Fixed Investment 11.9 12.4 13.2 13.7 13.9 13.9 13.6 16.9

Nonresidential 6.6 7.8 8.1 8.8 9.8 9.6 9.8 12.9Structures 4.4 4.6 4.2 4.0 4.5 3.6 2.9 3.0Equipment and Software 3.1 3.9 4.4 5.1 5.6 6.1 7.0 9.9

Residential 6.0 4.9 5.5 5.2 4.1 4.4 3.8 4.0Structures 6.0 4.8 5.4 5.2 4.0 4.3 3.7 3.9Equipment .0 .1 .1 .1 .1 .1 .1 .1

Government Gross Investment 4.8 4.7 4.7 4.6 4.5 4.4 4.1 3.8Defense 1.3 1.0 .6 .6 .9 1.1 .9 .6Nondefense 3.4 3.5 3.6 3.6 3.5 3.4 3.3 3.1

Consumer Durable Goods 4.5 5.2 5.8 6.2 6.3 7.5 7.3 8.4Education 1.5 1.7 1.8 1.6 1.6 1.6 1.6 1.6

Equipment, Software, Structures / 59.7 63.2 70.1 73.4 80.2 81.0 84.3 85.6Private Nonfarm Labor

Residential Capital per Capita 8.3 9.3 12.3 18.6 24.2 27.0 29.1 30.9Consumer Durables per Capita 5.1 5.1 5.6 7.0 8.3 8.6 8.7 8.2Government (Nondefense) .5 .6 .8 1.1 1.4 1.5 1.6 1.7

per Capitaa The entries are derived from chain-weighted data. Consequently, components do not necessarily sum to totals.Source: The measure of the labor force is from the U.S. Bureau of Labor Statistics, population is from the U.S. Bureau of the Census, and all otherdata are from the U.S. Bureau of Economic Analysis and can be found in Table 5 of the Survey of Current Business.


1980s, the stock of residences per capita grew 5.5 per-cent annually; since then, only 1.7 percent. The stock ofconsumers’ durable goods per capita rose 2.4 percentuntil the early 1980s, only to change negligibly overthe subsequent 15 years. The stock of public capitalgoods (nondefense) per capita increased 5.4 percentbefore the early 1980s, 1.3 percent afterward. By thesemeasures, housing and public capital have constitutedthe principal forms of investment in tangible assetssince the early 1960s, and the accumulation of all capi-tal assets has decelerated significantly during the past15 years.

Composition of Businesses’ Fixed Investment

The two broad categories of businesses’ invest-ment, nonresidential construction spending and pro-ducers’ purchases of durable equipment and software,each comprise a variety of capital assets. During thepast three decades, the allocation of businesses’ capitalbudgets among these assets has shifted substantially(Tables 2 and 3).

Since the early 1960s, businesses’ purchases ofequipment have shifted strongly toward informationprocessing equipment.1 This equipment and related

software represented just over 18 percent of produc-ers’ expenditures on equipment and software in theearly 1960s. By the late 1990s, this share exceeded 44percent, with most of the growth occurring in comput-ers, software, and communications equipment. At thesame time, the shares of industrial equipment andtransportation equipment fell from just over 28 and 29percent, respectively, to just over 18 and 20 percent.

The composition of investment in nonresidentialstructures did not change as much as that for equip-ment. In general, the share of construction allocated toindustrial, commercial, hospital, and institutionalbuildings increased over the past four decades, whilethe shares of public utilities and farms declined.

More interesting than these trends are the cyclesin spending on structures. After the price of oil andgas soared in the 1970s, the investment in wells rosesharply. Petroleum and gas wells’ share of construc-

1 The data in these tables show the composition of nominalspending. As noted in Appendix 1, the chain-weighted measures ofthe components of investment spending in 1996 dollars do not addto the chain-weighted measure of total investment spending. In thecase of equipment, the components sum to almost 160 percent of thetotal in the early 1960s, compared to just over 100 percent of the totalby the late 1990s.


tion then fell by two-thirds after the price of oil andgas fell in the 1980s. Similarly, the construction ofcommercial buildings increased substantially withthe growth of service industries in the 1970s and1980s. This investment subsequently fell once theconstruction boom produced a surfeit of space by thelate 1980s. Changing technologies in the past twodecades also allowed many of these industries to usespace more efficiently. Electric utilities’ share of non-

residential construction spending tended to increasewith the use of electricity until the 1970s. After risingelectric rates and public policy fostered conservationin the use of electric power, this share fell by two-thirds during the 1980s and 1990s. Finally, the shareof construction devoted to hospitals rose throughoutmuch of the last four decades, but fell after the 1980sas changes in government policies and private healthcare programs reduced the demand for hospital beds.

Table 2

Equipment Investment by Type, as a Percent of Total Equipment InvestmentYears

Type of Equipment 61–65 66–70 71–75 76–80 81–85 86–90 91–95 96–99

Information processing equipment and software 18.2 21.2 24.2 26.8 36.8 40.5 42.5 44.5

Computers and peripheral equipmenta 1.8 3.5 3.7 4.3 8.7 9.8 9.5 10.4Softwareb 1.0 2.4 3.6 4.0 6.5 9.7 13.5 16.7Communications equipment 8.4 8.3 8.7 9.8 11.9 11.7 10.1 10.1Instruments 2.2 2.4 3.0 3.5 4.2 4.7 5.5 4.5Photocopy and related equipment 1.7 2.3 3.1 2.9 2.8 2.7 2.8 1.8Office and accounting equipment 2.9 2.3 2.1 2.4 2.6 1.9 1.3 1.0

Industrial equipment 29.1 29.3 27.1 26.0 23.1 21.6 20.5 18.4Fabricated metal products 2.7 3.0 4.0 4.2 3.3 2.1 2.0 1.6Engines and turbines 1.2 1.5 1.8 1.0 .7 .7 .7 .6Metalworking machinery 5.9 7.4 5.9 6.0 5.0 4.6 4.6 4.3Special industry machinery, n.e.c. 6.7 6.2 5.3 4.7 4.9 5.5 5.1 4.7General industrial, including

materials handling, equipment 6.5 5.9 5.5 6.1 5.4 5.2 4.7 4.3Electrical transmission, distribution,

and industrial apparatus 6.1 5.4 4.6 4.0 3.8 3.6 3.2 3.0

Transportation equipment 28.1 26.8 25.2 24.1 20.1 19.0 19.7 20.6Trucks, buses, and truck trailers 9.9 9.7 10.4 9.7 8.2 8.0 9.2 11.8Autos 11.7 8.9 8.9 8.1 7.5 7.3 7.0 5.4Aircraft 2.3 4.3 2.3 2.6 2.6 2.6 2.5 2.3Ships and boats 1.2 1.2 1.6 1.6 .9 .4 .3 .3Railroad equipment 3.0 2.8 2.1 2.2 .8 .6 .8 .8

Other equipment 25.4 23.4 24.5 24.5 20.8 19.6 17.9 17.0Furniture and fixtures 4.5 4.0 3.7 3.7 4.5 5.0 4.4 4.2Tractors 3.1 3.1 3.3 3.4 2.1 1.8 1.7 1.7Agricultural machinery, except tractors 3.9 3.8 4.4 4.0 2.2 1.8 1.7 1.5Construction machinery, except tractors 3.4 3.5 3.8 4.0 2.6 2.6 2.1 2.4Mining and oilfield machinery 1.4 1.1 1.5 2.1 1.6 .4 .4 .5Service industry machinery 4.1 3.8 3.1 2.6 2.6 2.7 2.2 1.9Electrical equipment, n.e.c. 1.2 1.0 1.1 1.5 1.7 1.8 1.9 1.6Other 3.7 3.1 3.3 3.3 3.4 3.4 3.4 3.1

Sum of Major Components 100.7 100.8 101.0 101.5 100.8 100.7 100.7 100.6a Includes new computers and peripheral equipment only.b Excludes software “embedded,” or bundled, in computers and other equipment.Source: BEA’s Survey of Current Business, Table 5.8. Data provided by Haver Analytics.


The composition of investment by industryreflects the cycles in mining, the growth of service andelectronics industries, and the greater role of financial institutions in leasing capital goods to other enterpris-es (Table 4). From the early 1960s to the late 1990s,financial institutions’ share of investment rose from1.8 percent to 9.7 percent of businesses’ capital spend-ing. Banks, finance companies, insurance companies,and other intermediaries have substituted leases forsome of their loans—companies that formerly bor-rowed to finance their own purchases increasinglyrent their assets.

II. Models of Businesses’ Investment

Forecasters and policymakers frequently attemptto explain the behavior of the aggregate capitalspending of businesses by means of concise statisticalmodels. These macroeconomic models essentiallylook beyond the details of each industry’s investmentspending or the demand for each type of capital good

in order to isolate the more fundamental influencesthat govern capital formation. This aggregateapproach confronts considerable difficulties in com-bining the diverse capital goods properly in order toconstruct useful aggregates. It also takes a large riskby not explicitly considering the various economicconditions that prevail in specific industries. But,against these costs, it offers the potentially substan-tial benefit of describing the common tide uponwhich the specific fortunes of these diverse industriesmight ride.

All models of investment recognize that business-es intend to profit from their investments. Yet, themodels express this common theme in distinctiveways as they describe the influence of economic condi-tions on investors’ perceptions of future profits and, inturn, on their demand for capital goods. Rising orders,for example, might foster investment. But, do theseorders principally influence the demand for invest-ment goods directly, through their effect on business-es’ cash on hand, or through a higher return on assets?Does this influence depend substantially on the cost of

Table 3

Structures Investment by Type, as a Percent of Total Nonresidential Structures InvestmentYears

Type of Equipment 61–65 66–70 71–75 76–80 81–85 86–90 91–95 96–99

Nonresidential buildings, excluding farm 60.5 60.0 57.6 49.6 56.8 71.5 66.3 70.4Industrial 14.9 18.7 15.0 15.2 12.4 13.5 16.0 12.8Commercial 24.0 23.3 27.5 23.6 31.0 39.9 31.9 36.0Religious 4.6 3.0 1.6 1.5 1.4 2.1 2.0 2.2Educational 3.2 3.0 1.8 1.0 1.2 2.2 2.9 3.7Hospital and institutional 4.8 5.1 6.7 4.9 5.3 6.0 7.0 5.6Othera 9.0 6.7 5.1 3.5 5.6 7.8 6.3 10.0

Utilities 22.7 25.6 27.5 26.4 18.1 15.4 18.9 15.4Railroads 2.6 2.5 2.2 2.7 1.9 1.4 1.6 1.9Telecommunications 5.2 5.7 6.8 6.0 4.7 5.1 5.2 5.0Electric light and power 9.3 11.8 13.8 13.7 9.3 6.7 8.5 4.7Gas 4.8 5.0 3.4 2.5 1.9 2.0 3.1 3.3Petroleum pipelines .8 .7 1.3 1.5 .3 .2 .5 .5

Farm 5.8 4.8 4.8 5.3 2.1 1.3 1.6 1.6Mining exploration, shafts, and wells 10.6 7.5 8.0 16.5 20.7 8.3 9.2 10.0

Petroleum and natural gas 10.0 6.9 6.9 15.0 19.6 7.8 8.4 9.4Other .7 .7 1.0 1.5 1.1 .5 .8 .6

Otherb 1.4 1.8 2.0 1.9 2.3 3.2 4.0 2.3Sum of major categories 101.0 99.7 99.9 99.7 99.9 99.8 100.0 99.7a Consists of hotels and motels, buildings used primarily for social and recreational activities, and buildings not elsewhere classified, such as

passenger terminals, greenhouses, and animal hospitals.b Consists primarily of streets, dams and reservoirs, sewer and water facilities, parks, and airfields.Source: BEA’s Survey of Current Business, Table 5.6. Data provided by Haver Analytics.


acquiring capital goods? The various models of invest-ment provide different perspectives that reflect theirdifferent theories of investors’ behavior.

This section presents six models of investmentspending by businesses, each representing an elemen-tal description of the relationship between investmentand various measures of economic conditions.Individually, the six models allow us to assess theirparticular explanations of investment spending.Together, they cover the principal factors at work inmost forecasting models, which often combine andextend the approaches taken by these basic models.

These basic models of investment spending, likemost, rest on a common fiction inasmuch as they com-bine diverse capital goods into a few aggregates, andthey treat all businesses as one investor. The models,

therefore, do not explicitly recognize differencesamong types of investment goods or the difficulties inconstructing aggregates (Appendix 1). Nor do theyrecognize differences among businesses’ technologies,products, goals, market power, size, and other circum-stances. The models also do not explicitly consider theparticular influences of rising energy prices, healthcare reforms, and changes in work rules or labor’sskills. As a result of these differences, no model ofaggregate investment rests on an unimpeachable foun-dation, especially as the relative fortunes of differentindustries or the contributions of different technolo-gies shift over time.

Because each of the basic models emphasizes oneview of investment, and because the success of eachview can vary with economic conditions, we should

Table 4

Investment by Industry, as a Percent of Total InvestmentYears

Industry 61–65 66–70 71–75 76–80 81–85 86–90 91–95 96–99

Mining 4.7 3.9 3.7 7.0 9.1 3.3 3.2 3.2Metal Mining .3 .3 .3 .5 .2 .1 .2 .1Coal Mining .3 .3 .4 .7 .5 .2 .3 .3Oil and Gas Extraction 3.8 3.0 2.7 5.4 8.1 2.7 2.5 2.5

Construction 2.2 2.1 2.2 1.8 1.0 1.1 1.2 1.6Manufacturing 14.5 17.7 15.6 15.3 14.1 12.9 14.3 13.7

Durable Goods 7.7 9.8 8.3 8.3 7.8 6.7 7.1 7.5Primary and Fabricated Metals 2.5 3.2 2.4 2.1 1.5 1.3 1.4 1.3Industrial Machinery and Equipment 1.1 1.6 1.5 1.6 1.5 1.2 1.2 1.3Electronic and Other Electric Equipment .7 1.0 1.0 1.1 1.6 1.3 1.5 1.9Motor Vehicles and Equipment 1.2 1.3 1.0 1.1 .9 .8 1.1 1.1

Nondurable Goods 6.8 7.9 7.3 7.0 6.2 6.1 7.1 6.2Food and Kindred Products 1.5 1.5 1.4 1.3 1.2 1.1 1.3 1.1Paper and Allied Products .9 1.0 .9 1.0 .9 1.1 1.0 .8Printing and Publishing .5 .6 .6 .6 .7 .8 .7 .8Chemicals and Allied Products 1.9 2.3 2.1 2.3 1.6 1.7 2.2 2.0

Transportation 5.1 5.5 5.0 5.4 3.8 3.3 4.1 5.0Trucking and Warehousing 1.4 1.2 1.3 1.2 1.1 1.2 1.4 1.5Transportation by Air .8 1.5 1.0 1.3 1.0 1.0 1.2 1.7

Communications 4.9 5.4 5.7 5.8 5.7 5.5 5.9 6.6Telephone and Telegraph 4.6 5.1 5.4 5.4 4.9 4.6 4.8 5.1Radio and Television .3 .3 .3 .4 .7 .9 1.1 1.5

Electric, Gas, and Sanitary Services 5.8 6.7 6.8 6.2 6.8 6.6 5.6 4.2Wholesale Trade 2.3 2.7 3.1 3.6 5.4 4.7 5.5 5.9Retail Trade 3.8 4.1 4.0 3.7 4.1 4.8 5.1 4.6Finance, Insurance, and Real Estate 44.7 39.4 41.4 39.3 39.8 46.8 42.3 41.7

Financial and Insurance Institutions 1.8 2.4 3.3 4.3 6.7 9.1 9.0 9.7Real Estate 42.7 36.8 37.7 34.7 32.6 37.1 32.8 31.3

Services 6.0 6.8 6.7 6.3 7.2 8.5 9.7 10.4Hotels and Other Lodging Places 1.1 .9 .8 .7 .9 .8 .7 1.0Auto Repair, Services, and Parking 1.0 1.1 1.1 1.3 1.2 1.0 2.2 1.5Health Services .8 .8 .8 .8 1.3 1.4 1.5 1.4

Source: Investment by industry is from self-extracting ZIP files available on the BEA’s web-site.


not expect any one of these models to prevail over theothers. Instead, these models often complement oneanother, as we should expect given their commonroots and the degree to which their particularapproaches amount to related ways of representingthe motives of investors.

Most of the models invoke similar frameworks.Investors conceive of an optimal amount of capital toemploy given recent business conditions. They thenadjust their investment spending in order to approachthat optimum, K*, gradually.

�Kt = �(K*t – Kt–1) 0<�<1.

The models can describe either net investmentspending, which is the change in the stock of capital asshown above, or as has been more common, grossinvestment, which also includes the purchases neededto maintain the stock of capital.

Int = �Kt

Igt = �Kt + �Kt–1

Igt = �K*

t + (� – �)Kt–1.

This partial adjustment reflects the many delaysand costs investors incur as they install new capital.It also reflects their intent to avoid overreacting totemporary changes in their circumstances. The mod-els typically express the optimal stock of capital as aweighted sum of past values of the variables thateach model deems most important for determininginvestors’ demand for capital, variables such asbusinesses’ output, cost of capital, or cash flow. Inadopting this method of extrapolating the past inorder to forecast the future, the models implicitlyassume that the correlations among past, present,and future values of these variables are stable.2

Otherwise, this approach could misrepresentinvestors’ willingness and ability to respond tochanging conditions.

The Accelerator Model

Because capital goods are a factor of production,the demand for new capital goods depends on busi-nesses’ plans for expanding production in the future.According to the accelerator model, businesses esti-mate their potential need for capital from the recentcourse of output. Consequently, their acquisition ofnew capital, their investment spending, is proportion-al to the difference between their requirements andtheir existing stock of capital (Clark 1917; Chenery1952; Knox 1952). According to the accelerator model,

businesses essentially cannot substitute one factor ofproduction for another in producing a specific flow ofoutput most efficiently.3

The equation for the accelerator model is the firstentry in Table 5. The terms, including current andlagged output, represent investment’s gradualresponse to changes in businesses’ output. Beforeintentions become expenditures, a demand for greaterproductive capacity must pass through stages of planning, approval, contracting, and installation.Furthermore, when businesses intend to invest aggres-sively, thereby straining their suppliers’ capacity fordelivering capital goods, their suppliers impose delaysby putting some projects on back order. Because these

2 If these parameters are not stable, then they should notchange too greatly, and they should tend to revert to their formervalues.

3The elasticity of substitution among factors of production islow, which is consistent with a Leontief technology.

Table 5

The Models of InvestmentAccelerator

n

It =∑aiQt–i+cKt–1i=0

Neoclassicaln Qt–i

n Qt–iIt =∑ai–––––– +∑bi–––––––+cKt–1i=0 UCCt–i i=0 UCCt–1–i

Modified Neoclassicaln n

It =[∑ai log(Qt–i )+∑bi log(UCCt–i)]Kt–1+cKt–1i=0 i=0

qn

It =∑ai[(qt–i–1)Kt–1–i]+cKt–1i=0

Cash Flown FIt =∑ai(––)t–i+cKt–1

i=0 Pk

Time Seriesn n

It =∑aiIt–i+∑biQt–ii=1 i=0

Explanation of SymbolsF cash flowI investmentK existing stock of capital goodsPK price index for capital goodsQ outputq ratio of financial markets’ valuation of capital

to its replacement costUCC user cost of capital


lags can be shorter for some projects (such as installingpersonal computers) than others (installing a newassembly line), and because some larger investmentprojects are installed gradually, a greater demand foroutput today lifts investment spending over manysubsequent quarters. Because investors seldom regardcapital goods as liquid assets, these lags on output alsorepresent their measured reactions as they distill tran-sient changes in the demand for their output frommore enduring changes in the growth of their markets.These fixed weights reflect the correlations among thecurrent and past values of output, which investorsapply to the recent course of output in order to derivetheir forecast of future output.

The lagged stock of capital serves two purposes inthe accelerator model. Because businesses’ demand fornew investment goods depends on the differencebetween their potential need for capital assets andtheir existing stock of capital, the coefficient on thisvariable partly represents the speed at which theyattempt to close this gap. Businesses also need toreplace and renew their capital assets as they age orbecome obsolete. To the degree productive capacitytends to decay at a constant rate, this last term in theaccelerator model also measures the investment thatbusinesses must make in order to maintain their pro-ductive assets. The first effect opposes the second. Thegreater is the existing stock of capital, other thingsequal, the fewer new investments businesses needundertake in order to reach their optimal stock of cap-ital. But, the greater is their capital, the more they mustinvest in order to maintain and replace aging assets.

The accelerator model is a simple description ofinvestment spending that relies on a short history ofoutput and the lagged stock of capital to determine thedemand for new capital goods. This simplicity exacts aprice, however. The structure of the model allows it toexplain investment best when the trend for the ratio ofcapital to output changes smoothly over time. Themodel dictates that the ratio of output to capital risessomewhat above that trend when the rate of growth ofoutput is unusually high. Because investment reactsslowly when output accelerates, the growth of thestock of capital rises toward that of output after somedelay. During this time, output rises relative to thestock of capital. A higher output-capital ratio persistsuntil output decelerates, and the conservative reactionof investors causes the growth of capital to fall moreslowly than that of output. This feature of the accelera-tor model—that the demand for capital depends onchanges in the growth of output—coupled withinvestors’ fixed lag in responding to the growth of out-

put, implies not only that the supply of capital servicesneeded to produce a quantity of output varies in anuneconomical manner, but also that investors fail tocomprehend fully their need for future capital assetseven when the growth of output increases and thenremains constant.

The accelerator model is a simpledescription of investment spending

that relies on a short history of output and the lagged stock of capital to determine the demand

for new capital goods.

These characteristics imply that the acceleratormodel likely explains businesses’ investment spend-ing best when the average growth of output over longperiods tends to be constant. Even when this growth isnot constant, the accelerator model nevertheless mightdescribe investment spending reasonably accurately,provided that investment depends strongly on therecent course of output and the average growth of out-put does not change too greatly.

The Neoclassical Model

Whereas the accelerator model proposes thatbusinesses’ demand for capital is nearly proportionalto their planned rate of production, the neoclassicalproposes that competitive businesses invest in orderto maximize their profits. The demand for new capi-tal, consequently, varies with output, the relativeprice of capital goods, interest rates, and the inci-dence of taxes (Jorgenson 1963; Hall and Jorgenson1967; Jorgenson 1971). The neoclassical model, there-fore, rests on a specific description of the economy’saggregate production function, which describes themaximal output that businesses can obtain from anystock of capital goods combined with other factors of production.

In maximizing their profits, competitive business-es choose the amount of capital that they must employto meet the demand for their output at least cost.Competitive businesses, individually, cannot influence


the prices at which they can sell their output or theprices that they pay to obtain capital goods or otherinputs. Altogether, these businesses supply the outputthat their customers demand at prevailing prices whenthe economy is in equilibrium. In these circumstances,the economy’s production function describes theamount of capital that businesses must employ inorder to meet their customers’ demand most prof-itably given prevailing prices.

The rate of return that competitive businessesearn on their optimal stock of capital equals their costof employing this capital, which includes their cost offunds, their net tax liabilities, and their capital con-sumption charges. With common simplifying assump-tions regarding the form of the production function,the optimal stock of capital in the neoclassical model isproportional to output divided by the cost of capital.4

(See Appendix 1.)Q*

K*= � ———.UCC*

As was the case for the accelerator model, thedemand for new capital goods is then proportional tothe difference between the optimal and the existingstocks of capital, because spending responds compara-tively slowly to changes in the demand for output.Investors consider the recent history of both outputand the cost of capital when they assess their potentialneed for capital goods in the future. Inasmuch asinvestors likely respond to changes in the course ofoutput differently than they do to changes in the costof capital, the neoclassical model admits two sets oflags for these variables (Bischoff 1971). To the degreethese lags are to reflect investors’ forecasts of outputand the cost of capital, this model, much like the accel-erator model, depends on correlations among currentand past values of these variables remaining fairly sta-ble over time. Like the accelerator model, the neoclas-sical model includes the lagged value of the stock ofcapital. Here too, its coefficient represents the rate atwhich investors renew and replace capital as well as

the rate at which they intend to close the gap betweentheir potential need for capital and their existing stockof capital.

The neoclassical model attempts to measure theotherwise unobservable but critical return on margin-al investments by specifying investors’ behavior insufficient detail. This approach allows the modelmore latitude in explaining investment spending,especially when the ratio of output to capital in theeconomy varies significantly in response to changes inthe cost of capital. However, if these specific assump-tions misrepresent the behavior of investors too great-ly, the model might be neither more general nor more

The neoclassical model appeals toforecasters and policymakers because

it attempts to define the optimalstock of capital by balancing thereturn on capital with the cost

of capital, two important elements in most theories of investment.

accurate than other approaches that appear to be lessrigorous. For example, if businesses recognize thattheir plans for supplying output influence prices and interest rates, then the neoclassical model mightpredict that investment rises too strongly in responseto a higher demand for output or a drop in the cost of capital. Conversely, if a greater demand for out-put coincides with individual companies’ loss ofmarket power, then investment spending mightexceed that predicted by the neoclassical model.Moreover, if the price of capital goods rises inresponse to businesses’ demand for more capital,then investment can rise more than the change in thecost of capital might predict.

Nonetheless, the neoclassical model appeals toforecasters and policymakers because it attempts todefine the optimal stock of capital by balancing thereturn on capital with the cost of capital, two impor-tant elements in most theories of investment. Theexplicit representation of the cost of capital in themodel also shows how changes in economic policydirectly influence the demand for capital.

4 The production function is Cobb-Douglas, businesses are per-fect competitors who minimize the cost of producing a given output,factors of production are paid their marginal products, capital mar-kets also are perfectly competitive, and investors, who have identi-cal assessments of future conditions, use linear extrapolations ofrecent economic conditions to form their expectations of future con-ditions. The Cobb-Douglas production function fixes the elasticity ofsubstitution between factors of production at 1, implying thatlabor’s and capital’s shares of output are constant. In the nationalaccounts, capital’s share is relatively constant near 1/3; labor’sshare, near 2/3.


A Modified Neoclassical Model

An alternative version of the neoclassical modelproposes that the stock of capital expands at a rate thatis a constant fraction of the rate required to reach itsoptimum. This alternative view also happens to sepa-rate the influence of output on investment from that ofthe cost of capital, rather than binding them in onevariable. Not only does this approach allow past val-ues of output and the cost of capital more distinctweights, it also allows the model to compare the contri-butions of output and the cost of capital in explaininginvestment spending.

Suppose the expansion of the stock of capital is afunction of the ratio of the optimal to the existing stockof capital.5

Kt K*t—— = (––––)� 0<�<1

Kt–1 Kt–1

Int �Kt—— = –––– ≈ �•(log(K*

t) – log(Kt–1))Kt–1 Kt–1

Igt �Kt—— = –––– + � ≈ �•(log(K*

t) – log(Kt–1)) + �.Kt–1 Kt–1

This description of investment, when combinedwith the expression for the optimal stock of capitalthat appears in the neoclassical model, yields a modelthat distinguishes the contribution of output from thatof the cost of capital.

log(K*t) = log(�) + log(Q*) – log(UCC*).

This division, which conveniently separates thecontribution of output from that for the cost of capital,recognizes more discretely any differences in the mag-nitude and timing of investment’s response to thesevariables. 6, 7

The q Model

The q model proposes that the demand for capitalvaries directly with the ratio of the market value of thecapital assets of businesses to the replacement value of

The q model proposes that thedemand for capital varies directly

with the ratio of the market value ofthe capital assets of businesses to the

replacement value of those assets.

those assets. This ratio, q, essentially compares thereturn on capital with the rates of return required byinvestors who finance that capital. Values of q thatexceed unity foster investment spending, while valuesof q that are well below unity depress the demand fornew capital goods (Tobin 1969, 1982).

The description of the demand for capitalbehind the q model is as old as financial theories ofinvestment. Investors’ demand price for capitalderives from the present value of the returns theyexpect to earn from their investment. When thisdemand price exceeds the cost of acquiring capital,investment spending increases. As the rate of invest-ment rises, the supply price of capital tends to rise.As the stock of capital rises, the most profitableinvestment opportunities are exhausted, and thedemand price for capital falls. Eventually, thedemand and supply prices of capital will becomemore nearly equal, thereby reducing the rate ofinvestment spending.

This theory applies to existing capital assets aswell as new capital goods. Financial markets continu-ally assess companies’ prospective returns. The result-ing valuation of their equity and debt securities is thedemand price for their assets. When companies’prospective returns rise relative to the rates of returnrequired by their shareholders and creditors, then thevalue of their securities will increase relative to thebook or replacement value of their capital assets.Accordingly, q was relatively high when the returns oncapital were relatively high in the 1960s and 1990s, andq was lowest when returns were lowest in the late1970s and early 1980s (Figure 2).

5 The second and third lines of the expression below followfrom the first because the log of the left side of the first line approxi-mately equals the rate of growth of the stock of capital.

6 If the elasticity of substitution between capital and labor werea constant other than 0 or 1, as in a constant elasticity of substitution(CES) production function, its value would be reflected in the differ-ence between the sums of the lag coefficients on the terms for outputand the user cost of capital.

7 The use of logs of the values of output and the cost of capitalpresumes that the statistical processes for the rates of growth ofthese variables are stable. Because this article estimates the othermodels with all variables expressed as proportions of the stock ofcapital, these models also essentially presume stable processes forthe rates of growth of output, the cost of capital, and cash flow.


The version of the q model that appears in thisarticle simply uses a short history of q to explaininvestment. These fixed lags would representinvestors’ optimal forecasts of future values of q if thecorrelations among the values of q remained relativelystable over time.

Because a direct measure of q reflects the valueof both existing capital assets and potential invest-ments, it does not isolate incentives for undertakingnew investments (Hayashi 1982). For example,should markets for companies’ products becomemore competitive, the rate of return on their existingcapital assets might not rise as much as that on newinvestment opportunities. In these circumstances, theaverage value of q would understate investors’demand for new capital goods. q also might repre-sent the incentives for investment poorly if existingassets cannot adapt to new tasks or technologies veryeconomically.8 Should a new technology raise thevalue of new investments more than that of existingassets, investment spending could rise more than qwould predict.

Some models of q, therefore, extend the basictheory with more explicit assumptions aboutinvestors’ behavior and with more explicit descrip-

tions of production functions, demand curves foroutput, supply curves for inputs, and other featuresthat govern investors’ decisions. These approachesoften imply a value for q on new investments.9 Inmost cases, these extensions yield investment equa-tions that, like the neoclassical model, depend on out-put, prices, and the cost of capital (Abel 1980; Hyashi1982; also Abel et al. 1996).

The versions of this model that use direct mea-sures of q (or of marginal q) are not very popularamong forecasters or policy analysts. The difficulty ofidentifying marginal and average returns can com-promise the performance of the model (Abel and

8 See, for example, Pindyck (1991). If companies cannot adjusttheir employment of capital and other factors of production withoutcost, companies are not perfectly competitive, factors of productiondo not earn their marginal products, tax considerations alter thevalue of new capital goods relative to existing capital, or not allinvestors expect capital assets to earn the same return, then the sim-ple description of q and its relation to the demand for capital can bemisleading. See, for example, Galeotti and Schiantarelli (1991).

9 These models also typically define a functional relationshipbetween q and marginal q. Accordingly, their descriptions of invest-ment in terms of marginal q induce investment functions in terms ofq itself. If investors believe their actions influence prices, however,neither q nor marginal q likely provides a “sufficient statistic” forinvestment spending.


Blanchard 1986). Moreover, projecting the prices ofstocks and bonds in the future is more daunting thanforecasting investment by other means. Nevertheless,the q model does provide one way of gauging thedegree to which the recent surge in stocks’ pricesmight correspond to the increase in investmentspending.

The Cash Flow Model

The previous descriptions of investment essen-tially assume that the demand for capital goods doesnot depend very greatly on the means by whichinvestors finance their capital spending. In the neo-classical and q models, the provision of financingaffects the demand for capital only by altering thecost of funds that are available to companies in fullyefficient capital markets, provided by fully informedsuppliers. The cash flow model recognizes that busi-nesses rely on three sources of funds—internal cashflow, new debt, and new equity—and that the yieldson debt and equity do not represent the full cost ofusing these funds (Meyer and Kuh 1957;Duesenberry 1958; Grundfeld 1960; Lintner 1967; andMyers and Majluf 1984).

Cash flow—profit after taxes plus depreciationallowances less payments to shareholders—consti-tutes the principal source of financing companies’ cap-ital budgets. Since the 1940s, nonfinancial corpora-tions’ purchases of capital goods seldom have strayedfrom their cash flow for very long (Figure 3).10

Accordingly, businesses’ internal cash flow has consis-tently represented more than 85 percent of their capitalbudgets. The highest peaks in spending relative tocash flow tend to occur when profits fall more abrupt-ly than capital spending during recessions.

Debt financing includes public issues of bonds orcommercial paper, private placements, loans, leases,and other securities that usually offer creditors prede-termined yields and claims against the earnings orassets of businesses. Since the 1940s, debt financingtypically has accounted for virtually all of the net exter-nal financing of businesses’ inventories, plant, and

10 Not only do nonfinancial corporations provide internal capi-tal markets for funding their own projects, but they also support thecapital spending of other companies through equity investments,loans, mergers, leases, joint development or marketing agreements,and other alliances (Gomes-Casseres 1996; Navin and Sears 1955;Baskin 1988; Baskin and Miranti 1997; Carosso 1970).


equipment. New issues of equity, which include com-mon and preferred stock or partnerships, seldom haverepresented a substantial source of funds since 1960.

Not only do businesses use debt to finance theirinvestment spending when their opportunities exceedtheir cash flow, they also might reduce their averagecost of capital by financing a portion of their capitalassets with debt. Businesses can deduct their interestpayments from their taxable income; they cannotdeduct their payments to their shareholders.Nonetheless, the appeal of debt financing eventuallydiminishes as managers and shareholders incur a larg-er risk of losing control of their companies with greaterleverage.11 Moreover, when creditors are less opti-mistic than borrowers, companies will regard the riskpremiums that they must pay on their debt as increas-ingly excessive as their leverage increases.12 An opti-mal degree of leverage balances the advantages ofdebt financing against its costs.

Businesses whose demand for new capital assetsgreatly exceeds their cash flows eventually might issuenew equity in conjunction with their debt in order tomaintain a satisfactory degree of leverage. Becausenew shareholders, almost by definition, are less opti-mistic and less assured than existing shareholders,they generally require a greater rate of return thanexisting shareholders. This new equity financing typi-cally is sufficiently expensive to be a last resort, under-taken only when it brings more competent manage-ment, allows existing owners to liquidate or diversifytheir assets, or enables companies to expand sufficient-ly rapidly to secure greater economic rents withoutincurring excessive leverage.

Cash flow serves two purposes. It finances capitalbudgets and, in reflecting the return on existing assets,it can represent the return investors might expect ofnew investments. The terms that contain lagged cashflows in the model represent both the adjustment ofcapital budgets to recent experience and the projection

of future earnings from past earnings. These lags alsomay represent changes in companies’ optimal choiceof leverage. Because this model typically finds thatinvestors respond slowly to changes in the growth oftheir cash flow, it predicts that companies’ leveragerises when the growth of their earnings subsides andthat leverage falls when their earnings accelerate.

The Time Series Model

Unlike the other approaches discussed in this arti-cle, the time series model appeals to no explicit theory.Investment spending depends on its history and the

The time series model appeals to noexplicit theory: Investment spending

depends on its history and the history of a few related variables.

history of a few related variables. This model assumesthat the trends and cycles evident in recent experienceare sufficiently stable to describe the course of capitalspending in the future. This approach may be regard-ed as a model in its own right or as a standard where-by other models may be judged.

The time series model’s simple appearance beliesthe reasoning upon which it rests. Investment candepend on many economic variables, all of which areembedded in a larger model of the economy. If,according to this model, these variables mutuallydepend on their lagged values, then an autoregressioncan represent investment spending when the fullmodel of the economy is sufficiently linear and the sta-tistical processes for its exogenous variables do notchange over time. This autoregression could expressinvestment simply in terms of its own lagged values,or it also could include the lagged values of other vari-ables. This study’s version uses both past investmentand output to explain investment spending.

Although time series models impose their ownstrong assumptions, proponents of this approachbelieve that other models require even strongerassumptions. To what degree does output determineinvestment, or does investment determine output, orare both determined by some other common factors?In order to cope with these distinctions, models

11 Borrowers assume commitments and constraints that inher-ently increase the cost of their funds as their leverage increases. Debtcontracts entitle creditors to a senior claim against borrowers’ assets.These contracts also can impose minimum loan-to-value ratios, cov-erage ratios (earnings relative to debt service charges), working cap-ital ratios (net short-term assets relative to long-term debt), or otherrestrictions on borrowers. Should a company fail to meet these stan-dards, it cedes some control over its operations to its creditors.

12 When creditors and shareholders have identical discountrates and regard a company’s prospects similarly, when interestexpenses are taxed the same as other corporate income, and whenbankruptcy costs are negligible, then the company’s average cost ofcapital (combining debt and equity financing) is independent of itsleverage (Modigliani and Miller 1958, 1963; Duesenberry 1958;Lintner 1967; Myers 1989).


invoke assumptions about the behavior of business-es, the structure of markets, and other potentiallycontroversial characteristics of the economy. If out-put and the cost of capital do not determine invest-ment spending, for example, the accelerator and neo-classical models are misspecified. The time seriesmodel avoids these problems by analyzing thedynamics of investment and related variables. But,in order to measure these dynamics, it assumes thatthe correlations among these variables remain stableover time.

However accurately autoregressions might fore-cast investment, they tell no stories. They cannotexplain why a tax cut might foster more investmentspending than a commensurate reduction in interestrates. Forecasting that investment will increase 10percent might not be as important as describing thereasons that demand likely will increase at this pace.

Forecasts frequently are judged by this reasoning.Furthermore, should changes in policy or the busi-ness environment alter the correlations among thevariables over time—which, for example, often is theintention of policymakers or the consequence oftechnological changes—then the time series modelcould fail to explain the course of investment.Autoregressions are not uniquely vulnerable in thisregard. But, other models hope to achieve greaterstability by modeling the structural determinants ofinvestment more explicitly, thereby more fully incor-porating the consequences of policy in the modelitself.13 The neoclassical model, for instance, allowschanges in corporations’ taxes to influence invest-ment’s response to output.

III. The Performance of the Models

This article estimates the six models of investmentspending from 1960 to 1990, applying each model toeach of the two major components of businesses’ fixedinvestment, durable equipment and software and non-residential structures. The estimated models were thenused to predict investment from 1991 to 1999.

13 Correlation coefficients among variables are not necessarilystable when they depend on values assumed by other variables orwhen variables are bound by nonlinear relationships. Modelsattempt to uncover more stable statistical relationships by recogniz-ing the structural links among variables (Haavelmo 1944;Duesenberry 1948; B. Friedman 1978; Sims 1982).


The time series model appears to fit spending bestthrough 1990 and forecast best during the remainderof the 1990s. The other models at best fit spending onlymoderately well until the late 1980s, when their pre-dictions generally began to exceed the rate of invest-ment by a substantial margin. After 1990, the models’forecasts initially continued to exceed investment inequipment and software, but their errors generally fellsignificantly by 1999. Their forecasts of investment innonresidential structures, however, continued toexceed spending by a substantial margin throughoutthe 1990s.

Estimating the Models

The estimates of each model reflect the historicalcorrespondence between investment spending andother macroeconomic variables. As a result of the shiftin the composition of the stock of durable equipmenttoward information processing equipment, whichbecame especially great during the 1990s (Table 2), noneof the models for gross investment in equipment andsoftware forecasted this spending very well after 1990.The neoclassical model, for example, predicted too littlegross investment spending relative to the stock of capi-tal during this interval, because its implicit estimate ofthe rate of depreciation of capital became too low whenthe composition of the stock of equipment shifted

(Figure 4). The model’s forecast of net investment, onthe other hand, is significantly more accurate.

Because models of aggregate investment, bydesign, omit the finer details associated with the com-position of capital and investment, the rate of deprecia-tion of capital, which has risen especially sharply inrecent years, is outside their ken.14 Accordingly, the fol-lowing describes the performance of the equations fornet investment spending. The structure of each modelcorresponds to the equations that appear in Table 5,except that all equations are divided by the laggedvalue of the capital stock. The models, therefore,explain the rate of growth of the stock of nonresidentialstructures and the stock of equipment and software.

Table 6 describes the models’ abilities to fit thedata through 1990. Figures 5 through 8 also show thecorrespondence between the models’ projections andthe course of investment for the period of estimation,which ends at the vertical line. In general, the modelsexplained the course of investment in equipment andsoftware better than that for structures. The times

Table 6

Selected Statistics for the Investment Period 1960:I to 1990:IV for the Models of InvestmentPercent

Mean Root Mean Percent of Percent ofAbsolute Squared Absolute Errors Absolute Errors Autocorrelation Number

Model Error Error Exceeding 0.66 std Exceeding 1.5 std Coefficient of Lags

Equipment

Time Series .05 .07 .0 .0 .01 4Accelerator .26 .32 34.5 .9 .95 12Neoclassical .34 .40 56.9 8.6 .97 12Modified Neoclassical .25 .31 40.8 1.7 .97 8q Model .30 .35 49.1 3.4 .95 12Cash Flow .33 .41 51.7 5.2 .96 12

Structures

Time Series .03 .04 1.6 .0 –.00 4Accelerator .11 .13 45.7 .9 .94 12Neoclassical .10 .12 39.7 .9 .94 12Modified Neoclassical .08 .10 28.7 .8 .92 6q Model .10 .12 40.0 .9 .94 12Cash Flow .10 .12 35.7 1.7 .94 12

14 The figure also shows that the rate of growth of capital hasbeen more volatile than gross investment. In the early 1970s, forexample, the rate of growth of capital varied between 1 and 2 per-cent, while investment relative to capital varied between 0.12 and0.15 percent. This discrepancy can be attributed partly to variationsin depreciation, mostly to variations in the valuation of the compo-nents of the aggregate stock of capital. (See Appendix 1.)


series model fit the data best for both components ofinvestment. Of the remaining models, the modifiedneoclassical model performed best.

The times series model fits investment in equip-ment and software remarkably accurately, conformingto almost 98 percent of the variation in spending.

The time series model appears to fitspending best through 1990 and

forecast best during the remainder of the 1990s.

Nonetheless, its fitted values reached their peaks ortroughs one quarter after those of investment, a seem-ingly minor quibble that can suggest greater problemswhen using the model to forecast investment verymany quarters in advance. The accelerator modelexplained only about 46 percent of the variation inspending. The peaks and troughs of its fitted valuesalso follow those of investment, albeit with a longerlag than the time series model, and the pattern of itsfitted values corresponds to that of investment muchless closely than did the projections of the time series

model. The modified neoclassical model, whichexplained about 51 percent of the variation in spend-ing, conformed to the data better than the neoclassicalmodel, which explained only 11 percent. In the late1970s both of these equations, like the acceleratormodel, failed to follow the substantial acceleration ofinvestment. They then failed to reflect the drop ininvestment during the last half of the 1980s. The qmodel’s projections, which varied much less thanthose of the other models, nevertheless explainedabout 34 percent of the variation in spending. It, too,failed to reflect the surge in capital formation in thelate 1970s followed by the subsidence in the early andlate 1980s. The cash flow model explained about 11percent of the variation in spending as a result of itsrelatively large errors in the mid 1960s and 1980s.

The times series model explained about 92 per-cent of the investment in nonresidential structures, aperformance much better than that of the other mod-els. The time series model’s one-quarter lag in explain-ing spending on new structures, like that for equip-ment and software, suggests a potential difficulty withthe model, however. The accelerator model failed toconform to the data, explaining only about 3 percent ofthe variation in spending. Again, the modified neo-classical model, which explained about 33 percent ofspending, fit the data better than the neoclassicalmodel, which explained only 11 percent. Neither

Table 7

Selected Statistics for the Forecast Period 1991:I to 1999:IV for the Models of InvestmentPercent

Mean Root Mean Percent of Percent ofMean Absolute Squared Absolute Errors Absolute Errors

Model Error Error Error Exceeding 0.66 std Exceeding 1.5 std

Equipment

Time Series .03 .07 .09 .0 .0Accelerator .20 .42 .50 61.1 16.7Neoclassical –.51 .51 .56 80.6 25.0Modified Neoclassical –.21 .27 .33 36.1 2.8q Model –.64 .64 .66 100.0 33.3Cash Flow –.24 .32 .39 38.9 13.9

Structures

Time Series –.02 .02 .03 .0 .0Accelerator –.27 .27 .30 86.1 52.8Neoclassical –.41 .41 .42 100.0 100.0Modified Neoclassical –.35 .35 .35 100.0 94.4q Model –.42 .42 .43 100.0 97.2Cash Flow –.33 .33 .34 100.0 77.8


explained the pattern of investment during the 1980sparticularly well, but the modified neoclassical modelbenefited by projecting a lower average rate of netinvestment. The q model, like the accelerator model,failed to conform to the data, explaining only 4 percentof investment. The cash flow model explained about20 percent of spending. It, like the neoclassical models,failed to conform to the data for the 1980s very well

and could not explain the significant drop in nonresi-dential construction during the late 1980s.

The Forecasts

Table 7 and Figures 5 through 8 describe the fore-casts of the six models of investment. These forecastsuse the actual values of the variables that appear on


the right side of the equations combined with the esti-mates of the coefficients from the data before 1991. Thestatistics in Table 7 indicate that the models’ averageerrors after 1990 are generally greater than their errorsover their period of estimation. Statistical theory coun-sels tolerance in this regard: Models’ errors ordinarilyincrease as they are applied to new data that differsubstantially from the data over which they were esti-

mated. By this standard, the models’ errors for equip-ment and software are small compared to their errorsbefore 1991. The comparatively large errors for nonres-idential structures, however, suggest that all modelsexcept the times series model continued to misrepre-sent construction as badly as they did in the late 1980s.

The time series model for investment in equip-ment and software performs nearly as well after 1990


as it did over the years to which it was fitted. Its one-quarter lag in forecasting spending persists through-out the forecast interval. Given that the remainingmodels had missed the subsidence in spending onequipment and software during the late 1980s, aslump that continued into the early 1990s, the fore-casts of most of these models recovered after 1992.The accelerator model’s forecasts least resemble the

course of spending—its forecast of a constant rate ofgrowth of capital strongly misrepresents the surge ininvestment. Both of the neoclassical equations, whichanticipated too much spending in the early 1990s,described the especially strong rise in spending after1993. The neoclassical model’s average error wasgreater than that of the modified neoclassical modelover this interval, partly because it continued to pre-


dict a higher average rate of spending. However, theneoclassical model predicted the acceleration ofspending during the late 1990s better than the modi-fied model. Although the q model also erred substan-tially during the 1990s by consistently forecasting anexcessive rate of spending, the model did forecast theacceleration of spending relatively well until 1999,when its error increased. The cash flow model, like

the modified neoclassical model, began the forecastinterval by forecasting too much investment. But, itserror over the interval fell, because it failed to forecastthe strong acceleration in capital formation—spend-ing overtook its forecast.

The time series model for investment in nonresi-dential structures performed nearly as well after 1990as it did over the years to which it was fitted. Its one-


quarter lag in forecasting spending persistedthroughout the forecast interval. The other modelsforecasted investment in nonresidential structurespoorly. After failing to explain a substantial drop ininvestment during the first third of the decade, theirerrors remained large throughout the 1990s. This per-formance suggests that a significant shift in thedemand for structures occurred in the late 1980s or

early 1990s, a shift unrelated to the price of structuresor to businesses’ earnings, sales, and cost of capital.The neoclassical and q models generally forecastedsteady growth in the stock of structures throughoutmuch of the 1990s. For about half of this period, how-ever, investment in structures fell and remainedremarkably low. Although this investment subse-quently recovered strongly, it did not exceed the rela-


tively modest rates it attained in 1989 and 1990. Notonly did the gap between the forecasts and spendingremain large in the 1990s, but the neoclassical and qmodels also failed to reflect the pattern of invest-ment, especially the slump in spending at the end ofthe decade. Although the performance of the cashflow model generally resembles those of the neoclas-sical and q models, the cash flow model’s forecast

stops rising in 1998 at the time that the growth of thestock of nonresidential structures fell.

Diagnosis

The time series model is the only model that useslagged investment to explain current investment, acharacteristic that is both an asset and a liability. The


time series model’s success rests on the inertia in capi-tal formation over the past four decades. Within thecontext of this model, last quarter’s rate of growth ofthe stock of capital provides more than 90 percent ofthe information for its forecast. The contribution ofgrowth in earlier quarters or of output is very modestby comparison. Accordingly, the inertia in capital for-

mation allowed the model to explain investment onequarter in advance during the 1990s as accurately as ithad in the previous 30 years. On the other hand, thisstrong dependence on last quarter’s investmentcaused its longer-run forecasts of capital formation todeteriorate steadily. Without a constant correction, itsforecast would more nearly resemble that of the accel-


erator model (Figure 9).15 Conversely, if the other mod-els were allowed to take into account their previousperiod’s error, their performance would resemble

more closely that of the time series model. Withoutthese constant corrections, however, we can see moreclearly the models’ ability to explain the determinantsof capital formation, particularly over intervals longerthan one quarter.

The accelerator model’s failure can be attributedto its attempt to reconcile its presumption of a

15 Because their errors are highly correlated (Table 6), the othermodels would fit the data and forecast spending much more accu-rately by taking last quarter’s forecast error or, equivalently, lastquarter’s spending into account.


smooth trend for capital-output ratio with the data(the gray lines in Figure 10). Through the early 1980s,the ratio of the stock of equipment and software to output rose on average 4.2 percent annually.Afterward, the ratio followed a different course andremained relatively constant. Therefore, the accelera-tor model’s coefficients, which strongly reflect thecourse of the ratio in the earlier period, do not coin-cide with the subsequent experience very well. Amore successful model for equipment and softwarewould need to cope with this break in the data. The

capital-output ratio for structures also failed to coin-cide with the accelerator model’s presumption of asmooth trend. This ratio fell relatively rapidly in theearly 1960s and late 1990s, and during the 1970s and1980s it varied considerably.

In the past, the accelerator model explainedinvestment with more success, partly because thedata for aggregate output and capital were con-structed using fixed-weight, rather than today’schain-weight measures. This innovation has alteredboth the trends and variations in capital relative to


output (the red line in Figure 10). In particular, thechain-weight measure of the capital-output ratio forequipment was constant during the last two decades,while the fixed-weight measure continued to rise.Also, the chain-weight measure of capital-outputratio for structures has been significantly morevolatile than the fixed-weight measure since the mid1980s. Much of the statistical behavior of capital for-mation and the models’ ability to explain capital for-mation, therefore, depends on the way that we meas-

ure the stocks of capital or flows of output andinvestment.

The neoclassical models succeeded to a greaterdegree than the accelerator model because the trendsin the capital-output ratios for equipment and struc-tures often corresponded with those for their cost ofcapital (Figure 11). The rising ratio of the stock ofequipment to output before the mid 1980s generallycoincided with a falling cost of capital (inverted scale).From the mid 1980s to the early 1990s, both the capital-


output ratio and the cost of capital changed compara-tively little. After the early 1990s, however, the cost ofcapital fell while the capital-output ratio remained rel-atively constant. For structures, the correspondencebetween investment and the cost of capital is more ten-uous. From 1960 to the early 1970s, the capital-output ratio fell while the cost of capital generally rose. Afterthe spike in the cost of capital during the oil crisis in1974 and 1975, the cost of capital generally rose, thenfell abruptly in the early 1980s back to its value of the

early 1970s. During much of this interval, the capital-output ratio tended to vary inversely with the cost ofcapital. Afterward, the cost of capital generally rosewhile the capital-output ratio fell until the 1990s, whenthe capital-output ratio and the cost of capital bothdeclined at a fairly consistent pace. For nonresidentialstructures, neither the concept of investment nor thecost of capital includes the cost of land, an importantcomponent in businesses’ decision to develop realestate. Also, the neoclassical model’s assumption that


markets are in equilibrium and the rents that compa-nies incur on real estate match the cost of capital ismost likely to fail for extended periods, especially afterexcessive development, for assets such as long-livedstructures. Finally, the neoclassical model, like theother aggregate models, cannot reflect the conse-quences of deregulation and technological change inconstruction, energy, telecommunications, transporta-tion, manufacturing, and managing office and ware-house space that have occurred since the 1970s.

The modified neoclassical model performed bet-ter than the neoclassical model, because it allows theinfluences of output and the cost of capital on invest-ment to be different. The modified model fit the databest by allowing the magnitude of the coefficients forthe cost of capital to be lower than that for output.Investment would respond less to a 1 percent changein the cost of capital than to a 1 percent change in out-put. The growth of investment and output, in otherwords, was relatively less volatile than the changes inthe user cost of capital during the past four decades.16

The cost of capital and output might have differenteffects for several reasons. For example, the variationin the measured cost of capital might exceed the varia-tion in effective rents (including the cost of land forstructures), or investors might anticipate that the vari-ations in the cost of capital or effective rents tend not tolast as long as those for output.

The q model produces the smoothest fit and fore-cast for investment, despite its dependence on theprices of equities. Because longer-run averages ofsecurities prices tend to vary much less than averagesover short periods, and because short-run variations insecurities prices do not coincide with short-runchanges in investment very well,17 this model seemsbetter suited to explain longer-run trends in invest-ment than short-run cycles, especially for equipmentand software.

Finally, the cash flow model suggests that capitalformation during the 1980s and early 1990s did notslump for want of internal funds for businesses’ capi-tal budgets. For much of this interval (except for thebrief period that saw the blooming of low-grade bondfinancing in the mid 1980s), cash flow predicted amuch higher level of spending. This model’s perform-

ance, like those of the accelerator, q, and neoclassicalmodels, seems to be compromised by attempting toreconcile the experience after 1980 with previous data.Despite relatively high cash flows, this model, like theothers, could not directly consider that the economicprofits redounding to businesses’ equity capitalremained near their post-World War II lows from theearly 1980s to the early 1990s (Figure 2), also a periodof relatively high real rates of interest. Afterward, theeconomic return on equity rose significantly, andinvestment in equipment and software increased morethan cash flow predicted, as businesses assumed moreleverage in pursuit of profit.

IV. Conclusion

According to the conventional models of invest-ment spending examined in this article, the macroeco-nomic view of businesses’ investment spending hasnot explained the trends and cycles in capital forma-tion since the mid 1980s as well as it did previously. Tosome extent, the structure of the models’ equationsand the themes that they emphasize might have lostnone of their relevance; instead, a change in the corre-lations among macroeconomic variables might haverequired some fine-tuning of their coefficients. Shouldthese correlations change only infrequently in smallways, with some allowance the models might contin-ue to enjoy considerable success. If, however, the sta-tistical relationships among macroeconomic datahave become less stable, then the efficacy of themodels themselves becomes more questionable. Forexample, the models apparently failed to representbusinesses’ perceptions of the profit on new invest-ments after the mid 1980s as they had in previousyears. The results suggest that recent changes in thecomposition of investment expenditures and changesin our industrial structure, at the very least, requireforecasters and policymakers to alter the ways inwhich they estimate and apply their macroeconomicmodels of investment spending.

The composition of investment in recent decadeshas been shifting toward equipment that decays com-paratively rapidly, and the relative prices of capitalgoods have been shifting significantly. In the past, tra-ditional models separated the investment in equip-ment from that in structures, partly because their char-acteristics were too distinct to reconcile in one equa-tion. As investors shifted expenditures from structuresto equipment, for example, the rate of depreciation of

16 This evidence would indicate that the elasticity of substitu-tion between capital and labor does not equal one if the cost of capi-tal equaled the marginal product of capital, which in turn equaledthe current remuneration of capital. (See Appendix 1.)

17 This finding is consistent with the modified neoclassicalmodel’s assigning a lower weight to the cost of capital than to thegrowth of output.


capital that appears as a parameter in a universalinvestment equation would need to change. Similarly,the shift of investment in equipment toward rapidlydepreciating information-processing equipment caus-es models of gross investment in equipment to err byan increasing margin as they underestimate the needto replace seasoned capital. This study partially com-pensated for this bias by recasting the models in termsof net rather than gross investment.

Ultimately, however, stable models of invest-ment might rest on still finer divisions of investmentspending, by separating manufacturing machinery,computers and software, and other types of equip-ment (Tevlin and Whelan 2000), or by distinguishingmanufacturing plants, office buildings, or wells andmines from other nonresidential structures. Indeed,substantial changes in the characteristics and relativeprices of the various capital goods might make thisapproach more compelling for other, more funda-mental reasons. Not only do such changes influencethe measurement of aggregates for capital, but theyalso alter the correlations among measures of capitaland other variables. In other words, the behavior ofinvestment spending or the stock of capital dependsnot only on the quantities of capital goods that consti-tute these aggregates but also on changes in the rela-tive values of these goods. Some changes in the pricesof capital goods can alter the performance of modelsof investment more directly. For example, the neo-classical, q, and cash flow models erred by forecast-ing too much investment in nonresidential structuresduring the 1990s, partly because the relative prices ofthese structures were sufficiently low to elicit thisstrong forecast. If the price of structures, more thanhad been customary before the 1980s, reflected weakdemand rather than the supply of cheap capitalgoods, then the models lacked sufficient detail to rec-

ognize this shift in order to forecast investment moreaccurately.

Changes in our industrial structure, therefore,warrant more attention to detail than is customary inthe traditional models of investment. For example, theapparently low rate of investment in nonresidentialstructures beginning in the 1980s partly reflected thedrop in drilling for petroleum and natural gas or in thebuilding of base-load electric power plants. Themotives for these cuts were not evident in the custom-ary macroeconomic data for businesses’ output, cashflow, or cost of capital. Similarly, the macroeconomicmodels alone cannot explain the rise of investment ininformation processing, which lifted aggregate invest-ment in durable equipment and software. These shiftsin the composition of investment also can weaken ourability to measure aggregate output and investment,especially when the relative prices of products and cap-ital goods change very greatly. As a result of suchchanges, including the rapid drop in the prices of manytypes of equipment, the national accounts adopted achain-weight technique for measuring real output andinvestment during the 1990s. Consequently, aggregatereal stocks of capital now vary to a degree with the val-uations of their elements. As our economic structurecontinues to shift and the relative prices of goods andservices continue to change very substantially, macro-economic models of investment will confront difficul-ties in measuring aggregate output and capital as wellas difficulties in explaining investment spending with-out appealing more explicitly to the motives ofinvestors in different industries. To the degree the rela-tive prices of capital goods shift, forecasters will notnecessarily be able to combine even relatively accurateforecasts of spending for different types of investmentgoods into a comparatively accurate forecast of totalinvestment spending.


Appendix 1

The Cost of Capital and the Return on Capital

Suppose investors consider purchasing a quantity ofcapital assets, K, at the price of PK per unit of capital. Thevalue of their investment after one period would equal theearnings of the capital plus its resale value:

P•MPK•� + PK•K(1 – �)(1 + π)(1 + �).

P denotes the net price of output, and MPK, the marginalproduct of capital, denotes the amount of additional outputthat each unit of the assets produces over the period. At theend of the period, the value of the capital reflects its depreci-ation, at rate �, and the rate at which its blue book priceincreases due to inflation, π, and to any change in its pricerelative to the prices of other goods, �.

If instead of purchasing this capital, investors had pur-chased an equally risky security whose expected real rate ofreturn for one period is r after taxes, then the value of theirinvestment would be

PK•K(1 + r)(1 + π).

For the investors’ expected return on capital to equalthis opportunity cost,

Pr ≈ –– MPK – � + �,PK

orPK–– (r + � – �) ≈ MPK.P

In the absence of corporate income taxes, the left side of thisexpression is the user cost of capital, and the right side is thereturn on capital.

The earnings of capital (P MPK) are taxed as corporateprofits at rate . This tax reduces the net marginal product ofcapital. Investors who purchase new capital might qualifyfor an investment tax credit, itc per dollar of eligible invest-ment. Investors also can deduct from their taxable incomedepreciation allowances with a present value of pvdep perdollar of investment. These allowances reduce the effectiveprice of capital goods. With these tax considerations, theequilibrium condition above becomes

PK–– (r + � – �)(1 – • pvdep – itc) ≈ MPK(1 – ),P

orPK (1 – • pvdep – itc)

MPX ≈ –– (r + � – �)––––––––––––––– UCC.P (1 – )

If the production function, which defines the maximaloutput, Q, that businesses can produce from specificamounts of capital and labor inputs, is Cobb-Douglas,

Q = AK�L(1–�),

then the marginal product of capital equals

QMPK = DK(AK�L(1–�)) = � ––.

K

Substituting this expression into that for the user cost of cap-ital and solving for K yields the stock of capital assets thatmaximizes profit

�Q �QK ≈ –––– = –––––––––––––––––––––––––––.

UCC PK(r + � – �)(1 – •pvdep – itc)–– (r + � – �) ––––––––––––––P (1 – )

Measuring the Stock of Capital Assets

All measurement of economic variables presumes sometheory. As the measurement of a variable becomes more fine-ly tailored to the specifications of a particular theory, itbecomes more accurate and informative for those whoaccept that theory, at the risk of becoming less compelling toothers. The art of measurement, therefore, is to achieve asolid foundation without compromising too greatly a vari-able’s general appeal.

Most of the models of investment in this study proposethat investors conceive an optimal amount of capital toemploy after they consider their opportunities for produc-ing goods and services at a profit. Investment is the processby which the stock of capital approaches this optimum.Accordingly, measures of stocks of capital as well as theflow of investment are essential elements of these models.

A fundamental feature of the theory of productionrequires that the quantities of inputs, including capital, bemeasured independently of the quantities of output as wellas the prices of inputs and outputs (Koopmans 1957).Accordingly, our measure of the quantity of capital that acomputer manufacturer employs ought not vary according tothe value of the computers that the manufacturer produces oraccording to the prices of the manufacturer’s buildings andequipment. The value of capital depends on its price or on theincome that it earns, but the contribution of the capital in theproduction function should not be defined by that income.

Unfortunately, combining various capital goods, differ-ing in type, technology, or vintage, into a well-defined aggre-gate is possible only in implausible circumstances (Fisher1969; M. Brown 1976; Burmeister 1976; Blackorby andSchworm 1988; Hulten 1991). Consequently, no measure ofthe stock of capital is superior to all alternatives; each impos-es its particular assumptions and poses its particular biases.The problem is not limited to the stock of capital. Estimatesof investment, GDP, and other aggregates that appear in theinvestment equations pose similar difficulties.


The U.S. Bureau of Economic Analysis and the U.S.Bureau of Labor Statistics each publish a measure of capital.Both begin with estimates of the quantity of capital for dis-tinct types of capital goods, adding newly purchased capitalgoods to the previous stocks of similar goods and subtract-ing the depreciation of seasoned capital goods (the perpetualinventory method). The BEA assumes that a greater share ofthe capital depreciates in its earliest years of service (geomet-ric decay); the BLS assumes that more of the depreciationoccurs in later years (hyperbolic decay). The BEA’s measureof capital sums the distinct stocks, weighting them by theirrelative prices using a chain-weighted index (Landefeld andParker 1997). The BLS’s measure of the supply of capitalservices essentially weights each elemental stock by the pro-portion of capital’s income that accrues to that stock.18

Although the two techniques have different theoretical prop-erties, they generally do not produce measures of capitalinputs that diverge very greatly or very persistently overtime, at least until the mid 1990s. And, both measures of cap-ital inputs change from year to year as the result both of thenet investment in new capital goods and of changes in theweights applied to the elemental stocks of capital.

The BLS derives each capital good’s share of incomethrough its user costs. Assuming each type of capital is paidits user cost, the stock of each multiplied by its user costshould sum to the income of all capital,

gross capital income = ∑Ki•UCCi

PKi (1 – •pvdepi – itci)gross capital income = ∑Ki•––– (r + �i – �i)–––––––––––––––––,P (1 – )

where the common opportunity cost of funds (r) in theexpression for the user cost is chosen to guarantee this equal-ity. Other things equal, the more rapidly capital loses itsvalue—the greater is (�–�)—the greater is its share of capi-tal’s income

Ki•UCCi PKi (1 – •pvdepi – itci)–––––––––––––––––– = (r + �i – �i)––– –––––––––––––––––.gross capital income P (1 – )

In other words, capital that depreciates quickly and whoseprice falls most rapidly over time—computers for example—must earn more income per dollar of its purchase price (PK)in order to compensate investors for their losses. The BLS’smeasure of capital services, therefore, tends to give thestocks of equipment and software more weight than theBEA’s measure, which relies on the price of capital goods.

The BLS’s estimate gives more weight to more prof-itable capital. To an engineer, a lathe that produces rotors fora return of $1 million when demand is great in the first halfof a year does not lose its intrinsic capacity for producingrotors if it then earns $100 thousand after demand falters inthe second half of the year. The BLS’s measure of capitalservices for this lathe, however, declines with the value of itsoutput. The BLS’s procedure essentially assumes that pro-duction is characterized by constant returns to scale, theeconomy is in equilibrium, that markets for all goods and

services are competitive, that those who finance businesses’capital assess its returns the same as the businesses do, andthe return to capital equals its marginal product.19

Economists and accountants continue to debate the propermethod of assigning earnings to a company’s various factorsof production, especially when the demand for its productsis not perfectly elastic. Also, investors typically require dif-ferent returns (r) from investments that pose different risks.Not only might risks differ, so might the timing of income.The measurement of the return on investment probablyshould not rely entirely on its income during the period inquestion. Because capital goods to a degree are illiquid,because many investments expand companies’ options forfuture activities, and because many enterprises and innova-tions take time to realize their full potential, a capital good’scurrent income might misstate its marginal product from itsowner’s perspective. Furthermore, when companies earneconomic rents that change from year to year or their utiliza-tion of illiquid investments in capital assets varies from yearto year according to the demand for their products, thenmeasures of the supply of capital services can change inways that do not represent the productivity of the underly-ing capital goods. Indeed, the returns to capital and rates ofcapacity utilization have varied substantially over the busi-ness cycle and over the decades, suggesting that variationsin earnings might reflect more than variations in the funda-mental supply of capital services.

The BEA’s measure of the stock of capital depends onthe prices of capital goods, which poses its own problems(Jorgenson and Landau 1989; Jorgenson 1992; Hulten 1991).The logic behind the BLS’s approach reveals that the price ofa capital good does not likely reflect its contribution in theproduction function. Consequently, weighting the variousstocks of capital goods by prices might give some very pro-ductive assets a relatively low weight and other less produc-tive assets more substantial weights.

Both the BLS’s and the BEA’s measures of capitalchange each year partly because of the weights that theyapply to the elemental stocks of capital goods change. TheBEA, in particular, adopted its chain-weighting technique inorder to avoid a difficulty that arises from fixing the weightsaccording to prices of a specific base year. However well cur-rent prices represent the contribution of various capitalgoods to the production function, the prices that prevailed in1996, for example, provide a less compelling lens for viewingeither today’s capital stock or that of 1986. Various hedonicadjustments might focus this lens better over the years, butthese adjustments become less precise as the technologyembedded in these goods changes, as output evolves, and as

18 The rate of growth of capital is the sum of the rates of growthof the stocks of the elemental capital goods, each multiplied by itsshare of capital’s income (Törnquist aggregation). See Diewert (1976).

19 For criticisms of these assumptions, see, for example, M.Friedman (1964, 1988), Mankiw (1989), Gordon (1990, 1992), andMorrison (1992). If the employment and remuneration of factors ofproduction adjust comparatively slowly, if the applications of exist-ing capital are not sufficiently flexible, or if companies are oligopo-listic competitors, then earnings can misrepresent the contributionof capital in the production function.


the structure of markets changes (Landefeld and Grimm2000). Although the chain-weight approach might improve comparisons in neighboring years, it does not improve com-parisons of the capital stock over more distant years.Furthermore, as is the case for the components of GDP,chain-weight measures of the constant-dollar components of

Appendix 2

Sources of Data

All data are from the U.S. Department of Commerce,Bureau of Economic Analysis, National Income and ProductAccounts (NIPA) except where otherwise noted. Measures ofstocks of assets and flows of goods or services are expressedin real chain-weighted 1996 dollars.

KE, KS: Capital stock of equipment and software, andstructures, respectively. Tevlin and Whelan (2000) providedquarterly estimates of the annual published data from theBureau of Economic Analysis’ National Income and ProductAccounts that adjusted the interpolation to accommodatethe accelerating depreciation of equipment and softwareduring the 1990s.

NFCGDP: Real gross domestic product for nonfinancialcorporate business; quarterly data expressed at an annualrate.

RE, RS: User cost of capital for equipment and software,and nonresidential structures.

RE = [(CE / CT) (.15 + D)] * [(1-ITC-TAXS * WE) / (1 – TAXE)]

RS = [(CS / CT) (.05 + D)] * [(1-TAXS * WS) / (1 – TAXE)]

CE, CS: Implicit price deflators for nonresidentialinvestment in equipment and software, and structures.

CT is defined as the GDP price deflator. The economicrate of depreciation is estimated at 0.15 for equipment andsoftware, and 0.05 for structures. D is the discount rate forafter-tax corporate profits, and equals the Standard & Poor’s500 index of common stocks dividend-price ratio, plus 4 per-cent, which is the estimated real rate of growth of nonfinan-cial corporations. This definition of D is inspired by theGordon growth model for valuing equities.

ITC, the investment tax credit for equipment, TAXS, thestatutory, and TAXE, the effective, tax rates paid by U.S. cor-porations, are taken from the DRI Model of the U.S.Economy. ITC is the weighted average of investment taxcredits for autos, office equipment, and other equipment.

WE, WS: The present value of one dollar of depreciation,allowances for nonresidential capital equipment and corporatestructures, taken from the DRI Model of the U.S. Economy.

q: The ratio of the market value of nonfinancial corpo-rations to the replacement value of their net assets.

Market value equals new equity issuance net of finan-cial assets (total financial assets less trade receivables, mutu-al fund shares, and miscellaneous assets) plus net interest-

bearing debt (the sum of bank loans, commercial paper,acceptances, finance company loans, U.S. government loans,and adjusted bonds (AB)).

AB = 0.5 * MTG + NYSEBOND * (0.5 * MTG + TEB + CB)MTG = commercial mortgagesTEB = tax-exempt bondsCB = corporate bonds

NYSEBOND: Market value as a percent of par value forall New York Stock Exchange listed bonds. Annual datacome from the NYSE Fact Book for various years. Quarterlydata were derived using a nonlinear interpolation based onthe pattern of 5-year Treasury note yields.

The replacement value of net nonfarm nonfinancial cor-porate assets is the sum of total corporate real estate, equip-ment and software, and inventories at year-end prices.Except for NYSEBOND, all data used to construct the qseries are taken from the Flow of Funds Accounts of the UnitedStates, Board of Governors of the Federal Reserve System.

F: Cash flow for businesses, using data from the Boardof Governors, Flow of Funds Accounts, for the nonfarm nonfi-nancial corporate business sector. Cash flow is defined asprofits less taxes and dividends, including the consumptionof fixed capital and the inventory valuation adjustment.

All regressions were estimated using ordinary leastsquares with no allowance for autocorrelation of the errors.The period of fit was 1960:I to 1990:IV, and forecast was1991:I to 1999:IV. Polynomial distributed lags were used inall of the models except the time series and some of the mod-ified neoclassical terms. During the past decade, the unchar-acteristically large increase in equipment spending, intensi-fied by the boom in the information processing and softwarecomponent, made it difficult to fit models regressed on thelevel of investment or the ratio of investment to the stock ofcapital. Similarly, the decline in new building and real estateexpenditures in the early 1990s was not an event modelscould predict based on past investment trends. Runningregressions on the growth of the capital stock improved thefit, but varying the length of lags, degree of polynomials, andendpoint constraints as described below was also necessaryto generate results that better described the recent invest-ment and capital stock trends. The relatively strong perform-ance of the time series model is, therefore, the result of statis-tical and not actual explanatory economic effects.

the capital stock do not add to the chain-weight measure ofthe constant-dollar value of the full capital stock.

This study uses the BEA’s measure of stocks of capitalgoods. In the absence of compelling arguments, Occam’srazor recommends the simplest measure, that which invokesthe least complex theory.


Quarterly Models of Investment in Equipment and Structures

Time Series

KE/KEt–1–1 = –.00081 + b1(KEt–1/KEt–2–1) + b2(KEt–2/KEt–3–1) + b3(KEt–3/KEt–4–1) + b4(KEt–4/KEt–5–1) + c1NFCGDP/KEt–1 +c2NFCGDP/KEt–2 + c3NFCGDP/KEt–3 +c4NFCGDP/KEt–4 + c5NFCGDP/KEt–5

b1 = 1.0564b2 = .2042b3 = –.2915b4 = .0613

Sum = 1.0304c1 = .0274c2 = –.0148c3 = –.0090c4 = .0012c5 = –.0045

Sum = .0003

KS/KSt–1–1 = .00015 + b1(KSt–1/KSt–2–1) + b2(KSt–2/KSt–3–1) + b3(KSt–3/KSt–4–1) + b4(KSt–4/KSt–5–1) + c1NFCGDP/KSt–1 +c2NFCGDP/KSt-–2 + c3NFCGDP/KSt–3 +c4NFCGDP/KSt–4 + c5NFCGDP/KSt–5

b1 = 1.1724b2 = –.0841b3 = –.0482b4 = –.0776

Sum = .9625c1 = .0125c2 = –.0031c3 = –.0121c4 = .0084c5 = –.0056

Sum = .0001

Accelerator12

KE/KEt–1–1 = –.0118 + ∑biNFCGDP/KEt–1i = 0

b1 = .0039b2 = .0034b3 = .0030b4 = .0025b5 = .0021b6 = .0016b7 = .0012b8 = .0007b9 = .0003

b10 = –.0002b11 = –.0007b12 = –.0011

Sum = .0167Polynomial distributed lag, 2nd order, 12-period lag length,no endpoint constraint.

12

KS/KSt–1–1 = –.0095 + ∑biNFCGDP/KEt–1i = 0

b1 = .0013b2 = .0007b3 = .0002b4 = –.0002b5 = –.0005b6 = -.0008b7 = –.0009b8 = –.0010b9 = –.0010

b10 = –.0008b11 = –.0006b12 = –.0004

Sum = –.0040Polynomial distributed lag, 3rd order, 12-period lag length,far endpoint constraint.

Neoclassical

12

KE/KEt–1–1 = –.0055 + ∑biNFCGDP/KEt–1 + i = 0

12

∑ciNFCGDP/REt–1/KEt–1i = 0

b1 = .0008b2 = .0015b3 = .0020b4 = .0025b5 = .0027b6 = .0029b7 = .0029b8 = .0027b9 = .0025

b10 = .0020b11 = .0015b12 = .0008

Sum = .0248First polynomial distributed lag term, 3rd order, 12-periodlog length, both endpoint constraints.

c1 = –.0005c2 = –.0011c3 = –.0017c4 = –.0021c5 = –.0023c6 = –.0025c7 = –.0025c8 = –.0024c9 = –.0022

c10 = –.0018c11 = –.0014c12 = –.0007

Sum = –.0212Second polynomial distributed lag term, 3rd order, 12-periodlog length, far endpoint constraint.


12

KS/KSt–1–1 = –.0044 + ∑biNFCGDP/RS/KSt–1 + i = 0

12

∑ciNFCGDP/RSt–1/KSt–1i = 0

b1 = .0005b2 = .0005b3 = .0004b4 = .0004b5 = .0004b6 = .0003b7 = .0002b8 = .00006b9 = –.00008

b10 = –.0002b11 = –.0004b12 = –.0006

Sum = .0015c1 = –.0006c2 = –.0004c3 = –.0003c4 = –.0001c5 = –.00002c6 = .00007c7 = .0001c8 = .0002c9 = .0002

c10 = .0002c11 = .0001c12 = .00004

Sum = –.0005Polynomial distributed lags, 3rd order, 12-period laglengths, no endpoint constraints.

Modified Neoclassical

4

KE/KEt–1–1 = –.0280 + ∑biLOG(NFCGDP) + i = 0

8

∑ ciLOG(RE) + d1LOG(KE)i = 0

b1 = .0172b2 = .0129b3 = .0086b4 = .0043

Sum = .0430First polynomial distributed lag term, 2nd order, 4-periodlag length, far endpoint constraint.

c1 = –.0041c2 = –.0036c3 = –.0030c4 = –.0025c5 = –.0020c6 = –.0015c7 = –.0010c8 = –.0005

Sum = -.0182d1 = –.0425

Second polynomial distributed lag term, 2nd order, 8-periodlag length, far endpoint constraint.

6

KS/KSt–1–1 = –.0656 + ∑biLOG(NFCGDP) + i = 0

c1LOG(RS) + c2LOG(RSt–1) + c3LOG(RSt–2) + c4LOG(RSt-3) + d1LOG(KS)

b1 = .0046b2 = .0038b3 = .0031b4 = .0023b5 = .0015b6 = .0008

Sum = .0161c1 = –.0039c2 = –.0005c3 = –.0005c4 = .0036

Sum = –.0013d1 = –.0228

Polynomial distributed lag, 2nd order, 6-period lag length,far endpoint constraint.

Q Model

12

KE/KEt–1–1 = –.0152 + ∑bi((q–1)*(KEt–1))i = 0

b1 = .00000020b2 = .00000037b3 = .00000051b4 = .00000061b5 = .00000068b6 = .00000072b7 = .00000072b8 = .00000068b9 = .00000061

b10 = .00000051b11 = .00000037b12 = .00000020

Sum = .0000068Polynomial distributed lag, 3rd order, 12-period lag length,both endpoints constrained.

12

KS/KSt–1–1 = –.0014 + ∑bi((q–1)*(KSt–1))i = 0

b1 = .0013b2 = .0007b3 = .0002b4 = –.0002b5 = –.0005b6 = –.0008b7 = –.0009b8 = –.0010b9 = –.0010

b10 = –.0008b11 = –.0006b12 = –.0004

Sum = –.0040Polynomial distributed lag, 3rd order, 12-period lag length,far endpoint constraint.


Cash Flow

12

KE/KEt–1–1 = –.0018 + ∑bi(F/CE/KEt–1)i = 0

b1 = –.0170b2 = –.0034b3 = .0074b4 = .0153b5 = .0204b6 = .0228b7 = .0222b8 = .0189b9 = .0127

b10 = .0037b11 = –.0081b12 = –.0228

Sum = .0721Polynomial distributed lag, 3rd order, 12-period lag length,no endpoints constrained.

12

KS/KSt–1–1 = –.0014 + ∑bi(F/CS/KSt–1)i = 0

b1 = .0083b2 = .0076b3 = .0069b4 = .0062b5 = .0056b6 = .0049b7 = .0042b8 = .0035b9 = .0028

b10 = .0021b11 = .0014b12 = 00007

Sum = .0542Polynomial distributed lag, 2nd order, 12-period lag length,far endpoint constraint.

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