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Long-run growth projections and the aggregate production function: a survey of models used by the U.S. government.


Long-run economic growth is an area of obvious interest to both economists and policymakers. This interest is evident in the large academic literature on economic growth and the considerable effort that policymakers undertake when projecting the growth of the U.S. economy. Accurate projections of future growth have clear implications for U.S government budget policy, the soundness of the Social Security and Medicare systems, and future standards of living in the United States.

This paper examines the methodology of four prominent government models - the Congressional Budget Office (CBO), the Social Security Administration (SSA), the Office of Management and Budget (OMB), and the General Accounting Office (GAO) - and finds that all are essentially simple Solow growth models in the neoclassical tradition. While the details differ, each agency utilizes a similar framework where potential output depends on the aggregate levels of capital, labor, and technology through the familiar aggregate production function. Long-run growth then results from the accumulation of primary inputs due to demographic changes, education choices, saving and investment decisions, and exogenous increases in total factor productivity.

The Congressional Budget Office (1997a,b,c, 1996, 1995) has the most sophisticated model of long-run growth and explicitly relies on an aggregate production function. CBO uses a detailed and fully developed model of the economy where potential Gross Domestic Product (GDP) growth is determined by a two-input, Cobb-Douglas production function in the nonfarm business sector. Output grows with increases in labor hours (due to exogenous population growth and demographic shifts), endogenous capital accumulation (due to investment and national savings rates), and exogenous increases in total factor productivity.

The Social Security Administration (1996, 1992) and Board of Trustees (1996) use a long-run growth model that, implicitly at least, is in the neoclassical tradition. Since SSA is primarily interested in wage growth and labor supply, it does not explicitly model an aggregate production function, endogenize capital, or examine the sources of growth. Rather, SSA simply defines potential GDP growth as the sum of the growth in labor hours and the growth in labor productivity without modeling labor productivity growth. Labor hours are projected from internal demographic trends, and labor productivity growth is set exogenously at historical rates. This approach, however, is easily reconciled with the aggregate production function.

The Office of Management and Budget (1997a,b) projects long-run real GDP using a framework very similar to SSA. OMB also is not interested in the sources of growth and instead focuses on the relationship between real output growth and the federal budget. Long-run real GDP projections are modeled as a function of demographic factors, which determine labor supply growth, and of exogenous increases in labor productivity.

The General Accounting Office (1996, 1995, 1992a,b), like the CBO, explicitly uses an aggregate production function that depends on growth in labor hours, an endogenously determined capital stock, and total factor productivity. GAO then examines the impact of federal fiscal policy on the rate of capital accumulation and economic growth. Projections of labor hours are again taken from SSA, and total factor productivity growth is exogenous.

The biggest difference between the models involves the relationship between capital accumulation and fiscal policy. Both CBO and GAO endogenize the capital stock by incorporating feedback relationships that link fiscal policy, national savings, and capital accumulation. These models both show that, given demographic trends, current U.S. fiscal policy is not sustainable in the long run. SSA and OMB, on the other hand, simply assume labor productivity will follow previous trends without accounting for the impact of fiscal policy on capital accumulation.

Despite differences in methodology and objectives, these models generate very similar estimates of future output. On a per capita basis, projected real output in 2025 is virtually identical in the SSA and the GAO estimates and differs by only about 10% from the CBO estimates. This is reasonable since all models rely on the same demographic projections from SSA and assume similar rates of exogenous technological progress. However, by assuming that past labor productivity growth rates will continue, SSA and OMB also implicitly assume that substantial changes in U.S. fiscal policy will be made. In addition, by simply using labor hours as the measure of labor input and assuming that growth in total factor productivity will continue, these models miss the likely slowdown in the growth of labor quality and overstate future growth.

These long-run models stand in sharp contrast to the recent academic literature on economic growth. Grossman and Helpman (1994) and Rome (1994), for example, survey the endogenous growth literature that emphasizes market power, spillovers, and increasing returns to scale as important sources of aggregate growth. The large empirical literature on economic growth also has moved away from the simple Solow model, although in a less systematic way. Sala-i-Martin (1997), for example, surveys the field and finds 22 non-traditional variables- e.g., political, religious, regional - that are "significant" in cross-section growth regressions.

While both of these approaches offer valuable insights into the nature of economic growth, the aggregate production function remains the appropriate tool for long-run growth projections. Within a single country, many of the variables that enter the cross-sectional regressions simply do not vary enough to impact long-run growth, while the inability to predict changes in market power or spillovers leaves the more complicated, endogenous models subject to the same criticism as the Solow model. This suggests that the basic neoclassical framework, even with the fundamental reliance on exogenous technological progress, is the appropriate starting point when projecting long-run economic growth for a single country.


Since the early work of Cobb and Douglas (1928) and Tinbergen (1942), economists have been interested in the concept of an aggregate production function, that posits a systematic relationship between the economy's total output and total primary inputs - e.g., capital and labor. The seminal paper of Solow (1957) integrated this approach with national income data, and the aggregate production function now serves as the basis for much of the applied and theoretical work on economic growth.

In this approach, aggregate output, Y, is a function of aggregate capital, K, aggregate labor, L, and the level of technology, A. If technology is neutral in the sense that all marginal rates of substitution are independent of the level of technology - i.e., "Hicks-neutral" technological change - then one can write

(1) Y = A*F(K,L)

where time subscripts have been suppressed. Methods for estimating K and L are described below and a detailed, quality-adjusted approach is described in Jorgenson (1996, 1990).

This function can be combined with the assumption of competitive factor markets and accounting identities to analyze the sources of growth. If all inputs receive their marginal product as factor payments and all income is paid to the factors, the growth rate of output can be decomposed as

(2) [Delta]Y = [v.sub.K]*[Delta]K + [v.sub.L]*[Delta]L + [Delta]A

where a A before a variable refers to the growth rate of that variable,

[v.sub.K] = [Delta]Y/[Delta]K K/Y

is capital's share of nominal income,

[v.sub.L] = [Delta]Y/[Delta]K L/Y

is labor share's of nominal income and, [Delta]A is, equivalently, the growth rate of technology, the growth in total factor productivity (TFP), or the famous "Solow residual." If all inputs are classified as either capital or labor, this amounts to assuming constant returns to scale.

This neoclassical framework models long-run growth as a function of only the primary inputs and the level of technology. Capital and labor are accumulated over time through various firm and household choices such as investment, saving, or education decisions, while technology is typically treated as exogenous. There is no role for intermediate goods like material or energy inputs as a source of long-run economic growth. Finally, exogenous technological progress remains an important, although still unexplained, source of long-run growth.

Although the aggregate production function has an appealing and intuitive feel, there has been considerable controversy regarding the existence of such a relationship. For an aggregate production function to exist, one must be able to aggregate different production techniques into a single aggregate function and aggregate heterogeneous outputs and inputs into aggregate indexes. Even those who developed the aggregate production function recognized these limitations. As Solow (1957, p. 312) states, "It takes something more than the usual 'willing suspension of belief' to talk seriously of the aggregate production function." The controversy regarding the existence of such aggregates, however, has been largely decided in favor of the aggregationists. Fisher (1992, p. xiii), for example, states "the existence of aggregate production functions in general and of an aggregate capital stock in particular is a purely technical question."

These "technical" questions, however, impose stringent restrictions on the form of production. Jorgenson (1990) enumerates the necessary conditions for the existence of an aggregate production function as follows: (i) Technology is separable in Value-Added. (ii) Value-Added is a function of capital, labor and technology. (iii) All sectoral Value-Added functions are identical. (iv) The capital and labor aggregating functions are the same for all sectors. (v) Each input receives the same payment in all sectors. These are clearly highly restrictive assumptions that place very specific constraints on the means of production.

Despite the stringent technical conditions necessary for exact aggregation, the use of an aggregate production function is widespread in both the academic literature and in Washington. Modern growth theory, international growth comparisons, aggregate productivity analyses, and long-run economic projections are typically based on an aggregate production function.

As an alternative to the aggregate production function, one could model economic growth as an aggregate of growth in different production sectors. A complete sectoral model of the economy integrates sectoral Gross Output production functions with input-output matrices, Value-Added measures, and the familiar components of Final Demand - consumption, investment, government purchases, and net exports. This approach has considerable data requirements but dispenses with some of the restrictive assumptions of the aggregate production function.

Jorgenson et al. (1987) present empirical results for this type of detailed sectoral analysis for 1948-1979. Jorgenson (1990, p. 26) extends the work through 1985 and concludes that "the aggregate production model is appropriate for studying long-term growth trends. However, the model is highly inappropriate for analyzing the sources of growth over shorter periods." In the context of projecting long-run growth, therefore, the aggregate production function is empirically defensible.


This section summarizes the key economic and demographic assumptions used in the long-run growth models used by four U.S. government agencies. In each case, the authors acknowledge the inherent uncertainty in this type of exercise but are forced to make very specific assumptions regarding the future of the U.S. economy.

A. Congressional Budget Office

The Congressional Budget Office (CBO) was created by the Congressional Budget Act of 1974 and charged with a mission of providing Congress with economic and budgetary information. This mandate included five-year baseline reports of the federal budget, as well as support of the Committee on the Budget in both the House and the Senate. A key objective of the CBO is impartial, nonpartisan analysis of the fiscal situation and, as such, CBO provides no recommendations on fiscal policy.

The Congressional Budget Office (CBO) currently works with two models of economic growth. A medium-term model, described in CBO (1997a), is used for budget projections over a 10-year period. A long-run growth model projects the U.S. economy until 2050 and is described in detail in CBO (1997c, 1995), implemented in CBO (1997b, 1996), and summarized below.

(i) Output Growth

The long-run CBO model is clearly based on the neoclassical model described above and is the most advanced model surveyed here. Although the CBO model contains five sectors (nonfarm business, farm, government, nonfarm housing, and households and nonprofit institutions), the nonfarm business sector represents the core of the model, accounting for 74% of real GDP in 1995. Note that this breakdown follows the National Income and Product Accounts (NIPA) as in Table 1.7.

Nonfarm business output is projected based on growth in the labor force, the rate of national savings (which determines investment and capital formation), and growth in TFP. The production function is well-specified and calibrated to historical data, while other sectors either grow proportionally with the nonfarm business sector or have their own submodels.

Potential output in the business sector is described with a Cobb-Douglas production function with Hicks-neutral technical change and constant returns to scale. Potential output, Y, depends on labor hours, H, capital, K, and TFP, A, as

(3) Y = A*[H.sup.0.3]*[K.sup.0.7]

where the output elasticities are taken from observed shares of labor compensation and capital income in nominal output (CBO, 1997c, 1995). CBO attributes this to Maddison (1987), Denison (1985), and Jorgenson et al. (1987).

(ii) Input Growth

CBO measures labor as total labor hours worked in the nonfarm business sector. Total labor hours are projected by combining average hours worked across age and sex classifications with general demographic trends. To control for cyclical variation in labor supply, CBO uses historical data to determine the relationship between hours worked and potential output. Potential labor is then projected from SSA's estimates of population growth, labor force participation, and hours worked, across age and sex characteristics. These projections show a considerable long-term slowdown in growth of the labor force. For example, total nonfarm hours grew 1.6% for 1979-1989 and CBO assumes only a 0.1% growth beyond 2020 (CBO, 1997b, p. 8). This reflects the familiar demographic changes associated with the aging U.S. population.

CBO measures capital as the flow of capital services used in nonfarm production, with a growth rate calculated from a Tornqvist index of four types of heterogeneous assets as

(4) [Delta]K = [summation of] [v.sub.j]*[Delta][A.sub.j] where j = 1 to 4

where [v.sub.j] is the share in total capital income and [A.sub.j] is the stock of capital, all for asset j. The four asset categories are producers' durable equipment (PDE), computer PDE, nonresidential structures, and inventories.

CBO calculates a stock of capital for each asset based on gross investment for each asset. Gross investment is determined from the exogenously determined savings rate, CBO's projections of national income, and nonfarm business' share of gross investment. For each of the four assets, the capital stock is calculated via the perpetual inventory method as

(5) [A.sub.j,t] = (1-[[Delta].sub.j])*[A.sub.j,t-1] + [I.sub.j,t]

where [A.sub.j,t] is the stock capital, [[Delta].sub.j] is the geometric rate of depreciation, and [I.sub.j,t] is gross investment, all for asset j at time t.

A key feature of the CBO model is that the rate of saving and investment depend on the state of the economy and fiscal policy. In the "No Feedback" scenario in CBO (1997b, p. xiv), "investment simply grows with the overall economy," while the "Feedback" scenario shows federal deficits partially crowding out investment and slowing the rate of capital formation. CBO (p. xiv) assumes that "private savers will offset half of the rise in the deficit and that foreign investors would continue to lend to the U.S."

CBO (1997b, p xiv) further assumes that TFP grows at 1% per year beyond 2007. This is slightly below historical averages for the private nonfarm business sector but well above estimates for more recent periods. According to the Bureau of Labor Statistics (1996), TFP in the nonfarm business sector grew 1.1% a year for 1948-1994 but has fluctuated from 1.9% for 1948-1973, to just over 0.1% for 1973-1990 and 0.3% for 1990-1994.

(iii) Projections

Since CBO explicitly incorporates economic feedbacks between national savings and capital accumulation, growth projections are not promising. Under the mid-range population assumptions from the Social Security Administration, 1% annual TFP growth, and no change in the government budget policies, CBO (1997b, p. xvi) projects that real GDP per capita will begin to decline after 2035 since "federal debt would displace private capital in housing and business plant and equipment." As the productive capital stock falls and labor hours grow more slowly, GDP growth will be driven primarily by the exogenous TFP growth.

CBO, however, does not see this as a realistic forecast of what will happen, but rather a prediction of what could happen if the present fiscal policy is maintained. CBO (p. xvi) believes that policymakers will alter policy to avoid the possibility of debt reaching "unthinkable levels." By endogenizing capital accumulation and, therefore, a portion of labor productivity growth, the CBO projections allow the valuable comparison of economic growth under alternative fiscal policies. Given the non-sustainability of current U.S. policy, this is an important contribution of the CBO model.

B. Social Security Administration

The Social Security Act of 1935 established the Board of Trustees to oversee the financial responsibilities of the Social Security system. The Board of Trustees report annually to the Congress on the financial and actuarial status of the Federal Old-Age and Survivors Insurance (OASI) Trust Fund and the Federal Disability Insurance (DI) Trust Fund, where these two programs combine to form the Old-Age, Survivors, and Disability Insurance (OASDI) program. The annual report focuses on the future financing of the OASDI by projecting future contributions (income), expected future expenditure (benefits), and trust fund assets.

To meet these objectives, the Social Security Administration (SSA) spends considerable effort on projecting future economic and demographic trends. Like CBO, SSA has two time frames for its projections. The "short range" analysis extends over the next 10 years and the "long range" analysis extends over the next 75 years. In both scenarios, the SSA focuses on projections of revenue from the payroll tax and future benefit expenditures. This paper examines the long-range model described in Board of Trustees (1996).

(i) Output Growth

Since long-run economic projections are inherently uncertain, SSA presents three alternative sets of assumptions regarding economic and demographic developments. The low cost scenario (Alternative I) is the most optimistic in terms of financing OASDI, the high cost scenario (Alternative III) is the most pessimistic, and the intermediate scenario (Alternative II) lies in between. These scenarios reflect different demographic and economic assumptions and thus different GDP projections. Alternative II is considered the "best estimates" by SSA, and all subsequent numbers in this analysis refer to this scenario.

SSA projects long-term real GDP growth based on "assumed rates of growth in employment, average hours worked, and labor productivity" (Board of Trustees, 1996, Section II.D). This simplified approach, however, implicitly utilizes an aggregate production function. Earlier documentation in SSA (1992, p. 15), in fact, clearly describes an aggregate production function by stating "potential GDP87 increases in accordance with changes in the size of the labor force, the amount of capital available, and the state of technology." The current methodology can easily be reconciled with a formal aggregate production function.

Consider an aggregate production function as in Equation (3) and define average labor productivity, ALP as


(SSA, 1995, p. 15). The growth rate in output is then

(6) [Delta]Y = [Delta]ALP + [Delta]H

where Equation (6) and the traditional growth accounting formula in Equation (2) imply

(7) [Delta]ALP = [Delta]A + [v.sub.K]*([Delta]K - [Delta]H)

SSA projects real GDP growth as the sum of the growth rate of hours worked and the growth rate of average labor productivity, a methodology clearly based on the aggregate production function. Since growth in ALP incorporates the impact capital accumulation, labor quality changes, and TFP growth, growth in potential GDP again depends on labor, capital, and total factor productivity in the long-run.

(ii) Input Growth

The projections of population and employment patterns depend on a multitude of economic and demographic factors such as "future marriage and divorce rates, birth rates, death rates, migration rates, labor force participation and unemployment rates, disability incidence and termination rates, retirement age patterns, productivity gains, wage increases, cost-of-living increases and many other economic and demographic factors" (Board of Trustees, 1996, Section I.F). SSA estimates of these variables typically vary for the first 5-to-25 years and then reach steady-state values, although life expectancy is an exception that is assumed to continually increase.

Since estimates of employment and hours worked vary due to the changing demographics of the U.S. labor supply, SSA uses internal projections of the U.S. population and the distribution across age and sex. The dominant trend is a slower growth rate for the working-age population as the baby boom generation nears retirement and the labor force participation rate of women begins to level off. Details on all demographic factors that are used in the current population projections can be found in SSA (1996).

The growth in the labor force is projected to fall from 0.9% in 1995 to 0.6% in 2010 and to 0.1% in 2070 (Board of Trustees, 1996, Table II.D.1). The unemployment rate is assumed to reach 6.0% in the steady state, compared to an average of 5.8% for 1966-1995. The aggregate labor force reflects varying growth rates, labor force participation rates, and unemployment rates across age and sex characteristics. Labor productivity is assumed to reach a steady-state growth rate of 1.4% in Alternative II.

(iii) Projections

SSA projects that real GDP will grow near 2.0% per year for 1996-2005. After that, real GDP growth slows steadily from 1.8% in 2010 to 1.2% in 2050 (Board of Trustees, 1996, Table II.D.1). The slowdown in projected growth primarily reflects the "slower growth in the working age population" (Board of Trustees, 1996, Section II.D).

C. Office of Management and Budget

The Office of Management and Budget (OMB) represents the economic arm of the Executive Office of the President of the United States and publishes several reports that analyze the U.S. federal budget and budget process. The most detailed report, OMB (1997a), contains economic and accounting analyses of the impact of the current budget.

OMB presents long-run projections of potential output for use in evaluating the future federal budget situation where "long-run budget projections must be based on a long-run demographic and economic forecasts" (OMB, 1997a, p. 25). The long-run projections are an extension of the OMB medium-term projections (1997-2007) that are found in the official U.S. budget (OMB, 1997b). The medium-term estimates are augmented with population and demographic data from the intermediate assumptions in the Social Security Trustees' report (Board of Trustees, 1996) to form long-run projections.

(i) Output Growth

The OMB model is essentially the same as the long range model presented by the SSA in Board of Trustees (1996) and described above. The real rate of "economic growth is determined by the expected growth of the labor force (assuming a stable unemployment rate) plus labor productivity growth" (OMB, 1997a, p. 25).

Cyclical variation is not considered an important factor in long-run growth since "changes in the average rate of growth of real GDP are mainly due to changes in the rates of growth of productivity and labor supply, and are not necessarily associated with changes in the average rate of unemployment" (p. 13). OMB attributes growth in labor productivity to "higher rates of investment" (p. 8) and to "initiatives in education, technology, and regulatory reform" (p. 10) while growth in labor supply is due to demographic factors.

(ii) Input Growth

OMB uses SSA data for its projections of the labor force where a decline in the birth rate and changing demographics as the baby boom generation ages lead to a slowing of growth for the labor force. OMB projects that population growth will slow from the current 1% per year to about 0.5% per year in 2030. OMB, however, assumes a higher rate of labor force participation than the SSA does, both in the medium term and over a longer time horizon, which leads to somewhat faster growth in real output.

In the medium term, OMB (1997a, p. 8) projects that labor productivity will increase to 1.2% per year "due to an expected boost in trend productivity growth that is likely to accompany higher rates of investment." In the long run, however, OMB projects a slight decline to 1.1% per year beyond 2007.

(iii) Projections

In the short run, OMB expects real GDP growth to rise from 2.0% per year in 1997 to 2.3% in 2002. After 2002, the labor force will grow more slowly, which will reduce the growth rate of the economy. OMB projects real GDP growth of 2.25% in 2007 and then a steady decline to 1.5% per year. OMB also offers alternative scenarios with higher and lower growth rates for both labor productivity and the labor force.

D. General Accounting Office

The U.S. General Accounting Office (GAO) was established by the Budget and Accounting Act of 1921. The primary mission of the GAO is to act as an independent auditor of the U.S. federal government and to evaluate and review all activities involving receipt or disbursement of public funds.

GAO uses a long-term growth model with the explicit purpose of analyzing the impact of the U.S. federal budget deficit on economic growth through 2025. The model, originally developed by the Federal Reserve Bank of New York (Harris and Steindei, 1991), was adapted by the GAO to the current function. The model is first discussed in GAO (1992a) and subsequently updated in GAO (1996, 1995). Details on the economic assumptions can be found in Appendix I of GAO (1995), and some estimates within the model are taken from CBO.

(i) Output Growth

GAO (1996, 1995) does not provide specific details regarding the current structure of the model, but GAO (1995, p. 20) states, "The model represents growth as resulting from labor force increases, capital accumulation, and the various influences affecting total factor productivity." GAO (1992a, p. 98) states, "These basic features reflect an approach to understanding economic growth that was originally developed in the 1950s ... the model incorporates simple representations of three sources of economic growth: increased labor input, capital accumulation, and the advance of 'total factor productivity'." Clearly, this is the Solow model again.

The core of the GAO model, described in the appendix of Harris and Steindei (1991), is a traditional Cobb-Douglas production function for the nonfarm business sector with constant returns to scale assumed. By rewriting Equation (2), one can get the basic growth equation as

(8) [Y.sub.t] = (1 + [v.sub.L]*[Delta]L + [v.sub.K]*[Delta]A)*[Y.sub.t-1]

that Harris and Steindei (1991) calibrate as

(9) [Y.sub.t] = (1 + 0.7*[Delta]L + 0.3*[Delta]K + [Delta]A)*[Y.sub.t-1]

There are five other sectors of the economy-housing services, farm, government, other, and rest of the world that combine with nonfarm business output to form aggregate real output. These sectors either grow linearly with labor (government, other), grow based on accumulated external assets (rest of the world), grow at a fixed rate (farm), or grow proportionally with the capital stock (housing services).

(ii) Input Growth

GAO focuses on the links between fiscal policy, national savings, capital accumulation, and economic growth. Under various fiscal policy alternatives, GAO predicts national income and assumes that nonfederal savings, defined as private plus state and local surpluses/deficits, remains a constant 16.5% of GDP. Since national savings "influences private investment and the next period's capital stock" (GAO, 1995, p. 22), the value of nonfederal savings is combined with the appropriate estimate of the federal deficit to determine national savings and gross investment. Gross investment then determines the rate of capital accumulation and influences the growth of real GDP.

As a measure of the growth of labor input, GAO (1995, p. 24) defines labor as the "growth in hours worked" and incorporates estimated from the intermediate (Alternative II) scenario of SSA. Total factor productivity is assumed to grow exogenously at 1% per year. Both the savings rate of 16.5% and the 1% growth in total factor productivity are chosen to equal 1992 values.

(iii) Projections

GAO (1996) also presents pessimistic forecasts of future U.S. growth and points to rising health care costs, Social Security costs, and interest payments as the principle factors that are driving federal obligations and are consuming an increasing share of national savings. GAO projects that if the federal government took no steps toward fiscal balance, then per capita GDP would grow just 0.2% per year for 1994-2025. In contrast, a sustained balanced budget past 2002 would translate to per capita GDP growth of 1.1% per year.

Like OMB, GAO is explicitly a long-run model of potential GDP growth and not a business cycle model. GAO (1995, p. 14) states, "The model reflects the interrelationships between the budget and the economy over the long term and does not capture their interactions during short-term business cycles." This long-term growth perspective is consistent with the aggregate production function approach.


This section compares, contrasts, and critiques the four government models. Table 1 summarizes the key features of each model. The main conclusion is that, despite different goals and purposes, the models are all based on the traditional aggregate production function and are strikingly similar in their long-run projections.

A. Basic Approach

As detailed above, all four government models are clearly evolved from the basic Solow growth model where growth depends on the accumulation of primary inputs (capital and labor) and where a large role exists for exogenous technological progress (TFP growth).

Consistent with this lineage, all of the models are full-employment, supply-driven models with little emphasis on aggregate demand effects. While one could argue that short-run, demand-side events influence the long-run growth of an economy - e.g., through incentive effects on the accumulation of inputs or hysteresis models of unemployment - it is reasonable that long-run projections are based on the supply side of the economy.

B. Output Comparisons

All four models use the same population projections, so GDP per capita is a good summary statistic for the models. The last row of Table 1 shows projected per capita GDP in 2025 measured in 1992 dollars. OMB does not report any estimates of future GDP, and this calculation could not be done with the OMB data.

CBO (1997b) presents several scenarios regarding the impact of future fiscal policy on the U.S. economy. The "stabilize" scenario assumes that the federal budget deficit remains a constant 1.7% of GDP throughout the projection period. In this case, CBO projects real per capita GNP of $35,400 in 1992 dollars (CBO, 1997a, Table 3). As a comparison, CBO estimates that a permanently balanced budget would increase this to $36,000 in 2025, while a continuation of the current policy would cause a decrease to $33,600.

SSA projects nominal GDP in 2025 for each demographic scenario. Under Alternative II, GDP was deflated with the SSA projection of CPI inflation and divided by the SSA population projections to estimate real per capita GDP in 2025 in 1996 dollars. This was further deflated with the actual GDP chain-type price index (Bureau of Economic Analysis, 1997) to generate a comparable estimate of $32,345 in 1992 dollars. The low cost and high cost scenarios, using the same deflators and population, are $30,386 and $35,702 in 1992 dollars.

GAO also presents GDP estimates under various scenarios. The "muddling through" scenario is most similar to the CBO as it assumes that the CBO deficit projections through 1999 are correct and that a constant deficit of 3% exists thereafter. Again, these numbers were deflated using the GDP price index to yield real per capita GDP of $32,630 in 2025. As a comparison, GAO's more extreme scenarios generate a range of $34,722 to $25,932 depending on the fiscal budget policy. Note that CBO reports GNP per capita, while SSA and GAO report GDP per capita. Since these two figures are relatively close - e.g., only $9 billion in 1996 - the difference is inconsequential on a per capita basis.

Despite very different methodologies, SSA and GAO have virtually identical estimates of per capita GDP. CBO is about 9% higher than both SSA and CBO, which reflects the slight differences in methodology. For example, CBO's "stabilize" scenario assumes a deficit of 1.7% of GDP while GAO's "muddling through" scenario assumes a 3% deficit. In both models, economic feedback effects are relevant, so the larger deficit in the GAO likely explains the difference.

C. Capital Accumulation

The fundamental difference across the four models is the treatment of capital accumulation. Both CBO and GAO treat capital formation as an endogenous variable that responds to fiscal policy, while SSA and OMB ignore capital formation and simply assume labor productivity will grow according to past trends. While both approaches are consistent with the Solow model, the feedback relationship between fiscal policy and capital accumulation provides more insight on current budget issues.

It is well known that the combination of an aging population, expanding entitlement programs, and rising health care cost represent a significant burden for the U.S. federal government. Auerbach (1997), for example, estimates that the U.S. fiscal imbalance - the permanent change in the federal deficit needed to stabilize national debt as a share of GDP - now stands at 5.3% of GDP. In addition, Auerbach shows that the Medicare and Medicaid programs, and not the more often cited OASDI program, are [TABULAR DATA FOR TABLE 1 OMITTED] the primary causes of future budget imbalances. Rising federal deficits can have adverse economic consequences through the savings/investment channel since as "deficits rise, they crowd out capital investment, and slow economic growth" (CBO, 1997b, p. 8).

By endogenizing capital accumulation, the CBO model allows comparisons of long-run growth under alternative fiscal policies. The CBO projections suggest that the changing demographics of the U.S. population make the current fiscal policy non-sustainable in the long-run (CBO, 1997b, Table 3).

GAO (1995) assumes that the non-federal savings rate equals 16.5% of GDP and that federal savings depend on the federal deficit. National savings then influence private investment, capital formation, and growth. GAO (1995, p. 4) also concludes that current policy is not sustainable: "Without any significant changes in spending or revenue, such an expanding deficit would result in collapsing investment, declining capital stock, and, inevitably, a declining economy by 2025." These types of policy conclusions are not possible unless one makes capital accumulation and economic growth responsive to fiscal policy.

SSA and OMB, on the other hand, ignore the potential impact of rising federal deficits on capital accumulation and growth. By simply assuming labor productivity growth will continue as in the past, SSA and OMB implicitly assume that capital accumulation and TFP growth will likewise continue. Given the projected rise in federal deficits and the impact on investment, this is likely to be overly optimistic. Although SSA and OMB explicitly recognize the importance of investment - "the primary factors that affect measured productivity are the quality of the labor forces, and the amount and effectiveness of investment in research, development, new plant, and equipment" (SSA, 1992, p. 19) and "an expected boost in trend (labor) productivity growth that is likely to accompany higher rates of investment" (OMB, 1997a, p. 8) - there is no attempt to model the impact of fiscal policy on the rate of capital accumulation.

The SSA and OMB projections could be interpreted as best case scenarios for the U.S. economy. That is, if the dire predictions of the CBO and GAO models spur the necessary changes in fiscal policy, then capital accumulation could well continue as in the past. These changes, however, are by no means guaranteed, and by ignoring the relationship between fiscal policy and capital accumulation, the SSA and OMB models are less valuable for projecting the growth of the U.S. economy.

D. Labor Input

All four models rely on demographic assumptions provided by the Social Security Administration. SSA in turn relies on data from the Bureau of the Census, the National Center for Health Statistics, the Immigration and Naturalization Services, the Center for Disease Control and Prevention, and others. (See SSA, 1996, for details.) Although all models are based on the SSA mid-range demographic projections, some differences do exist. The OMB, for example, assumes a higher rate of labor force participation and thus a larger growth rate in labor input.

Each model uses hours worked as the basic measure of labor input. This approach, however, ignores differences in productivity across labor types, which is an important source of economic growth. Jorgenson (1990), for example, estimates that about one-third of the growth contribution from labor for 1947-1985 comes from increases in the quality of labor, and Mankiw et al. (1992) show human capital to be an important determinant of growth.

Recent evidence, however, shows that the growth in labor quality was exceedingly fast over the past 40 years and that this impact from human capital accumulation is not sustainable. Jones (1997) argues that growth in U.S. per capita GDP, a rough proxy for labor productivity, will slow to one-fourth of its post-war average due to slower growth in labor quality, R&D investment, and trade concerns. In addition, the U.S. Census Bureau reports that 82% of adults over 25 have at least a high school education in 1996, up from 24% in 1940 (Day and Curry, 1997). Since educational accumulation must eventually level out, models with exogenous labor productivity growth based on historical averages are likely to overstate future economic growth.

Note that this criticism also applies to the CBO and GAO models even though they do not rely on estimates of labor productivity growth. By failing to account separately for changes in human capital, those long-run models implicitly include the growth contribution of labor quality in the TFP residual and thus are also likely to overstate future TFP growth.

There is now evidence that labor quality has been a large source of economic growth and that this growth is likely to slow in the future. Quality-adjusted labor quality series have been estimated by many researchers, but they have not been incorporated into the growth models used by the U.S. government agencies. By explicitly modeling labor quality as a source of growth, these models could provide more accurate growth projections for the U.S. economy.

E. Uncertainty

A final issue to be raised is the inherent uncertainty that applies at all levels of these models - e.g., TFP growth, fertility rates, death rates, marriage rates, and the extent of crowding out. While all four models acknowledge this uncertainty, only CBO provides probability analysis to quantify the uncertainty. CBO simulates its long-run model under 750 alternatives with different demographic and productivity assumptions (CBO, 1997b, Box 3) and concludes that there is only a 32% chance that the debt to GDP ratio will be below 200% in 2035. SSA, OMB, and GAO, on the other hand, provide results under various alternatives regarding policy and demographic assumptions but do not explicitly assign probabilities. (See Pizer, 1998, and Lee and Tuljapurkar, 1997, for examples of growth projections that explicitly incorporate a stochastic structure and report confidence intervals.)

A final source of uncertainty relates to the non-sustainable nature of current fiscal policy. If current policy is indeed not sustainable, then the necessary changes to fiscal policy introduce additional uncertainty since it is unclear how or when fiscal policy will change or how economic agents will react. A sudden increase in taxes to balance future budgets, for example, would surely have an adverse impact on labor supply and investment. Incorporating these effects, however, is a difficult task that remains to be done.


Economic growth has recently experienced a major revival among academic economists. A complete survey of the literature is well beyond the scope of this paper. For a detailed review, see Jorgenson (1996), Barro and Sala-i-Martin (1994), Grossman and Helpman (1994), and Romer (1994). Instead, two areas of major interest - cross-section empirical work and endogenous growth models - are broadly compared to projections of long-run growth for a single country.

This resurgence was largely motivated by the question of convergence - do poor countries "catch-up" to rich countries in terms of per capita output? Solow (1970) and Kuznets (1971) began the revival with a neoclassical approach, but subsequent work quickly evolved to include factors not found in the original Solow model. In a recent summary of the expanding empirical literature on growth and convergence, Sala-i-Martin (1997) documents 62 variables that are significant in some cross-section growth regressions. After identifying three variables (initial level of income, life expectancy, and primary school enrollment) that are "good a priori," 22 other variables are found to be "significant" when regressions with all combinations of each set of three explanatory variables are estimated. Note that the "good" variables are consistent with the neoclassical framework.

These other variables represent a large range of factors, many of which are not present in the neoclassical model. For example, religious variables (e.g., the fraction of the population that is Confucian or Muslim), political variables (e.g., Rule of Law and Number of Revolutions and Coups), and regional variables (e.g., Absolute Latitude) are all found to be important sources of cross-sectional variation in economic growth and are all absent in the neoclassical model.

In the context of long-ron growth projections, however, many of these variables have little relevance. For a particular country like the United States, they will either be fixed, e.g., Absolute Latitude, or will change only slowly, e.g., the religious variables. As such, they serve a limited role as a determinant of long-run growth for a single country. These variables are significant in the cross-sectional context precisely because of the substantial variation across countries. When examining a specific country over time, however, they add little predictive information about future growth prospects.

Endogenous growth models, on the other hand, turned to non-traditional mechanisms such as increasing returns to scale, investment or R&D externalities, and market power as fundamental sources of long-run growth. With regard to these nontraditional mechanisms, however, there remain convincing arguments for the neoclassical framework as a tool for long-run projections. On empirical grounds, the recent work of Mankiw et al. (1992) and Islam (1995) suggest that, when correctly specified, the Solow model fits the data. In particular, Islam (1995) argues that the basic neoclassical model is consistent with the observed rates of convergence once the assumption of identical technologies across countries is dropped.

Furthermore, the endogenous growth models are driven by factors that cannot be projected with any more certainty than the exogenous increases in TFP in the neoclassical model. While these alternative forces may in fact be driving long-run growth, strong assumptions still need to be made. Finally, the empirical work of Jorgenson (1990) shows that aggregate production function provides a reasonable description of post-war growth for the U.S.

Given the recent empirical success of the neoclassical model in explaining growth and the limitations of the endogenous growth models as a predictive tool, one can argue that the simplicity and intuition in the neoclassical model make it the appropriate tool for long-run growth projections. The U.S. government agencies, therefore, seem justified in their reliance on the neoclassical model.


This paper summarizes the long-run growth models of four prominent government organizations. The Congressional Budget Office, the Social Security Administration, the Office of Management and Budget, and the General Accounting Office all utilize an aggregate production function that models economic growth as a result of the accumulation of capital and labor inputs and exogenous increases in total factor productivity.

This approach follows a long history in the economics literature and is firmly grounded in the neoclassical tradition of Solow and others. These four models, however, differ in certain important features, most notably the modeling of capital accumulation. The CBO and GAO models explicitly include an impact of fiscal policy on investment, while SSA and OMB ignore this relationship. The subsequent exogeneity of labor productivity growth makes the SSA and OMB models much less useful in evaluating the future of the U.S. economy. In addition, all four models could be improved by including a specific role for human capital that is consistent with U.S. trends. By failing to account for the slowing accumulation of education and skills, these models may significantly overstate future economic growth.

The empirical work of Mankiw et al. (1992) and Islam (1995) show that the neoclassical framework does well in explaining cross-country growth patterns, while the work of Jorgenson (1990) shows that the aggregate production function provides a reasonable model of long-run economic growth for the United States. Since the other important factors in the growth literature are either irrelevant for a single country or hard to project, the traditional aggregate production function remains the appropriate starting point when projecting long-run economic growth.


CBO: Congressional Budget Office D: Disability Insurance GAO: Genera Accounting Office GDP: Gross Domestic Product OASDI: Old-Age, Survivors, and Disability Insurance OASI: Old-Age and Survivors Insurance OMB: Office of Management and Budget SSA: Social Security Administration TFP: Total factor productivity

I would like to thank Dale Jorgenson and two anonymous referees for helpful comments on an earlier draft. John Sturrock and Ben Page at CBO and Stephen Goss at SSA provided assistance in understanding the long-range models. The conclusions in this paper are those of the author and do not necessarily reflect The Conference Board or its staff.


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Author:Stiroh, Kevin J.
Publication:Contemporary Economic Policy
Date:Oct 1, 1998
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