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Appendix
CThe Models Used to Analyze the Supply-Side Macroeconomic Effects of the President’s Budgetary Proposals
The Congressional Budget Office (CBO) used three models—a "textbook" growth model, a life-cycle growth model, and an infinite-horizon growth model—to estimate the supply-side effects of the President’s budgetary proposals from 2009 to 2018, the period covered by CBO’s current 10-year baseline projection. (Estimates generated by those models are presented in Chapter 2.)
The textbook growth model is an enhanced version of a model developed by Robert Solow, a pioneer in the theory of growth accounting.1 The textbook growth model incorporates the assumption that economic output is determined by the number of hours of labor workers supply, the size and composition of the capital stock (for example, factories and information systems), and total factor productivity—which represents the state of technological expertise. The model is not forward-looking: The people it represents base their decisions about working and saving entirely on current economic conditions. In particular, they do not respond to expected future changes in government policy. Moreover, instead of incorporating effects from demand-side variations in the economy, the model assumes that output is always at its potential (or sustainable) level.
The estimates that CBO developed using the textbook growth model incorporate the effects that changes in marginal tax rates specified in the President’s budgetary proposals would have on the number of hours worked. (CBO made separate calculations of the effects of tax rates.)
The President’s budgetary proposals would increase federal deficits over the 10-year budget window. However, as described in Chapter 2, most of the increase would result from two proposals that, in CBO’s judgment, would have little effect on national saving (government and private saving combined). Excluding those proposals, the rest of the President’s budget shows deficits that are projected in the textbook growth model to have a modest negative effect on the capital stock. The proposals would slightly increase consumer spending, relative to the amount in CBO’s baseline, and that in turn would crowd out investment. The textbook growth model predicts that changes in marginal tax rates on capital have no direct effect on private-sector spending.
Incurred deficits can lead to higher private saving for several reasons, including a response to higher interest rates.
Another factor affecting the results is that the reduction in national saving would not entirely translate into reductions in domestic investment. Instead, part of the reduction would be reflected in increased borrowing from abroad, which allows the domestic capital stock to increase more rapidly than the capital stock (which is mainly but not entirely domestically located) owned by U.S. citizens.2
The textbook growth model accounts for those tendencies by including two assumptions, each based on past relationships. First, the model assumes that every dollar of deficit leads people to increase their private saving by 40 cents and thus reduces national saving by only 60 cents. Second, the model assumes that every decline of $1 in national saving leads to a 40 cent increase in the amount of foreign capital invested in the United States. Together, those assumptions imply that a $1 increase in the budget deficit results in a 40 cent increase in private saving, a 24 cent increase in capital inflows (24 cents equals 60 cents times 0.4), and a 36 cent decline in domestic investment.
Life-Cycle and Infinite-Horizon Growth Models
Like the textbook growth model, the life-cycle and infinite-horizon growth models ignore demand-side effects. Those models differ from the textbook growth model in several fundamental ways, however.3 Each assumes that people decide how much to work and save to make themselves as well off as possible over a lifetime. That behavior is calibrated so that such macroeconomic variables as the total amount of labor supplied and the size of the capital stock match that in the U.S. economy. In the life-cycle and infinite-horizon models, people’s spending changes by a relatively large amount in response to changes in the after-tax rate of return on their saving—more, in some cases, than appears consistent with historical experience.
The life-cycle and infinite-horizon models are designed to consider the fact that people make decisions on the basis not only of information about the present but in keeping with their expectations about the future. The President’s proposals for any given year can affect government spending and revenues over the 10-year projection period, and any deficits or surpluses that accumulate over that period can affect budgetary decisions in later years. People’s expectations about those developments—correct or not—can affect their behavior long before the changes materialize. Analysts disagree, however, on the extent to which expectations influence people’s economic decisions, the time horizon over which people plan, or the future policy shifts they actually expect. CBO therefore analyzed the President’s proposals using a wide range of assumptions about the extent of people’s foresight and the expectations they might have about future policies. That approach yields a range of plausible estimates about how those proposals could affect economic growth.
The households in the life-cycle and infinite-horizon models are assumed to be forward-looking, to form expectations about future economic and policy developments that are rational and consistent with the model, and to alter their behavior accordingly. They are assumed to have perfect foresight about the future of the economy as a whole and about policies. The models assume the opposite of the range of possibilities in the textbook growth model. Most people’s foresight actually falls somewhere between those two extremes, but using those two somewhat dramatic assumptions allows CBO to encompass the broadest possible range of responses to the President’s budgetary proposals.
Although the life-cycle and infinite-horizon models do not provide a role for unpredictable fluctuations in aggregate output, the models do assume that individual households face unforeseeable (and idiosyncratic) fluctuations in their income against which they cannot buy insurance.4 Faced with that uncertainty, households hold some additional, "precautionary" savings as a buffer against potential drops in income. Because the precautionary motive to save is not strongly affected by changes in tax rates, households’ savings do not respond as much to policy changes as they would in models that do not include the precautionary motive. That, in turn, makes CBO’s model somewhat more realistic than models in which households are assumed to have no uncertainty about their future income.
Because people’s behavior as represented in the life-cycle and infinite-horizon models depends in part on future policies, those models lead analysts to make assumptions about budgetary policies beyond 2018 (the end of the10‑year projection period). Policies that increased deficits during the projection period would yield greater debt payments, requiring higher taxes or lower spending than would have been the case under CBO’s baseline assumptions. Policies that reduced deficits would require the opposite.
Assumptions about how and when to finance the increased deficits can influence the estimated economic effects of the President’s proposed policies over the 2009–2018 period. In the models, people anticipate the offsetting policies and plan accordingly. In its analysis, CBO used two assumptions about how the budget would be stabilized after 2018: Either marginal tax rates or government spending would be adjusted. (Spending adjustments are assumed to be spread roughly equally across government purchases of goods and services—which the models assume do not substitute for private spending—and transfer payments.) In either case, those adjustments are assumed to be phased in over the 10 years from 2019 to 2028.
The life-cycle and infinite-horizon models differ in their assumptions about how far ahead people look in making their plans. The life-cycle model is calibrated so that the probability of death at a given age matches current U.S. mortality rates, and people are assumed to consider the effects of future economic or policy changes only for themselves but not for their children. In the infinite-horizon model, people behave as though they expect to live forever—behavior that is effectively equivalent to acting as though the well-being of their descendants is as important to them as their own well-being. Although many people care about their descendants, there is evidence against the assumption used in the infinite-horizon model that people care as much about their descendants as they do about themselves.5
The difference in the models’ time horizons has an important effect on the resulting estimates. Although people in both models anticipate changes in policy under the President’s budgetary proposals, older generations in the life-cycle model know that they could retire or die before a policy change occurs. Consequently, anticipation of policy changes tends to have a smaller effect on people’s current behavior in the life-cycle model than it has in the infinite-horizon model.
Another characteristic that affects the models’ estimates is the degree to which the domestic economy is open to the flow of foreign capital. That is important because foreign capital determines both how easily domestic investment can be financed by sources other than domestic saving and the degree to which budgetary policies can affect wage and interest rates. CBO used two opposite assumptions in the life-cycle model about how open the economy is to flows of capital to and from other countries. One assumption was that the economy is completely closed—no capital can flow into or out of the United States. The other was that the economy is completely open and cannot affect world interest rates—capital flows freely into and out of the country to keep the domestic interest rate equal to a constant world rate. The U.S. economy effectively operates somewhere between those two extremes; even though it is relatively open to investment, it is so large that it can influence world interest rates. By using the two assumptions, CBO obtained a range of results that bounds the probable effects of the modeled policy changes.
For a detailed description of the textbook growth model, see Congressional Budget Office, CBO’s Method for Estimating Potential Output: An Update (August 2001).
The ultimate effect of increased borrowing from abroad depends on whether one is examining domestic output (which reflects the return to the domestic capital stock) or national income (which reflects the return to the capital stock owned by U.S. citizens).
For a detailed description of the life-cycle model, see Shinichi Nishiyama, Analyzing Tax Policy Changes Using a Stochastic OLG Model with Heterogeneous Households, CBO Technical Paper 2003-12 (December 2003). For a description of a model very similar to the infinite-horizon model, see S.R. Aiyagari, "Optimal Capital Income Taxation with Incomplete Markets, Borrowing Constraints, and Constant Discounting," Journal of Political Economy, vol. 103, no. 6 (December 1995), pp. 1158–1175.
Accounting for both aggregate uncertainty and idiosyncratic uncertainty in income creates significant computational difficulties.
See Paul Evans, "Consumers Are Not Ricardian: Evidence from Nineteen Countries," Economic Inquiry, vol. 31, no. 4 (October 1993), pp. 534–548; Fumio Hayashi, Joseph Altonji, and Laurence Kotlikoff, "Risk Sharing Between and Within Families," Econometrica, vol. 64, no. 2 (March 1996), pp. 261–294; and T.D. Stanley, "New Wine in Old Bottles: A Meta-Analysis of Ricardian Equivalence," Southern Economic Journal, vol. 64, no. 3 (January 1998), pp. 713–727.
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