Article

Financial Crowding Out: Theory with an Application to Australia

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1986
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The aim of this paper is to analyze the extent to which public spending crowds out private production and capital formation. The analysis is carried out within the context of an intertemporal general equilibrium model, and a computational version of the model is developed and applied to Australia. The approach is especially relevant for policy analysis because it allows the consideration of disaggregated fiscal measures, such as changes in individual tax rates, and at the same time incorporates macro-economic aspects of fiscal policy, such as rules for deficit financing and the interaction between government deficits, interest rates, and inflation. In addition, by disaggregating the private sector, a comparison can be made of the extent to which individual industries are affected by public sector spending policies. Crowding out has usually been examined in two different but related contexts. In the first, the public sector purchases large quantities of goods and finances them either by taxes or by borrowing. To the extent that the goods purchased are used to produce public goods, they will no longer be available for private sector production, which will therefore be forced to decline. The second context is “financial crowding out,” which occurs when the government increases its borrowing requirements and thereby drives up the interest rate. Credit is thus made more expensive for the private sector, which is forced to curtail any capital formation that is not self-financed. (Indirect crowding out may also occur because rising interest rates may cause current consumption, and hence demand for the output of the private sector, to fall.)

Financial crowding out has traditionally been analyzed within the context of aggregative macroeconomic models.1 There are severe limitations, however, to this approach. Borrowing requirements differ among industries, so that one would also expect the effect of the government’s borrowing on the private sector to vary. The aggregation of demand also precludes any analysis of the relative effects of fiscal policies on the welfare of different consumer groups. In addition, because models are usually valid only for small changes, it is difficult, if not impossible, to estimate the effects of large increases in government borrowing. Finally, governments often attempt to increase tax revenue and borrowing simultaneously. Because aggregative macroeconomic models do not normally separate tax revenues from government expenditure, such policies cannot be dealt with properly.1

The question of resource crowding out is increasingly being examined within the framework of computational general equilibrium models of taxation. Such models, originally inspired by the work of Harberger (1962, 1966) on tax incidence, have been developed in Shoven and Whalley (1972, 1973), Shoven (1976), Fullerton (1982, 1983), Fullerton and others (1981), Miller and Spencer (1977), Piggott and Whalley (1983), Feltenstein (1983), and Whalley (1975,1977,1982), among others, to examine incidence and welfare implications of changes in tax and trade regimes. The advantages of these models in comparison with macroeconomic ones have been discussed at length in Shoven (1983); among them is the ability to deal with large changes in government policies, with disaggregated taxes, and with the analysis of the welfare implications of taxation on individual consumer categories. There are, however, a number of disadvantages in computational general equilibrium models. These models have been almost exclusively “real”; that is, the public sector is constrained to have a balanced budget, owing to the absence of financial assets that could finance a deficit. Because there is no money, and hence no price level or interest rate, these models do not allow the analysis of financial crowding out.

Research in which certain types of computational general equilibrium models are expanded to include financial assets has been carried out by several authors. Clements (1980) allowed for domestic credit expansion in a model of the United States, although such expansion was exogenous with respect to public sector expenditure and revenues. Feltenstein (1980), in a model of Argentina, permitted the existence of domestic and foreign financial assets, whose endogeneity of supply was dependent on the balance of payments. Slemrod (1981) constructed a computational general equilibrium model incorporating portfolio choice by consumers. For the policymaker the major flaw in these models is that they do not permit both endogenous public deficits and private investment.

The model constructed here is dynamic; it has two periods, with the notion of a past (before period 1) and a future (after period 2). Both consumers and firms have perfect foresight, so that the prices, tax liabilities, and transfers received from the government in period 2 are correctly anticipated in period 1.3 The model is closed by assuming that, in period 2, consumers save—that is, hold debt—according to an exogenous savings rate.4

Firms in the private sector are constrained to cover current expenditures by current revenue, but capital formation is financed by the sale of bonds. The government, in contrast, sets its program of expenditure in real terms and is not required to cover costs from tax revenues; any deficit it incurs is covered by its issuing a combination of money and bonds. The government is sensitive, however, to the effect that its deficits may have on interest and inflation rates. Accordingly, it will gradually cut its spending as real interest and inflation rates rise above predetermined targets. Consumers are required to hold money to cover transaction costs, and they purchase bonds in order to save for the future. With perfect foresight there is no risk, so that to the consumer private and government bonds are identical. The equilibrium condition on privately issued debt is that new capital produced in period 1, which comes on line in period 2, must yield a return in period 2 equal to the obligations on the bonds that financed it. The government, in contrast, must add the debt obligations incurred in period 1 and coming due in period 2 to its current expenditures in the period.

Consumers maximize intertemporal utility functions and derive a demand for bonds as a method of saving. As the interest rate rises, consumers tend to satisfy the Fisherian relation and shift their consumption to the future, releasing resources to the government. The private sector may thus suffer from both resource and financial crowding out.5

The model includes profit, income, and sales taxes and allows for direct transfer payments by the government to consumers. The price level is endogenous, so that the inflationary effects of various government policies may be analyzed. There is also an investment function, with the level of investment being driven by the interest rate. Section I presents a formal description of the model, and Section II describes a computational version of the model and its application to Australian data. This exercise should serve not only to illustrate the workings of the model but also to allow certain qualitative judgments about Australian fiscal policies. Section III presents conclusions, a few qualifications, and some directions for further research.

I. The Model

In this section a formal description is given for production, consumption, government finance, and investment, as well as for the conditions of intertemporal equilibrium.

Production

The structure of production is Leontief in intermediate and final production, whereas value added is produced by smooth production functions.6 Because the model incorporates perfect foresight in both production and consumption, production may be represented by a nonstochastic block-diagonal matrix whose components refer to goods that are different in their dating (see Debreu (1959) for a discussion of the use of dated commodities). If goods i = 1,…, N refer to goods produced in period 1, and goods N + 1,…, 2 N refer to goods produced in period 2, then the structure of the production matrix for intermediate and final goods is

The upper block of the matrix refers to first-period production, the lower block to second-period production. Corresponding to each activity is a continuous function fj(Ki, Li) that produces value added for the jth activity using capital and labor from the corresponding stocks that exist in period i. To be specific, assume that the value-added functions are Cobb-Douglas in nature, hence of the form

In addition, there are investment activities, Hi(Ki, Li), that operate in period i, using inputs of capital and labor existing in that period, and that produce capital goods for period i + 1.7 The investment is carried out by the private sector. Because the capital that is produced in one period becomes available only in the next, the investment firm must pay for the input costs of its production in the current period but will receive the revenue from that capital in the next period.8 To simplify demonstration of the existence of an equilibrium, it is assumed that the investment functions exhibit decreasing returns to scale9 and are of the form

Capital in period 2 is then given by the depreciated initial capital stock, plus whatever new capital has been produced in period 1. If K0 is the initial stock of capital at the beginning of period 1, δ is the rate of depreciation, and L0 is the initial stock of labor, then

where K2 is the stock of capital at the beginning of period 2.

The government also produces public goods through a smooth production function that uses capital and labor of the current period as inputs.10 Let Qi(Ki, Li) denote this function in period i and, for simplicity, also assume the function to be Cobb-Douglas in nature; hence,

The government is assumed to determine, at the beginning of period i, the real level of output of public goods to be produced:

where Qi is the real quantity of public goods to be produced in period i, in such a way as to minimize the cost of production.

Consumption

There is a single generation of consumers who live for the entire period of the model. Because they may have initial endowments of capital and financial assets, it is implicitly supposed that they were alive before period 1. The consumers perfectly anticipate all prices of period 2 while in period 1.11 The individual consumer maximizes a utility function, U, that has as arguments the levels of consumption in each of the two periods.12 Thus,

where xi (with i≤N) refers to the ith consumption good in period 1, xi (with i>N) refers to the ith consumption good in period 2, and Li refers to consumption of leisure in period i. To be specific, the utility function is assumed to be of the form

Suppose that (di) reflect the consumer’s rate of time preference u, uniformly across goods, so that in addition, u is uniform across all consumers. Hence, leisure enters the utility function, but money, bonds, and capital do not.13

The consumer maximizes his utility function, subject to a set of intertemporal budget constraints, and it is assumed that capital markets are imperfect in that consumers cannot borrow against future income.14 A consumer has an initial allocation of money and bonds, M0 and B0, at the beginning of period 1; if he is a shareholder in the capital goods-producing firm, the consumer will also hold capital, K0.15 Let pKi, pLi, pMi, and pBi represent the prices of capital, labor, money, and bonds, respectively, in period i, and let TRi represent whatever transfer payments the government pays to consumers during period i, whereas γi, represents this particular consumer’s share in those transfers.

Bonds are considered to be long term, so that a consumer owning a bond receives its par value as an interest payment in each period that he owns the bond. Because this payment is made in units of money, his income from the bond in period i is pMi. He also has the possibility of selling the bond at market prices pBi. The consumer’s income in period 1, I1(p1), is then given by

In addition, the consumer has a second-period budget constraint. If he has purchased quantity xB1 of bonds in period 1, he then receives the coupon value of those bonds in units of money in period 2, this being equal to pM2xB1. The consumer’s income in period 2, I2,(p2) then becomes

where xM1 is the quantity of money that the consumer holds in period 1.16

The consumer, in solving his utility-maximization problem, has two simultaneous budget constraints, as well as a closure rule to be described shortly. Suppose that the consumer faces ad valorem taxes on his purchases of consumption goods, and let

where ti represents the vector of tax rates levied on the N intermediate and final goods produced in period i. Further, denote the prices of the intermediate and final goods in each of the two periods. The consumer has, in addition, a money demand function, uniform across all consumers, in which demand for nominal cash balances depends on the value of current consumption and the nominal interest rate. Leisure is not included as a determinant in the demand for money because income taxes are withheld at the source.

Suppose now that νi, the velocity of money, is not constant but is a function of the nominal interest rate. The nominal interest rate in period, i,ri, is defined by

Suppose also that

so that the velocity of money is directly related to the nominal interest rate. Hence,

or, in a somewhat more familiar form,

The total value of the consumer’s consumption in period 1 and period 2 must be equal to or less than the corresponding income; hence

where pMi xMi is given by equation (16) and Ii(pi) is given by equations (10) and (11). To close the model, some assumption must be made about consumers’ holding debt in period 2. Accordingly, suppose that demand for bonds in period 2 is equal to the long-run savings rate of the economy, assumed to be constant. Thus, where 1/z is equal to the long-run savings rate. One thus avoids making the assumption, equivalent to debt neutrality, that the consumer supposes that the portion of his savings held in government debt must eventually be repaid by higher taxes.

The following maximization problem for the consumer therefore results:

such that

It is straightforward to solve equations (21) in the form of a Lagrangian to obtain the following solution:

The demand for money, xMi, is given by equation (16), whereas the demand for bonds, xBi, is derived from Walras’s law in each period as

Having calculated the individual consumer’s demand for all goods plus financial assets in each period, one may turn to the derivation of aggregate supply and, accordingly, excess demand functions.

Financing the Central Government and the Formation of Capital

Using the individual industry’s value-added functions given in equation (2), cost-minimizing levels of the use of capital and labor for the jth sector in period i are obtained:

where tKi and tLi represent the tax rates levied on capital and labor, assumed to be uniform across sectors, in the ith period, and VAj represents the required inputs of value added, in real terms, to the jth sector. The interpretation of tKi is a profit tax levied on capital, whereas tLi may be thought of as an income tax that is collected at the source—that is, a withholding tax. The nominal value added, vaj, is given by

and intertemporal Leontief prices, p(p), may be calculated as

Total demand for the jth intermediate and final good, xLj, may be derived as

where xj is the kth consumer’s demand for intermediate or final good j, as in equation (22). The vector of activity levels, w, of the 2N activities required to produce this level of demand may then be derived as

Let yKpj, yLpj be the corresponding requirements of column j for capital and labor and let yKpi, , yLpi be the total requirements for capital and labor by private industry in period i. The total taxes, Ti, collected by the central government in each of the two periods may now be calculated.

The government uses capital and labor to produce public goods in each of the two periods. Suppose that the real quantity of these public goods is given by Q1, Q2. The government has a Cobb-Douglas production function, given in equation (6). From this function may be derived the cost-minimizing quantities of capital and labor, yKGi, yLGi, used by the government in producing Qi, and the total cost to the government, Gi, of producing Qi.

The deficit of the central government in period 1, D1, is then given by

so that if D1 is negative the government runs a surplus. It is assumed that a surplus is paid out as transfer payments to consumers, but financing must take place in the case of a deficit.17 Here one must first make a connection between real interest rates and the level of the government’s real expenditures. It is possible for a particular program of expenditures to be technologically feasible—in the sense that it does not require inputs of capital or labor beyond the capacities of the economy—yet at the same time to lead to a deficit representing a level of real debt greater than what people are willing to hold. To avoid this problem of an unbounded supply of money and bonds, a functional relationship will be imposed between the real level of government expenditure and the instantaneous real interest rate and rate of inflation. Accordingly, define Qi in the following way: let hi be a continuous function and Qi some fixed, target level of output of public goods, and let πi be the rate of inflation in the ith period.18 Thus,

Real output of public goods will therefore be equal to the initial target Q if both the rate of inflation πi and the real interest rate Ri are below corresponding target rates. As the real interest or inflation rates rise above target, the level of real government output of public goods approaches zero.

The resultant deficit, given by equation (28), is financed by a combination of money and bonds. Accordingly, let yBGi be the government’s bond issue in period 1, and let Bi be a continuous function such that

Thus, the nominal value of bond financing is a continuous function of the nominal deficit, not including debt repayment, and no sale of bonds takes place if there is a surplus. The change in the supply of money, y˜M1 , is then given by

so that debt repayment is made in money.

In period 2 the formation of the government deficit is somewhat different, since the government must pay not only for its current consumption but also for its debt obligations incurred in period 1.

Accordingly,

Of course B1 would equal B2 if the government chooses to maintain the same financing rule in period 2 as in period 1.19

It is assumed that capital formation is carried out by the private sector and that it is fully financed by the sale of bonds, which are identical to the bonds sold by the government. Suppose, then, that the rate of return on capital in period i + 1 is pk(i+1).20 The total return on quantity Hi of new capital that was formed in period i and that comes on line in period i + 1 is then Pk(i+1). If CHi is the cost-minimizing cost of producing Hi, then future debt obligations must be equal to the return on capital. Hence,

The investment firm, having found a level of investment Hi such that Hi, CHi satisfy equation (31), then sets its sale of bonds, yBpi:

Excess Demand Functions and the Conditions for Intertemporal Equilibrium

The presence of an intertemporal input-output matrix allows the vector of excess demand functions to be confined to the space of prices corresponding to capital, labor, money, bonds, and transfer payments, indexed by their time period. Accordingly, given an arbitrary vector of prices, p, the nominal value added per unit of output may be derived for each of the 2N sectors producing intermediate and final goods, as in equation (24). Equation (25) then gives Leontief prices for each of the two periods, and equations (26) and (27) give total demand for intermediate and final goods, along with the corresponding level of production required of each activity in the Leontief matrix. The total inputs of capital and labor required in each period by the private production sector and the government may also be derived.

The requirements of capital and labor in each period also include their use in investment, which is determined by equations (3) and (33). The total supplies of the capital and labor in period i—that is, yKi, yLi—are then

where y^K1,y^Li are the aggregate inputs to public and private production and investment in period i, and H1 is the level of real investment in period 1.

The change in the money supply in period i, y˜M1, is given by equation (31), so that the total supply of money in each period, yMi, is

The supply of bonds in each period, yBi, is given by

where yBGi is the government’s bond issue in period i, and yBpi is private bond issue for investment financing.

An aggregate supply vector y has now been derived, where

This supply vector is augmented by two additional dimensions, corresponding to transfer payments in each of the two time periods. Accordingly, define y(p), the augmented supply vector, by

where Di is the government deficit in period i.

The derivation of an augmented demand vector x(p) is now straightforward. Because xKi = 0 and because equation (30) gives individual demands for leisure, money, and bonds in each period, summing across consumers gives the aggregate demands, xLi,xMi,xBi. The aggregate demand vector x is then defined by

Finally, the augmented demand vector x(p) is defined by

where TRi represents the proxy for government transfer payments that enters the consumer’s maximization problem, as in equations (21). The aggregate excess demand function u(p) is then defined as

therefore it must be shown that there exists some price p* such that u(p*)≤0.21

II. An Application to Australia

The Australian economy is a suitable example for application of the model because a trade sector may be introduced without modifications to the model’s theoretical structure. In addition, it is also reasonable to make the assumption of a small country that is a price taker in world trade. To use the model for simulation analysis, it is necessary to demonstrate first that it replicates reasonably accurately the Australian economy for a particular benchmark period. This section will therefore first describe the data used and then will give the results of the benchmark simulation for two successive years. The analysis will then proceed to various experiments with different rules for financing the government budget deficit, as well as for the level of real government expenditure.

Until late 1982, Australia operated under a system of fixed exchange rates and capital controls. The model simultaneously derives a solution for two periods, so the years 1981-82 have been chosen for the benchmark solution. This choice avoids the problem of having to construct a mechanism for exchange rate determination, and the capital account may be treated as exogenous. The model’s technology for Australia is represented by a 30-by-30 input-output matrix, constructed for 1977, in which activities 29 and 30 are complementary and competing imports, respectively (Australia, Bureau of Statistics (1983)). The matrix was not updated for 1981 and 1982. The model’s technology is thus represented by a 60-by-60 block-diagonal matrix. The coefficients for the Cobb-Douglas functions representing production of value added in each period are given by the relative shares of capital and labor in each activity in the 1977 matrix (Australia, Bureau of Statistics (1983, Table 11)), with no technological change assumed between periods. Coefficients for capital and labor in the investment function are also derived from relative shares of capital and labor aggregated across industries, as inputs to investment (Australia, Bureau of Statistics (1983, Table 18)). The resultant coefficients—ai, bi as in equation (3)—are

where the subscripts 1 and 2 refer to 1981 and 1982, respectively, here and in what follows. Thus, capital has a larger share as an input to investment than does labor, and no change in technology is assumed between periods. In computation, the coefficients are scaled proportionally so as to be slightly less than unity.

Targets for real government expenditure on goods and services, as a percentage of gross national product (GNP), are taken to be the actual values for 1981-82 (Norton, Garmston, and Reserve Bank of Australia (1984, Table 2.1)). Accordingly,

The coefficients for the government production of public goods function—βi, 1 - βi, as in equation (5)—are derived by simply deducting the government wage bill from total government expenditures (Australia, Bureau of Statistics (1984b, Tables 1 and 25)). The corresponding coefficients for capital, βi, in the two periods are thus

Finally, the rate of depreciation of capital—δ as in equation (4)—is taken to be 5 = 0.0629.22

The net effective rate of sales taxes was chosen to represent the uniform sales tax rate across sectors. This simplification seems justified because the Australian tax system charges uniform sales tax rates on all goods except private motor vehicles and certain household durables. The sales tax rates, ti in period i across sectors (Norton, Garmston, and Reserve Bank of Australia (1984, Table 2.30)) are thus

The tax rate on labor use, tLi (an income tax withheld at the source), is taken to be the average personal income tax rate. The tax rate on capital, tKi is taken to be the corporate income tax rate, which is a flat rate in Australia. The corresponding rates (Norton, Garmston, and Reserve Bank of Australia (1984, Table 2.29)) are thus

The tariff rate on complementary imports is zero, but on competing imports it was 0.16 in 1981 and 0.15 in 1982, uniformly across goods (Australia, Bureau of Statistics (1984a, Table 13)).

The model has three consumer categories: high-income Australian, low-income Australian, and rest of world. One first needs to derive initial allocations of capital, labor, money, and bonds for each of these categories. Initial allocations are taken to be holdings at the end of 1980. Total initial allocations of capital and labor are taken to be the aggregate gross operating surplus and the total wage bill for 1980. Thus, a unit of capital or labor is defined as that which earned $A 1 in 1980 (Norton, Garmston, and Reserve Bank of Australia (1984, Table 5.5)). It is assumed that this income is divided entirely among Australian consumers, with shares derived from survey data giving sources of income by income level (Australia, Bureau of Statistics (1981, Table 11)). Initial holdings of money were, for the Australian consumers, taken to be the stock of M2 at the end of 1980 (International Monetary Fund (1984)). The shares in this stock of money were assumed to be equal to the relative shares of wage plus capital income for the two Australian consumer categories. The initial allocation of money for the rest of the value of exports will come about only through changes in Australian export prices. There is no wealth effect for the rest of the world. In particular, changes in the exchange rate are represented by corresponding changes in the rest of the world’s initial allocation of money. A 10 percent devaluation would be represented by a 10 percent increase in the rest of the world’s initial holdings of money, and there would also be a corresponding increase in the quantity of domestic money needed to import one unit of foreign goods. Finally, the initial holdings of bonds by the Australian consumer categories are taken to be the interest obligations on Australian government securities on issue in 1980.23 Thus, a bond is defined as that security which earned $A 1 of interest in 1980, corresponding to the definitions of capital and labor in terms of earning flows. The initial allocations are then as shown in Table 1.

Table 1.Initial Allocations(In millions of 1980 Australian dollars)
GoodAustralian 1 (Low-Income)Australian 2 (High-Income)Rest of the World
Capital9,48829,4770
Labor22,67039,0500
Money15,35040,41011,500
Bonds5801,8100
Source: Norton, Garmston, and Reserve Bank of Australia (1984).
Source: Norton, Garmston, and Reserve Bank of Australia (1984).

To obtain budget elasticities for consumption of intermediate and final goods, the addilog estimates of marginal budget shares given in Bewley (1982) were used. These estimates are made for two categories of consumers: those with weekly household incomes of $A 50 and $A 350 based on 1976 data. The categories of low-income and high-income Australian consumers and the corresponding distribution shares are thus made to correspond to the 1980 nominal values of these income levels. There is a somewhat higher level of aggregation in these budget shares than in the input-output matrix, and it was decided to assign input-output categories to each of the consumption categories rather than construct a transformation matrix. Marginal budget shares are also treated as being equal to average shares so that marginal shares correspond to the specification of the consumer’s utility functions. Average budget shares are taken to be equal in both 1981 and 1982 and are shown in Table 2.24 In addition, there is assumed to be an elastic labor supply, with each Australian consumer having an elasticity of demand for leisure of 5 percent. This figure was not empirically derived but was determined by fitting the overall model to the benchmark years.

Table 2.Average Budget Shares(In percent)
CommodityCorresponding

Input-Output

Sector
Low-Income

Australian
High-Income

Australian
Rent24, 2519.62.0
Fuel122.20.2
Food1, 2, 4, 522.05.3
Alcohol, etc.64.45.0
Clothing7, 88.25.8
Durables9, 10, 11, 15, 16,
17, 18, 19, 21, 228.39.5
Health272.71.0
Transport2315.220.9
Recreation288.514.4
Miscellaneous269.014.2
Source: Bewley (1982).
Source: Bewley (1982).

The final element in the structure of the consumer’s demand system is a money demand function, as in equation (16). A partial adjustment mechanism is assumed, whereby the money stock adjusts with a lag to the level desired by consumers. Accordingly,

where M, M-1 are the stocks of broad money in the current and past period, Md is the current quantity of money demanded, and β is the unobserved speed of adjustment. Equation (16) converts into logarithmic form as

where r is the current interest rate, and C is the nominal value of current private consumption including taxes. Substituting and setting a1 = 1 allows the condition required for homogeneity to be obtained:

Equation (50) was estimated using annual Australian data for the period 1950-82. The interest rate is the nominal yield on short-term (two-year) Australian Treasury bonds (all data come from International Monetary Fund (1984 and various issues)). The resultant equation estimate is

The figures in parentheses are t-statistics; DW is the Durbin-Watson test statistic; R2 is the coefficient of determination. With M assumed to equal M-1, the required condition for long-run stability, parameters may then be identified. Thus,

Returning to the form of equation (16), PMiXMi=aebr(1+ti)p˜iXi,, allows one to obtain

Values now exist for all required parameters in the model, and attention may turn to the simulation of the benchmark years. A key instrument of government policy that is allowed to be endogenous to the model is the choice of the mix between money and bonds used to finance the government’s budget deficit. It was determined in solving the model that weights of 40 percent money and 60 percent bonds in 1981, and 60 percent money and 40 percent bonds in 1982, yielded the most accurate approximation of the actual macroeconomic variables in those years. A version of Merrill’s (1972) fixed-point algorithm was used to solve the model. Merrill’s method relies on a shrinking subdivision of the price simplex, and the theoretical structure of the version used here is based on Shoven (1974). The algorithm operates on the space of excess demands for capital, labor, money, bonds, and transfer payments in each of two periods while there is identical market clearing in the markets for intermediate and final goods. A similar methodology is described in Feltenstein (1979). The algorithm stopped when all excess demands were less than 0.1 percent of the corresponding total supply. The initial solution yields equilibrium relative prices for scarce factors and financial assets as shown in Table 3.

Table 3.Equilibrium Prices, Benchmark
GoodPrice

(Index numbers)a
1981
Capital86.7
Labor80.1
Money100.0
Bonds94.6
Transfer payments0.0
1982
Capital68.3
Labor97.1
Money89.0
Bonds80.0
Transfer payments0.0

Prices are normalized, with the price of 1981 money being the numeraire. In particular, the zero price of transfer payments in both periods indicates that there is a budget deficit.

Prices are normalized, with the price of 1981 money being the numeraire. In particular, the zero price of transfer payments in both periods indicates that there is a budget deficit.

The interest rate in period i is then defined as pMi/pBi•, the inflation rate in period 2, π2, is given by

(There is no definition of an endogenous first-period inflation rate because there is no endogenous price level prior to period 1.) Here pLj is the Leontief price of the jth intermediate or final good; Wj is the corresponding weight in the Australian gross domestic product (GDP) deflator; pMi, pBi are the ith period prices for money and bonds, respectively; goods 1-30 refer to 1981 intermediate and final goods; and goods 31-60 refer to 1982 goods. Actual and simulated interest and inflation rates can now be compared, as is done in Table 4. National income in period i, GDPi, may then be defined as the value of expenditure in period i, in terms of money in periodi, as in Table 5.

Table 4.Simulated Versus Actual Values for Interest and Inflation Rates, Benchmark Case(In percent)
ItemSimulatedActual
1981
Interest ratea5.811.5
Inflation rateb10.010.0
1982
Interest rate11.313.1
Inflation rate11.210.4

The two-year Australian Treasury bill rate is used for the actual figures. See Norton, Garmston, and Reserve Bank of Australia (1984, Table 2.27).

The 1981 simulated inflation rate is taken to have its actual value for the purpose of the conditions for boundedness in equation (29).

The two-year Australian Treasury bill rate is used for the actual figures. See Norton, Garmston, and Reserve Bank of Australia (1984, Table 2.27).

The 1981 simulated inflation rate is taken to have its actual value for the purpose of the conditions for boundedness in equation (29).

Table 5.Simulated Versus Actual Values, Benchmark Case
In Billions of

Australian Dollars
In Percentage of GDP
ItemSimulatedActualSimulatedActual
1981
GDP130.8a130.8100.0100.0
Tax revenuesb43.045.232.834.6
Government expenditureb48.049.836.738.0
Budget surplus (deficit)-5.0-4.6-3.9-3.5
Gross private investmentc20.821.715.916.6
Exports of goodsd20.018.715.314.3
Imports of goodsd22.819.217.414.7
Trade balance-2.8-0.5-2.1-0.4
1981
GDP149.8147.9100.0100.0
Tax revenuesb50.952.634.035.6
Government expenditureb57.057.438.138.8
Budget surplus (deficit)-6.1-4.8-4.1-3.2
Gross private investmentc21.426.914.318.2
Exports of goodsd18.719.112.512.9
Imports of goods425.922.417.315.1
Trade balance-7.2-3.3-4.8-2.2

The simulated figures are normalized so that 1981 simulated and actual gross domestic product (GDP) are equal.

See Norton, Garmston, and Reserve Bank of Australia (1984, Table 2.1).

Ibid. (Table 5.7a).

Ibid. (Table 1.1).

The simulated figures are normalized so that 1981 simulated and actual gross domestic product (GDP) are equal.

See Norton, Garmston, and Reserve Bank of Australia (1984, Table 2.1).

Ibid. (Table 5.7a).

Ibid. (Table 1.1).

Table 5 shows that the model gives a reasonably close approximation of the actual outcomes in Australia for 1981-82.25 The difference between the model’s results and those normally reported in applied general equilibrium work is also noteworthy. Interest and inflation rates are particular to this model, as are budget deficits financed by money and bonds and balance of payments deficits financed by losses in reserves. The model, of course, also generates supply of and demand for scarce factors and financial assets, as well as intermediate and final goods, indexed by time period.

The analysis turns to two counterfactual simulations. For the first example, suppose that a single change has taken place: in both 1981 and 1982, the target for government expenditure as a percentage of GDP has risen by 10 percent. Thus, government expenditures on goods and services are targeted at 38.4 percent of GDP in 1981 and 39.0 percent in 1982. The solution shown in Table 6 for the macroeconomic variables is the result.

Table 6.Counterfactual Simulation 1:10 Percent Increase in Government Spending
Item19811982
In

percent
In

billions of

Australian

dollars
In

percentage

of GDP
In

percent
In

billions of

Australian

dollars
In

percentage

of GDP
Interest rate14.723.0
Inflation ratea17.217.8
GDP153.6100.0187.0100.0
Tax revenues51.133.364.634.6
Government expenditure60.639.578.842.2
Budget surplus (deficit)-9.5-6.2-14.2-7.6
Gross private investment22.116.126.914.4
Exports of goods20.013.018.610.0
Imports of goods25.516.630.716.4
Trade balance-5.5-3.6-12.1-6.4

The inflation rate is calculated with respect to the price level generated in the benchmark simulation (see Table 3).

The inflation rate is calculated with respect to the price level generated in the benchmark simulation (see Table 3).

Note from Table 6 that, compared with the benchmark case, both real and nominal interest rates have increased sharply in response to higher government deficit financing. As might be expected, the rate of inflation has risen, and the trade balance and budget deficit have deteriorated. The rate of growth in real GDP has risen from 3.3 percent in the initial example to 3.9 percent in this case, whereas gross private investment has remained approximately constant as a percentage of GDP. The reason for this apparent absence of crowding out can be seen by observing the equilibrium relative prices for factors and financial assets, presented in Table 7.

Table 7.Equilibrium Prices Under Counterfactual Simulation I(Index numbers)
GoodPrice (Benchmark)Price (Simulation I)
1981
Capital86.7105.8
Labor80.197.5
Money100.0100.0
Bonds94.687.2
Transfer payments
1982
Capital68.379.3
Labor97.1111.0
Money89.079.0
Bonds80.064.2
Transfer payments

The money prices of capital and labor have risen relative to the benchmark case. In particular, the higher wage rate has caused the supply of labor to increase. This outcome depends critically, however, on the choice of an elastic labor supply. The higher price of capital in 1982 indicates that, although the cost of investment has risen (reflected by the higher interest rate), the rate of return on capital has also risen, and the two changes approximately cancel each other out. There is also a demand effect as the higher interest rate causes consumers to reduce their money holdings, increasing consumption. Thus, tax revenues have increased as a percentage of GDP; that is, an inflation tax is evident.

For the final example, suppose that government expenditure on goods and services stays the same in real terms as in the benchmark case, the results of which are reported in Table 5, but that the government’s rule for financing its budget deficit changes. Under the new rule, 100 percent of the deficit will be financed by the sale of bonds, so that the deficit is not monetized. This example will indicate whether changes in financing rules can have an impact on the real economy, and the results are presented in Table 8.

Table 8.Counterfactual Simulation II: 100 Percent Bond-Financed Deficit
Item19811982
In

percent
In

billions of

Australian

dollars
In

percentage

of GDP
In

percent
In

billions of

Australian

dollars
In

percentage

of GDP
Interest rate12.724.5
Inflation rate11.016.6
GDP144.5100.0174.1100.0
Tax revenues48.033.260.234.6
Government expenditure52.636.467.238.6
Budget surplus (deficit)-4.6-3.2-7.0-4.0
Gross private investment22.715.724.313.9
Exports of goods20.013.918.610.7
Imports of goods24.617.129.416.9
Trade balance-4.6-3.2-10.8-6.2

The rate of growth of real GDP is 3.4 percent, or approximately what it was in the benchmark case. Note that the nominal and real interest rates have risen, the latter somewhat more than in the case of increased government spending. Gross private investment as a percentage of GDP has fallen in both years, compared with the benchmark case, primarily because there has been insufficient demand stimulus and corresponding increased returns on capital to outweigh the increased interest costs to investors. Thus, a moderate degree of crowding out of the private sector does take place under a government deficit wholly financed by bonds.

III. Conclusions and Qualifications

The paper has presented an intertemporal general equilibrium model that can be used to analyze crowding out of the private sector. The model is disaggregated in both production and consumption and assumes perfect foresight for all agents. For a tractable empirical application, the model posits a time horizon of two periods with a single generation of consumers, although there would be no difficulty in extending the model to multiple periods. Private investment is financed wholly by debt and competes for private savings with government debt, which is issued with money to finance the deficit. The exchange rate is fixed, and capital flows are assumed to be exogenous. A particular closing rule that is not debt neutral was assumed, and an intertemporal equilibrium was proven to exist.

A fixed-point algorithm was derived to solve the model, and an application was made to Australian data. A benchmark solution was calculated for 1981-82, the last two years during which the Australian exchange rate was fixed, and yielded a reasonably accurate approximation to the actual outcomes of the Australian economy during those years. Two counterfactual simulations were then carried out. In the first, an increase in government expenditure brought about a slight increase in real income, with no significant change in the proportion of income allocated to private investment. There was, however, a significant increase in the real interest rate and in the government’s budget deficit, as well as a loss in reserves through the trade account. In the second simulation, an increase in the debt-financed proportion of the government’s deficit was found to have no significant effect on real income, although there was a decrease in both years in the level of private investment. Thus, a degree of crowding out does take place.

The results of the model are quite sensitive to the elasticity of the labor-leisure choice, as well as to the closing rule for holding debt in the second period. Some of the simulation results would not hold in a model with a longer time horizon. In particular, continued increases in government expenditure and deficit would not continue to stimulate real income as inflation accelerates. Future research, therefore, might extend the time horizon, possibly in the form of an intergenerational model, as well as introduce a floating exchange rate and an endogenous capital account.

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Mr. Feltenstein, a Senior Economist in the Country Policy Department of The World Bank, was a member of the Fiscal Affairs Department of the Fund when this paper was written. Most of the research was carried out while the author was visiting the University of Melbourne, and a theoretical version of the paper was written while he was at the Stockholm School of Economics. He would like to thank Lars Bergman, Willem Buiter, Ken Clements, Allan Powell, John Shoven, and Nicholas Stern for many helpful suggestions. The views expressed here do not necessarily represent those of The World Bank or the Fund.

See Tanzi (1978) and Aghevli and Khan (1978) for models which do distinguish between taxes and expenditures.

The model may thus be interpreted as generating a rational expectations equilibrium. The minimum needed to introduce a dynamic framework is two periods, but there would be no difficulty in extending the models to several periods. For a study of perfect foresight equilibria, see Brock and Turnovsky (1981).

This “closure” rule is made for purely technical reasons. One must allow for some future after the final period in order to avoid the requirement that in that final period all debt be fully paid off, so that no customer would hold debt. Alternative approaches would be to have infinitely lived consumers, or to introduce an overlapping generations structure. The closure rule will, in particular, ensure that the model does not generate Ricardian debt equivalence.

The model does not, however, yield a mechanical one-to-one correspondence between public deficits and crowding out because the rising interest rate will not only have the above-mentioned effects but may also increase the overall level of private savings.

This formulation is used because of the eventual goal of an empirical application and has been described in greater detail in, for example, Fullerton and others (1981) and Feltenstein (1980).

The investment function could also require intermediate and final goods as inputs, but for simplicity of exposition it will require only capital and labor.

It would also be possible to have investment activities distinguished by firms if firm-specific capital were available, as in specifications by Fullerton (1983) and Dervis, De Melo, and Robinson (1982).

Decreasing returns to scale will allow the derivation of a single-valued investment response. If desired, one could choose the parameters such that 1 - ai - b = εi, with εi arbitrarily small. Any investment function with decreasing returns to scale would be equally acceptable.

Rather than having the government operate its own production function, it would also be possible to have the government buy directly from the private sector. Introducing a government production function allows, however, the direct representation of changing public policy toward the relative importance of hiring capital or labor. If, for example, the government wished to increase employment, it could, in the model, change the weights given to capital and labor in its production function. A more sophisticated version of the model would have public goods enter consumers’ utility functions directly, or increase productivity.

A rational expectations equilibrium is being defined in which consumers’ expectations of period 2 are perfectly fulfilled. If the model contained more than two periods, it would be quite possible that information available for the time period after period 2 might be used to determine the consumers’ choices in periods 1 and 2.

There are K>0 consumers in the model; to avoid unreadable subscripts, however, the consumer demand parameters will not be indexed. It should be noted that these parameters, along with initial allocations, are not uniform across consumers. One might also wish to include public goods in the consumers’ utility function, although that has not been done here.

Proof of the existence of equilibrium does not depend on this form of the utility function; any continuous utility function would be valid. This particular form permits an analytic solution to the demand function.

Another approach—for example, in Grandmont (1977) and Grandmont and Laroque (1975)-—is to have consumers borrow from the central bank against future income but to have no borrowing by the central bank. Several technical problems are involved with allowing borrowing to go in both directions, which essentially is equivalent to the requirement of irreversibility of production.

It will be assumed that initial holdings of bonds, B0, are entirely composed of government debt. Initial private debt would be inconsistent with the specified intertemporal investment decision.

The interpretation of the price of capital in capital i, pKi, is that it is a rental rather than a sales, or cost of production, price. There is no secondary market for capital, since the conditions on private investment are such that the rate of return on capital is always identically equal to the interest rate. Thus all savings decisions are made by purchases of bonds, and capital gains are realized by the sale of bonds.

These transfer payments are not identically equal to the sum of the transfer payments included in the consumer’s budget constraints, although at equilibrium they will be.

Here π2(CPI2/pM2)/(CPI1/pM1), where CPIi is a weighted average of the period-i Leontief prices. It may be assumed that π1 is exogenous (in practice, taken to be the actual inflation rate in that year).

Thus, the interest obligations incurred by the government in period 1 are paid off in period 2 in units of money, rather than being rolled over in new bond sales. This form of payment is not essential to the model, but it does allow a simpler proof of the boundedness of the supply of bonds in period 2.

For i = 2, assume that pK3 = (1 + π2)Pk2.

The proof of this result is available from the author upon request.

This figure is taken from the ORANI general equilibrium model of Australia (see Dixon and others (1982)).

See Norton, Garmston, and Reserve Bank of Australia (1984, Table 2.22). Recall the assumption that there are no outstanding initial holdings of privately issued bonds.

Within a particular consumption category, the elasticities for the input-output sectors are derived from relative consumption shares. Budget shares for the rest of the world are taken to be the shares in total exports of goods of each input-output category.

That the simulated interest rate in 1981 is lower than the corresponding actual rate is primarily a result of the decision to take the initial allocation of bonds as comprising only outstanding government debt and not incorporating private debt. Inclusion of initial private debt (which, as a fixed cost, is technically not feasible) would tend to lower the 1981 price of bonds and raise the interest rate.

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