# A multilevel government model of deficits and inflation.

I. IntroductionThe debate over deficits centers around their impact on investment, employment, prices, and interest rates. Both theoretical and empirical studies of deficits delve into the inflationary impact (or crowding out) effects of deficits at the national level. To the authors' knowledge, there is a dearth of such studies at the state (or provincial) level of government. The objective of this paper is to develop a macro model of the state (provincial) economy which incorporates important features of the national economy. This model is intended to isolate the inflationary effects, if any, of deficits at the provincial or state (state hereinafter) level of government. A model of this type is useful in view of the recent rise in state governments' deficits. In federalist or multilevel countries such as Canada and Australia, for instance, many states face budgetary woes stemming from reduced federal support for state governments, rapidly rising costs of federally mandated programs such as education and medical care, and slow economic growth.

This paper establishes a link between state government deficits and inflation arising from such deficits. The results indicate that inflation in a state responds to the national and international movements of prices and is affected by the level of the deficit. What differentiates the current model from federal government models is that state governments cannot monetize their debt. Thus, it is assumed that the money supply is exogenous with respect to state government debt. This removes an important source of endogeneity from the model.

The remainder of the paper is divided as follows. Section II present a brief review of the literature. Section III develops a model tracing the equilibrium effect of deficits. Section IV concludes the paper and the federal model, which allows for the establishment of a link between state and overall inflation, is presented in Appendix II.

II. Review of the Main Issues

The usual debate about government deficits centers around the impact of deficits on investment, employment, prices, and interest rates. Within the neoclassical framework, the method of financing government deficits affects the level of aggregate demand. For instance, a bond-financed deficit - as opposed to tax-financed deficit - causes real interest rates to rise at full employment. Thus, investment and net exports are crowded out [Yellen, 1989].(1) In an open economy, a rise in real interest rates engenders an influx of foreign capital which, in turn, causes the country's currency to appreciate. This phenomenon retards the economy's competitiveness in the world market. In a closed economy, the upward pressure on interest rates crowds out investment.

The foregoing paradigm has been challenged by proponents of the Ricardian equivalence theorem [e.g., Barro, 1974, 1978; Kormendi, 1983] as well as Keynesians [e.g., Eisner, 1986, 1989]. The Ricardian equivalence theorem argues that economic agents perceive the implied future taxes of debt financing. Thus, the net worth of the private sector is invariant with respect to debt or tax financing.(2) The Keynesian position argues that under conditions of less-than-full employment, increases in current consumption need not imply any borrowing from the future or future generation of taxpayers. The otherwise unutilized resources finance consumption which, in turn, encourages more, not less, investment.

Essentially, the debate over government deficits hinges on whether or not government debt is net wealth. As Barth et al. [1986] suggest, as long as the rate of growth of output [Mathematical Expression Omitted] exceeds the rate of interest (I), then public debt is unambiguously net wealth. The reason is that in such circumstances, future taxes are not necessary to service the debt. Economic growth will accommodate indefinite deficits without jeopardizing the taxing capacity of the economy. If [Mathematical Expression Omitted] is less than I, then the status of national debt is ambiguous. Government debt will be considered "net wealth only to the extent that current generations do not fully discount the increase in future tax liability to service the debt, which in this case cannot be serviced solely with revenues generated by economic growth" [Barth et al., 1986, p.28]. If I exceeds [Mathematical Expression Omitted] and there is no primary surplus (revenues less outlays net of interest payments), then federal debt will grow more rapidly than the economy.

The inflationary effect of government deficits depends upon the means by which the deficit is financed and the impact of the deficit on aggregate demand. In a Ricardian equivalence world, government deficits financed by issuing bonds have no effect on inflation [Barro, 1978; McCallum, 1984]. Essentially, a deficit is always financed by issuing or retiring interest-bearing debt. Sargent [1986] points out that in order for the Ricardian regime to hold, deficits must be temporary and they must eventually be offset by future surpluses. If deficits persist, governments will eventually have to increase the monetary base, which will generate inflation. Bryant and Wallace [1980] and Sargent and Wallace [1981] show that a persistent stream of large deficits will eventually force a government to increase the money supply, thereby raising inflation. In both of these papers, the inflationary effect of government deficits depends on the debt repayment regime that is in place.

Barro [1979] concludes that when governments wish to smooth interest rate movements, they increase the money supply to offset higher interest rates that result from issuing bonds. In this case, bond-financed deficits indirectly lead to higher inflation. The monetarist position maintains that, for example, the central bank's purchases of government bonds increases high-powered money and, thus, the money supply. This, ultimately, leads to a rising level of prices. McCallum [1984, p.134] uses a perfect foresight version of the competitive equilibrium model to investigate the theoretical validity of a monetarist hypothesis which asserts "that a constant, per capita budget deficit can be maintained without inflation if it is financed by the issue of bonds rather than money." He finds the monetarist hypothesis to be valid under conventional definition but invalid if the deficit is defined to be exclusive of interest payments.

Dwyer [1982] outlines three hypotheses concerning the inflationary impact of deficits. First, the increased value of outstanding bonds and perceived wealth should increase total spending and prices. Furthermore, deficits lead central banks to purchase a portion of the debt, thus increasing the money supply and prices. Finally, deficits are a result of inflation rather than the other way around. The final hypothesis is such because along with a rise in the anticipated rate of inflation, "the nominal value of bonds must increase, i.e., the government will run a deficit to keep the same anticipated real amount of bonds" [Dwyer, 1982, p. 315].

Thus far, the empirical evidence on the inflationary effects of deficits is inconclusive. This stems from different theories of deficits and inflation. Dwyer [1982] and Crozier [1976] found no significant evidence to support the idea that inflation is caused by deficits. Barro [1989] found empirical support for the view that deficits are a result of inflation. His results were congruent with an earlier study by Horrigan [1985], whose findings provided strong support for the same view that deficits are a consequence of inflation. Darrat [1985] also examined the link between deficits and inflation. He concluded that over the estimation period, both monetary growth and federal deficits significantly influenced inflation. Additionally, he found that federal deficits bore a stronger and more reliable relationship to inflation than monetary growth. Eisner [1989] examined the impact of deficits on inflationary pressure to see whether structural deficits contribute to inflation. He found [p. 87] "no support for the proposition that the federal budget deficit, by any measure, contributes to inflation. If anything the opposite appears to be true." Eisner suggested that the true story of inflationary tendencies of the late 1970s and early 1980s stemmed not from budget deficits or excess demand but from the major supply shocks.

All of the papers discussed above deal with the issue of deficits at the level of the federal government rather than nonfederal governments. In contrast, Kneebone [1989] develops a model of nonfederal governments to determine the stability conditions for a monetary rule in which the money supply is restricted to grow within certain bounds. However, Kneebone is primarily concerned with the stability properties of the equilibrium and the interdependence of economic policy between state governments and the federal government. He is not interested in the inflationary effects of nonfederal government deficits. An important feature of Kneebone's model is that he assumes that the monetary authorities only chose to monetize the debt of the federal government.

III. The Model

The model developed in this section attempts to add to the literature by examining the factors that influence the rate of inflation at the state level. Although it is recognized that decisions by one level of government may have an impact upon the behavior of other levels of government since their financing constraints are interdependent, this interdependence is not explicitly specified in the model. It is the purpose of this paper to exclusively analyze the inflationary effects of state government deficits rather than the interdependence of economic policy. The size of state deficits is related to the federal deficit through transfer payments. However, the interaction between federal and state deficits is not specifically incorporated in the model. Rather, it is assumed that transfer payments are exogenous to the state and the size of the federal deficit is exogenous.(3) Accordingly, all variables are in terms of state levels unless otherwise specified.(4)

In addition, it is assumed that the money supply is exogenous to the state, since the federal government sets monetary policy and the monetary authorities choose not to monetize the debt of the state governments. Each state, however, can affect the nominal interest rate through changes in the demand for money. The sensitivity of the interest rate to changes in the demand for money at the state level is directly related to the size of the state. (See Appendix II for the effect of the state on the demand for money.)

To determine the inflationary effects of state deficits, one must simultaneously determine the effect of state deficits on state inflation and on overall inflation, since overall inflation is just a weighted average of inflation at the state level. Accordingly, one must specify a state model and a federal model. The state model is developed in this section, while the federal model is constructed in Appendix II.

It is assumed that capital and goods flow freely between the states. The interstate flow of capital insures that the nominal interest rate does not vary across states. Likewise, flow of goods insures the same thing about goods' prices. This implies that all states face the same real interest rate.

To derive the goods' market equilibrium condition at the state level, begin with:

[Y.sub.t] = [C.sub.t] + [I.sub.t] + [G.sub.t] + X[N.sub.t]. (1)

The value of state output is given by the sum of consumption, investment, government expenditures, and net exports.

Following Turnovsky [1985] and Kneebone [1989], consumption is specified as a positive function of disposable income and wealth and a negative function of the expected real rate of interest:

[Mathematical Expression Omitted].

By including the effect of the interest rate on consumption, one allows for the so-called credit effect.(5)

Real wealth at the state level is defined by:

[Mathematical Expression Omitted].

State wealth is determined by the proportion of the real money supply held by the state and the stock of outstanding federal and state bonds held by each state. If b = 0, the Ricardian equivalence hypothesis holds and government bonds are not perceived as net wealth. However, if 0 [less than] b [less than or equal to] 1, then bonds are perceived as net wealth.

Investment is negatively related to the expected real interest rate:

[Mathematical Expression Omitted].

Government expenditures, including interest payments, are financed by: 1) running a deficit and issuing bonds; 2) tax revenues; and 3) net transfer payments. These payments are the difference between receipts by a state government from the national government and payments to municipal governments:

[G.sub.t] = D[F.sub.t] + [T.sub.t] + T[R.sub.t], (5)

where:

[Mathematical Expression Omitted].

Finally, net exports are defined by the difference between the value of exports and imports. Exports amount to:(6)

[Mathematical Expression Omitted],

whereas imports are given by:

[Mathematical Expression Omitted]

where [Mathematical Expression Omitted] is Dornbusch's [1980] terms of trade.

States export goods and services to other states and foreign markets. Hence, exports are directly related to foreign income [Mathematical Expression Omitted], income in the rest of the country [Mathematical Expression Omitted], and the ratio of prices to foreign prices, given by [Mathematical Expression Omitted]. By similar argument, imports are a positive function of state income ([Y.sub.t]) and a negative function of the price ratio.

To solve for equilibrium, the aggregate demand curve, substitute (2) through (7) into (1) and simplify:

[Mathematical Expression Omitted],

where:

[Lambda] = 1 - [c.sub.1] + [m.sub.1]

[Mathematical Expression Omitted].

Equation (8) shows that state income is negatively related to the real interest rate, which is determined at the federal level.(7) In addition, it is a function of real wealth, which depends on the Ricardian equivalence hypothesis and the size of the state deficit.

The aggregate-supply curve or the domestic wage-price sector is given by (see Duck [1984, p.65]):

[Mathematical Expression Omitted]

This equation assumes that money-wage inflation is generated by an extended Phillips curve at the state level and that the rate of unemployment is related to the degree of product-market disequilibrium. As the state output gap falls, the rate of inflation declines. As given in Duck [1984], [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are exogenous to the current model.

To solve for the rate of inflation, equate (8) to (9), aggregate supply equal to aggregate demand, and substitute in for the national price level and real rate of interest equations (A12) and (A11) taken from the national model in Appendix II:

[Mathematical Expression Omitted],

where:

[Lambda] = 1 + [m.sub.1] - [c.sub.1]

[Theta] = [c.sub.3]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

Equation (10) is a quasi-reduced form equation for the rate of inflation. It shows that the rate of inflation is positively related to the expected rate of inflation and the real interest rate, which is determined at the federal level.

To solve for the expected rate of inflation, first use an adaptive expectation given as:

[Mathematical Expression Omitted].

By iterating back in time, (11) links the unobservable variable - expected state inflation - to actual inflation in all previous periods. However, [Alpha] [less than] 1 implies that actual inflation in any previous period has less of an effect on current expectations the further back in time one goes.

Set the expected rate of inflation to be a function of the previous two periods:

[Mathematical Expression Omitted]

and then substitute (12) into (9) to obtain the reduced form equation for the rate of inflation:

[Mathematical Expression Omitted].

Equation (13) shows that state inflation is a function of trend income foreign inflation, the rate of depreciation of the exchange rate, the expected rate of inflation given by lagged inflation, and the government deficit.

There is a feedback between state inflation and overall inflation. When state governments run deficits, it leads to an increase in both state level aggregate demand and, consequently, overall aggregate demand. This, in turn, affects the demand for money and interest rates. The inflationary effect of state deficits depends on the size of the state relative to the overall economy and the slope of the aggregate supply curve, which is a function of the coefficient [a.sub.1] and the multipliers [Lambda] and [Mathematical Expression Omitted] in (13). Equation (13) readily lends itself to a proper empirical testing of the link between deficits and the rate of inflation of a multilevel state. In addition, by substituting (3), the wealth constraint, into (13), one can test for the existence of the Ricardian equivalence hypothesis.

Next, rather than assuming that the expectations are formed adaptively, the model can be solved by assuming that expectations are formed rationally' Set aggregate demand ([Mathematical Expression Omitted]) equal to aggregate supply ([Mathematical Expression Omitted]) from (8) and (9):

[Mathematical Expression Omitted].

To solve the model, take expectations of (8) and (9) and equate the expectation of ([Mathematical Expression Omitted]) to ([Mathematical Expression Omitted]). This yields the expected price level:

[Mathematical Expression Omitted].

Equation (15) states that the expected price level is a function of the expected levels of fiscal and monetary variables, trend income, and expected overall inflation.

Finally, to solve for the rate of inflation, set [Mathematical Expression Omitted] and substitute for [Mathematical Expression Omitted] from (15):

[Mathematical Expression Omitted].

The effect of the state deficit depends on the sign of:

1/[Lambda][a.sub.1] D[F.sub.t] - (1/[Lambda][a.sub.1] + 1/[Psi])D[F.sup.e].

[Mathematical Expression Omitted].

As in the case of adaptive expectations, the link between state and overall inflation is modeled in Appendix II. Essentially, state deficits will have an effect on overall inflation through changes in federal aggregate demand. The effect of the state deficit on overall inflation depends on the size of the state deficit, the slope of the aggregate supply curve, [a.sub.1], and the size of the multiplier, [Lambda]. Unlike the case of adaptive expectations, (16) relates inflation to not only the expected size of the deficit but also to the unexpected component of the deficit.

IV. Conclusion

The objective of this paper was to construct a macroeconomic model that is testable and explains the inflationary effects of state deficits. Two models are developed, one using adaptive expectations and a second which assumes that expectations are formed rationally.

The results suggest that when expectations are formed adaptively, state deficits are directly related to inflation. However, the degree to which state deficits affect inflation is an empirical question. Conversely, when expectations are formed rationally, the model indicates that inflation is a function of the deviation of the actual deficit from the expected deficit, the forecast error. A negative forecast error, for example, will exert downward pressure on the rate of inflation. Essentially, the aggregate demand curve shifts out by less than expected and, thus, the actual rate of inflation will be below the expected inflation rate.

The model differs from federal models in that it not only incorporates the inflationary effects of international trade but also the impact of interregional trade. Higher national prices spill over into states through trade and cause inflation at the state level.

In addition, it is assumed that state governments cannot monetize their debt. Growth in the money supply is, thus, independent of state level deficits. This removes an important source of endogeneity that exists in federal models. In federal models, bond- financed deficits are found to be inflationary when governments are forced to monetize their debt. How soon this occurs depends on the debt repayment regime. However, at the state level, the link between deficits and inflation is more direct since monetizing the debt is not an issue.

[TABULAR DATA FOR APPENDIX I OMITTED]

APPENDIX II

Federal Model

Equations (13) and (18) are derived from a model of the federal level that is similar to the state-level model. The superscript c denotes values at the federal level.

The goods' market is specified in equations (A1) to (A6):

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted],

where:

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

The money market equilibrium condition is given by:

[Mathematical Expression Omitted].

Following Turnovsky [1977, p.135], the real money demand at the federal level is determined by income, real interest rates, expected inflation, and wealth. Federal demand for money is a positive function of income, inflation, and wealth but a negative function of the real interest rate. Since the federal government controls the real money supply,

([MS.sub.t]/[P.sub.t]), money markets must clear at the federal level rather than the state level.

Equation (A8) shows that real demand for money, [Mathematical Expression Omitted], is a weighted average of demand for money at the state level:

[Mathematical Expression Omitted],

where:

[Mathematical Expression Omitted],

I = states (1,..., n), and w = weights.

National income is just a weighted average of state incomes. Thus, the nominal interest rate is affected by the level of income at the state level. A rise in state income will lead to an increase in the demand for money and, holding the money supply constant, will increase the interest rate.

Equations (A1) to (A7) can be combined to generate an equation for the aggregate demand curve at the federal level:

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

To solve for the real interest rate, substitute (A10) into (A8) and (A9):

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

Equation (A11) can also be solved for the federal level of income. To solve for the level of output in the federal economy, solve the IS-LM model for [Mathematical Expression Omitted] instead of ([Mathematical Expression Omitted]).

[Mathematical Expression Omitted],

where:

[Mathematical Expression Omitted].

1 Eaton [1981, p. 44] concludes that his results "suggest that to a limited degree deficit finance will yield greater capital growth than income tax finance."

2 The Ricardian equivalence theorem has its own detractors. See, for instance, Bernheim [1989] and Gramlich [1989].

3 See Kneebone [1989] for a model that incorporates the interdependence between federal and nonfederal governments.

4 See Table A1 for a complete list of variables and their definitions.

5 As Turnovsky [1985] points out, this specification is closest to Ando and Modigliani's [1963] consumption function.

6 In this paper, exports and imports are also inclusive of interstate trade. That is, goods and services sold by individuals and firms in State A to firms and individuals in State B are referred to as A's exports. Similar treatment applies to imports.

7 Use has been made of Cebula [1987], Eisner [1986], Turnovsky [1985] in deriving the IS-LM portion of the method.

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-----. "Comment from Unreconstructed Ricardian," Journal of Monetary Economics, 4, August 1978, pp. 569-81.

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Author: | Abizadeh, Sohrab; Benarroch, Michael; Yousefi, Mahmood |
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Publication: | Atlantic Economic Journal |

Date: | Jun 1, 1996 |

Words: | 4165 |

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