THE EFFECT OF PUBLIC DEBT ON STATE AND LOCAL ECONOMIC GROWTH AND ITS IMPLICATION FOR MEASURING DEBT CAPACITY: A SIMULTANEOUS

EQUATIONS APPROACH

Qiushi Wang

University of Nebraska at Omaha

A draft for ABFM, Chicago

October 2008

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I. Introduction

Public debt has been a relatively underworked area in public administration, yet it is a very important issue in government finance. In essence, with the assumption that bonded borrowings can not be used for non-capital expenditure, the debt actually plays a role that helps adjust the public capital investment to its optimal level, given the fixed schedule of borrowing costs and tax costs for a particular jurisdiction. If no debt was allowed, jurisdictions will have to rely solely on their current revenue or savings from past revenues, and this will cause underinvestment in public infrastructure. Existing literature typically focuses on one of the following three facets of public debt: borrowing costs and risk of default, debt burden and debt capacity, and the relationship between capital investment and regional economy, but none of them has taken a holistic view that take account of the problem all at a time. In fact, public debt has very complicated impact on state and local finance and many of these impacts are simultaneously determined by a set of endogenous and exogenous variables. For example, the debt level for a particular jurisdiction usually depends on its economic situation and some other factors such as management performance, political environment, etc. The jurisdiction’s economic situation is in turn, determined by such factors as past and current capital investment in infrastructure; the level of capital investment will play an important role in deciding how much debt the jurisdiction will borrow, after an optimal share of debt against tax financing has been chosen. This simple example reveals that the real effect of public debt can only be studied in this simultaneous system.

This dissertation will contribute to the literature in following ways:1. Explicitly link debt to capital investment and state local economy and examine its

impact in a simultaneous equation system;2. Use a better measure as well as a large and updated dataset to estimate the above

equation with both pooled cross-sectional and panel data technique;3. Propose a new method to estimate debt capacity.

II. Literature Review

2.1 Debt level

In general, borrowing level, both the aggregated borrowing level for the whole financial market across the nation and the individual borrowing level for each jurisdiction, is positively associated with borrowing costs. First, an increase in the overall borrowing level will increase the borrowing costs for all municipal borrowers and this is sometimes called the “squeezing out” effect, because the more governments borrow, the less the private sector can borrow (Needs lit. here). Study shows that this effect turns out to be relatively small, from a low .37 basis points to a high of approximately 9.0 basis points increase in bond interest cost for every $1 billion increase in state and local

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borrowing level. (Tuccillo & Weicher, 1981; Kormendi & Nagle, 1981). On the contrary, the effect of jurisdictions’ own borrowing level appears to be dominant. Capeci (1990) shows that a million dollar increase in the size of an individual bond issuance will lead to an increase of 3.5 basis points in the borrowing costs.

Cunningham(1989) attempts to explain debt level by using both cross-sectional and time-series data. In his model, the equilibrium amount of debt is determined by equating the marginal welfare burden of debt with that of taxes. His model also incorporates the political argument that higher income residents prefer debt financing while lower income residents prefer tax finance, because the former benefit most from a lower tax burden. He finds that his dependent variable, which is the debt over personal income ratio, is positively related to income and unemployment, but is not related to past capital spending and expected population growth.

How state and local governments make decisions on issuing revenue bonds has not been well explained by the literature. Descriptive studies of revenue bonds usually focus on the perceived costlessness to the jurisdiction (Clark & Neubig, 1984; Clark, 1985). The income from the particular investment project, rather than government revenue, is used to service the debt. Allman (1982) proposes a model of revenue bond supply, in which the elected official tries to satisfy the voters by providing as many services as possible. Because the increasing user fees are considered a sign of increasing demand for revenue bonds, the supply of revenue bonds is assumed to be positively related to the recent user fee trend. His empirical results support this assumption, but a problem arises when only a small fraction of revenue projects use user fees to service the debt. But so far the literature has not yet addressed the association between the revenue bonds level and the overall cost of borrowing for that jurisdiction. It is an important assumption in this dissertation that as the overall level of debt, including GO and RB, increases, the cost of debt for the jurisdiction will also increase. This assumption will be tested by my empirical work.

2.2 Cost of debt

Literature on the costs of borrowing for state and local governments is reviewed in this section. In the United States, the majority of governmental borrowings takes the form of municipal bonds, and therefore takes place in the financial market. The theoretical frame work about debt that this paper is going to develop is exactly based on the assumption that governmental debt is all public traded and there is no implicit debt. Suppose the governmental debt is not in the bond format (this is indeed the case for many developing countries, China for example), and the financial market is not the venue for its transaction, the analytical framework will be completely different. Furthermore, it is argued that jurisdiction is not price taker in the financial market, because the jurisdiction-specific factors can affect borrowing costs. Like in the market for other goods, the price of financial products is also determined by demand and supply, but there are reasons to believe that the financial is not fully competitive. The number of suppliers of fund in the market is limited and each of them may have certain monopolistic power, implying that

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they can lend the funds to the “highest bidder” and reap more supplier surplus. It is to be noted that the “highest bidder” doesn’t only refer to the price, but also the risk. As the CAPM model shows, the real interest cost depends on a risk free interest rate plus a risk premium.

Measurement is another important issue in the study of borrowing cost. Over the past decade, a large body of literature has focused on this issue, taking one of the three different paths: net interest rate (NIC), true interest rate (TIC) and reoffer yield. Hopewell and Kaufman (1974) have a complete discussion of NIC and TIC. Both of them measure the interest cost of the entire bond issue and the key difference between the two is the time value of money. The reoffer yield is the interest cost for one particular maturity of the whole issue. It has several advantages such as easier control for general level of interest rate (Peng, 2000), but a big concern is that it does not include the cost of underwriter spread. Comparing the three methods, Peng (2000) concludes that TIC is the best measurement of the actual interest cost to the issuer, but NIC and offer yield may be more accessible to researchers.

Temple (1990, p.14) presents the tax exempt rate facing the ith jurisdiction with the following two equations:

and

where and are jurisdiction i’s interest costs on its general obligation bonds and

revenue bonds, respectively. and are the level of general obligation and revenue

bond issued by jurisdiction i during a particular period of time. is a vector of variables

that contains information on jurisdiction i’s credit worthiness while consists of particular factors of the projects being financed, such as the predicted profitability. Further, Temple (1990) concludes that the costs of each type of borrowing (GO and RB) are positive function of the size both types of borrowing. Findings from Hendershott and Kidwell (1978), Leonard (1983), and others seem to support this conclusion. With respect to the interaction effect between GO and RB bond, Hendershott and Kidwell (1978) and Kidwell, et. al. (1984) imply that the interest costs associated with issuing general obligation bonds will increase with increase in the level of revenue bond issues and vice versa. Epple and Spatt (1986) cite evidence from the WPPSS’s default and argues that such large-size default has had an adverse effect on that state’s GO borrowing costs, even if the jurisdiction typically is not responsible for repayment of revenue bonds.

Capeci (1990) studies the effect of local fiscal policy on the jurisdiction’s borrowing cost. Using a sample of 243 bonds issued by New Jersey bond issuing entities, he finds that the amount borrowed per dollar of property value has a positive impact on the borrowing cost while the level of discretionary revenue per dollar of property value has a negative effect. Similarly, other researchers also find the positive relationship between bond issue volume and interest costs (Leonard, 1983; Hendershott & Kidwell, 1978). Hendershott and Kidwell (1978) also notice that a change in the supply of tax-exempt

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bonds may have effect on the interest costs in that particular regional market relative to the interest costs nationwide. Kidwell, Koch and Stock (1984) empirically prove that jurisdictions exempt from state income tax on the interest from bonds can issue bonds at lower interest cost.

The cost of borrowing depends on its own level of borrowing while the latter also depends on the borrowing cost that the jurisdiction is facing. In corporate finance research, the introduction of endogenous borrowing costs serves to limit borrowing and results in an optimal debt/equity structure (Barnea, et. al. 1981). In the public sector, such endogeneity will also result in an optimal structure of debt/tax ratio for jurisdictions (Temple, 1990).

Factors other than borrowing level also play an important part in the determination of jurisdictions’ borrowing costs. Although the exact information on the evaluation criteria of the three major rating agencies is unknown to the public, studies (needs lit) have approximated their process and it is widely believed that factors reflecting the financial health and the overall ability of the jurisdiction to repay the principal as well as interest are included in . These factors are the ratio of total general obligation debt to the taxable wealth in the jurisdiction, GO debt per capita, GO debt as a percentage of personal income, among others. , however, may contain specific information on the

project, other than the common ones in , because the revenue bond financed project rely on its own proceeds to repay the revenue bond debt. Cook (1982) divides these factors into five broad categories: issue characteristics, issuer characteristics, marketing, regional market conditions and others (revenue versus GO bonds, size of issue, etc.). Some of these explanatory variables will be employed in the estimation model. Since the interest of borrowing is used in this dissertation only to control for the possible simultaneity, I will not go into further depth of this issue.

The interest cost is an important consideration for jurisdictions to make borrowing

decisions. And it is partly responsible for the debt level to show a diminishing return with respect to the local economic growth. This will be further discussed in later sections.

2.3 Debt financing vs. tax financing

This section will discuss state and local governments’ decision on how to finance capital projects and the determinants of the portion that is financed by general obligation bonds. For the private sector, Miller (1977) argues that in the equilibrium, the market value of any firm must be independent of its capital structure even interest payments are fully deductible in computing corporate income taxes. Auerbach (1979), and Feldstein, Green and Sheshinski (1979), however, challenge Miller’s point of view by claiming that a unique optimal debt-equity ratio will exist if the cost of capital varies with the degree of debt finance, or “leverage”. Nadeau (1989) holds a similar view that the fact that interest costs vary with the level of borrowing may serve to guarantee a unique optimal point of debt. In the public sector, capital expenditures are financed by a combination of taxation, general obligation bonds and intergovernmental transfers. Among these three sources, intergovernmental transfers can largely be considered exogenous, and analogous to the

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private firm’s choice between debt financing and equity financing, the jurisdiction has the power to choose between debt financing and tax financing, or the debt share. Since the public borrowing costs also vary with the degree of borrowing, there may also be a unique optimal debt/tax ratio for each jurisdiction. Temple (1990) applies this analytical framework to the determination of optimal debt share. She assumes government official selects the mix of financing methods that minimizes the cost of a dollar of per capita public expenditure to the residents of the jurisdiction, in particular, to the median voter of the jurisdiction (p.23). Her analytical framework will be revisited in more detail in Chapter 3.

The existence of statutory control on debt may have impact on officials’ ability to adjust the debt share to the optimal level. There are two common types of restrictions on jurisdictions’ borrowing practice. First is the restriction that debt is only to be used to finance capital projects. Second is that debt should be limited to a certain percentage of some assessed value in the jurisdiction, or the “debt ceiling”. The first restriction is assumed to be true for GO bonds, because there is no evidence that suggests otherwise. It will be argued in this dissertation that the debt ceiling, however, is not binding, an assumption that has also been made be Gordon and Slemord (1986).

Another theory is also relevant to the optimal debt and tax share. Adams (1977), Asefa, et. al. (1981), Gordon and Slemord (1986) and Metcalf (1989) argue that municipal governments issue bonds in order to earn arbitrage. The direct form of municipal bond arbitrage consists of issuing tax exempt bonds and investing the proceeds in higher yield taxable bonds, but it is limited by law (it has been largely eliminated by TRA 86). Alternatively, jurisdictions can engage in other two types of indirect arbitrage. Since governments can earn pre tax rate of return on taxable investment, residents in higher tax bracket may prefer that their governments save for them by collecting more tax revenues and using the proceeds to invest in taxable securities, because these residents would earn lower rate of return on their own investments. In contrast, jurisdictions can take advantage of the different yields on tax-exempt and taxable securities by issuing tax-exempt bonds and using the proceeds to lower tax rate. This substitution of bond for tax may be preferred by residents in lower tax bracket, because they can use the extra income gained from lower tax rate to invest in taxable securities and earn the greatest after tax yield. In their empirical work, this type of bond supply model usually includes such important determinants as the federal marginal tax rate of the residents in the jurisdiction and the marginal tax rate implied by the tax-exempt/taxable bond yield ratio.

2.4 Capital investment in the infrastructure and economic growth

The neoclassic model of economic growth dates back to the late 1950s, with some early contributions made by Frank, Ramsey (1928), Harrod (1939) and Domer (1946). Solow (1956) and Swan (1956) build a model that adopts the neoclassical form of the production function. Their specification assumes constant return to scale, diminishing returns to each input, per capita variables and some positive and smooth elasticity of substitution between each input. The Cobb-Douglas production function and

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mathematical methods of dynamic optimization and differential equations are widely used to generate some general equilibrium of the economy, based on a set of strict assumptions some of which will be relaxed in variations of the main model. Attention has also been given to the government which plays an important part of regulator as well as consumer and producer in the economy. In a various modifications of Ramsey model, government purchase, tax effects, etc. and some government economic policies (monetary policy for example) are studied1. This dissertation will not go into the depth of these macroeconomic theories, but will borrow the languages and techniques from this tradition to analyze the government’s behavior in borrowing and public capital investment. More closely related to this dissertation is the literature focusing on the public sector, which will be presented next.

In the early 1990s, the Congress Budget Office and the Associated General Contractors of America estimated the gap between the investments needed to provide adequate public infrastructure and available resources to fund these projects range from $17.4 billion to $71.7 billion. Associated with this problem is the concern about the possible adverse effect on economic growth (Deno & Eberts, 1990). Pubic capital plays an important role in regional economic growth because it provides such goods and services as highways, bridges, sewer systems and water treatment facilities which can be viewed as inputs in the production (Meade, 1952). Helms (1985) and Garcia-Mila and McGuire (1987) find that capital expenditures on highway have a positive and significant effect on state personal income. Mera (1975) and Costa et al. (1987) examine the effect of capital stock, instead of capital expenditures, on the manufacturing, and find it to be positive. Several other studies also find the positive relationship between public capital and production output at the regional level (Eberts, 1986; Deno, 1988).

The literature explaining the demand for local public infrastructure is more extensive. Determination of the level of public investment (or capital stock) usually follows the median voter model with the additional characteristic that public goods not only are consumption goods that enter the utility function, but also influence personal income growth through the production function. Based on this insight, Duffy-Deno and Eberts (1989) derive a model that links the capital stock and investment. Empirical studies, Borcherding & Deacon (1972) for example, consistently find large and statistically significant income elasticity for some form of public expenditure such as highway and water-sewer.

Finally, the simultaneity between public capital investment and income is addressed in Duffy-Deno and Eberts (1990). Comparing the OLS and 2SLS results for their model, they conclude that simultaneity is found for the public investment variable but not for public capital stock.

2.5 Debt Affordability Models in State Governments2

1 For a more complete overview of growth models, refer to Barro & Sala-i-Martin (2004). 2 This section is based on the discussion in Bartle, J. R., Kriz, K. A., & Wang, Q. (2006), which will be later referred to as BKW.

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Debt capacity and debt affordability are two closely related concepts that are frequently mentioned by debt studies in “measuring the ability to handle debt” (Hildreth & Miller, 2002, p.100). According to Hildreth (2005), debt capacity is “the amount of financing that may be issued by the State within legal constraints without overextending the State’s ability to repay its obligations. Debt capacity is a measurement of the extent of additional debt that can be issued in the future given the State’s existing debt level” (p. 17); whereas “debt affordability refers to the burden associated with repaying debt.” Similarly, Ramsey and Hackbart (1996) defines debt capacity as “the level of debt and /or debt service relative to current revenues (or debt ceiling) that an issuing entity could support without creating undue budgetary constraints that might impair the ability of the issuer to repay bonds outstanding or make timely debt service payments (1996). “To be affordable, the repayment of debt should not cause a jurisdiction’s tax rate to increase to uncompetitive levels in order to cover the debt service, nor should the repayment of debt negatively impact the provision of ongoing public services” (Hildreth, 2005, p.17). Their article intends to answer the debt affordability question: “how much debt can government afford?” by establishing a model that includes the consideration of uncertain future revenue and expenditure, but debt capacity also serves as a means to explain the debt-related issue. Political and legal factors however, are not primary concern of their article. While a significant body of literature on “how much debt is right” exists for private sector (Piper & Weinhold, 1982), much less research has focused upon the measurement of the optimal debt levels for state and local governments (Bernard, 1982). Debt affordability is typically estimated in either one of these two types of comparison or a combination of the two: one is comparing debt level to some indicators of itself—debt ceiling approach and the other is comparing debt level to that of others—benchmarking approach. In the former, a dependent variable that indicates debt capacity, usually debt outstanding or annual debt service is contrasted against indicators such as revenue, personal income, population, property value or historical debt (Ramsey, Gritz & Hackbart,1988, p. 231) A mandatory ceiling, based on experts’ recommendation or policymakers’ judgment, is then set to regulate borrowing. In a benchmarking approach, agencies first select a “bench” to compare with, such as national median or the median of a peer group, and then calculate debt capacity according to this “bench”. A third approach is regression, usually incorporated with time series elements. Each of the methodologies described above can be further divided into subcategories which modify the original model in a certain way or focus on a specific aspect of the original model. Ramsey, Gritz & Hackbart (1988) conducted a survey of debt capacity measures in twelve states. But as pointed out by Hildreth and Miller (2002), the currently used methods to assess debt capacity are largely inaccurate, biased and unsatisfactory. They discuss some of these deficiencies in their paper and conclude by saying “the ability to afford capital requires more empirical study, not just the indiscriminate application of normative debt capacity rules” (p.113). They also suggest that the effect of public capital investment be further investigated. This dissertation is an effort just in that direction.

III. Theory

3.1 General overview

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To develop a theory of public debt, it is important to first understand the real role that debt plays in state and local economy. In essence, the possibility to borrow provides state and local governments with the ability to adjust the costs for funding the expenditure, especially capital expenditure, to an optimal level, given that both the costs of tax and borrowing are known to the administrator. In other words, governors choose a debt level (or debt/capital outlay ratio) at where marginal tax cost equals marginal debt cost (all- included true interest cost). Under current law, the financing of the expansion of the state and local capital stock undoubtedly will rely on both bond proceeds and on current tax revenues. Debt constitutes an alternative source of finance and it is clear that without the debt alternative, governments will have to rely solely on tax revenues and it follows that the costs for capital investment will rise substantially, making some capital project impossible to happen. Studies have shown that underinvestment in infrastructure will hurt the economy. This is especially true when taking account of the fact that the costs of state and local bonds are relatively low thanks to their tax exempt status. As the analysis of this dissertation is going to show, contrary to what many believe, too little debt is equally harmful to a jurisdiction as too much debt is.

Three assumptions need to be made before setting up a theoretical framework for analyzing the relationship between debt, economic growth and capital investment. First, government is assumed to be well-informed and responsible, and it will make a financing choice between tax and debt that will minimize the costs to the median voter in the jurisdiction. Second, with respect to its economic function, government is also assumed to think of achieving better economic performance as its ultimate goal and do everything it could to maximize the economic growth of the jurisdiction. This is a debatable yet very important assumption for this paper. In the past, several assumptions regarding government’s borrowing behavior have been made, such as minimizing default risk, weighing the electoral costs and benefits of debt financing (Ellis & Schansberg, 1999), among others. It is my opinion that all these assumptions from previous literature are of lower level and each of them focuses on only one specific aspect of government’s behavior about debt. This analysis will stand on a higher ground that will bring together all other assumptions. If we classify a government’s functions into several areas and one of them is economic, it is quite safe to assume next that all a government does is to achieve better economic performance, e.g. higher GSP growth rate, higher income per capita, lower employment rate, etc. A better economy will definitely reduce the jurisdiction bond default risk and it will also help satisfy politicians’ interests in pleasing their voters. Whether to borrow or not to borrow and how much to borrow is essentially a financial decision, not a political one, therefore standard economic theory on administrators’ maximization or minimization can be applied to the analysis of debt. Lastly, it is assumed there is a median voter who makes decisions on debt by maximizing his or her utility subject to budget constraint, after having been informed of all relevant information.

3.2 A model of borrowing cost

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The jurisdiction’s decision on bond or tax financing depends on the marginal cost of bond and tax finance. A wise and responsible governor should choose to borrow or increase tax where the price of an additional dollar of bond exactly equally and that of additional dollar of tax. In recent years, a large body of literature has focused on the cost of borrowing, largely taking the true interest costs approach (details in chapter 2). In general, these studies suggest that borrowing cost facing the ith jurisdiction is positively related with such factors as outstanding level of general obligation (GO) bonds, revenue bonds(Capeci, 1994, Hendershott & Kidwell,1978), but negatively related with credit rating and financial certification (Kriz 2000, Peng, 2000). Economic variables such as income, income to debt ratio and growth rate in per capita income are also used to explain the borrowing cost for a jurisdiction in some studies. Leonard (1983) finds that both the coefficient for income/debt ratio and that for the growth rate have negatively significant impact on borrowing cost. For the purpose of this analysis, the borrowing cost

on its GO ( ), per capita personal income 3, and other factors can be written as a function4:

(1) where , and

The vector includes all other issuer and issuance characteristics other than current debt

that affects the jurisdiction’s borrowing costs. Specifics about will be presented in the chapter of estimation.

Most researchers assume that borrowing cost is a linear function of debt level (Temple, 1990) and personal income (Kriz, 2000; Peng, 2000). This linearity predicts that as the debt level goes up, the interest rate tends to go up as well. As described as is, the debt level here is in absolute terms, not in relative terms. Hendershott and Kidwell (1978) posit a relative supply theory about bond issuance and conclude that when the supply of municipal bonds increases in one particular state, higher yield is needed to attract more investors to buy the bonds. Therefore, the debt level, even without taking its relative weight to the jurisdiction’s economy size into account, can have a positive effect on the jurisdiction’s borrowing cost. The absolute economic size as measured by per capita income is predicted to have a negative effect on borrowing cost, because income can serve as a good indicator of the taxpayer’s ability to pay (income tax accounts for a large part of state and local government revenue). So the higher the jurisdiction’s per capita income is, the lower the possibility that the jurisdiction will default or defer payment on its bonds, and consequently the lower interest cost for its bonds. Specified this way, the borrowing cost function can be written as5

(2) ,

3 The level of per capita income is used here, but the growth rate of income will be introduced in the dynamic function. 4 The derivation used here is similar to Temple (1994).5 Parameters e and f are assumed constant across jurisdictions. The subscripts on r, hI and Z are dropped for simpler notation.

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where = level of current capital outlay Y = per capital personal income

= level of current capital outlay funded by debt (or )

= a function of other factor that influence borrowing cost

Related literature also reveals there might be a simultaneous relation between the level and the cost of borrowing, and that is exactly why state and local governments can’t issue bonds at a given market rate. The existence of endogenous borrowing costs and the fact that interest costs rise with the amount of bonds issued make it possible to determine a unique optimal share of debt against tax financing for each jurisdiction, given that the costs of tax are also known to the decision maker. This dissertation will take this simultaneity issue into account by explicitly including a function of borrowing cost into the estimation.

3.3 A model of debt level

Temple (1990) assumes that the official chooses the debt share that minimizes the median voter’s price of the jurisdiction’s capital expenditure, therefore the price P of a dollar of public capital expenditure I in period one to a representative resident in the jurisdiction can be written as:

(3)

where h = the share of bond-financed capital spending = the net cost (after deductibility) to the individual of each dollar of tax-

financed expenditure; = the net cost facing the individual in period 2 of a dollar of tax-financed

expenditure; = jurisdiction i’s cost of borrowing, where = ( , ); and

= the discount factor used to calculate the present value of individual’s future tax liability due to the debt finance.

Equation (2) stands for the average cost of a dollar of capital expenditure to the individual. Setting the marginal cost of debt equal to marginal cost of tax, without specifying the functional form of , we get:

To determine the optimal debt share , it is necessary to specify a particular function form for i’s jurisdiction’s borrowing cost. Following Temple (1994) and others, this function is assumed to be linear and can be written as (2). Equation (2) captures the fact

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that cost of municipal borrowing will increase as the level of borrowing as well as other factors increase. Substituting (2) into (3), taking first derivative with respect to and setting it equal to zero, we get the optimization solution for

(4)

Through comparative static, equation (4) generates a set of testable hypotheses

a) the level of state and local capital outlay I (-),b) the other cost of borrowing factor Z (-)c) the rate of discount D (+)d) the per capita income Y (+)e) the current tax price (+)f) the future tax price (-)

Optimal debt share is negatively related to the investment level I. An increase in

investment I will increase the borrowing cost r (from equation (3)) and consequently reduces the debt level. In the above analysis, all variables but h are assumed to be exogenous, but it might be the case that the debt share itself is a function of investment I, through their relationship with borrowing cost r. This possible endogeneity might be responsible for the predicted negative relationship between the debt share and the level of capital investment. Eberts and Fox (1992) posit that the optimal debt share (the share of total city funds obtained through borrowing in their paper) will increase with the level of capital investment due to the concerns of the residents for tax-smoothing. In this dissertation, this problem will be avoided because the possible endogeneity will be controlled for by explicitly including an equation for borrowing cost and an equation for investment level into a simultaneous system. As specified in equation (1), the cost of borrowing will increase as the level of G and other factors Z increase. As a result, the other factors vector Z as a whole is predicted to have a negative impact on debt level. It is important to mention that specific factor(s) in Z may or may not follow the predicted sign for Z vector as a whole, because the specific functional form is undecided. Higher discount rate D means that the current debt burden will become smaller to the resident in the future, so the resident prefer more and more debt financing in the current period as D increases. The personal income Y has a positive impact (since q < 0) on debt share. This indicates that when a jurisdiction’s per capita income raises, it will rely more on debt to finance capital project. This happens probably because higher per capita income will reduce borrowing interest costs and therefore make borrowing a more attractive financing method as compared to taxing. Finally, residents who pay a higher tax price are expected to prefer postponing their tax liability until future, so higher tax price will positively influence debt share; on the contrary, residents facing higher future tax price

would rather pay more tax now than in the future, resulting in a lower debt share.

It should be noted that (4) can be rewritten as

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(5)

where equals level of current capital outlay funded by debt ( ) for the jurisdiction, after an optimal debt share has been chosen.

This equation suggests that once the current, future tax prices, discount rate and other issuer and issuance characteristics are fixed, there exists a unique debt level that minimizes the price of public capital expenditure P for the jurisdiction. The public investment I is assumed to be exogenous in equation (4) and (5), but studies show that this might not be the case. So we now turn to look at the determinants of I.

3.4 A model of public capital investment

Following Temple (1990), the analysis of the determinants of public investment will adopt a median voter model.

In a particular jurisdiction, a median voter’s utility function is written as

(6)

where K = the flow of services from the accumulated capital stock possessed by states and localities. The capital term in the utility function is equal to

, where I is the level of current capital expenditures,

d is the depreciation rate, and is the level of the capital stock in the previous period.

E = the level of state and local current non-capital expenditures, including service on debt.

X = a composite bundle of private and federal goods and services consumed by the individual.

The individual chooses the amount of each good to consume by maximizing utility subject to both the government’s and his or her own budget constraint. The individual’s budget constraint is written as

(7) where

and where

Y = the individual’s pre-tax income, = the price to the individual of a dollar per capita capital expenditure

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= the price to the individual of a dollar per capita current expenditure

= the price to the individual of a dollar of the composite good.

The government’s budget constraint is as follows

(8)

where T = total tax revenue

hI = the total proceeds from GO bonds F = grants

E = current expenditure I = capital investment

Since the per capita tax revenue T = = , and from (7) we get

, so the combined budget constraint of individual and government is

(9)

The median voter maximizes utility subject to the combined budget constraint. Assuming a Cob-Douglas utility function and the optimal debt share has already been decided, the problem becomes

Maximize

Subject to (9):

Substituting (4) into (9), setting the first derivatives equal to zero and solving for I

(10)

Some of the economic factors that influence the level of investment, as indicated by the comparative statics, are as following

a) the per capita personal income Y (+)b) the intergovernmental revenue F (+)c) the size of the capital stock in the previous period (-)d) the rate of discount D (+)e) the future tax price (-)f) the cost of borrowing factors Z (-)

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The desired public investment level that maximizes a median voter’s utility is a positively related to personal income. Higher per capita personal income will raise tax revenue, so it will make the jurisdiction able to make more investment in infrastructure. Additionally, higher income may also call for more investment in public infrastructure. Increases in intergovernmental revenue will also increase the investment level, because even if the intergovernmental revenue may not be directly used to fund infrastructure, it may still lead to higher investment level due to substitution effect. Last one period’s capital stock has a negative impact on current capital outlay. This is so probably because the more the existing capital stock in the previous period, the less likely the jurisdiction need for more investment in the current period. Future tax price is negatively related to public investment level for the same reason as described earlier. Finally, other variables such as D, and those included in the Z vector influence the investment level through their effects on the debt share. Some studies show that the investment level I rely on infrastructure needs as well as the cost of capital investment, but not on debt share or method of financing. This is similar to the statement that the market value of any private firm must be independent of its capital structure (Miller, 1977). Temple (1990) doesn’t have debt share in her derivation of I , but she then includes it in the estimation. Her findings show that the debt share variable is insignificant in the determination of investment level.

3.5 A model of economic growth and public investment

Personal income Y is routinely used in growth models as an independent variable standing for outcome. Solow-Swan and Ramsey models serve as example. It has also been found to be a significant determinant in a variety of models attempting to explain borrowing costs (Kriz,2000; Peng, 2000, p.49 )and regional capital investment (Deno & Eberts, 1991), but very few of them consider income, investment and borrowing costs together. Even fewer are the studies that link personal income to debt. Deno and Eberts (1991) use a simultaneous system to explain the relationship between income and investment at local level, but they ignore the problem of debt; Temple (1990) finds the simultaneity between debt share and investment at state level, but she assumes personal income is exogenous in the system. Existing literature seems to suggest that economic growth (measured as personal income per capita), public capital investment, debt (debt level or debt share) and borrowing costs are all interrelated. For the first time, this dissertation attempts explore these four variables together in one system. In addition, most current literature analyze state and local economic problem in a static framework, but this may not be appropriate since the time elements of economic activities are not taken into account. To address this deficiency, my dissertation develops a model for regional economic growth using a dynamic approach.

In a neoclassical macroeconomics with endogenous growth, assuming the government purchases of goods and services, G, enter into the production function as

15

pure public goods, the function for aggregated outcome, Y, is written as (Barro & Sala-i-Martin, 2004, pp. 24-26)

(11)

where = the flow of output produced at time t = capital investment = labor input = technology = time

The total capital investment at time t can be written as

where = private capital investment at time t

= government capital investment at time t

= private capital investment at time t

= government capital investment at time t From previous notation

= where

(11) becomes

(12)

Now define the jurisdiction’s public investment rate at time t, as

(13)

Let denote the net increase in output : . must be a function

of , and t, so

(a)

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Now consider a time period T, during which the output would increase from its

initial value to its maximum value , or

(b)

Max (c)

The question at hand now becomes: under (a) and (b), find a that satisfy (c). This is

equivalent to its dual problem: when , minimize T. For simplicity, we set T=1 (year), so

, (e)

(f)

Summarizing, our objective is to find a that minimizes at every point of time, under the conditions (a) and (e). This problem can be solved by constructing a Hamiltonian function6:

(g)

Solving for to find an optimal control path , we get

(h)

It is necessary to specify the function in (a) so as to derive the relationship between

and Y (t). First, we define the relative growth rate of output as . If the

private investment at time t, is held constant, the relationship between the public

investment rate u and relative growth rate of output can be approximately described as follows. When u is relatively small, will increase as u increases, because increase in the public investment will improve the infrastructure such as highway, sewer system, etc. and therefore facilitate economic growth; when u is relatively large, however, over-investment in infrastructure may occur, and government spending on other non-capital projects will fall (hurting other government functions that may help economy grow), as a result, will decrease as u increases. It is most helpful to think about the two extremes: suppose for now there is no private sector in the economy, if the government invests nothing in capital infrastructure for a certain period t , u = 0 (suppose this period is

6 For a discussion of Hamiltonian function, please see Chiang & Wainwright (2005).

17

sufficiently long that the flow of services from past capital investment can be neglected), the economy of the jurisdiction will stop growing or even gain a negative growth, because the economy relies on such essential publicly provided goods as road, electricity, water, etc. to function healthily; conversely, if the government invests all of its revenue in the infrastructure , the economy will also stop growing or even worse, other the producing and other sections of the economy will have little resource as input. With the private sector in the economy, things may look differently, because, for example, private firms may assume some of the government’s functions such as building roads, producing tap water, etc, but the government investment will still exhibit the same basic pattern as described above, just on a smaller scale. This analysis here is analogous to the Golden Rule of Capital Accumulation first introduced by Phelps (1966). It is believed that this concave pattern of saving described by Phelps not only is valid on consumption, but also on the economic growth through its effects on consumption. Having laid that groundwork, we can now write out the simplest form of function that complies with the pattern of Golden Rule: (i)

where a and b are constant and positive

(i) implies that (j)

Substituting (j) into (h) gives

(k)

The solution for (k) is

, (l)

This solution implies that if a benevolent social planner is ever to choose a u to maximize

growth rate for a certain period t, he or she would choose , and the growth rate

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achieves its maximum at . In addition, the minimum time T needed for to

grow from to is found at .

Substituting into equation (j), we get

(14)

To maximize (14) is equivalent to maximizing (12) if we differentiate both side of (12) with respect to t, and from (l) we know that the maximum value of can be found at

.

If we substitute into (14), we get

(15)

Although the specific function of (12) is not derived here, we are already able to generate a set of testable hypotheses based on (12) and (15), and on standard macroeconomic theory as outlined in Barro & Sala-i-Martin (2004)

a) the government long-term debt (+)

b) the government long-term debt squared (-)

c) the previous period per capita personal income of Y (-)d) the per capita labor input L (+)e) the per capita private capital (+)7

The optimal control model for public investment and economic growth rate certainly draws on a set of assumption, but the model and some of the assumptions will be put to test by the data.

Many macroeconomic models assume a non-distorting lump-sum tax to simplify the analysis, but in reality US is using a progressive or regressive tax system which is always distorting. The possibility of issuing debt not only makes it possible for public investment to adjust to its optimal level, but also helps keep tax rate low—and consequently reduce its negative impacts on economic growth. As a mediator, debt itself may have no direct relationship with local economy, but it affects the economic growth through two devices: 7 Here we adopt a Solow-Swan model which assumes positive and diminishing returns to private inputs.

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public investment and tax. As shown earlier, public investment rate—and therefore the debt and debt share, may exhibit a quadratic relationship with growth. But the impact pattern of tax is not clear. For now, it is possible to assume that taxes are distorting and have linearly negative effects on the economy. So it’s possible to add another hypothesis to be tested:

f) the tax rate(income and property) T (-)

3.6 The simultaneous equation system and hypotheses

From above analysis, we obtain a set of four-equation system that will be estimated in the next chapter. Hypotheses generated from these equations will be tested. For simplicity, the equations are presented only with endogenous variables; exogenous variables for each equation are denoted as , , , respectively . Details about these

exogenous variables will be discussed in the chapter of estimation.

1) Debt level equation:

= (Y, )

2) Cost of borrowing equation:

r = r ( , Y, )

3) Public capital investment equation:

= (Y, r, )

4) Economic growth equation:

= ( , , , Y)

5) Identity based on equation (9)

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IV. Empirical Research

4.1 General Procedure

This dissertation will adopt both cross-sectional and panel data framework. The rationale behind the cross-sectional framework is threefold. First, it is my belief that the general pattern of regional economic growth rate and debt of probably is not going to change over time. It is show in the derivation of the model, the quadratic relationship between economic growth and debt actually stems from the quadratic relationship between saving rate (or investment rate) and economic growth. As long as the latter pattern doesn’t change over time, we have no reason to believe that the former will change. If this is the case, a multiple-year pooled cross-section data will provide such good features as increased sample size, more precise estimators and test statistics with more power (Wooldridge, 2006, p. 449). This is especially true when taking into account the fact that many states maintain a very low borrowing level and only a few states has a significant debt burden. If we don’t pool the historical state data together, the predicted quadratic relationship between debt and economic growth may not be found. Second, a cross-sectional framework is superior to time-series in explaining the cross-state variations. In terms of their borrowing behavior, states are very different from one to another. Some have tighter restrictions on borrowing than others, some issue more revenue bonds instead of general obligation bonds, so on and so forth. In addition, as suggested by some researchers, the bond markets in the United States are segmented: many state and local bond issues are marketed in local or regional markets and bonds issued by jurisdictions within a state are viewed as closer substitutes by an investor than an in-state and an out-of-state bond (Hendershott and Kidwell, 1978). Therefore, it is of interest to investigate the cross-sectional differences between states. Last, some previous studies on debt and public investment have also adopted a cross-sectional framework. These studies include Cunningham8 (1989) and Temple (1990).

On the other hand, the changes over time can not be neglected. Many important variables that will be used in the estimation, such as economic growth rate, public investment, etc., are serially correlated in nature. Tax reforms like TRA 86 has had a huge impact on state and local borrowing pattern, so failure to include the time elements in the estimation will significantly impair the explanatory power of the model. The most appropriate method to capture both the cross-sectional differences and the changes over time is the panel data approach. Capeci (1991), for example, uses a panel data set to study the credit risk and bond yields. It is especially informative to compare the results from both approaches.

4.2 Estimation Model

For the most part, the variables included in the estimation follow the equations developed in Chapter 3. To determine the other independent variables through ,

8 He also conducts a time-series analysis in the same dissertation.

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this research draws on a variety of studies. Among other, Cook (1982), Kriz (2000) and Peng (2000) survey the independent variables that are used to determine default risk and borrowing costs for municipal bonds; Temple (1994) studies the determinants of state and local borrowing (debt share in her paper); Duffy-Deno and Eberts (1990) provide clues for the independent variables to be used in a simultaneous equation system explaining public infrastructure and economic growth.

(1) Debt equation

totalltdoutffc = capout, cpi, totalltdissng, lnpersinc, igr, genrev, spenlim, Capst_1, taxes

where

totalltdoutffc = total long-term full faith and credit debt outstanding capout = per capita capital outlay (-) cpi = consumer price index (+) totalltdissng = total long-term debt issue non guaranteed (+) lnpersinc = log per capita personal income igr = per capita intergovernmental revenue (-) genrev = per capita general revenue (-) spenlim = a binary variable of spending limit (-) Capst_1 = last one period of per capita capital stock (-) taxes = state per capita taxes (+)

(2) Borrowing costs equation

r = r ( , Y, Issue size, credit rating, bond insurance, maturity, call provision, bank qualification, tax status, general interest rate, interest rate volatility, number of bids, income/debt ratio, income, GSP change, relative supply)9 (see Kriz, Peng, p.182)

(3) Public investment equation

capout = lnpersinc, igr, totalltdoutffc, taxes, Capst_1

where

capout = per capita capital outlay lnpersinc = log per capita personal income (+) igr = per capita intergovernmental revenue (+)

totalltdoutffc = total long-term full faith and credit debt outstanding (+) taxes = state per capita taxes (+)

Capst_1 = last one period of per capita capital stock (-)

9 Due to data availability, this equation is not going to be estimated in the simultaneous equation system, but some of its elements are incorporated in the other three equations.

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(4) Economic growth equation

lnpersinc= unem, ltdebtsqu, totalltdoutffc,age1865,capout,Capst_1

where lnpersinc = log per capita personal income (+) unem = unemployment rate (-)

ltdebtsqu = long term debt (totalltdoutffc) squared (-) totalltdoutffc = total long-term full faith and credit debt outstanding (+)

age1865 = percentage of population between 18 and 65 (+)capout = per capita capital outlay (+)

Capst_1 = last one period of per capita capital stock (+)

4.3 Data and Descriptive Statistics

Instead of using the debt data from each issuing entities, I aggregate the state and local borrowing levels within each state so as to explain the interstate difference in total state and local bonds issued. The unit of observation is per capita borrowing for each state. This is consistent with the method used in Feldstein and Metcalf (1986), and Temple (1990). A potential weakness of this aggregated state data is the loss of heterogeneity within states. Since we are more interested in the interstate differences, and more importantly, the borrowing activity by some local government is actually carried out by the state, it might be more appropriate to use the state aggregate data.

Data to be used in this dissertation come from various sources. Many demographic and economic variables are available from U.S. Census, U.S. Bureau of Economic Analysis, or other U.S. departments; data of private sector are obtained from Federal Reserve Bank at St. Louis; information on bond issues is collected from the Securities Data Company. Information on municipal bond issuance is from the Securities Data Company.

To obey the law of parsimony, I use as few variables as possible. The descriptive statistics is presented in the following table:

Variable Obs Mean Std. Dev. Min Max

lnpersinc 902 9.505419 .1828811 9.057997 10.0531unem 861 6.498606 2.123177 2.4 18ltdebtsqu 902 9.41e+12 2.77e+13 0 2.58e+14totalltdou~c 902 1865802 2435420 0 1.61e+07age1865 902 .6108336 .0199096 .5458851 .6557377capout 1347 223.2147 151.53 32.73 1803.66Capst_1 1300 5454.072 3926.04 148.68 32647.38cpi 902 117.1591 30.53942 60.6 163

23

totalltdis~g 902 730164.3 1162723 0 1.00e+07igr 902 440.1211 152.9914 183.2218 1164.703genrev 902 1749.048 1096.98 825.1176 12867.75taxes 1200 1148.66 594.2977 235.84 6316.4

spenlim 902 .1718404 .3774509 0 1

4.4 Pooled Cross-sectional Analysis

As Wooldridge (2006, p.449) points out, estimating a pooled cross sectional dataset with OLS raises only minor statistical complications. To account for the possibly different distributions in different years, a year dummy will be added to the model.

The model that will be estimated in this dissertation is a simultaneous system with four endogenous variables and a number of exogenous variables. As outlined in Wooldridge (2006), Green (2008) and Gujarati (2003), the OLS method is not appropriate for estimating such a simultaneous equation system, because the error term in on equation is generally correlated with the other endogenous variable(s) that is/are included in that equation as explanatory variable(s). To correct for this simultaneity bias, 2SLS method is called for. The 2SLS method basically address the simultaneity bias by first predicting the value of each endogenous variable with the whole set of included exogenous variables as instruments and then estimating equation with the predicted value of endogenous variables by OLS. 3SLS, which is a system method of estimation (Green, 2008) will also be applied. According to Green (2008, p.383), 3SLS is generally superior to 2 SLS for it is asymptotically efficient whereas 2SLS is not; but there are cases where 2SLS is more favorable (Wooldridge, 2002, pp.198-199). Therefore, compare the results from 2SLS and 3SLS will provide a more complete picture. The rank-order condition is assumed to be met because a relatively large number of exogenous variables will be included in the system. The endogeneity has been tested by Hausman test.

Applying 3SLS with STATA, I obtain the following estimates for the three equations. Z scores are reported in parentheses.

(1) Debt equation

D = 7.93 – 149604.1 capout + 6615.0 cpi + .04 totalltdissng + 1.1e+07 lnpersinc (-3.27) (-8.15) (0.5) (0.34) (3.12)

+ 6150.3 igr – 72.1 genrev + 204602.4 spenlim + 2279.8 Capst_1 + 17355.4 taxes (2.13) (-.14) (.57) (5.64) (7.08)

N=861 = -14.85

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(3) Public investment equation

I = -732.56 + 74.8 lnpersin +.04 igr – 6.6e-06 totalltdoutffc +.117 taxes + .02Capst_1 (-3.30) (3.14) (2.32) (-12.67) (15.18) (20.98)

N=861 = .78

(4) Economic growth equation10

Y = 7.92 - .02unem – 6.38e-15 ltdebtsqu + 1.06e-07totalltdoutffc + 2.45age1865 + (44.47) (-10.43) (-5.59) (7.03) (8.04)

+7.7e-03capout -9.46e-06Capst_1 (9.31) (-3.34)

N=861 = .62

Heteroskedasticity and autocorrelation-consistent estimates:

Y = 7.26 - .03unem – 2.19e-15 ltdebtsqu + 5.22e-08totalltdoutffc + 3.70age1865 + (70.07) (-15.42) (-11.27) (20.01) (21.87)

+4.4e-04capout -3.84e-06Capst_1 (7.90) (-1.90)

N=861 = .74 F =331.65

A C test was conducted and the endogeneity was found for the three dependent variables, all significant at very small confidence intervals, but the overidentification test suggests that there might be more endogenous variables in the model. This problem, however, will probably be fixed when the borrowing cost equation is incorporated to the system.

4.5 Panel Data Analysis

10 Heteroskedasticity was detected and the second equation reported the heteroskedasticity and autocorrelation-consistent numbers using the 2SLS method (ivreg2, robust command in STATA). These numbers are just slightly different from 3SLS estimates.

25

Panel data analysis is gaining popularity in empirical studies because it has some major advantages over purely cross-sectional or time-series datasets. As Hsiao (2003, p.5) summarizes in his book, panel data give a researcher a large number of data points, thus increasing the degrees of freedom and reducing the collinearity; panel data set allow a researcher to capture more complex patterns that can not be addressed by other data set; and panel data can eliminate the effects of any missing variables that are correlated with explanatory variables. Data on state governments are panel data by nature (and usually a balanced panel data), for this reason a panel data analysis will be conducted so as to capture cross-sectional as well as time varying effects of some of the key variables in the model. A panel dataset is typically analyzed by either the fixed effects (FE) approach or the random effects approach (FE), or both. According to the discussion in Wooldridge (2006), fixed effects estimation should be used when we assume that the unobserved effect is correlated with each explanatory variable; conversely, if we assume the unobserved effect is not correlated with any of the explanatory variables, random effects estimation should be used. The key difference between random and fixed effect estimation is whether or not allow observations of each time period (usually a year) to have a different intercept. For a fixed effects approach, the first step is to transform the panel data into a time-demeaned data by subtracting its mean from each variable and then estimate it by a pooled OLS estimator. For a random effects approach, GLS estimation is needed because the composite error terms in each period are serially correlated. In the present research, many key variables such as income, growth rate, debt level or debt ratio, etc, are all time-varying; additionally, there is no reason to believe that any unobserved effect is uncorrelated with the explanatory variables in the model. As a result, fixed effects approach might be more appropriate. In fact, FE is widely thought to be a more convincing tool for estimating panel data set, because it allows arbitrary correlation between unobserved effects and independent variables, while RE does not (Wooldridge, 2006, p. 497). In this study, both RE and FE will be implemented for comparison purpose; will be reported and a Hausman test will also be conducted. When panel data are combined with simultaneous equation, more complications arise. Assuming there is no identification problem, two methods can be used to estimate the model: the purged-instrumental-variable method and the maximum-likelihood method11. The former consists of two steps: the first is to eliminate the unobserved effects from the equation of interest using the fixed effects transformation and the second step is to find proper instrumental variables for the endogenous variables in the transformed equation (Wooldridge, 2006, p. 571). Unlike in the cross sectional setting, instruments needed here must change over time for convincing analysis. This can be a very challenging task and when no good instruments are available, one has to rely on maximum-likelihood method, which is efficient, but more complicated in computation.

Since the STATA does not have a command for estimating 3SLS with the panel data for panel data, I use the 2SLS panel data command “xtivreg” instead. Both fixed effect

11 These two methods are proposed by Chamberlain (1977) and Chamberlain & Griliches (1975), respectively. For more complete discussion, see Hsiao (2002), pp. 129-140.

26

and random effect are estimated for the equation of main interest—the economic growth equation. Results are presented as follows. (Dependent variable is log per capital personal income.)

Fixed Effects Random Effects

Coef. Z Coef. Z

totalltdoutfcc 4.78e-08 11.94 4.95e-08 13.25 unem -.02 -21.27 -.02 -21.37 ltdebtsqu -1.86e-15 -7.54 -1.94e-15 -8.20 age1865 3.99 17.38 3.86 18.00 capout 4.32e-04 17.61 4.26e-04 17.77 Capst_1 6.65e-06 1.79 5.56e-07 0.23 _cons 7.02 47.94 7.13 53.21

N = 861 : within = .78 N = 861 : within = .78 =0.77 Between = .64 =0.74 Between = .70

F =53.66 Overall =.68 F =53.66 Overall =.73

4.5 Discussion

An important finding from these estimates is that, as predicted, state and local long term debt does appear to have a quadratic relationship with economic growth as measured by per capita personal income. Based on this sample, a single maximum debt level can be calculated. This is theoretically as well as practically useful, because this suggests a new way of measuring debt capacity for public finance managers. Other variables in the economic growth equation largely bear the signs as predicted in the previous chapter. The human capital, as measured by population of age above 18 and under 65 has a large and very significant impact on regional economy. The public investment as measured by capital outlay is also significant and positive, as expected. Besides the unemployment rates have negative effects on the economy, which is also consistent with theory. The last one period capital stock variable needs more discussion. It is significant at 1% level in the 3SLS estimation, but when the model is corrected for heteroskedasticity, it is only significant at 5% level. More importantly, its negative sign is not as predicted. In fact, this strange behavior of public capital stock has been found in previous empirical works. Some author use current capital stock, other use lag(s) of capital stock, but the results remain the same. A possible explanation is that while the overall capital stock is not significant, the individual items of capital stock, such as capital stock in highway, utilities, etc, can be very significant and positive. Compare the

27

3SLS results with the robust results, the estimates of coefficients are about the same, but generally more significant, with exception of capital outlay and capital stock variables.

Although this paper focuses on the economic growth equation, some variables in the other two equations are also of interest to explain. The debt equation may not be well defined, because the R square turns out to be a negative number when estimated with 3SLS. This is probably due the omission of the borrowing cost equation. It is worth noting that, as expected, both income and taxes have positive effect on debt. In fact, these two variables are routinely used as indicators of a jurisdiction’s debt capacity. The public investment equation provides solid empirical evidences for the theory present earlier. Income has a positive impact on public investment, and so do the intergovernmental revenue, taxes and last period capital stock (if more lags of capital stock are included, this effect may be reversed). It is interesting that debt appears to be negatively related to public investment. When a square term of debt is included, this negative effect is reduced, but will not disappear. This may suggest that worries about borrowing costs may dominate incentives to invest more in public infrastructure. So when a jurisdiction has to borrow money to finance capital project, the level of investment actually drops due to concerns about the increased debt costs. In the contrary, if capital project is funded by tax dollars, people will have no such concerns—this is just why tax has a positive impact on public investment.

The fix effects model and the random effects model of panel data generate very similar results for equation (4). Since we have no reason to believe that the unobserved effect is uncorrelated with each explanatory variable, the fixed effects estimates may be more appropriate in this case. Again, the quadratic relationship between debt and income is found and it is more significant than in the pooled cross-sectional analysis. Other variables are also slightly more significant than before. The capital stock variable now bears a positive sign, but again it is not significant at 5% level.

V. Conclusions and Implications

Empirical results show that debt has a nonlinear relationship with economic growth, and consequently, a unique optimal debt level can be calculated with respect to economic growth. This finding has a lot of practical meaning, especially for measuring a jurisdiction’s debt capacity and determining how much debt it can afford. Moreover, hypotheses are tested with an expanded and updated dataset and found to be consistent with previous literature. By applying the simultaneous panel data method, this paper takes account of the time elements as well as the simultaneity for the first time. When the borrowing cost equation is included in this estimation, the results would be more robust. This also has limitations. First, some variables derived from theoretical framework, future tax price for example, were not included in the estimation due to lack of reliable measure. Second, some variables that are assumed to be exogenous may turn out to be endogenous, as indicated by the C test. Future studies should address this problem by identifying them and include more equations in the simultaneous system.

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