1 Introduction

Virtually all state governments in the USA, unlike the federal government, operate under explicit or implicit balanced budget rules (see Poterba 1995, for a good discussion). Although the submission or passage of a balanced budget is required for many states, the actual budget may well be in deficit. States can use rainy day funds or borrow to carry this deficit forward to future years (Poterba 1995). In this paper, we assess the extent to which state government spending in the USA is influenced by balanced budget rules or forward-looking behavior. Our main contribution to the literature is methodological. As discussed below in the literature review, existing studies’ methodologies may not comprehensively analyze the spending behavior of state governments. We propose and estimate a general intertemporal model of state government spending that allows for habit formation and precautionary saving with asymmetry in balanced budget rules using a panel data framework allowing for heterogeneity among states. Our study adds to the extensive debate about the pros and cons of fiscal or balanced budget rules (see Fatás and Mihov 2006; Canova and Pappa 2005) with new empirical evidence from our more comprehensive analysis of state government spending.

There are two disparate strands of studies that analyze state government spending.Footnote 1 On the one hand, given that state governments are subject to balanced budget rules, there are many studies that examine the effects of these rules on state fiscal policy (see Poterba 1994; Eichengreen and Bayoumi 1994; Bohn and Inman 1996; Sørensen, Wu, and Yosha 2001; Clemens and Miran 2012; Smith and Hou 2013). They are, by and large, based on ad hoc specifications, including a variety of right-hand side variables to explain government spending or revenue. Most notable is a study by Fatás and Mihov (2006), who specify state spending in a log form as a function of gross state product (GSP), lagged spending, and control variables such as the current and lagged value of an index of oil prices and the current inflation rate, as well as a linear time trend.

On the other hand, a few studies on state government spending evaluate the possibility of forward-looking behavior by state governments (Holtz-Eakin et al. 1994; Dahlberg and Lindstrom 1998; Borge and Tovmo 2009). This line of analysis is akin to studies of private consumption wherein consumers are assumed to take an intertemporal forward-looking view in their decisions. This model may be useful for analyzing state government spending, because it allows states to make spending decisions on the basis of their expectations about future resources by borrowing against future revenue to finance current spending. Evidence on intertemporal state spending is mixed, however, and these studies do not necessarily inform on the effects of balanced budget rules. They test for myopic (rule of thumb) or liquidity constraints to see whether government spending follows current resources. State governments, however, may consume their current resources because they are constrained by explicit or implicit balanced budget rules and not because of myopia or liquidity constraints. This implies that there is a distinction between a test of balanced budget rules and of current resources. The test of balanced budget rules is based on a binding legal constraint, but the test of current resources is based on a binding liquidity constraint.

We improve on the empirical work in these various previous studies in several ways by providing a general intertemporal model of state government spending, along with new empirical evidence. First, state governments are often buffeted by uncertain revenue or spending streams. To buffer against these uncertain events, many have rainy day funds (formally known as “budget stabilization funds”) that allow them to save for an unexpected revenue shortfall or to make up for a budget deficit to help stabilize spending over time (Knight and Levinson 1999; Poterba 1995; Fatás and Mihov 2006; Wagner and Elder 2005). The existence of rainy day funds suggests a precautionary saving motive for state government spending, which has not received much attention in the literature.Footnote 2 The intertemporal model that fails to account for precautionary saving is likely to overstate the response of state government spending by an amount related to the uncertainty or risk facing states.

Second, habit formation has been found to be a potentially important explanatory variable for private consumption (Dynan 2000). In the context of state government spending, habit formation might arise as a result of biennial budgeting, which occurs in a number of states (see Snell 2011), or pre-commitments on certain spending items that are costly to adjust in response to revenue fluctuations. This may be due to transaction costs or other costs, like the effort needed to change plans (see Chetty and Szeidl 2016). Habit formation may also arise because of adjustment costs associated with the political process. That is, changes in spending may be difficult to implement in either direction. If so, when the “optimal” choice changes, it can take governments some time to get there. Such an idea relates to a public choice theory called structure-induced equilibrium (SIE),Footnote 3 which addresses the question of how legislatures make decisions. It appears that committee structure is important, but that agenda setters matter, too. Agenda setters (say, key legislative leaders) have power over what proposals can be taken up and create a barrier to change, because new proposals must be superior to old proposals for them. This creates slow adjustments to shocks or rigidities in spending that manifest as what we term “habits.”Footnote 4

Following Hall (1978), Holtz-Eakin et al. (1994) argue that, if state governments behave rationally, lagged spending growth rates should not explain current spending growth, but if habit formation is an important component of state spending decisions, the Holtz-Eakin et al. (1994) procedure is likely mis-specified.

Third, previous studies on government spending hinge on the premise that balanced budget rules (which vary across states in terms of their severity) induce a symmetric response of spending to increases or declines in revenue (Borge and Tovmo 2009). While such rules could be binding in the case of a revenue shortfall, state governments may not mechanically increase spending when they face an increase in revenue. That is, when they face a decline or shortfall in revenue, state governments might have to reduce their spending correspondingly. Alternatively, state governments might increase spending in response to a positive revenue surprise, but seek ways around the rule when there are negative shocks to avoid painful spending cuts. This would be consistent with a ratchet model of state government spending. In these models, governments want to increase spending, but never want to decrease spending. Thus, spending will likely fall much more slowly than revenue, at least compared with the case where revenue is rising (see Watson and Scott 2014). In particular, cutting spending on popular programs that are considered “sacred cows,” such as Medicaid, is hard to do, especially when revenue is declining (Sørensen and Yosha 2001). All of this implies that spending responses to increases in revenue could differ from responses to revenue declines. This asymmetry has not been recognized in many previous studies, but it is important for fully understanding the broader effects of balanced budget rules (which is an objective of Fatás and Mihov 2006).Footnote 5

The existence of balanced budget rules may make it appear odd that we would apply a forward-looking model to states’ spending behavior. We do not assert that the model makes for a literal description of states’ decision making, but we believe that it nonetheless provides a useful framework in which to contextualize the study. A priori, knowing that many states use budget stabilization funds naturally raises the question of a precautionary saving motive. Similarly, prior commitments on spending or adjustment costs associated with the political process might generate spending patterns that resemble the formation of habits. By allowing for heterogeneity across states, the model allows for essential flexibility, as well as the theoretical rigor that we argue is helpful for fully understanding how state governments make their spending decisions.

The proposed model is formulated with the familiar Euler equation of the intertemporal optimization problem in a panel data framework with explicit allowance for heterogeneity of states by incorporating state characteristics, and is estimated with US data on state governments for the period of 1968–2016. The model nests several alternative specifications such as a traditional intertemporal model that previous studies consider, as well as a balanced-budget constraint model with symmetric or asymmetric responses in government spending, an intertemporal model with habit formation and precautionary saving, and a composite model that includes all of these features. Additionally, while many state governments are subject to balanced budget rules, the nature and scope of these rules vary cross-sectionally; hence, we allow for different responses in states with varying degrees of strictness in their balanced budget rules.

Our study, unsurprisingly, does not find evidence for forward-looking behavior in state government spending. In general, balanced budget rules are a significant constraint on state governments. We do find, however, some modest evidence that there are differences among states in how these constraints bind. Those states with fiscal rules imposing tighter constraints exhibit asymmetric responses to changes in revenue. For some groupings, their spending on current operations does not apparently react to declines in revenue, but it reacts significantly to increases in revenue. For example, an increase in revenue of 1 percentage point leads to a rise in current operation expenditure of between 0.7 and 0.8 percentage points, depending on the specification. States with looser restrictions generally also behave as though they form habits in their spending decisions, as spending growth in the previous year is an important predictor of current year spending growth. Precautionary saving is relatively unimportant for most states. When we look at the results over different time periods, we find that responses to spending have tended to become more symmetric in recent years (since 2000) than they were in prior years.

These results allow us to reconsider previous studies of the business cycle effects of balanced budget rules. Fatás and Mihov (2006) find that states with tight balanced budget rules have more procyclical fiscal policies, but they also have less volatile state economic cycles. Canova and Pappa (2005) find that balanced budget rules make little macroeconomic difference for states whether they have tight or loose rules. We find that states with tight and loose budget rules behave differently in response to revenue shocks, but we cannot statistically reject the hypothesis that they behave equally in many cases, in line with the Canova and Pappa (2005) findings. States with tight rules are more likely to behave as though they can avoid spending cuts in the face of revenue declines, even as states with loose rules do not. In particular, for states with tight fiscal rules, these constraints induce substantial procyclical spending, conditional on revenue increases, which may lead to increased local economic volatility in upturns.

2 The theoretical framework

We present a forward-looking intertemporal model of state government spending as a frame of reference to develop an appropriate empirical model to be discussed in the next section. As pointed out in the introduction, while some previous studies on state government spending take this approach (Holtz-Eakin et al. 1994; Dahlberg and Lindstrom 1998; Borge and Tovmo 2009), they are limited in scope and analysis. We assume that states’ intertemporal spending behavior might be treated in a similar manner as that of private consumers, for which there is an increasingly large number of studies in the literature. We draw upon this literature (for a good survey, see Deaton 1992; Browning and Lusardi 1996) and provide a cogent intertemporal model of state government spending within a panel data framework with allowance for heterogeneity of states. While obviously not a literal description of states’ actions, the purpose of this is to provide an idealized baseline against which to compare actual observed government spending behavior.Footnote 6

A representative state government’s within-period utility function is expressed as \(u(G_{i,s}, \varvec{Z_{i,s}})\) with the subscript i indexing states and s referring to time, i.e., year \(s=t,t+1, \ldots ,t+\infty\). \(G_{i,t}\) is state government consumption spending, and \(\varvec{Z_{i,t}}\) is a vector of state characteristics, to be used as control variables. This function is continuous, increasing, and strictly concave in \(G_{i,t}\). We assume that the within-period utility function takes a CRRA form, so the state government’s lifetime preferences are:

$$\begin{aligned} U = \sum _{s=t}^{\infty } \bigg ( \frac{1}{1+\rho }\bigg )^{s-t} \frac{1}{1-\alpha } \bigg (\frac{\hat{G}_{i,s}}{\psi (\varvec{Z_{i,s}})}\bigg )^{1-\alpha }, \end{aligned}$$
(1)

where \(\rho\) is the rate of time preference (assumed to be constant), \(\alpha\) is the coefficient of constant relative risk aversion, and \(\hat{G}_{i,s}\) is consumption spending services. Consumption spending services incorporate the habit formation process, and we assume that the habits of state spending are determined by the state’s consumption spending in the last period. This allows us to represent consumption services as \(\hat{G}_{i,s} = G_{i,s}-\gamma G_{i,s-1}\) where the parameter \(\gamma\) measures the strength of habit formation (Dynan 2000). Habit formation has the effect of relaxing the assumption of intertemporal separability maintained in existing studies on state spending. The index \(\psi (\varvec{Z_{i,s}})\) measures an equivalence scale for states and is parameterized as \(\psi (\varvec{Z_{i,s}}) = \exp (\varvec{\theta ^{\prime } Z_{i,s}})\) where \(\varvec{\theta }\) is a vector of parameters. The scale is intended to capture cross-sectional variation in spending across states that is solely due to differences in population characteristics, and it is needed to bring states of different composition to comparable welfare levels.

In our idealized conceptual framework, there are perfect capital markets so that the state government can freely borrow and lend against future revenue or resources at a given interest rate to finance spending or accumulate assets. The state government faces the following intertemporal financing constraint:

$$\begin{aligned} W_{i,s+1} = (1+r_{i,s}) W_{i,s} + R_{i,s} - G_{i,s} , \quad \forall s \ge t , \end{aligned}$$
(2)

with

$$\begin{aligned} \lim _{T \rightarrow \infty } \prod _{s=t+1}^{T} (1+r_{i,s})^{-1} W_{i,t+T+1} \ge 0 , \end{aligned}$$
(3)

where \(W_{i,s}\) is the state’s net wealth at the beginning of time s, \(r_{i,s}\) is the state-specific interest rate from time s to \(s+1\), and \(R_{i,s}\) is state government revenue or current resources at time s. We allow the interest rate to vary across states because they face different financing or credit conditions. Equation (2) describes the evolution of net wealth over time, while Eq. (3) rules out perpetual debt financing.

The state government’s problem is to maximize

$$\begin{aligned} E_t \bigg [\sum _{s=t}^{\infty } \bigg (\frac{1}{1+\rho }\bigg )^{s-t} \frac{1}{1-\alpha } \bigg (\frac{\hat{G}_{i,s}}{\psi (\varvec{Z_{i,s}})}\bigg )^{1-\alpha }\bigg ], \end{aligned}$$
(4)

with respect to \(\hat{G}_{i,s}\) for all i and s, where \(E_t\) is the expectation operator conditional on the information available to the state government at time t, subject to Eq. (2) with the initial condition on wealth and terminal condition Eq. (3). This gives rise to an Euler equation for the intertemporal allocation of consumption spendingFootnote 7:

$$\begin{aligned} E_t \bigg [ \bigg (\frac{1+r_{i,t+1}}{1+\rho }\bigg )\bigg (\frac{\exp (\varvec{\theta ^{\prime } Z_{i,t+1}})}{\exp (\varvec{\theta ^{\prime } Z_{i,t}})}\bigg )^{\alpha -1} \bigg (\frac{G_{i,t+1}-\gamma G_{i,t}}{G_{i,t}-\gamma G_{i,t-1}}\bigg )^{-\alpha }\bigg ] = 1 \end{aligned}$$
(5)

Under rational expectations, Eq. (5) implies

$$\begin{aligned} \bigg (\frac{1+r_{i,t+1}}{1+\rho }\bigg ) \bigg (\frac{\exp (\varvec{\theta ^{\prime }Z_{i,t+1}})}{\exp (\varvec{\theta ^{\prime } Z_{i,t}})}\bigg )^{\alpha -1} \bigg (\frac{G_{i,t+1}-\gamma G_{i,t}}{G_{i,t}-\gamma G_{i,t-1}}\bigg )^{-\alpha } = 1 + e_{i,t+1} \end{aligned}$$
(6)

where \(e_{i,t+1}\) is the forecast error at time \(t+1\) that is uncorrelated with variables known at time t, with \(E_t (e_{i,t+1})=0\) and \(Var_t (e_{i,t+1}) = \sigma _{i,t+1}^2 = E_t e_{i,t+1}^2\).

The Euler relation in Eq. (6) is nonlinear. Taking natural logs on both sides of this equation and rearranging, we have

$$\Delta \ln (G_{i,t+1}-\gamma G_{i,t}) {}= -\frac{1}{\alpha } \ln (1+\rho ) + \frac{(\alpha -1)}{\alpha } \varvec{\theta ^{\prime } \Delta Z_{i,t+1}} + \frac{1}{\alpha }\ln (1+r_{i,t+1}) - \frac{1}{\alpha } \ln (1+e_{i,t+1})$$
(7)

where \(\Delta \ln (G_{i,t+1}-\gamma G_{i,t})\) is the growth of spending services. We approximate the growth of spending services as \(\Delta \ln (G_{i,t+1}-\gamma G_{i,t}) \approx \Delta \ln G_{i,t+1} - \gamma \Delta \ln G_{i,t}\) (see Muellbauer 1988) and rewrite Eq. (7) to obtain a log-linearized Euler equation for spending growth with habit formation:

$$\Delta \ln G_{i,t+1}{}= -\frac{1}{\alpha } \ln (1+\rho ) + \frac{(\alpha -1)}{\alpha } \varvec{\theta ^{\prime } \Delta Z_{i,t+1}} + \frac{1}{\alpha } \ln (1+r_{i,t+1}) + \gamma \Delta \ln G_{i,t} - \frac{1}{\alpha }\ln (1+e_{i,t+1})$$
(8)

This equation summarizes the conceptually relevant determinants of state spending growth: time preference, anticipated changes in the state’s demographics or circumstances, the interest rate, past spending habits, and unanticipated events. The effect of the interest rate on spending growth measures the elasticity of intertemporal substitution, which is inversely related to the coefficient of relative risk aversion.

Now, if we take a second-order Taylor approximation for \(\ln (1+e_{i,t+1})\) in Eq. (8), we get \(\ln (1+e_{i,t+1}) = e_{i,t+1} - \frac{1}{2} e_{i,t+1}^2\) so that \(E_t [-\ln (1+e_{i,t+1})] = \frac{1}{2} \sigma _{i,t+1}^2\). Substituting this result into Eq. (8) yields

$$\Delta \ln G_{i,t+1} {}= -\frac{1}{\alpha } \ln (1+\rho ) + \frac{(\alpha -1)}{\alpha } \varvec{\theta ^{\prime } \Delta Z_{i,t+1}} + \frac{1}{\alpha } \ln (1+r_{i,t+1}) + \gamma \Delta \ln G_{i,t} + \frac{1}{2\alpha } \sigma _{i,t+1}^2 + v_{i,t+1}$$
(9)

where \(v_{i,t+1} = -(e_{i,t+1}-(1/2)(e_{i,t+1}^2 - \sigma _{i,t+1}^2))/\alpha\) so that \(E_t (v_{i,t+1}) = 0\). Equation (9) characterizes spending/saving decisions for states in the presence of precautionary saving with habit formation. The variable \(\sigma _{i,t+1}^2\) is a measure of uncertainty or risk-facing states that drives the precautionary saving motive. The more uncertainty there is about revenue or spending and the more risk averse states are, the greater is precautionary saving. This leads states to decrease current spending but to increase future spending, resulting in higher expected spending growth. Moreover, the presence (absence) of insurable or diversifiable risk leads states to decrease (increase) their precautionary saving. In fact, federal grants provide some insurance against state-specific downturns (Asdrubali et al. 1996; Sørensen, Wu, and Yosha 2001), decreasing the need for precautionary saving by states. The coefficient for \(\sigma _{i,t+1}^2\), \(\frac{1}{2\alpha }\), which measures the degree of relative prudence, is closely linked to the coefficient of relative risk aversion.

3 The empirical model

The intertemporal model of state government spending presented above is based on forward-looking behavior, but it does not allow for the balanced budget rules facing most state governments. These rules are likely to affect intertemporal spending behavior, so accounting for them is essential for fully understanding state government spending. Moreover, as discussed in the introduction, we should have an empirical model that enables us to test for possible asymmetry in balanced budget rules. To do so, we propose the following model for the empirical analysis:

$$\Delta \ln G_{i,t} {} = \beta _t + \varvec{\beta _z^{\prime } \Delta Z_{i,t}} + \beta _r \ln (1+r_{i,t}) + \beta _R^{+} \Delta \ln R_{i,t}^{+} + \beta _R^{-} \ln \Delta R_{i,t}^{-} \nonumber \quad + \beta _L \Delta \ln G_{i,t-1} + \beta _{\sigma } \sigma _{i,t}^2 + \varepsilon _{i,t}$$
(10)

where \(\beta\)’s are parameters to be estimated and \(\varepsilon _{i,t}\) is the forecast error. The coefficients \(\varvec{\beta _z}\) measure the response of the state’s spending growth to a change in idiosyncratic or state-specific variables, while the coefficient \(\beta _r\) describes the effect of the interest rate on spending growth. \(\Delta \ln R_{i,t}\) is growth of revenue or current resources, and \(\Delta \ln R_{i,t}^{+}\) and \(\Delta \ln R_{i,t}^{-}\) are defined as follows. \(\Delta \ln R_{i,t}^{+} = \Delta \ln R_{i,t}\) if \(\Delta \ln R_{i,t} \ge 0\) and \(\Delta \ln R_{i,t}^{+}=0\) otherwise, and \(\Delta \ln R_{i,t}^{-} = \Delta \ln R_{i,t}\) if \(\Delta \ln R_{i,t} < 0\) and \(\Delta \ln R_{i,t}^{-} = 0\) otherwise. The coefficients \(\beta _R^{+}\) and \(\beta _R^{-}\) measure potential asymmetry of spending responses with respect to changes in current resources.Footnote 8 The coefficient \(\beta _{L}\) captures the effect of habit formation on spending; habit formation predicts \(\beta _L > 0\). The coefficient \(\beta _{\sigma }\) describes the effect of local economic uncertainty on spending growth. In addition, the time fixed effect \(\beta _t\) is introduced to capture year-specific effects that are common to all states.

Equation (10) nests several alternative models, which are delineated in Table 1. Some discussion of these models is in order. (1a) Balanced budget requirements dictate a tight relationship between state governments’ revenues and expenditures. If state governments are constrained in their spending by the balanced budget rules, the implication is that \(\beta _R \ne 0\), which we can test. This model does not allow for asymmetry of spending with respect to changes in revenue. Under asymmetric balanced budget rules, spending should respond more strongly to either revenue decreases or increases. Under symmetric balanced budget rules, however, spending should respond symmetrically to increases and decreases in revenue. (1b) If spending responds to increases in revenue differently relative to revenue declines, then we expect that \(\beta _{R}^{+} \ne \beta _{R}^{-}\). If, however, there is a symmetric response, \(\beta _R^{+} = \beta _R^{-}\). (2) The forward-looking model allows state governments to smooth their spending over time. This model is familiar and underlies previous studies on intertemporal state spending with no balanced budget rules (Holtz-Eakin et al. 1994; Dahlberg and Lindstrom 1998; Borge and Tovmo 2009). (3) In the habit formation model, lagged spending growth affects current spending growth, so we expect \(\beta _L > 0\). (4) In the precautionary saving model, state governments save not only to smooth consumption over the lifetime but also to hedge against uncertain future revenue or spending streams. This requires testing the hypothesis that \(\beta _{\sigma } = 0\). (5a) If state government spending is determined by many factors such as current resources or precautionary saving, we can test if \(\beta _R \ne 0\) and \(\beta _{\sigma } \ne 0\). (5b) If there is an asymmetric response of spending to current resources, \(\beta _R^{+} \ne \beta _R^{-}\) and \(\beta _{\sigma } \ne 0\).

Table 1 Model alternatives
Full size table

We intend to estimate the general intertemporal model of state government spending, summarized by Eq. (10), with data from the USA. We will pursue an instrumental variables approach. This is necessary because most of the explanatory variables, excluding state characteristics, may not be strictly exogenous. In fact, as demonstrated by Poterba (1994), Bohn and Inman (1996), and Wagner and Elder (2005), state governments will often try to address revenue shortfalls by raising taxes as well as cutting spending. As an instrument for current general revenues, we use the current and lagged value of growth in intergovernmental revenue. Our implicit assumption is that intergovernmental revenue changes will influence changes in current operation expenditure only via its effect on current general revenue. Of course, with respect to spending on health programs like Medicaid, this is unlikely to be strictly true, as there may be simultaneity in the determination of current expenditure on health programs and federal transfers to states. In an appendix, we demonstrate that our results are not sensitive to excluding spending on health and hospitals from our current expenditure measure. We use the lag of the interest rate as an instrument for the contemporaneous interest rate.Footnote 9

Dynan (2000) shows that, when estimating a consumption model with habit formation, the coefficient on the lagged spending variable may be confounded by serially correlated measurement error. To address this issue, we also instrument for lagged current operations expenditure growth with a set of dummy variables that indicate growth in elementary and secondary school enrollment. Specifically, we generate a dummy variable indicating whether enrollment growth in state i in year t is less than the 5th percentile of the entire sample distribution, a dummy variable indicating whether enrollment growth is between the 5th and 10th percentiles, a dummy for whether it is between the 10th and 25th percentiles, a dummy for whether it is between the 25th and 75th percentiles, a dummy for whether it is between the 75th and 90th percentiles, one for whether enrollment growth is between the 90th and 95th percentiles, and one for whether it is above the 95th percentile in the whole sample distribution.

Estimation of the composite model, Eq. (10), requires a measure of the state government’s uncertainty about its revenue, or the state economy in general, which induces them to have a precautionary saving motive. To obtain such a measure, we assume that GSP growth depends on state-specific factors as well as aggregate fluctuations in the economy, and that there is persistence in GSP growth. Thus, we take GSP growth in deviation from GDP growth and specify it as an AR (autoregressive) process by controlling for state-specific variables:

$$\begin{aligned} \Delta \ln {\text {GSP}}_{i,t} - \Delta \ln {\text {GDP}}_t = \delta (\Delta \ln {\text {GSP}}_{i,t-1} - \Delta \ln {\text {GDP}}_{t-1}) + \varvec{\eta ^{\prime } X_{i,t}} + u_{i,t} \end{aligned}$$
(11)

where GDP is gross domestic product, \(X_{i,t}\) is a vector of state-specific control variables, and \(u_{i,t}\) is the forecast error that represents unobservable factors. \(\delta\) is a measure of persistence in GSP growth after controlling for state-specific variables. We assume that \(u_{i,t}\) is a serially uncorrelated Gaussian process, with \(Var (u_{i,t})=\sigma _{i,t}^2\).

In the spirit of an ARCH (autoregressive conditional heteroskedasticity) process (Ahn et al. 2017), we use \(u_{i,t}^2\) as a proxy variable for \(\sigma _{i,t}^2\).Footnote 10 If we assume rational expectations regarding \(\sigma _{i,t}^2\), then

$$\begin{aligned} u_{i,t}^2 = \sigma _{i,t}^2 + \omega _{i,t}, \end{aligned}$$
(12)

where \(\omega _{i,t}\) is the forecast error so that \(E_t \omega _{i,t} = 0\). After substituting for \(\sigma _{i,t}^2\) in Eq. (9) using Eq. (12), we obtain

$$\Delta \ln G_{i,t}= \beta _t + \varvec{\beta _z^{\prime } \Delta Z_{i,t}} + \beta _r \ln (1+r_{i,t}) + \beta _{R}^{+} \Delta \ln R_{i,t}^{+} + \beta _{R}^{-} \Delta \ln R_{i,t}^{-} + \beta _L \Delta \ln G_{i,t-1} + \beta _{\sigma } u_{i,t}^2 + [ \varepsilon _{i,t} - \beta _{\sigma } \omega _{i,t}]\ .$$
(13)

OLS (ordinary least squares) estimation of Eq. (13) results in biased and inconsistent estimates because \(u_{i,t}^2\) is correlated with the error term \([\varepsilon _{i,t}-\beta _{\sigma } \omega _{i,t}]\); thus, we need an instrument for the proxy variable, which we choose to be \(u_{i,t-1}^2\).

In contrast with intertemporal models adopted in previous studies examining state spending, such as Holtz-Eakin et al. (1994), Dahlberg and Lindstrom (1998), and Borge and Tovmo (2009), our model allows for habit formation and precautionary saving with asymmetry in balanced budget rules within a panel data framework that accounts for heterogeneity among states. A number of additional studies on US state government behavior examine the effects of balanced budget rules on state fiscal policy (see Poterba 1994; Eichengreen and Bayoumi 1994; Bohn and Inman 1996; Sørensen, Wu, and Yosha 2001; Sørensen and Yosha 2001; Clemens and Miran 2012). They, by and large, adopt ad hoc specifications by including a variety of explanatory variables to predict government spending or revenue. For example, Sørensen, Wu, and Yosha (2001) estimate budget surpluses and changes in spending as a function of changes in GSP for US state and local governments. Fatás and Mihov (2006) specify spending for US state governments in a log form as a function of GSP growth, lagged spending, and control variables, such as the current and lagged value of an index of oil prices, the current inflation rate, and a linear time trend. Estimating this equation individually for each state, they then assess variation in the cyclicality and volatility of spending across states. Our paper reassesses these issues with a more general model of state government spending that allows for forward-looking behavior and asymmetric balanced budget rules, potentially providing new perspectives relative to previous studies in the literature.

4 Data and summary statistics

The preceding empirical model offers a guide as to the data to use in the empirical analysis. They include state government revenue and expenditure, variables for state characteristics, the interest rate, GSP, and GDP. Our data span the years 1963–2016 (depending on the variable), with 1963 representing the first year for which the Bureau of Economic Analysis has information on GSP and 2016 being the last year for which we have detailed state government finance data. In our analysis, we include only the lower 48 US states, dropping Alaska and Hawaii. This is a common practice in the literature on state-level public finance (see, for example, Sørensen, Wu, and Yosha 2001; Fatás and Mihov 2006; Bohn and Inman 1996).

Our primary data source is the Annual Survey of State Government Finances, conducted by the US Census Bureau. The Census data include information on revenue (by source, including intergovernmental revenue, our primary instrument) and expenditure categories (by function) for state governments, as well as debt and cash-on-hand variables. For our measure of state spending, the key variable of interest in our model, we choose current operations expenditure.Footnote 11 This includes spending on a variety of state government functions, including education, highways, and police, among others, but it excludes capital outlays, interest payments, insurance payouts, and subsidies. We use general revenue as our measure of state income, which includes tax revenue, charges, and transfers from other governments, but excludes revenue from utilities, insurance trusts, or liquor stores. State finance variables are transformed into real terms using the implicit deflator for state and local government consumption and gross investment, which is obtained from the Bureau of Economic Analysis. GDP is also obtained from the Bureau of Economic Analysis.

For the interest rates facing state governments, there are no widely available data for state-specific interest rates. Our preferred option is to construct an “implicit” interest rate for each state, which is calculated as a state government’s interest expenditure in year t divided by its debt outstanding in year \(t-1\). This measure has the benefit of exhibiting cross-sectional variation in every year of our dataset, but it is fundamentally a “backward-looking” measure that may not reflect what a state’s true borrowing costs are at the moment that spending decisions are made. Thus, we also consider the Moody’s Baa corporate bond yield, which would be a forward-looking measure of interest rates and may be a reasonable approximation of the average state’s borrowing costs, but this measure has no cross-sectional variation. We find that our results are not particularly sensitive to the choice of interest rate measure.

To allow for variation in spending growth across states, we incorporate a number of control variables. We include population growth and annual growth in nonfarm payrolls for each state,Footnote 12 which come from the Bureau of Labor Statistics. By controlling for population growth, we allow states that are growing to respond in kind with greater spending without imposing homothetic preferences. Growth in nonfarm payrolls proxies for the contemporaneous state of the local economy, which would otherwise influence spending on social programs. We also consider the relative importance of oil production in the state-level economy, since we want to abstract from resource fluctuations induced only by commodity price changes. We construct a variable indicating the share of oil and gas extraction in a state’s nominal GSP in a given year, which is then interacted with year fixed effects, which we also include. Political variables may also affect state spending, so we include a dummy variable taking a value of 1 if the governor is in the Democratic Party and 0 otherwise, as well as dummies for whether the Republican or Democratic Party has complete control of the legislature, and a dummy for whether the same party controls both the executive and legislative branches within a state. These controls allow for differences in the political tastes for spending and come from the Book of the States. Finally, we include the current value of growth in public elementary and secondary education enrollment, which comes from the Annual Survey of School System Finances (published by the Census Bureau) and the National Center for Education Statistics. We do not include state fixed effects, which are obviated by the fact that we estimate our model in first differences, as guided by our theoretical model.

While state governments are constrained by explicit or implicit balanced budget rules, the nature and scope of these rules vary across states. We allow for a number of possible variations in the relative strictness of state balanced budget rules in our analysis. We start with the classification constructed by the Advisory Commission on Intergovernmental Relations (ACIR).Footnote 13 This is an index of fiscal rules stringency on a scale of zero to ten, with zero indicating no balanced budget rule and ten indicating the tightest possible conditions. This classification system has been employed in a number of papers in the literature, including Poterba (1994), Poterba (1995), Eichengreen and Bayoumi (1994), Sørensen, Wu, and Yosha (2001), and Bohn and Inman (1996). For the purposes of our study, we will consider a state to have a “tight” balanced budget rule if their classification according to the ACIR system is 10, and to have a “loose” balanced budget rule otherwise. The main reasoning behind choosing this cutoff is that it results in a nearly even split of the sample.

More finely detailed criteria that make a given state’s balanced budget rule “tight” or “loose” are discussed in Bohn and Inman (1996) and Fatás and Mihov (2006). Bohn and Inman (1996) uncover evidence that the most important factor is the existence of a “no carry-over” provision, which prevents state governments from counting an incurred deficit in year t toward the budget balance in year \(t+1\). Other significant criteria that inform whether or not a state’s balanced budget rule is strict or not include whether the governor needs only propose a balanced budget or the legislature needs to pass one, whether rules are constitutional or statutory, whether they are enforced by elected or appointed state supreme courts, whether a referendum must be passed to issue new debt, and whether the state governor has a line item veto. We consider splitting our sample according to all of these criteria.

Table 2 Summary statistics
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Table 2 contains summary statistics for the main variables in our analysis for the whole sample period. The various panels of Fig. 1 further break down the summary statistics for revenue and expenditure growth by state and by year, respectively. It is apparent from this figure that, even within states and within years, there is substantial variation in revenue and spending growth, which facilitates our investigation of the intertemporal spending behavior of state governments. The bottom left panel of Fig. 1 displays the number of positive growth episodes by state. Revenue for state governments falls in a considerable number of years, and many years see at least a few states experiencing revenue declines (see the bottom right panel of Fig. 1). This will be helpful for us as we examine the extent to which responses to revenue growth are asymmetric, that is, whether state governments react differently to increases or decreases in revenue. Table 3 shows whether each state is considered to have a tight or loose budget rule according to the ACIR classification system.Footnote 14

Fig. 1
figure 1

Distribution of changes in spending and revenue by state and by year. The top two panels in the figure report summary statistics for growth in current operations expenditure separately by state (a) and by year (b). The middle two panels in the figure report summary statistics for growth in general revenue separately by state (c) and by year (d). All values are expressed in percentage points. The boxes represent the interquartile ranges, while the whiskers reflect values 1.5 times the interquartile range. The bottom two panels report the number of positive general revenue growth episodes by state (e) and by year (f)

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Table 3 Budget rule classification
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5 Estimation and results

A number of studies have been conducted analyzing intertemporal state government spending, with mixed evidence. Holtz-Eakin et al. (1994) formally introduced an intertemporal model of government spending and found that state and local government spending in the USA is primarily determined by current resources in line with balanced budget rules. Dahlberg and Lindstrom (1998), using panel data on Swedish municipalities, found that their spending decisions are largely determined by rational, forward-looking decision makers. Borge and Tovmo (2009) found that, for Norwegian local governments, their spending behavior in general is not perfectly forward-looking. They attribute it to both liquidity constraints imposed by balanced budget rules and myopic behavior. None of these studies allows for precautionary saving and habit formation with asymmetry in balanced budget rules.

We reexamine these studies and present the results of estimating the model for different kinds of states to ascertain whether state government spending (if only for a subset of states) in the USA is governed by balanced budget rules or forward-looking behavior. To account for time-specific effects that are common to all states, we estimate the model with year fixed effects. We essentially treat the stringency of the budget rules as exogenous, which is common in most of this literature. In many cases, these rules are embedded in state constitutions, which long predate the sample period which we study. For the interest rate, we use the state-specific implicit rate calculated as a state government’s interest expenditure in the current year divided by its debt outstanding in the previous year. As discussed in Sect. 3, we treat contemporaneous revenue growth, lagged spending growth, the state-specific interest rate, and the time-varying idiosyncratic conditional variance as endogenous variables and estimate the model via two-stage least squares (2SLS), using as instruments the current and lagged value of intergovernmental revenue growth, the lagged interest rate, the lagged value of the conditional variance, and a set of dummy variables capturing lagged growth in enrollment in public elementary and secondary education.

5.1 OLS estimation

Although our main results rely on instrumental variables estimation, it is instructive to consider ordinary least squares estimation as a starting point for the investigation. These results can be found in Appendix Tables 10 and 11, for the symmetric and asymmetric models, respectively. The symmetric model indicates that, in general, state current operation expenditure growth rises by about 0.3–0.4 percentage points with every percentage point change in the growth rate of general revenue. This applies to all states, regardless of the relative strictness of their balanced budget rules, and it applies to both increases and decreases in revenue. OLS estimation would then suggest that states are not forward-looking, responding symmetrically to both positive and negative changes in general revenue.

Interestingly, our coefficient estimates for the lag in spending growth are significantly negative in nearly all cases. This is difficult to reconcile conceptually with the theory on consumer behavior that allows for a positive effect of habits, but not a negative one, and further bolsters the argument for an instrumental variables approach, as in Dynan (2000).

Our results suggest that there are significant behavioral differences between states according to whether or not the governor must submit a balanced budget to the legislature, whether or not the government can carry over a deficit into the following fiscal year, and whether or not there is a statutory limit on the ability to carry deficits over. Those that must submit balanced budgets and that face statutory constraints on carrying deficits forward are more likely to respond to changes in interest rates than are those that do not face such constraints. Those that do allow deficits to be shifted to the next year also respond more to the interest rate (if not significantly so), and they have the more negative coefficient on lagged spending growth.

With the OLS estimates as a benchmark, we turn to the main part of our analysis, which relies on instrumental variables estimation.

5.2 IV estimation: symmetric model

We start with the symmetric model, in which we impose the constraint that state governments respond similarly to both positive and negative changes in general revenue. Table 4 contains the first-stage F-statistics for each of the endogenous variables in the model. We note that for the full sample estimation, as well as for a number of splits of the data, the conventionally used standard of an F-statistic above 10 holds for all of the endogenous variables. Where the threshold is not met, it is likely because the sample sizes are relatively small and we are unable to cluster standard errors, since there are too few states for which to do so. For example, there are only 441 observations in which the state governor must submit a balanced budget. In our results, we focus on those samples where the weak instruments condition is less likely to hold (where the first-stage F-statistics exceed 10). Appendix Table 14 contains the results for the other samples, which are not radically different.

Table 4 First-stage F-statistics for symmetric instrumental variables model
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Looking first at the full sample results, contained in Table 5, we find a strongly significant reaction of state government spending to revenue changes. The coefficient is 0.70, and it is significant at the 1 percent level (though we can reject that states respond exactly one-for-one with unexpected revenue changes). This implies that we can reject the hypothesis that states are forward-looking, and it is likely that balanced budget rules impose a significant constraint. There is no evidence of an effect of the interest rate, further bolstering the view that state governments are not forward-looking. We do find evidence of significant habit formation, with a coefficient on lagged spending growth of 0.19, significantly different from 0 at the 1% level, and there is also modest evidence for a precautionary savings motive, as the coefficient on the conditional variance term (which serves as a proxy for state-level economic uncertainty) is 0.02 and significant at the 10% level. Importantly, there is no evidence that the overidentifying restrictions on our instruments are rejected, as the p value for the J-statistic is 0.91, well above conventional significance levels. We interpret the combination of the relatively high F-statistics found for the full sample first stage, reported in Table 4, with the failure to reject the overidentifying restrictions as support for our instrumental variables strategy.

Table 5 Estimation of state government spending model: IV results for symmetric model
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Next, we ask whether state government behavior is similar across splits in the sample. The two splits that we consider are whether or not the state has an ACIR budget rule classification of 10 or something less than 10 and whether the state has an elected or appointed supreme court. These are the two sample splits for which we have sufficiently large first-stage F-statistics for both subsamples. The ACIR applies a rating of 10 to the states that have especially tight balanced budget rules. For supreme courts, Bohn and Inman (1996) reason that elected courts, being answerable to voters and not politicians, might be more vigorous about enforcing balanced budget rules.

We do not find any strong evidence of significant differences across the two sample splits. In both cases, states with both weak and strong budget rules respond significantly positively to revenue changes. They also do not react to changes in interest rates, and they exhibit similar degrees of habit formation. States with loose rules according to the ACIR classification system show a marginally significant precautionary saving motive, as do states with an elected supreme court. That said, we fail to reject that the model’s main parameters are equal across the sample splits, as the bottom line in each panel of the table reveals.

This implies that our symmetric model produces results consistent with the findings of Canova and Pappa (2005). In that paper, strict and loose balanced budget rules are not found to generate significantly different behavior on the part of state governments. Here, too, we find that, in spite of big differences on paper, there is not much actual difference in the behavior of states, depending on whether their balanced budget rules are tight or loose.

5.3 IV estimation: asymmetric model

We next turn to our asymmetric model, where we relax the restriction that state governments must respond proportionally to both increases and decreases in general revenue. Table 6 contains the first-stage F-statistics for our instruments. For the asymmetric model, we must include instruments for both positive changes in general revenue (\(\Delta \ln R_{i,t}^{+}\)) and negative changes in general revenue (\(\Delta \ln R_{i,t}^{-}\)). We alter our instrument set by substituting the contemporaneous value and the first lag of both positive and negative changes in intergovernmental revenue for the contemporaneous and lagged value of intergovernmental revenue growth.

Table 6 First-stage F-statistics for asymmetric instrumental variables model
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For each of our endogenous variables and a number of sample splits (including the full sample), we find that our first-stage F-statistics easily clear the threshold value of 10, indicating that our chosen instruments have strong explanatory power for the endogenous variables in the model. Turning to the main results in Table 7, we focus on the full sample, the split according to whether or not the state has an ACIR rating of 10, the split according to whether the state has an elected supreme court, and the split according to whether there is a state constitutional provision against carrying deficits into the next fiscal year.Footnote 15

Table 7 Estimation of state government spending model: IV results for asymmetric model
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We are mainly interested in assessing whether or not states respond differently when revenue declines, compared with when it rises. The results of our asymmetric model do not provide strong evidence for this notion. In the full sample, we find a higher point estimate on revenue increases (0.75) than on revenue decreases (0.58), but the difference between them is not significant. We continue to find significant habit formation, but there is no evidence for a reaction to interest rate changes or a precautionary saving motive.

Comparing states with an ACIR balanced budget rule rating of 10 with those having a rating below 10 or comparing states whose constitutions restrict carrying deficits forward to those without such a constraint produces similar findings. Most notably, the states with the tighter restrictions are more likely to respond positively to increases in revenue, raising spending growth by around 0.70 percentage points for every 1 percentage point increase in revenue, while not responding significantly at all to decreases in revenue. Despite this substantial difference in point estimates, there is still no statistically significant evidence that the coefficients are different. For the sample of states with the strictest possible budget rule ratings according to the ACIR, the p value for a test of the null that \(\beta _R^+ = \beta _R^-\) is only 0.18, fairly distant from conventional significance levels. Further, there is no strong evidence that the set of parameters are different across sample splits in any of the three splits illustrated in the table.

Therefore, while we find a suggestion that there may be asymmetric responses for some states, we do not find systematic behavioral differences with respect to positive or negative revenue growth for any group of states, nor is there strong evidence that any one group of states behaves in a statistically different manner from another. This provides further evidence for the argument, expressed in Canova and Pappa (2005), that the nominal strictness of balanced budget rules may not actually lead to real differences in spending decisions.

5.4 Alternative model specifications

Our main results thus far are that state governments do not make spending decisions as though they are forward-looking, that they are subject to significant habit formation, and that while some groups of states have fairly different coefficient point estimates on revenue increases relative to revenue decreases, the evidence for a statistically significant difference is lacking. In this subsection, we pursue three alternative specifications. We first split the sample according to time period, looking at early, middle, and more recent periods. Then, we split the sample according to whether each state follows a biennial budget cycle. Finally, we demonstrate that our results are not sensitive to the exclusion of state government expenditure on health and hospitals, a specification motivated by the fact that simultaneous determination of Medicaid expenditure and federal aid to states may prove a threat to our instrumental variables strategy.

Table 8 reports results from estimating the model separately for three time periods, 1968–1983, 1984–2000, and 2001–2016. We perform our estimation in each time period for the full group of states, as well as for states with the strictest and loosest budget rules, according to ACIR.

Table 8 Estimation of state government spending model for different time periods
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We do observe some differences for each different time period. In the earliest sample, dominated by the 1970s, states appeared to significantly respond to revenue increases but not to revenue decreases. The coefficient on revenue increases hovers around 0.4 percentage points for every percentage point change in positive revenue growth, depending on the specific specification. In no case can we reject that the reaction to revenue increases is the same as that to revenue decreases, similar to our finding for the full sample asymmetric model.

In the middle period, covering the late 1980s and the 1990s, the pattern is similar, with positive revenue changes leading to positive spending changes, while negative revenue changes do not spark any change. That said, the magnitude of the coefficients is much greater in this middle period, as there is about a one-for-one reaction of spending growth to positive revenue growth. Still, we cannot reject the equality of the responses to positive and negative revenue changes.

Finally, in the most recent period, the result is rather different. Since the turn of the millenium, state governments have exhibited similar responses to both positive and negative revenue changes (and of a high magnitude, between 0.6 and 1.0), and p values on tests of equality between these responses are higher even than in earlier periods, in general. What is more, it is in this period of history that we find the strongest evidence of habit formation for states with the tightest balanced budget rules, as they have a habit coefficient of 0.47, significant at the 1% level.

In summary, over time, states have begun changing their spending decisions as a result of revenue changes more aggressively, for both increases and decreases in revenue, and habit formation, at least for states with the tightest rules, has become a more important determinant of spending decisions.

We also consider whether states’ decision making is related to whether or not they employ biennial budget cycles (setting spending plans for 2-year periods, as opposed to on an annual basis). The results of such an analysis are found in Table 9, with the first line of the table replicating the first line in Table 7 for comparability. Those states that budget on a biennial basis apparently behave like those states with the tighter balanced budget rules (in fact, there is a strong overlap between them), raising spending growth by 0.85 percentage points for every surprise one percent growth in revenue. These states do not significantly react to revenue losses. We can marginally reject the null hypothesis that the responses to increases and decreases in revenue are equal, with a p value of 0.10. States budgeting annually, on the other hand, behave similarly with respect to both increases and decreases in revenue growth, and we fail to reject the null hypothesis that the key model parameters are the same for states with annual or biennial budget cycles.

Table 9 Biennial budgeting: IV results for asymmetric model
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Finally, in Appendix Tables 16 and 17, we show that we get very similar results as in our benchmark model when we exclude expenditures on health and hospitals from our measure of state government current expenditure. This suggests that possible simultaneous determination of federal transfers to states and expenditure on Medicaid programs is not a threat to our identification strategy.

5.5 Business cycle effects of balanced budget rules

Balanced budget rules require that spending follows the path of revenue. A central issue in the discussion of balanced budget rules is whether these rules make spending procyclical and hence amplify business cycle volatility in the state economy. A few studies seek to investigate this issue empirically for US states (Fatás and Mihov 2006; Canova and Pappa 2005). Our study brings a new perspective to this investigation. Fatás and Mihov (2006) find that states with tighter balanced budget rules have more procyclical fiscal policies, but they also have less volatility in the state economy.Footnote 16 Part of this stems from the inability of states with tight fiscal rules to introduce volatility into the economy with larger increases in government spending when times are good. As we noted in Sect. 3, the analytical framework of Fatás and Mihov (2006) is not based on possibly forward-looking behavior by state governments, and it does not allow for asymmetric responses to balanced budget rules. In contrast to their work, we construct a general intertemporal model that embeds balanced budget rules with asymmetric responses to changes in revenue, demonstrating that states with tighter rules do behave differently in response to increases and to decreases in revenue. Such asymmetries are important for a fuller understanding of these fiscal rules.

We use Tables 5 and 7, which capture our main findings, to re-examine the business cycle effects of balanced budget rules. In the symmetric specification of the model estimated only on states with relatively tight budget rules, we find a coefficient of 0.59 on revenue growth, smaller than the coefficient on revenue growth for states with loose rules (0.77). Such a finding does not accord with the results of Fatás and Mihov (2006), who find that states with tight fiscal rules tend to operate a more procyclical fiscal policy. Examining the asymmetric specification, however, allows for a more complete picture. For the pooled sample, the coefficients on revenue increases and decreases are positive, suggesting that balanced budget rules, in general, generate procyclicality in spending. The coefficient on revenue increases, however, is a bit larger (0.75) than that on revenue decreases, which is 0.58, implying that states as a whole increase spending with increases in revenue more than they cut with decreases in revenue. This appears to indicate that there is greater procyclicality in spending associated with increases in revenue than with decreases in revenue. That said, the coefficient on revenue increases is not large enough to conclude that increases in revenue might exacerbate booms with increased volatility in spending.

When we examine states with loose budget rules, we observe that, at least qualitatively, they behave in a fashion similar to the sample as a whole. Their reactions to positive and negative revenue changes are both positive (implying again that balanced budget rules induce procyclicality of spending with respect to both increases and decreases in revenue), but they are somewhat closer to each other than in the full sample. The coefficient on revenue increases is 0.77, and the coefficient on revenue decreases is 0.79. This makes it hard to refute the claim that, in states with loose budget rules, greater procyclicality (and hence volatility) in spending is associated with both increases and decreases in revenue.

For states with tight balanced budget rules, the coefficient on revenue increases is 0.71, suggesting that states experience nontrivial procyclicality with respect to revenue increases during expansions. The estimated coefficient on revenue declines in states with tight rules is a much lower 0.13, and this difference takes on some economic significance, allowing for a more nuanced understanding of the Fatás and Mihov (2006) results. The greater procyclicality of fiscal policy in tight rule states is mainly a consequence of spending increases during good times. Economic downturns are not associated with the same kind of spending procyclicality.

Canova and Pappa (2005) also analyze the macroeconomic effects of balanced budget rules in US states. They point out that the two-step procedure employed by Fatás and Mihov (2006) may produce biased results, and they propose a different methodology based on a vector autoregression (VAR). They find that balanced budget rules make little difference in macroeconomic fluctuations for states with tight and loose rules, further arguing that the presence of rainy day funds effectively allows states to limit expenditure cuts at times of binding constraints. Our results are more consistent with these findings, especially in light of the fact that we cannot, in general, reject that states with very tight or very loose balanced budget rules have equal parameters governing their decision-making processes.

Our estimates might also be employed to assess the broader macroeconomic impacts of a change in revenue. Clemens and Miran (2012) estimate the income multiplier on changes in state government spending to be around $0.77 per dollar. The fact that this value is less than one indicates some crowding out of private activity by increases in state government expenditure. Using this estimate, we can calculate a “back-of-the-envelope” measure of the response of state personal income (Y) growth with respect to changes in revenue growth. Note that:

$$\begin{aligned} \frac{\partial \Delta \ln Y}{\partial \Delta \ln R} = \frac{\partial \Delta \ln Y}{\partial \Delta \ln G} \frac{\partial \Delta \ln G}{\partial \Delta \ln R} \approx \frac{\Delta Y}{\Delta G} \bar{\Big (\frac{G}{Y}\Big )} \frac{\partial \Delta \ln G}{\partial \Delta \ln R}, \end{aligned}$$
(14)

where \(\frac{\Delta Y}{\Delta G}\) is the government spending multiplier and \(\bar{\Big (\frac{G}{Y}\Big )}\) is the average ratio of current operations expenditure to state personal income. The final term on the right-hand side would be our regression estimates (from Tables 5 and 7) of the response of government expenditure growth with respect to revenue growth. Evaluating this expression reveals that this response with respect to revenue increases is 0.04% in the whole sample, 0.03% in the tight rule states, and 0.04% in the loose rule states. With respect to revenue decreases, we find reactions of income of 0.03% in the whole sample, 0.01% in states with tight budget rules, and 0.04% in states with loose budget rules. These figures support the notion that tight balanced budget rules raise state-level income volatility in the face of positive shocks, but not conditional on negative shocks.

6 Conclusion

This paper has presented an intertemporal model of government spending that accounts for habit formation and the precautionary nature of saving by state governments with a treatment of asymmetry in balanced budget rules, estimated on panel data for US states. In general, we find that balanced budget rules are a significant constraint on state governments, as we cannot reject that expenditures on current operations rise significantly with revenue growth.

This is in line with some previous results in the literature, such as Holtz-Eakin et al. (1994) and Borge and Tovmo (2009). While this finding holds in the overall sample, we do find some very modest evidence for a slightly different pattern in states, depending on the relative strictness of their balanced budget rules. Specifically, we find some evidence for the hypothesis that states with very tight fiscal rules exhibit asymmetric responses to changes in revenue. They do not appear to change spending significantly when revenue falls, but they increase spending when revenue rises. That said, in general, we cannot statistically reject that the responses to revenue increases and decreases are equal in most of our specifications, and we generally do not reject the null of equal coefficients across our various splits in the sample. In addition, we find that habit formation may be a significant influence on spending in all states, but especially in those with relatively tight balanced budget rules in the most recent years of our data. There is not much evidence for precautionary saving as an important driver of state governments’ spending decisions.

Our analysis is more in line with the findings of Canova and Pappa (2005), who conclude that balanced budget rules make little macroeconomic difference for states, whether they are loose or tight. Our findings help to expand upon the work of Fatás and Mihov (2006), who conclude that states with tighter balanced budget rules have more procyclical fiscal policies but also less volatile state economies. We find that the greater procyclicality of policy in these states is driven by increases in spending when the state economy is entering an expansionary period. This raises the possibility that, conditional on an expansion, states with tighter rules might amplify (not mitigate) local economic volatility.

It may be noted that our main finding that balanced budget rules are a significant constraint on state governments does not mean that a forward-looking model is not appropriate in the analysis of state government spending. This finding applies to the typical state government, but we still find that precautionary saving and habit formation are relevant concepts for state government behavior. Even for those states for which the model fails, there is value in establishing exactly how this canonical framework falls short in describing state government spending behavior.