Evidence from a half century of experience by states identifies nonlinearities in the effects of debt and fiscal policy on growth.  Effects are Keynesian for low to moderate levels of debt and stimulus but anti Keynesian for sufficiently high levels of debt or stimulus. Results are broadly consistent with models by Barro (1999), Judd (1987), and others

Gray, Jo Anna

Stone, Joe A.

Munich Personal RePEc Archive

MPRA
Munich Personal RePEc Archive
Debt and nonlinear fiscal policy:
evidence from the states
Jo Anna Gray and Joe A. Stone
University of Oregon
6 June 2012
Online at https://mpra.ub.uni-muenchen.de/39731/
MPRA Paper No. 39731, posted 28 June 2012 20:50 UTC
1 
 
 
 
 
Debt and Nonlinear Fiscal Policy: Evidence from the States 
Joe A. Stone  
University of Oregon 
April 2012 
 
 
 
 
Abstract 
Evidence from a half century of experience by states identifies nonlinearities in the effects of 
debt and fiscal policy on growth.  Effects are Keynesian for low to moderate levels of debt and 
stimulus but anti Keynesian for sufficiently high levels of debt or stimulus. Results are broadly 
consistent with models by Barro (1999), Judd (1987), and others. 
 
 
*Corresponding author: 
Joe A. Stone 
Department of Economics 
University of Oregon 
Eugene, OR   97403 
Telephone:  541-346-4663 
Fax:          541-346-1243 
E-mail:        jstone@oregon.uoregon.edu  
 
 
JEL Codes: A00, E00, H00 
Keywords: fiscal policy, debt, growth 
   
2 
 
Introduction 
Burgeoning levels of  national debt, the ‘Great Recession” and the largest peacetime 
fiscal stimulus in U.S. history have spurred intense interest in whether debt reduces the 
effectiveness of fiscal stimulus, and in particular, whether or not the effects of fiscal stimulus can 
be non Keynesian. Based on a half century of evidence from states, this study extends recent 
cross-national investigations by Reinhart and Rogoff (2010, 2011) and others. We pursue 
answers to three questions: 1) Does the effect of fiscal stimulus depend on the initial stock of 
government debt, as suggested by Judd (1987) and others?  2) Do the effects depend on the 
magnitude of the stimulus? 3) Even when borrowing finances spending on education and public 
infrastructure does the effect of stimulus decline and eventually turns negative as the level of 
debt rises? 
Why Nonlinearities? 
Why might we expect nonlinear effects for fiscal policy implicit in our questions? For the 
first question, Judd (1987) extends the Barro (1989) model of endogenous growth to demonstrate 
that effects of fiscal stimulus can be either Ricardian or Keynesian, depending in part on the 
level of outstanding debt. For questions two and three, the Barro (1989) model predicts 
nonlinearities that arise from the decreasing returns and increasing opportunity cost of 
investments in public capital. Evidence of Barro-type nonlinearities are reported, for example, in 
Bania et al (2007). For question 2, one might also expect nonlinearity for practical reasons 
related to difficulties in spending a large amount of funds in productive ways in a limited amount 
of time. Of course, in a purely Keynesian context, how funds are spent is a secondary issue. 
3 
 
Why States? 
Sub national states of a large country offer several attributes useful in identifying 
nonlinear effects of fiscal policy. For example, they  i) often provide substantial variation needed 
to identify nonlinearities, while ii) also sharing similar legal and political systems; and iii) are 
small economies subsumed within a large common currency area. These attributes make them a 
useful quasi-experimental environment in which to study the effects of fiscal policy. Even so, 
some attributes also limit the extent to which results can be applied in other contexts. For 
example, states share well-integrated, highly mobile markets for capital and labor; are not able to 
monetize their debt; and all but one state (Vermont) has some form of constitutional limitation 
on deficits.  
Data and Empirical Specification 
We rely on data for 49 states at five-year intervals over the half century from 1957 to 
2007. We omit Alaska due to the dominance of the Alaska pipeline and the consequent outlying 
variances in fiscal variables relative to other states.  Five-year interval data allows a longer 
observation period than the available higher-frequency annual data, which for state and local 
public expenditures only begins in 1977, and has the advantage of increased power to identify 
middle-frequency factors related to non-cyclical, intermediate-run variations in growth. 
The data for state and local government fiscal variables are taken from the Census of 
Governments. Related economic, demographic, and other data for corresponding years are from 
the Bureau of Labor Statistics or the Department of Commerce (for personal income). Table 1 
reports summary statistics for the 441 observations of the five-year-interval data used to estimate 
equation (1).  
4 
 
Our baseline regression equation for the log-change in real personal income in a state is 
expressed by equation (1) below. We rely on a difference-in-differences empirical specification 
with fixed state and period effects. Thus, the specification incorporates state-specific trends for 
growth and period-specific effects common to all states. To address simultaneity issues, we rely 
on a recursive structure, with beginning-of-period predetermined explanatory variables,  
including the initial state unemployment rate to account for state-level cyclical influences. 
(1)     yit = c + ci + ct + b1di(t-1) + b2di(t-1)2 +  b3Di(t-1) + b4Di(t-1)*di(t-1) + b5Di(t-1)2 + BZit-1 + eit  
yit is growth, the log-change in real personal income per capita for state i in period t; c is a fixed 
intercept, ci is a state-specific intercept common to all periods, and ct is a period-specific intercept 
common to all states; d and D, respectively, are the budget deficit and outstanding debt1; bs are 
coefficients for the deficit and debt variables; B is a vector of coefficients for other components 
of the government budget constraint, denoted by Z; and eit is a random error unique to state i in 
period t. All fiscal variables and are expressed as percentage points of state personal income. 
To account for the government budget constraint in period t-1, we include the lagged 
deficit and debt variables, taxes in quadratic form, and omit one element, a general cross section 
of expenditures and revenues not already explicitly included, such as health, welfare, education, 
public infrastructure, fee revenue, and federal transfers.. Hence, for linear effects, a change in 
any explicitly included expenditure category,  requires a compensating change in an omitted 
category. In theoretical terms, eliminating a budget category introduces the budget constraint into 
                                                            
1 To avoid negative numbers for the deficit, we subtract the largest state deficit in the sample 
from each state’s deficit, so that changes are relative to the most negative deficit. 
 
5 
 
the model, as in Barro (1989). Empirically, it avoids linear dependence among elements of the 
government budget constraint, as discussed in Mofidi and Stone (1990) and Bania et al. (2007).  
We also incorporate a number of other control variables, including the lagged 
unemployment rate to account for cyclical variations, and contemporaneous federal transfers to 
the state (fed) to account for contemporaneous external revenue transfers.3 Both the common 
period effects and the unemployment rate help to limit any significant  autocorrelation in the 
residual errors, a condition necessary for the recursive identification structure to yield unbiased 
estimates. To gauge robustness of our primary estimates, we also include an index of the 
strictness of the state’s constitutional budget limitations as aninteraction with the deficit in 
estimates not reported here.4  
Results 
Table 2 reports our primary estimates for the growth equation (1).  The overall fit of the 
equation (an R-squared of 0.51) is strong for a difference equation with so little autocorrelation. 
Fiscal terms  
The linear coefficients for deficit and debt are both Keynesian (i.e., significantly 
positive), but their quadratic terms are both negative, so that the linear effects are less Keynesian 
as the levels of stimulus and debt rise.  The same is true for the significantly negative interaction 
between debt and the deficit. Consistent with Barro (1989) and results in Bania et al. (2007), the 
tax coefficients also exhibit positive linear and negative quadratic effects. Results for other fiscal 
variables are not of immediate interest, but are also consistent with results in Bania et al. (2007). 
                                                            
3 The contemporaneous budget constraint implies that a change in external revenues is offset by a compensating 
change in either expenditures or revenu 
4 The index was constructed by ACIR, the American Council on intergovernmental Relations. 
ACIR (2006). Estimates are available by request from the author. 
6 
 
Robustness 
 The estimates in Table 2 are not qualitatively sensitive to several alternative 
specifications, including controls for either the current or lagged state-level unemployment rate 
or for a measure of the restrictiveness of constitutional budget limitations and its interaction with 
our deficit measure of fiscal stimulus. In addition, tests of Granger causality yield equivalent 
results for the fiscal variables, including the negative interaction between debt and the deficit. 
Results are sensitive to omitting either the state or period fixed effects. 
Discussion 
The pattern of coefficients for the deficit, debt, and their interaction identifies 
nonlinearities in the effects of fiscal policy. Effects are Keynesian for low levels of debt and 
moderate amounts of stimulus but anti Keynesian for sufficiently high levels of debt or stimulus. 
 Are these patterns relevant within the sample range of our data? At the sample 
minimum (near-zero) values of the deficit and debt, the marginal effects of the two are 
significantly positive and ‘Keynesian.’ At their median values however, the marginal 
effects are zero or near zero and ’non Keynesian.’ Even more starkly, the marginal effects 
are negative and ‘anti Keynesian’ at the maximum sample values of the deficit and debt. 
Results based on evidence from sub national states are limited in their relevance to 
conclusions about effects of national policies. Even so, the nonlinearities found here are 
broadly consistent with theoretical results in Judd (1987) and Barro (1999).  They are also 
broadly consistent with empirical results in Rogoff and Reinhart (2009, 2010) and Adam 
and Beevan (2011), though at moderate levels of debt and stimulus our results are less 
optimistic for Keynesian fiscal policy.  Non-Keynesian effects emerge at well under the 
7 
 
ratio of debt to income found in Rogoff and Reinhart – i.e., at roughly 40%, less than half 
the Rogoff-Reinhart debt-income ratio of 90%.  But at low levels of stimulus, our results 
are consistent with theirs; non Keynesian effects don’t emerge until a debt-income ratio of 
90 to 100% is reached, roughly equivalent to the Rogoff-Reinhart ratio for the emergence 
of non-Keynesian effects. 
 
 
 
 
  
8 
 
References 
Adam, C.S., Beevan, D.L., 2011. Fiscal deficits and growth in developing countries.  
Cornell/ISPE Conference on Public Finance and Development.  ISSN: 1471-0498. 
 
American Council on Intergovernmental Relations, 2006. Archived site. 
http://govinfo.library.unt.edu/amcouncil/index.html. 
 
Bania, N., Gray, J.A., Stone, J.A. 2007. Growth, taxes, and government expenditures: growth 
hills for U.S. states. National Tax Journal 60:2, 193-204. 
 
Barro, R.J., 1999. Government spending in a simple model of endogenous growth.  Journal of 
Political Economy 98:5, S103-26.   
Judd, K.L., 1987. Debt and distortionary taxation in a simple perfect foresight model. Journal of 
Monetary Economics 20, 51-72. 
 
Mofidi, A., Stone, J., 1990. Do state and local taxes affect economic growth? Review of 
Economics and Statistics 72:4, 686-91. 
Rogoff, K.S., Reinhart, C.M., 2010. Growth in a time of debt. American Economic Review 
100:2, 573-78.  
Rogoff, K.S., Reinhart, C.M., 2009. This Time Is Different: Eight Centuries of Financial Folly.  
Princeton University Press, Princeton, N. J. 
  
9 
 
Table 1.   Summary Statistics (49 states, 1957-2007) 
 
 GROWTH     DEFICIT     DEBT   TAXES FED     OTHER UR 
 Mean  12.09696  8.33101  17.27186  10.07454  3.56646  3.46196  5.93001
 Median  11.39058  8.32130  16.62510  10.01384  3.36572  3.24844  5.58333
 Maximum  30.14108 11.59415  42.69089  17.74776  7.67741  8.40369  15.45000
 Minimum -9.92664 -0.00041  4.52034  7.13326  0.91310  1.28115  2.00000
 Std. Dev.  5.55975  0.99403  5.61312  1.32966  1.26775  1.26555  2.10587
        
 # Obs.  441  441  441  441  441  441  441 
        
Note:  See text for description of data and variables. 
 
        
        
        
        
        
        
 
  
  
10 
 
Table 2. Growth and Fiscal Policy Estimates (49 states, 1957-2007) 
 
Variable Coefficient        Robust s. e. t-Statistic Prob.  
C/c -1.12033    0.01889 -5.93013 0.0000
DEFICIT(-1) 8.43557 1.90326 4.43217 0.0000
DEFICIT(-1)^2 -0.40362 0.10433 -3.86868 0.0001
DEBT(-1) 1.09612 0.41823 2.62085 0.0091
DEBT(-1)^2 -0.00880 0.00505 -1.74050 0.0826
DEFICIT(-1)*DEBT(-1) -0.08477 0.04120 -2.05733 0.0404
TAXES(-1) 4.22053 1.72668 2.44431 0.0150
TAXES(-1)^2 -0.14133 0.08179 -1.72785 0.0848
FED(-1) 2.12859 0.50375 4.22549 0.0000
OTHER(-1) -1.31311 0.53678 -2.44628 0.0149
             
Other controls                         yes  
Period effects 
State effects 
 yes
 yes   
    
R-squared      0.51222              
Adjusted R-squared 0.42281  
S.E. of regression 4.21929  
Sum squared resid 6604.703  
Durbin-Watson stat 2.51165  
Number of obs.         440  
  
 
 


Debt and nonlinear fiscal policy: evidence from the states

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Debt and nonlinear fiscal policy: evidence from the states

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