133 discussion of this variable choice, see Chapter 5 and Appendix C.
23
State and year- specific differences are controlled for using dichotomous variables.
6.2.2 Methodology
In each regression model, several specification problems will be addressed. First, endogeniety is a concern in this research, specifically simultaneity between state fiscal
stress and state actions to address it. In other words an increase in fiscal stress may cause the frequency and size of state actions also to increase. When the dependent variable and
at least one explanatory variable are jointly determined, the explanatory variable is correlated with the error term, violating the classical regression assumptions Wooldridge
2006. This relationship may result in the independent variable, state responses, being inappropriately attributed to changes to the dependent variable, instead of the reverse
Studenmond 2006. Endogeniety, specifically simultaneity, results in biased estimators. To address these concerns, results from Chapter 5 and efforts in similar research Hou
2003, Hou 2004 are considered to correct this bias. In the previous chapter, descriptive analysis showed that the level of fiscal stress did not have a strong effect on state use of
actions. The lack of connection between level of fiscal stress and the types of state action taken suggests the limited extent to which fiscal stress effects state response. Endogeniety
is addressed here by following previous scholars and lagging state responses by one year Hou 2003; Hou 2004; Poterba 1994.
Second, serial correlation is a concern with a panel dataset. Serial correlation violates the classical assumption that different observations of the error term are
uncorrelated with one another Studenmund 2006. When the order of the observations
23
Appendix C shows the regression analysis using an alternative coding of the structural balance variable. The structural balance variable is only marginally significant for the budget fiscal stress when the structural
balance variable is coded using the 2005 and 2008 values. The difference between the two regression models suggests the structural balance variable is not very robust.
134 has meaning, in this case a time series, serial correlation is likely to occur since the error
term in year 2 may depend on the error term in year 1. As a result, the correlation between error terms will not equal zero. First-order serial correlation occurs when the
current value of the error term is a function of the previous value of the error term. While serial correlation does not cause bias in the coefficient estimates, the estimates may still
be different from the true beta and the standard errors may be biased, resulting in inaccurate hypothesis testing. To test for first-order serial correlation, the Wooldridge test
for panel datasets is conducted.
24
When serial correlation is found, Prais-Winsten OLS estimation is used to correct for it. Prais-Winsten OLS estimations are also used by
scholars using similar datasets Hou 2003; Hou 2004. Third, heteroskedasticity is a concern in the dataset. Heteroskedasticity occurs
when the variance of the error terms is not constant Wooldridge 2006. Heteroskedasticity does not result in biased or inconsistent OLS estimates; however, the
standard errors are no longer reliable for constructing confidence intervals and t-statistics. With states as the unit of analysis, it is possible for unobserved factors across states to
result in not constant error terms. Heteroskedasticity is tested for in each model using the Breusch-Pagan test for heteroskedasticity. For models that have a significant p-value,
robust standard errors are used. Fourth, without controlling for time-invariant factors from year to year and within
states, the specification is vulnerable to omitted variable bias. To address this issue, time and state-specific effects are controlled for using year and state dummy variables.
The dataset used for the initial analysis is a panel dataset with 50 states
25
over eight years 2002 to 2009. The three independent variables of interest, as defined above, are the
24
The Durbin-Watson test does not work on panel datasets. The Wooldridge test xtserial in STATA sets a null hypothesis of no serial correlation.
25
New York is not included for 2002.
135 expenditure, tax, and rainy day actions taken within a fiscal year. The regression equation
below describes the model of fiscal stress within the states. The expenditure, tax and rainy day actions are included in the same model because the analysis attempts to tease
out the effect
26
of reducing expenditures, raising taxes, and using rainy day fund balances while holding the other responses constant. The other variables included in the model –
economic, political, and institutional factors – are control variables used in previous research Hou 2003; Jimenez 2009; Poterba 1994.
Two-way scatter plots were used to identify outliers for each dependent- independent variable model. With budget fiscal stress as the dependent variable and the
three independent variables of interest tax and fee increases, expenditure cuts, and rainy day fund use, two states, Alaska and Wyoming, consistently deviated from the scatter
plot groupings. Similar analyses were done for the cash, long-run and service-level fiscal stress dependent variables. Alaska was an outlier for the cash fiscal stress model,
Nebraska and Wyoming outliers for the long-run fiscal stress dependent variable and Alaska and Nevada outliers for the service-level fiscal stress dependent variable. These
state outliers were removed from the relevant regression model. To address the first two questions: 1 Are some states able to navigate better
through periods of fiscal stress than other states?, and 2 Are certain state responses more effective at reducing or alleviating fiscal stress?; the effects of institutional factors
as well as expenditure cuts, tax increases, and rainy day fund use on fiscal stress will be tested.
26
Literature shows that the three state responses are not used in a vacuum. Indeed states may use one instead of the other in a trade-off Maag and Merriman 2007. However, a correlation matrix shows
relatively low correlation between the enacted change in tax revenues as a percent of total tax revenue, percentage change in expenditures, and change in rainy day fund balance as a percent of total general
expenditures 0.05 between the tax and expenditure variables, -0.02 between rainy day fund and tax variables, and 0.19 between expenditure and rainy day fund variables.
136 STRESS
it
= β
1
EXPENDITURE
it-1
+ β
2
TAX
it-1
+ β
3
RDF
it-1
+β
4
BBREQ
it
+ β
5
TEL
it
+ β
6
ECONOMIC
it-1
+ β
7
POLITICAL
it
+ β
8
STRUCBAL
i2008
+ γ
t
+ ε
it
i = 50 or 49 t = 8 2002-2009
To address the third question, 3 Does the choice of response by a state in one period of economic downturn affect its experience of fiscal stress through a subsequent
period of economic downturn?, the dataset will be restricted to three years 2007-2009. The model below includes the three state actions in 2002. In 2002, states experienced
higher levels of fiscal stress due to the effects of a national and subsequently regional and state recession.
STRESS
it
= β
1
EXPENDITURE
it-1
+ β
2
TAX
it-1
+ β
3
RDF
it-1
+β
4
EXPENDITURE
i2002
+ β
5
TAX
i2002
+ β
6
RDF
i2002
+ β
7
BBREQ
it
+ β
8
TEL
it
+ β
9
ECONOMIC
it-1
+ β
10
POLITICAL
it
+β
11
STRUCBAL
i2008
α
i
+ γ
t
+ ε
it
i = 50 t = 3 2007-2009
6.3 Findings Descriptive Statistics
