Tax-spend or fiscal illusion?
Young, Andrew T.
[My opponent] tells us that first we've got to reduce spending
before we can reduce taxes. Well, if you've got a kid that's
extravagant, you can lecture him all you want to about his extravagance.
Or you can cut his allowance and achieve the same end much quicker.
--Ronald Reagan (1980)
The attractiveness of financing spending by debt issue to the
elected politicians should be obvious. Borrowing allows spending to be
made that will yield immediate political payoffs without the incurring
of any immediate political cost.
--James Buchanan (1984)
What is the intertemporal relationship between U.S. federal
government expenditures and revenues? Do variations in revenues cause
variations in expenditures (tax-spend) or is causation the other way
round (spend-tax)? Alternatively, is causation bidirectional or
nonexistent? Understanding the "revenue-expenditure nexus" has
important implications for the political economy of fiscal policies.
For example, if causation is in the tax-spend direction, then there
are at least two interpretations. First, there is the conventional
tax-spend hypothesis associated with Milton Friedman (1978): Government
wants to and will spend whatever is made available. If tax revenues are
increased, spending will increase; if tax revenues are lowered, the
beast is starved. Revenues have a positive causal relationship to
expenditures. This view has led various proponents of limited government
to encourage tax cuts that are not conditional on offsetting spending
cuts. The ultimate goal is for eventual spending cuts as a result of
"starving the beast." (1)
On the other hand, a negative causal relationship from revenues to
expenditures may exist due to fiscal illusion (Wagner 1976, Buchanan and
Wagner 1977). Niskanen (1978, 2002, 2006) finds a negative correlation
between federal expenditures and tax receipts. He states, "The most
direct interpretation [is] a demand curve [where] federal spending is a
negative function of the tax price" (Niskanen 2002: 184). A tax
increase may make taxpayers hostile toward government spending as they
are forced to directly reckon with its costs. (2) Likewise, tax
decreases may lessen the perceived cost of government spending,
increasing the quantity demanded.
For proponents of limited government, understanding which of these
relationships best explains reality is critical in terms of policy.
Believers in conventional tax-spend or "'starve the
beast" may applaud the type of tax cuts associated with Ronald
Reagan and George W. Bush because, despite the lack of simultaneous
spending cuts, lower taxes are expected to constrain future spending.
Alternatively, believers in fiscal illusion may view such tax cuts as
counterproductive because they perversely encourage even greater
spending by decreasing its perceived (by the electorate) price. Fiscal
illusionists may instead encourage tax increases (especially during
times of budget deficits) because they force the public to confront the
costs of excessive spending, hopefully decreasing their tolerance for
it.
Ultimately, which relationship best describes the
revenue-expenditure nexus is an empirical question and several recent
studies using U.S. federal time series data provide evidence for the
conventional (Friedman-type) tax-spend hypothesis. Examples include Bohn
(1991), Mounts and Sowell (1997), Koren and Stiassny (1998), Garcia and
Henin (1999), and Chang, Liu, and Candill (2002). However, Baghestani
and McNown (1994) find that there is no relationship between revenues
and expenditures, and Ross and Payne (1998) provide evidence favoring
the spend-tax hypothesis. Payne (2003) provides an excellent survey of
the literature for the United States and other nations. All of the
recent studies follow the example set early on by Miller and Russek
(1989) in estimating error-correction models that allow for long-run
fiscal synchronization (cointegration).
Recent U.S. evidence for the fiscal-illusion hypothesis is scant.
One exception is a recent paper by Romer and Romer (2007a). They use a
measure of "tax changes taken for long-run purposes" based on
narrative evidence from government sources (developed in Romer and Romer
200719). Regressing changes in federal spending on contemporaneous and
lagged values of this measure, they find that tax cuts are positively
associated with significant increases in expenditures. This sort of
perverse effect is precisely the type a fiscal illusionist may fear is
associated with tax cuts unaccompanied by spending cuts. However, Romer
and Romer do not consider an intertemporal budget constraint for the
government and control for budgetary disequilibria in an
error-correction framework. Doing so is standard in the literature. This
criticism is also applicable to the early findings by Niskanen (1978).
Darrat (1998, 9,002) finds evidence of the fiscal illusion hypothesis in
the context of the revenue-expenditure nexus for Turkey, Lebanon, and
Tunisia.
The existing literature uniformly imposes symmetry on revenue
effects in expenditure equations. This constraint may bias results
toward the conventional tax-spend hypothesis because it is based on
simple adherence to a budget constraint. In contrast, the fiscal
illusion hypothesis--based on the public's subjective perceptions
of the cost of government spending--is more plausibly associated with
asymmetric responses. For example, individuals may be more sensitive to
tax increases, seeking to assign blame for those shocks, while tax
decreases are more passively accommodated. This may be due to
irrationality, but not necessarily. Tax decreases (relative to spending)
create future tax liabilities that may or may not be paid during the
individual's lifetime. Tax increases, on the other hand, are
realized with certainty. Also, an insensitivity to tax decreases
relative to increases is consistent with the loss-aversion hypothesis
put forth in the prospect theory of Kahneman and Tversky (1979, 1991).
In this article, I evaluate the conventional tax-spend hypothesis
versus the fiscal illusion hypothesis by analyzing quarterly data from
1959:3 to 2007:4 on U.S. federal revenues and expenditures within an
error-correction framework. The findings suggest that (a) decreases in
taxes do not Granger-cause changes in federal expenditures while (b)
increases in taxes significantly and negatively affect expenditures.
Following Ewing et al. (2006), I also allow for asymmetric responses to
long-run budgetary disequilibria. The findings, (a) and (b) from above,
are robust to allowing for error-correction asymmetries. This result
suggests that fiscal illusion-type effects are present even when
controlling for different potential types of intertemporal adjustment to
the government's budget constraint.
This article is organized as follows: First, I describe the data
and explore their relevant properties for the analysis that follows.
Second, I present an overview of the error-correction framework and
present the basic results. Third, I explore the robustness of the basic
results to asymmetries in the error-correction process. Fourth, I
conclude with a brief summary and discuss the policy implications of my
results.
The Data and Their Relevance
Quarterly data on total receipts and expenditures for the U.S.
federal government from 1959:3 to 2007:4 are used in this study. (3) The
data are transformed into natural logs and then scaled by the natural
log of GDP. (4) These data are basically identical to those used by
Ewing et al. (2006) except for slightly longer coverage. Figure 1 plots
the scaled time series. Among other features, the persistent budget
deficits of the 1980s are clearly visible, as are the subsequent and
short-lived Clinton surpluses and the return to deficits under George W.
Bush.
Augmented Dickey-Fuller (1979) and Phillips-Perron (1988) unit root
tests (Table 1) fail to reject a unit root for both the scaled revenue
(r) and expenditures (x) series. For their first differences (At and
[DELTA] x), however, the unit root hypothesis can be easily rejected.
Therefore, I focus the analysis on these differenced variables, for
which summary statistics are provided in Table 2.
[FIGURE 1 OMITTED]
Incorporating [DELTA] r and [DELTA] x into an error-correction
framework makes sense if r and x are not only nonstationary but also
cointegrated. I estimate the following relationship by OLS,
(1) [r.sub.t] = [beta][x.sub.t] + [[epsilon].sub.t].
The error term associated with the above relationship should be
stationary if the two variables are cointegrated. In other words,
revenue and expenditure levels are ultimately tied to one another by a
(long-run) budget constraint. Augmented Dickey-Fuller (ADF) and
Phillips-Perron tests both reject the unit root hypothesis at the 1
percent significance level. (5)
Empirical Framework and Results
Given that U.S. federal government revenues and expenditures are
cointegrated, it is appropriate to exploit an error-correction
framework. Indeed, Bohn (1991), Mounts and Sowell (1997), Koren and
Stiassny (1998), Gareia and Henin (1999), and Ewing et al. (2006) are
all based on error-correction models (ECMs). A standard ECM system is,
(2) [DELTA][x.sub.t] = [[gamma].sub.0] +
[[alpha].sub.1][DELTA][x.sub.t-1] + ... +
[[alpha].sub.p][DELTA][x.sub.t-p] + [[beta].sub.1][DELTA][r.sub.t-1] +
... + [[beta].sub.[rho]][DELTA][r.sub.t-p] + [rho][[??].sub.t-1] +
[u.sub.t]
(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [[??].sub.t] is the period t estimated residual from the
cointegrating relationship (1). The system, (2) and (3), is estimated by
OLS. Since the focus of this article is on evaluating the conventional
tax-spend hypothesis versus the fiscal illusion hypothesis, I restrict
reporting to results from expenditure equations such as (2).
Equation (2) represents the standard hypothesis in the literature
whereby changes in revenue have symmetric effects on expenditure
changes. I estimate (2) for lag lengths (p) of 1 through 8. The Akaike
information criterion (AIC) suggests a lag length of 4 (AIC = -9.2459).
The results of that regression are presented on the left-hand side of
Table 3. Similar to several previous studies, the hypothesis that the
coefficients on revenue changes are jointly 0 is rejected at the 5
percent significance level. This suggests that revenue changes
Granger-cause changes in expenditures. Furthermore, Granger causality is
based on a positive coefficient on the 4th lag of [DELTA]r
([[beta].sub.4]). The interpretation of Granger causality here is in
terms of the conventional tax-spend hypothesis. With about a 2-year lag,
increases (decreases) in federal government receipts result in increases
(decreases) in federal government expenditures.
Now consider an alternative ECM where revenue increases and
decreases are allowed to affect expenditures asymmetrically:
(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [D.sup.POS] = I if [DELTA]r > 0 and 0 otherwise;
[D.sup.NEG] = i if [DELTA]r < 0 and 0 otherwise. (6) Specification
(4), in a straightforward way, allows for changes in federal government
revenues to have different effects on expenditures depending on whether
those revenue changes are positive or negative. I estimate (4) for lag
lengths (p) of 1 through 8. The AIC again suggests a lag length of 4.
The right-hand side of Table 3 presents the results of
incorporating asymmetric effects. The first statistic to note is the R2,
which rises from 0.1482 to 0.1930 when asymmetric effects are permitted.
This result is to be expected given the greater number of explanatory
variables. However, the AIC, which imposes a penalty for including
additional variables (explanatory power being equal), also falls
slightly from -9.2334 to -9.2452, despite the addition of four
additional terms. These statistics suggest that the data are more
consistent with the asymmetric model than with the symmetric
alternative.
In the case of the asymmetric ECM, the null hypothesis of no
Granger causality cannot be rejected at the 10 percent significance
level for negative revenue changes. However, the null hypothesis can be
rejected for positive changes at the 5 percent significance level. That
revenue increases Granger-cause expenditure changes is based on
significant coefficients on the 2nd and 3rd lags of [DELTA]r: -0.2340
and 0.1866 respectively, both significant at the 5 percent level. Given
these coefficient estimates, a reasonable interpretation is that an
increase in federal receipts leads to a decrease in government
expenditure about two quarters later. This is inconsistent with
conventional tax-spend and consistent with fiscal illusion effects. The
relative point estimates imply that the associated expenditure decrease
only partially reverses itself in the following quarter. However, the
null hypothesis that [[beta].sub.1.sup.POS] + [[beta].sub.2.sup.POS] +
[[beta].sub.3.sup.POS] + [[beta].sub.4.sup.POS] = 0 cannot be rejected.
Robustness to Asymmetric Error Correction
We can now examine the robustness of the earlier results with
respect to an extension of the basic ECM explored by Ewing et al.
(2006). These authors apply the threshold autoregression (TAR) and
momentum threshold autoregression models (M-TAR) of Enders and Granger
(1998) and Enders and Sildos (2001) to test the symmetry assumption of
the ECM with respect to budgetary disequilibria. Based on these models,
Ewing et al. (2006) reject the symmetry null hypothesis.
Checking the robustness of the present results to asymmetric
adjustment to budgetary disequilibria is important. If, for example, the
federal government adjusts more quickly to large deficits than to
surpluses or small deficits (say, because large deficits are ultimately
not sustainable and politicians or the electorate recognize this) then
the ECM is misspeeified. In particular, the negative relationship
between tax increases and spending may not be indicative of the fiscal
illusion story told above but may, instead, be capturing the (omitted)
mechanism through which adjustment to budgetary disequilibrimn occurs.
In other words, if deficits get large enough, adjustment occurs through
raising taxes and decreasing spending.
TAR and M-TAR models are estimated using the residuals
([[??].sub.t]) from the estimated cointegration relation, (1). Each
model is based on estimating,
(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where, for TAR and M-TAR respectively,
(6) [I.sub.t] = 1 if [[??].sub.t-1] [greater than or equal to]
[tau] and 0 if [[??].sub.t-1] < [tau]
(7) [I.sub.t] = 1 if [DELTA][[??].sub.t-1] [greater than or equal
to] [tau] and 0 if [delta][[??].sub.t-1] < [tau]
The threshold, [tau], is determined endogenously using Chan's
(1993) method:
(i) arrange the [[??].sub.t] 's (TAR) or
[DELTA][[??].sub.t]'s (M-TAR) in increasing order, (ii) exclude the
smallest and largest 15 percent of the observations, (iii) choose [??]
out of the remaining 70 percent of observations associated with the
smallest SSR from OLS regression of (5).
Given [[??].sub.TAR] and [[??].sub.M-TAR,] for each model the
relevant null hypothesis is [H.sub.0]: [[rho].sub.1] = [[rho].sub.2]
(i.e., symmetric adjustment to budgetary disequilibria). As well, the
threshold values can be used to estimate an ECM with both short-run and
long-run asymmetric effects.
(8) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
[FIGURE 2 OMITTED]
In (8), [[rho].sub.1] represents the effects of above-threshold
budgetary disequilibria and [[rho].sup.2] represent the effects of
below-threshold budgetary conditions.
Table 4 demonstrates that, for a choice of either p = 2 or 4 in
estimating (5), the chosen TAR or M-TAR thresholds are the same
([[??].sub.TAR] = 0.0025 and [[??].sub.M-TAR] = 0.0040). This outcome is
reassuring because, though the MC favors p = 2 for both TAR and M-TAR,
the threshold is not sensitive to a chosen lag structure consistent with
the p = 4 used in the previous regressions.
Results of estimating (8) using I's defined by the estimated
thresholds are presented in Table 5. One interesting result is that,
while both TAR and M-TAR models strongly reject symmetric adjustment to
budgetary disequilibria, the nature of the asymmetry is completely
different depending on the model. So the M-TAR results suggest that
[[rho].sub.2] is statistically significant and large relative to
[[rho].sub.1] , which is insignificant. Ewing et al. (2006) report M-TAR
results and, based on those, argue that expenditures only respond to
"worsening" budgetary conditions (by which they mean
below-threshold disequilibria). However, the TAR model results suggest
the exact opposite: expenditures respond only to above-threshold
disequilibria. (Note that the TAR model's [R.sub.2] is slightly
higher.) (7)
Whether more faith is placed in the M-TAR or TAR results is of
second-order importance for the issues explored here. The important
point is that a range of adjustments to budgetary disequilibria have
been allowed for and the earlier results are robust: Revenue increases
Granger-cause expenditure changes two quarters later, and the effect is
negative and only partially reversed in the following quarter. One
notable difference is in the M-TAR model where the null hypothesis of no
Granger causation can be rejected for negative (as well as positive)
revenue changes. Taken at face value, the MTAR model associates
decreases in federal revenues with conventional tax-spend effects.
However, it is again noted that the R2 is in favor of (i.e., higher in
the case of) the TAR model where only revenue increases Granger-cause
expenditures.
Conclusion
The existing literature on the U.S. federal government
revenue-expenditure nexus is mixed. There exist studies supporting no
short-run causal relationship between revenues and expenditures, as well
as both spend-tax and tax-spend views. Within the literature claiming to
establish a causal link from changes in revenues to expenditures, the
conventional, Friedman-type tax-spend view has been almost ubiquitous.
Evidence of the competing fiscal illusion hypothesis has largely been
absent. According to this hypothesis, increases (decreases) in revenues
increase (decrease) the perceived cost of government leading to
decreases (increases) in the quantity demanded of expenditures.
Using quarterly U.S. data from 1959:3 to 2007:4, I demonstrate that
allowing revenue increases and decreases to asymmetrically affect
expenditures in an otherwise standard error-correction model leads to
evidence of fiscal illusion. Specifically, conventional tax-spend
partial correlations appear to be those associated with revenue
decreases but are not significant in a Granger-causal sense.
Alternatively, revenue increases Granger-cause decreases in federal
government expenditures. This result is robust to incorporating
asymmetric, long-run adjustments to budgetary disequilibria
(error-correction).
For advocates of reining in an expanding federal government, the
results here do not provide strong support for
"starve-the-beast" type of policies. Perhaps
counter-intuitively, the findings suggest that tax increases--even
temporary--may serve to decrease expenditures by forcing the public to
reckon with the cost of government spending. The findings suggest that
the electorate has to be clearly presented with the bill to recognize
the cost of government, rather than being allowed to run up a tab.
This article should be viewed as a starting point for
reconsideration of the importance of the fiscal illusion hypothesis.
This reconsideration comes at an important time. The current decade has
been characterized by the reappearance of federal budget deficits and
the repeated call for tax cuts with offsetting cuts in spending. Aside
from the econometric results presented in this article, recent
experience may support a healthy skepticism toward
"starve-the-beast" policies.
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(1) See Tempelman (2006) for a review of the historical development
of academic and political arguments for and against the "starve the
beast" view.
(2) This hypothesis assumes that people do not behave as farsighted
members of infinitely lived dynasties (Barro 1974).
(3) These data are taken from the Bureau of Economic Analysis,
Table 3.2, Federal Government Current Receipts and Expenditures. Data
are in billions of dollars and are seasonally adjusted.
(4) The data are taken from the BEA Table 1.1.5, Gross Domestic
Product. They are in billions of dollars and seasonally adjusted.
(5) The ADF statistic is -2.73 (p-value = 0.01) and the
Phillips-Perron statistic is -2.96 (p-value = 0.00). Although economic
intuition suggests that a long-run balanced budget condition must hold,
I also estimate (1) including an intercept. The resulting residuals are
also stationary and have a correlation of 0.91 with the baseline
residuals.
(6) The issue of [DELTA]r = 0 does not occur in the data.
(7) Ewing et al. (2006) use a two-lag specification where the M-TAR
[R.sub.2] is slightly higher than in the TAR model. However, the key
point seems to be that, while differences in explanatory power are
small, the choice of TAR or M-TAR results in one or another wildly
different conclusions concerning asymmetric error-correction.
Andrew T. Young is Assistant Professor of Economics at the
University of Mississippi. He thanks Bill Shughart, Paul Pecorino,
participants at the 2008 Southern Economic Association meetings in
Washington, D.C., and at a 2008 West Virginia University economics
department seminar for helpful comments. He also thanks Jim Dorn and an
anonymous referee.
TABLE 1
UNIT ROOT TESTS ON U.S. FEDERAL REVENUES
AND EXPENDITURES
Statistic r x
ADF -2.58 -1.65
(0.29) (0.77)
Phillips-Perron -2.48 -1.19
(0.34) (0.91)
[DELTA]r [DELTA]x
ADF -16.23 -9.07
(0.00) (0.00)
Phillips-Perron -16.23 -15.55
(0.00) (0.00)
NOTES: Both the ADF and Phillips-Perron tests include
constants and linear trends. Numbers in parentheses
are p-values. Data cover 1959:3 to 2007:4.
TABLE 2
SUMMARY STATISTICS FOR U.S. FEDERAL REVENUE AND
EXPENDITURE CHANGES
[DELTA]r [DELTA]x
Mean 0.000568 0.000577
Maximum 0.018119 0.000280
Minimum -0.018119 -0.008454
Standard Deviation 0.003352 0.002531
Correlation -0.183460 -0.183460
Correlation with
[DELTA]r(-1) -0.156136 -0.016313
[DELTA]r(-2) 0.115866 -0.074998
[DELTA]r(-3) -0.071234 0.079624
[DELTA]r(-4) 0.033348 0.166100
Correlation with
[DELTA]x(-1) -0.082363 -0.119555
[DELTA]x(-2) 0.023534 0.248538
[DELTA]x(-3) -0.048255 0.039941
[DELTA]x(-4) 0.145869 0.023482
NOTE: After differencing, the data cover 1959:4 to 2007:4.
TABLE 3
RESULTS OF ESTIMATING EXPENDITURE ECM EQUATION
Coefficient Symmetric Coefficient
[[beta].sub.1] 0.0293 [[beta].sub.1.sup.NEG]
(0.0541)
[[beta].sub.2] -0.0429 [[beta].sub.2.sup.NEG]
(0.0545)
[[beta].sub.3] 0.0812 [[beta].sub.3.sup.NEG]
(0.0536)
[[beta].sub.4] 0.1508 *** [[beta].sub.4.sup.NEG]
(0.0528)
[[beta].sub.1.sup.POS]
[[beta].sub.2.sup.POS]
[[beta].sub.3.sup.POS]
[[beta].sub.4.sup.POS]
[rho] 0.0330 * [rho]
(0.0192)
[R.sup.2] 0.1482 [R.sup.2]
AIC -9.2334 AIC
F-stat 2.5254 ** F-stat
([[beta].sub.1] = ([[beta].sub.1.sup.NEG] =
[[beta].sub.2] = [[beta].sub.2.sup.NEG] =
[[beta].sub.3] = [[beta].sub.3.sup.NEG] =
[[beta].sub.4] = 0) [[beta].sub.4.sup.NEG] = 0)
F-stat
([[beta].sub.1.sup.POS] =
[[beta].sub.2.sup.POS] =
[[beta].sub.3.sup.POS] =
[[beta].sub.4.sup.POS] = 0)
F-stat 1.7934 F-stat
([[beta].sub.1] + ([[beta].sub.1.sup.POS] =
[[beta].sub.2] + [[beta].sub.2.sup.POS] =
[[beta].sub.3] + [[beta].sub.3.sup.POS] =
[[beta].sub.4] = 0) [[beta].sub.4.sup.POS] = 0)
Coefficient Asymmetric
[[beta].sub.1] -0.0160
(0.0902)
[[beta].sub.2] 0.1066
(0.0977)
[[beta].sub.3] -0.1087
(0.0977)
[[beta].sub.4] 0.2084 **
(0.0945)
0.0062
(0.0933)
-0.2340 **
(0.0929)
0.1866 **
(0.0874)
0.1025
(0.0874)
[rho] 0.0381 **
(0.0171)
[R.sup.2] 0.1930
AIC -9.2452
F-stat 1.8660
([[beta].sub.1] =
[[beta].sub.2] =
[[beta].sub.3] =
[[beta].sub.4] = 0) 3.0974 **
F-stat 0.1304
([[beta].sub.1] +
[[beta].sub.2] +
[[beta].sub.3] +
[[beta].sub.4] = 0)
NOTES: *, **, *** denote significance at the 10 percent, 5 percent,
and 1 percent levels, respectively. Numbers in parentheses are
standard errors. "Symmetric" indicates results from estimation
of (2); "Asymmetric" indicates results from estimation of (4).
TABLE 4
ESTIMATED THRESHOLD VALUES FOR TAR AND
M-TAR MODELS
Coefficient TAR M-TAR
p=2
[[rho].sub.1] -0.3345 *** -0.0198
[[rho].sub.2] -0.0455 -0.2522 ***
[tau] 0.0025 0.0040
(1959.3; 0.0029) (1959.4; 0.0030)
AIC -8.1785 -8.1796
p=4
[[rho].sub.1] -0.3266 *** -0.0222
[[rho].sub.2] -0.0352 -0.2440
[tau] 0.0025 0.0040
(1959.3; 0.0031) (1959.4; 0.0030)
AIC -8.1719 -8.1574
NOTES: *, **, *** denote significance at the 10 percent, 5 percent,
and 1 percent levels, respectively. Numbers in parentheses are,
first, the date associated with the threshold residual value and,
second, the SSR associated with the model regression using that
threshold. The parameter estimates of [[rho].sub.1] and
[[rho].sub.2] correspond to equation (5).
TABLE 5
RESULTS OF ESTIMATING TAR AND M-TAR VERSIONS OF
EXPENDITURE EQUATION
Coefficient TAR M-TAR
[[beta].sub.1.sup.NEG] -0.0088 -0.0635
(0.0864) (0.0917)
[[beta].sub.2.sup.NEG] 0.1430 0.1503
(0.0941) (0.0984)
[[beta].sub.3.sup.NEG] -0.0833 -0.1010
(0.0939) (0.0965)
[[beta].sub.4.sup.NEG] 0.1735 * 0.2116 **
(0.0910) (0.0934)
[[beta].sub.1.sup.POS] 0.0022 0.0256
(0.0894) (0.0925)
[[beta].sub.2.sup.POS] -0.2557 *** -0.2328 **
(0.0892) (0.0925)
[[beta].sub.3.sup.POS] 0.1502 * 0.1777 **
(0.0843) (0.0864)
[[beta].sub.4.sup.POS] 0.0988 0.0886
(0.0758) (0.0784)
[[rho].sub.1] 0.1791 *** 0.0134
(0.0384) (0.0200)
[[rho].sub.2] 0.0060 0.0932
(0.0182) (0.0293)
[R.sup.2] 0.2627 0.2168
AIC -9.3249 -9.2645
F-stat 1.8045 2.3887 *
([[beta].sub.1.sup.NEG] =
[[beta].sub.2.sup.NEG] =
[[beta].sub.3.sup.NEG] =
[[beta].sub.4.sup.NEG] = 0)
F-stat 3.2385 ** 2.9064 **
([[beta].sub.1.sup.POS] =
[[beta].sub.2.sup.POS] =
[[beta].sub.3.sup.POS] =
[[beta].sub.4.sup.POS] = 0)
F-stat 0.0007 0.1240
([[beta].sub.1.sup.POS] =
[[beta].sub.2.sup.POS] =
[[beta].sub.3.sup.POS] =
[[beta].sub.4.sup.POS] = 0)
F-stat 16.4425 *** 5.2746 **
([[rho].sub.1] = [[rho.sub.2])
NOTES: *, **, *** denote significance at the 10 percent, 5 percent,
and 1 percent levels, respectively. Numbers in parentheses are
standard errors.
