1. 1
Do Households Internalise Public Debt?
1. Introduction
The controversial issue over whether government bonds are considered part of household net wealth has been a
founded problem in the economic literature for decades. The importance of such question can be easily seen
given the implications on the underlying economic theory. If an increase in public net debt is indeed perceived to
produce an income effect in any given household, then fiscal policy can be used to stimulate consumption and
therefore aggregate demand (Modigliani 1961). This follows the more widely recognised method of modelling
consumer spending, as postulated by Keynes (1936), in which the government can intervene in the economy
through government expenditure and taxation.
Nevertheless, if households internalise public debt the previous scenario changes considerably. Initially brought
forward by Ricardo (1820), and later revised by Barro (1974), the Barro-Ricardo Equivalence Theorem assumes
that consumers are fiscally aware and adjust their consumption behaviour according to the current situation of
the government’s public finances. This stands in strict contradiction to the Keynesian view, implying that fiscal
policy is ineffective in stimulating the economy.
In spite of the substantial implications for government policy and hence the economy, literature on the subject is
yet to reach conclusive results. The purpose of this paper is thus to model household consumption using a set of
fiscal variables, namely public deficit and net public debt, and empirically assess the validity of the Ricardian
Equivalence Theorem.
2. Theory
The Ricardian Equivalence Theorem suggests that an individual’s consumption pattern over time is the result of
an ultra-rational behaviour in which utility is maximised subject to an after-tax lifetime budget constraint (Ricardo
1820). Thus, provided that individuals are fiscally aware and fully consider the future tax burden that will be
required to service the debt, introducing higher taxes today or in the future will be equivalent as far as consumers
are concerned. This has very important implications for government policy since it suggests that financing
expenditure through either higher taxation or bonds will have an identical effect on consumption: the present
value of the individual’s net wealth will remain equal (Cunningham & Harberger 2005).
The theory has, however, been highly criticized over the years, most notably because of its crude assumption that
households have an infinite lifetime. If an individual were to die before higher taxes were introduced, then he
would benefit from a positive wealth effect. A way to circumvent this restriction was given by Barro (1974), who
introduced the notion of intergenerational altruism. If the utility of an individual today is affected not only by his
welfare but also that of his children, then he would behave as if he would live forever. Following a tax for deficit
swap today, the individual would do so by leaving the future generation an amount, in the form of bequests,
which would fully compensate them for the higher taxes in the future.
In order to assess the validity of the Barro-Ricardo Theorem, several economists have undergone empirical
research. In spite of this, the results found in the literature are mixed, this being largely explained by the
employment of different econometric techniques and data sets. The standard way to test for equivalence is
nonetheless to model household consumption by including a set of fiscal variables (Stanley 1998).

2. 2
0 1 2 3 4 5 6t t t tt t t tC G WY Tx B Tr µα α α α α α α= + + + + + + + (0.1)
Where ∁ 𝑡 is household consumption, 𝑌𝑡 is personal income, 𝐺𝑡 is government expenditure, 𝑊𝑡 is household net
wealth, 𝑇𝑥𝑡 is tax revenue, 𝐵𝑡 is net public debt and 𝑇𝑟𝑡 is government transfer payments. Kochin (1974)
estimated a similar function over the years 1952-1971, although having used disposable income and the deficit.
This allows testing directly the general restriction that a $1 tax for deficit swap will leave consumption unaffected.
Although significant results are found in favour, Kochin uses consumption on non-durables and services which is
not in line with the original theory.
Feldstein (1982) undertook the standard approach, allowing for the fact that marginal propensities to consume
out of pre-tax and after tax income might not be the same. He used data from 1930-1977 and was the first one to
employ instrumental variable estimation to correct for the endogeneity found in the tax variable. The lagged tax
variable was used as an IV although it is not entirely uncorrelated with the error term. Overall, Feldstein found no
evidence that supports Ricardian Equivalence.
Kormendi (1983) used a consolidated approach and is hitherto the strongest supporting evidence of equivalence.
The permanent income hypothesis was used to model household consumption over the period 1931-1976. More
recently, a paper by Perelman and Pestieau (1993) has found mixed results while using an error correction model
(ECM). Overall, both the strict Keynesian and Ricardian view were rejected.
3. Model
The model will follow a more recent attempt by Perelman and Pestieau (1993) to test for Ricardian Equivalence
by making use of an ECM. The approach is similar to that of Kochin (1974) in which fiscal variables, namely
government deficit and net public debt, are used along with disposable income and household net wealth to
model private consumption:
0 1 2 3 4t t tt t tC WYD DEF B µα α α α α= + + + + + (0.2)
Following the strict assumptions implied by the theory, two tests can be performed and these involve imposing
the restrictions that 𝛼1 + 𝛼2 = 0 and 𝛼3+ 𝛼4 = 0 . The former suggests that a $1 tax for debt swap leaves
consumption unchanged while the later implies that households do not consider government bonds to be part of
net wealth. This follows from the underlying fact that Household Net Wealth includes household holdings of
treasury bills. Conversely, the Keynesian view suggests that 𝛼2 = 0 and 𝛼4 ≥ 0 such that 𝛼3 + 𝛼4 ≥ 0, meaning
that government bonds will produce a net wealth effect.
4. Data
The variables used in the model follow directly from equation (1.2) and span across the period 1948-2007.
Personal Consumption Expenditures and Disposable Income were both taken from the National Income and
Product Accounts Tables (NIPA) found in the U.S Bureau of Economic Analysis. Net Public Debt and Total
Government Surpluses and Deficits were taken from the Historical Tables of the U.S Office of Management and
Budget. Lastly, the measure of Household Net Wealth was taken from the Flow of Funds Account provided by the
Board of Governors of the Federal Reserve System.

3. 3
All variables were initially deflated by the Implicit Price Deflator for Gross Domestic Product, also found in the
NIPA, and turned into constant 2005 hundred-dollar units. Furthermore, annual population estimates provided by
the United States Census Bureau were used to express the variables in per capita terms.
Descriptive statistics are presented in appendix two. Although Household Wealth and Public Debt do not have a
normal distribution, as shown in table two, this did not influence the normality of the residuals when the model
was estimated.. Two correlation matrices, presented in table three, were also calculated and show a high
correlation between the variables. This, however, should not pose a problem since the variables were estimated
in first differences.
In addition, the model was also estimated in log-linear form such that all variables were transformed to
logarithms. Descriptive statistics are reported in appendix seven, table five, and show that the normal distribution
of the variables has improved slightly, as signalled by a higher Jarque-Bera P-value. Taking the log of the deficit
variable involved adding a constant to ensure that the minimum observation was equal to one (Gujarati 2009).
Finally, visual plots of both the Deficit and Public Debt, figure one and two respectively, encouraged the inclusion
of three dummy variables following three possible structural breaks in the data. The first coincides with one Oil
Shock starting in 1979 and the Savings and Loan crisis which signal the change in the trend of public debt levels.
The second one spans over the period 1992-007 and accounts for the end of the Cold War, and the respective fall
in government expenditure, and the increase in tax revenue following the period leading up to the collapse of the
dot.com bubble. The third dummy covers the post-collapse period 2000-2007.
5. Empirical Analysis
5.1 Unit Root Tests
One problem found when estimating equation (1.2) is that the series might not be stationary processes.
Stationarity implies that certain statistical properties of the data, namely the mean and the variance, must be
constant and that the covariance be independent of time (Gujarati 2009). If non-stationary variables are used in
time series analysis by the method of ordinary least squares (OLS), then the estimates will be invalid and result in
a “spurious regression” (Granger and Newbold 1974).
In order to test for the presence of a unit root, the method suggested by Dickey and Fuller (1979) can be adopted,
whereby three different regressions are estimated:
1 1
2
p
tt t i t i
i
y y yγ β ε− − +
=
∆ = + ∆ +∑ (0.3)
0 1 1
2
p
tt t i t i
i
y y ya γ β ε− − +
=
∆ = + + ∆ +∑ (0.4)
0 21 1
2
p
tt t i t i
i
ty y ya aγ β ε− − +
=
∆ = + + + ∆ +∑ (0.5)
The parameter in which we are interested is γ and under the null hypothesis 0
: 0H γ = , equation (1.1) becomes
a pure random walk, (1.2) a random walk with a drift and (1.3) a random walk with a drift and trend. Further lags
of each variable are used in order to account for autocorrelation and were selected using the Schwarz Bayesian
Information Criterion. The results are presented in appendix three.

4. 4
All the variables are integrated of order one except for the deficit variable for which the data rejects the null of
unit root when the test is performed both with an intercept and with a drift and a linear trend. Not accounting for
structural breaks can bias the test towards non stationarity (Perron 1989). However, the null of unit root is
rejected irrespective of whether breaks are included. The visual plot, shown in figure one, suggests the variable to
be trend stationary (TS) over the period 1948-1992 with a structural break thereafter, yielding mixed results
between stationary and TS. Re-running the test over the aforementioned period results in a TS process.
5.2 Error Correction Model
Given the presence of (1)I processes, a test for cointegration was performed using the popularised Engle-
Granger (1987) methodology which is still applicable to the n-variable case (Enders 2009). This allows determining
whether a relationship exists in the data such that variables will adjust in order to correct for disequilibria in the
long run. The test involves estimating (1.6) and performing a unit root test on the residuals tê . If these are found
to be stationary, then t
y and tz are said to be cointegrated of order (1, 1). A different set of critical values
(Mackinnon 2010) is used since the residuals are only estimates.
0 1 t tt
y ezβ β= + + (0.6)
Once a cointegrating relationship is found, an Error Correction Model (ECM) such as (1.7) can be estimated where
11 12
&a a are the short run impact coefficients and ya is the speed of adjustment coefficient.
11 11 121 1
1 1
( ) ( )t t iy ytt t t i
i i
i iy y ya a a az zβ ε− −− −
= =
 =+ − + ∆ + ∆ +
 ∆ ∑ ∑ (0.7)
Since equation (1.2) is not a cointegrating vector, the error correction term was estimated as the residual in the
relationship between consumption, disposable income, household net wealth and net public debt. The
requirement that all variables included in the ECM must be integrated of the same order meant that the deficit
variable had to be dropped. Results, presented in appendix four, show that the statistic for the ADF test is above
the critical value found in Mackinnon (2010). The residuals are hence stationary and the variables are
cointegrated such that the ECM can now be estimated as:
1 1 2 3 5 6
1
( ) ( ) ( ) ( )t i t it c t t i t i ct
i
i i i iC a a ê a C a a W aYD B ε− −− − −
=
 = + + ∆ + ∆ + ∆ + ∆ + ∑∆ (0.8)
The optimal lag length for each variable was selected using the General-To-Specific (Gets)1
modelling approach by
Hendry (2001), in which a maximum of two2
lags were allowed in the unrestricted model. The dependant variable
was also lagged in the cases where serial autocorrelation was found. The model is presented in appendix five.
1
The procedure is explained in appendix 5, box 3 notes
2
This is a general rule of thumb for annual data which avoids over parameterizing the model and hence save degrees of
freedom

5. 5
5.3 Diagnostics
Before undergoing any analysis, the model had to be subject to three standard tests in order to ensure no linear
regression analysis assumption was violated. Normality of the residuals was checked using the Jarque-Bera
statistic. The null is the joint hypothesis that the skewness and excess kurtosis are zero. The second test
performed checks that the residuals are not serially correlated and was done using the Breusch-Godfrey LM test
which has a null of no serial correlation. Finally, the last test reports whether the error term has constant variance
(homoskedastic) and was performed using the White test which has a null of no heteroskedasticity. Violation of
any of these can result in inefficiency and bias of the model.
The results are presented in appendix five, box two, and show that the model passes all aforementioned tests, as
shown by the failure to reject the null hypothesis in all three. The Chow test was also performed to account for
structural breaks in the pre-specified dates: 1979, 1992 and 2000. The results, shown in box three, suggest the
structural break in the year 2000 to have been the only significant one. Despite this, running the model with the
dummies (D79, D92 & D2) presented contradicting results, in which only the intercept dummy3
for the break in
1979 was found to be significant. The model with D79 is found in appendix six and the standard tests are in box
four. All coefficients have the expected sign and as before, no problem is reported. The model has also improved
slightly, as suggested by a relatively higher explanatory power ( 2
R adj ) and a lower Schwarz information criteria.
A final test was performed to check for general mis-specification. The test used was the Ramsey RESET test which
involves adding a non-linear combination of the fitted values to help improve the overall explanatory power of
the model. The model is mis-specified if these are significant in explaining the dependant variable. The null of no
mis-specification is rejected, as shown in box four.
The most common causes for the rejection follow from omitted variables or wrong functional form. Attempts
were made to correct the former by including more lagged terms of the dependant variable to solve a possible
dynamic mis-specification4
, especially given the autocorrelation test result. This, however, proved ineffective such
that a log-linear model was then considered following the study of Blinder and Deaton (1985)5
. Subsequent to the
logarithmic transformation, all variables were retested for unit roots and for the existence of a cointegrating
relationship. Appendix eight, table five, shows that all variables remain (1)I processes, apart from the deficit
variable, and appendix nine, box five, shows the residuals are stationary such that an ECM is still applicable.
The “Gets” approach by Hendry (2001) was used to select the number of lags for each variable and the modified
ECM with the standard test results is in appendix ten, box six and seven. The coefficients have the right sign and
no problem is found since the null for the three main tests cannot be rejected. Furthermore, the Ramsey RESET
now signals that the model is correctly specified and the last step involved retesting the model for structural
breaks. Chow test results, shown in box seven, reject the existence of a structural break in all three dates. D79
and D92 were, nonetheless, found to be significant for particular variables. The final model (1.9) is in appendix
eleven and only includes the significant dummies.
3
Interaction dummies were also included for all three variables but found to be insignificant and therefore not reported
4
Dynamic Mis-Specification can result from omitting lagged terms of the dependant variable
5
The paper uses a similar model and suggests the results should not be overly sensitive to either linear or log-linear
regression

6. 6
10.006 0.740 0.066 0.106ln 0.593ln lnln
(0.002)** (0.068)* (0.027)** (0.031)* (0.100)*
0.005 79 0.015 92 0.086 79. 0.431 92.ln ln
(0.003)*** (0.005)* (0.042)** (0.201)**
t tt tt
t t
W êYD BC
D D D DB YD
−= + + + −∆∆ ∆∆
− + − −∆ ∆
(0.9)
All the relevant tests (box eight) indicate that the linear regression assumptions are met and the Ramsey test
suggests that there are no problems, as shown by a failure to reject the null. Finally, the long run estimates (1.10)
are shown below (appendix 9).
0.397 0.831 0.149 0.034ln lnln ln
(0.025)* (0.019)* (0.019)* (0.006)*
t tt tC WYD B=− + + +
(0.10)
5.4 Interpretation
Overall, the regressors in (1.9) can explain around 81% of the variability in consumption, as shown by the
goodness of fit of the model. The coefficients on the variables of interest have the correct sings and are all
significantly different from zero. As expected, net income and wealth have a positive effect on household’s
decision to consume, although the propensity to consume out of disposable income fell considerably (-0.431)
after 1992.
The restriction that the coefficient on disposable income should be symmetrical to that of the deficit cannot be
tested. However, the remaining restriction imposed on the coefficient of the Net Public Debt provides supporting
evidence against the Ricardian Equivalence Theorem. The initial Ricardian restriction implies that the coefficient
on net debt should be negative but equal in magnitude to the coefficient on net wealth. Nevertheless, as shown
by the model, net debt has an overall positive effect on consumption, most notably in the period preceding the oil
shocks, when the coefficient on the variable is shown to be (0.106). Arguably, the effect is much lower after the
oil shocks in 1979 (0.02) but remains positive nonetheless.
The coefficient on the lagged residual is negative and highly significant, thus reinforcing and validating the
existence of a long run relationship among the variables. Any disequilibria in the previous period is corrected at
an annual rate of around 59%. Finally, the long run estimates in (1.10) are also all positive and significant,
providing further evidence that the Ricardian Equivalence does not apply in the long run either.
6. Conclusion
Although the literature on the subject is quite vast, the number of empirical papers which have adopted an
appropriate methodology to account for the use of non-stationary data is yet limited. The current paper,
therefore, attempts to test the Ricardian Equivalence Theorem in light of this by making use of an Error
Correction Model. The analysis performed on annual data from the United States over the period 1948-2007 fails
to find any relevant evidence of household “ultra” rationality. Instead, households appear to be short-sighted or
“myopic”, not fully recognising the increased liabilities that greater levels of public debt will bring in the form of
higher taxes. This is in line with the more widely accepted Keynesian view, in which fiscal policies can affect the
overall state of the economy.

7. 7
Bibliography
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Dickey, D, A. & Fuller, W, A. (1979). “Distribution of the Estimators for Autoregressive Time Series With a Unit
Root”. Journal of the American Statistical Association, Vol. 74, pp 427-431.
Cunningham, J, P. & Harberger, A, C. (2005). “Microeconomic Tests of Ricardian Equivalence”. Unpublished paper.
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Enders, W. (2009). Applied Econometric Time Series. 3rd
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Engle, R, F. & Granger, C, W, J. (1987). “Co-integration and Error Correction: Representation, Estimation and
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Feldstein, M. (1980). “Government Deficits and Aggregate Demand”. Journal of Monetary Economics, Vol. 9, pp.
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Granger, C, W,J. & Newbold, P. (1973). “Spurious Regression in Econometrics”. Journal of Econometrics, Vol. 33,
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Gujarati, Damodar, (2009). Basic Econometrics. 5th
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Mackinnon, J.C. (1996). “Numerical Distribution Functions for Unit Root and Cointegration Tests”. Journal of
Applied Econometrics, Vol. 11, pp. 601-618.
MacKinnon, J.G. (2010). Critical Values for Cointegration Tests. (1227). Queen's University, Canada.
Modigliani, F. (1961). “Long-Run Implications of Alternative Fiscal Policies and the Burden of the National Debt”.
The Economic Journal, Vol.71, pp.730-755.
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Verbon and Winden ed, pp. 181-194.
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1361-1401.
Ricardo, D. (1951). “The Works and Correspondence of David Ricardo”. Edited by P. Sraffa, Cambridge University
Press, Cambridge.
Stanley, T. D. (1998). “New Wine in old Bottles: A Meta-Analysis of Ricardian Equivalence”. Southern Economic
Journal, Vol. 64, pp. 713-727.

8. 8
Appendices
Appendix 1: Variable Description
Table 1: Variable Description
Variable Description Expected Sign
Ricardo Keynes
Cons Personal Consumption Expenditure NA NA
YD Disposable Income = (Personal Income – Personal Income Tax) + +
Def Total Government Surplus/Deficit = (Government Spending – Receipts) - 0
W Household Net Wealth + +
B Net Public Debt - +
D79 D79=1, over the period 1979-2007, 0 elsewhere NA NA
D92 D9=1, over the period 1991-2007, 0 elsewhere NA NA
D02 D02=1, over the period 2001-2007, 0 elsewhere NA NA
Appendix 2: Descriptive Statistics
Table 2: Descriptive Statistics
Variable Mean Median Maximum Minimum Std.Dev. Jarque-Bera
(P-Value )
Cons 168.56 156.09 305.04 82.17 68.99 0.08
YD 186.29 175.52 325.37 87.93 73.16 0.11
Def -6.85 -5.80 7.04 -21.07 6.55 0.43
W 963.65 788.84 2116.79 433.17 464.94 0.01
B 99.76 84.37 169.29 52.27 38.79 0.03
D79 0.21 0 1 0 0.41 0.00
D92 0.13 0 1 0 0.34 0.00
D02 0.13 0 1 0 0.34 0.00
Note: The Jarque-Bera statistic follows a Chi-Square distribution with a null hypothesis of normal distribution.
Table 3: Correlation Coefficients
Cons YD DEF W B
Cons - - - - -
YD 0.99 - - - -
Def -0.47 -0.49 - - -
W 0.98 0.97 -0.38 - -
B 0.81 0.79 -0.34 0.81 -
∆Cons ∆YD ∆DEF ∆W ∆B
∆Cons - - - - -
∆YD 0.76 - - - -
∆Def - - - - -
∆W 0.48 0.31 0.16 - -
∆B 0.25 0.16 -0.27 0.28 -

9. 9
Figure 1: Deficit against Time Figure 2: Public Debt against Time
Appendix 3: Augmented Dickey Fuller Test Results
Table 4: ADF Results
Variable Levels First Differences Conclusion
0a Lag
0
&a t Lag
0a Lag
Cons 2.21 1 -1.37 1 -4.54 0 (1)I
YD 3.28 0 -1.79 0 -6.68 0 (1)I
Def -3.23 1 -3.88 1 NA NA (0)I
W -2.97 3 0.17 3 -6.41 2 (1)I
B -0.95 1 NA NA -3.52 1 (1)I
Def* -1.80 0 -4.31 0 NA NA (0)I
Note: The critical values at a 5% level of significance are -2.91 and -3.49 for intercept and intercept and linear
trend respectively. A single test was performed on the deficit variable* between the years 1948-1992 and the
critical values at a 5% level of significance are -2.93 for intercept and -3.52 for intercept and trend. Critical Values
were taken from Mackinnon (1996).
Appendix 4: Regression Results for Error Correction Term
2.654 0.754 0.027 0.045
(0.941)* (0.016)* (0.003)* (0.012)*
t tt t tC W eYD B=− + + + +
Note: The standard errors are in parentheses and * denotes significance at a 1% level. The 2
R provides a measure
of goodness of fit of the model and the 2
.R adj is adjusted for the number of parameters in the model. The
Breusch-Godfrey LM is a test for first order correlation and follows an F-distribution with a null of no serial
correlation. The p-value for the test with one and two lags is in brackets. The ADF test was performed on the
residuals te and the critical value for the cointegration test with intercept and no trend is -3.95 at a 10% level of
significance (Mackinnon 2010).
-25
-20
-15
-10
-5
0
5
10
50 55 60 65 70 75 80 85 90 95 00 05
DEF
40
60
80
100
120
140
160
180
50 55 60 65 70 75 80 85 90 95 00 05
B
2 2
0.999; . 0.999;
22.973[0.00] 1
4.479; ( )
12.401[0.00] 2
( ) 4.127
R R adj
Lag
Schwarz criterion LM test
Lags
ADF test µτ
=
= =
= −
Box 1:


10. 10
Appendix 5: Regression Results for Error Correction Model
2
1 2 1
0.087 0.572 0.015 0.104 0.1011
(0.413) (0.077)* (0.004)* (0.041)** (0.044)**
0.218 0.084 0.489
(0.088)** (0.076) (0.101)*
t t ttt
t t t
WYD B BC
Cons Cons ê
−
− − −
=− + + + −∆∆ ∆ ∆∆
+ + −∆ ∆
Note: The White test is a test for heteroskedasticity and follows a chi-square distribution with the null hypothesis
of homoskedasticity. White cross terms have been included and the p-value for the test is shown in brackets. As
before, * denotes significance at a 1% level, ** at 5% and *** at 10% significance level. The Ramsey Reset Test is a
general mispecification test and follows an F-Distribution with a null hypothesis of no mispecification.
Note: The Redundant Variable Test follows an F-distribution with a null hypothesis of variable redundancy. Used
with the General-To-Specific approach, it involved selecting the most insignificant coefficients in a two step
procedure. If found insignificant after testing, as signalled by a high P-Value, the variables were dropped. The
Chow Breakpoint Test is used to test for structural breaks in the model and involves estimating two models: one
before the break is found and one after. If the coefficients on the variables are signifficantly different in the two
periods, the test will signal the existence of a structural break. The test follows an F-distribution with a null
hypothesis of no structural break at the specified date.
Appendix 6: Regression Results for Error Correction Model after accounting for Structural Breaks
2
1 2 1
0.062 0.544 0.013 0.175 0.091
(0.375) (0.069)* (0.003)* (0.042)* (0.040)**
0.261 0.128 1.782 790.579
(0.080)** (0.069) (0.095)* (0.514)*
t t ttt
t t t
WYD B BC
DCons Cons ê
−
− − −
=+ + + + −∆∆ ∆ ∆∆
+ + − + −∆ ∆
2 2
2
2
0.659[0.421] 1
0.792; . 0.763; ( )
0.357[0.702] 2
3.943; ( ) 1.570[0.456]
( ) 43.989[0.142]; Re ( ) 2.112[0.040]
Lag
R R adj LM test
Lags
Schwarz criterion Jarque Bera
White Test Ramsey set Test
χ
χ
= =
= − =
=
Box 2:


1 11
22
Re ( ): int ( ):
1; 0.710 1979 0.593
2; 0.362 1992 0.149
2000 0.093
t tt
tt
dundant Variable Test P Value Chow Breakpo Test P Value
Step Break inWB YD
Step Break inW YD
Break in
− −−
−−
− −
∆ ∆ ∆
∆ ∆
Box 3:
 
2 2
2
2
2.781[0.102] 1
0.834; . 0.806; ( )
1.611[0.211] 2
3.791; ( ) 0.401[0.818]
( ) 45.374[0.373]; Re ( ) 1.979[0.054]
Lag
R R adj LM test
Lags
Schwarz criterion Jarque Bera
White Test Ramsey set Test
χ
χ
= =
= − =
=
Box 4:



11. 11
Appendix 7: Descriptive Statistics
Table 5: Descriptive Statistics After Logs
Variable Mean Median Maximum Minimum Std.Dev. Jarque-Bera
(P-Value )
Cons 5.04 5.05 5.72 4.41 0.41 0.13
YD 5.15 5.17 5.78 4.48 0.41 0.13
Def 3.77 3.81 4.07 3.39 0.16 0.18
W 6.77 6.67 7.66 6.07 0.45 0.16
B 4.53 4.44 5.13 3.96 0.38 0.05
D79 0.48 0 1 0 0.50 0.01
D92 0.27 0 1 0 0.45 0.00
D02 0.12 0 1 0 0.32 0.00
The constant (k=50.719) was added to the deficit variable before logarithmic transformation to ensure the
minimum observation was equal to one.
Appendix 8: Augmented Dickey Fuller Test Results after Logarithmic Transformation
Table 6: ADF Results after Logs
Variable Levels First Differences Conclusion
0a Lag
0
&a t Lag
0a Lag
Ln(Cons) 0.39 0 -3.00 0 -6.61 0 (1)I
Ln(YD) -0.40 0 -2.18 0 -8.68 0 (1)I
Ln(Def) -3.23 1 -4.05 1 NA NA (0)I
Ln(W) 0.50 0 -2.78 1 -6.37 1 (1)I
Ln(B) -0.75 1 -2.24 1 -3.63 0 (1)I
Note: The critical values at a 5% level of significance are -2.91 and -3.49 for intercept and intercept and linear
trend respectively.
Appendix 9: Regression Results for Error Correction Term after Logarithmic Transformation
0.397 0.831 0.149 0.034ln lnln ln
(0.025)* (0.019)* (0.019)* (0.006)*
t tt tC WYD B=− + + +
Note: The critical value for the cointegration with intercept and no trend is -3.95 at a 10% level of significance
(Mackinnon 2010).
2 2
5
16.434[0.00] 1
0.999; . 0.999; ( )
8.179[0.00] 2
6.046
( ) 4.523
Lag
R R adj LM test
Lags
Schwarz criterion
ADF test µτ
= =
= −
= −
Box :


12. 12
Appendix 10: Regression Results for Error Correction Model after Logarithmic Transformation
10.005 0.713 0.071 0.039ln 0.489ln lnln
(0.002)** (0.070)* (0.029)** (0.021)*** (0.108)*
t tt tt
W êYD BC −= + + + −∆∆ ∆∆
Appendix 11: Regression Results for Error Correction Model after Logarithmic Transformation
10.006 0.740 0.066 0.106ln 0.593ln lnln
(0.002)** (0.068)* (0.027)** (0.031)* (0.100)*
0.005 79 0.015 92 0.086 79. 0.431 92.ln ln
(0.003)*** (0.005)* (0.042)** (0.201)**
t tt tt
t t
W êYD BC
D D D DB YD
−= + + + −∆∆ ∆∆
− + − −∆ ∆
2 2
2
2
0.329[0.568] 1
0.751; . 0.732; ( )
0.309[0.735] 2
6.459; ( ) 1.845[0.397]
( ) 21.07[0.099]; Re ( ) 0.006[0.939]
Lag
R R adj LM test
Lags
Schwarz criterion Jarque Bera
White Test Ramsey set Test
χ
χ
= =
=− − =
=
Box 6:


1 22 1
2 11 2
Re ( ): int ( ):
1; ln 0.573 1979 0.113ln lnln
2; ln 0.472 1992 0.216ln lnln
2000 0.
t tt t
t tt t
dundant Variable Test P Value Chow Breakpo Test P Value
Step Break inW ConsB YD
Step Break inW ConsB YD
Break in
− −− −
− −− −
• − • −
∆ ∆ ∆ ∆
∆ ∆ ∆ ∆
Box 7:
 
303
2 2
2
2
0.615[0.436] 1
0.814; . 0.784; ( )
0.438[0.648] 2
6.475; ( ) 0.519[0.771]
( ) 35.379[0.312]; Re ( ) 0.972[0.329]
Lag
R R adj LM test
Lags
Schwarz criterion Jarque Bera
White Test Ramsey set Test
χ
χ
= =
=− − =
=
Box 8:

