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This article was downloaded by: [George Mason University]On: 30 September 2014, At: 02:18Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number:1072954 Registered office: Mortimer House, 37-41 Mortimer Street,London W1T 3JH, UK
Journal of Applied StatisticsPublication details, including instructions forauthors and subscription information:http://www.tandfonline.com/loi/cjas20
Multivariate-based causalitytests of twin deficits in theUSAbdulnasser Hatemi-J & Ghazi ShukurPublished online: 02 Aug 2010.
To cite this article: Abdulnasser Hatemi-J & Ghazi Shukur (2002) Multivariate-based causality tests of twin deficits in the US, Journal of Applied Statistics, 29:6,817-824, DOI: 10.1080/02664760220136159
To link to this article: http://dx.doi.org/10.1080/02664760220136159
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Journal of Applied Statistics, Vol. 29, No. 6, 2002, 817-824
Multivariate-based causality tests of twinde® cits in the US
ABDULNASSER HATEMI-J.1 & GHAZI SHUKUR2, 1International BusinessSchool, JoÈ nkoÈ ping University and SkoÈ vde University, and 2Department of Statistics,University of VaÈ xjoÈ , Sweden
abstract This paper provides an alternative methodology for testing the causality direc-tion between twin de® cits in the US. Rao’s multivariate F-test combined with the bootstrapsimulation technique has appealing properties, especially when the data-generating processis characterized by unit roots. In addition the results show that the eþ ect of structuralbreaks are of paramount importance when the causality tests are conducted. In muchcontemporary applied econometrics there is all-too-little attention given to the possibilityof changes in the economic process.
1 Introduction
In the literature it has been established that there is a positive relationship betweenbudget de® cits and current account de® cits, and this is termed the twin de® citsphenomena.1 The budget de® cit is de® ned as total government expenditures minustotal tax revenues. The current account is a record of receipts from the sale ofgoods and services to foreigners, the payments for goods and services bought fromforeigners, the interest income received from and paid to foreigners, and gifts andother transfers received from and paid to foreigners. The current account de® cit isde® ned as the diþ erence between revenues and costs from trade plus net transfersto the country. There are several ways in which budget de® cits can aþ ect currentaccount de® cits. In a conventional Mundell- Fleming model, it is assumed that anincrease in budget de® cit would cause an increase in interest rates, with capitalin¯ ows and appreciation of exchange rates as eþ ects. These eþ ects, in turn, resultin an increase in current account de® cit. According to Keynesian absorption theoryan increase in budget de® cit would induce domestic absorption and hence import
Correspondence: Abdulnasser Hatemi-J., Department of Economics and Political Sciences, University ofSkoÈ vde, PO Box 408, SE-541 28, SkoÈ vde, Sweden.
ISSN 0266-4763 print; 1360-0532 online/02/060817-08 © 2002 Taylor & Francis Ltd
DOI: 10.1080/02664760220136159
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818 Hatemi-J. & G. Shukur
expansion, which will increase current account de® cits. Feldstein & Horioka (1980)® nd that saving and investment are highly correlated in the US economy, causingcurrent account de® cits and budget de® cits to move together. Another contraryview regarding these two macro-aggregates is provided by the Ricardian Equivalencetheorem, which claims that changes in the path of government expenditures (ortaxes) do not aþ ect real interest rates, the quantity of investment, and/or currentaccount de® cits.
Several empirical studies have con® rmed the existence of a positive relationshipbetween the twin de® cits in the US economy. The purpose of the present study isto investigate the direction of causality between these variables. This issue isimportant from a policy-making point of view in order to remedy the twin de® cits.Removing twin de® cits is assumed to be a precondition for the economy to thrive.
Here, in addition to the singlewise Likelihood Ratio test (LR) and the systemwiseRao’s F-test, we apply the bootstrap multivariate simulation technique in combina-tion with Rao’s F-test, to see which de® cit precedes the other, or whether theycause each other simultaneously. The advantages of previously mentioned testmethod are that it performs well even when the time series are non-stationary, it isnot based on a speci® c distribution and, ® nally, it can be used irrespective of thecointegration properties of the data.
This paper is organized as follows: Section 2 presents the basis of our data set.Section 3 discusses the order selection of the model, while Section 4 describes themultivariate test methodology for Granger causality. Finally, in Section 5, wepresent our main results and draw some important conclusions.
2 Data
The data used in this study consist of budget de® cits (BD) and current accountde® cits (CAD) on a quarterly basis for the period 1975Q1-1998Q2 from Inter-national Financial Statistics. We have seasonally adjusted the data by running eachvariable through the X-11 ® lter.
Tests for non-stationarity have been applied using the KPSS (Kwiatkowski et al.1992) and Perron (1989) unit root test methods. The results, presented in Tables1 and 2, reveal that each variable is characterized by one unit root. This is inaccordance with the graphical inspection of the time series, is are not presentedhere but is available on request. The ® gures show that the data generating processfor each variable could be well described by one unit root, since each variableappears to be stationary after being diþ erenced once.
3 The order of the VAR model
The order of the vector autoregressive (VAR) model often plays a crucial role inempirical analysis and hence special care should be taken in selecting the optimallag length. To this end, we applied Akaike information criterion (AIC), SchwarzBayesian criterion (SBC) and the multivariate likelihood ratio (LR) test.2 We ® rstestimated the AIC and SBC that indicated the lag length two and three respectively.To choose between these two lags we performed a LR multivariate test adjustedfor small samples. The result was in favour of lag length two. It is important tomention that we have tested for autocorrelation in the residuals by using theBreusch- Godfrey multivariate test. The null hypothesis of no autocorrelation couldnot be rejected at the conventional signi® cance levels. When testing for normality,
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Multivariate based causality tests of twin de® cits 819
Table 1. Test for unit roots using the KPSS test.a
Truncation lags ® 0 1 2 3 4
H0 :I(0), H1: I(d)BDsa series 1.21 0.69 0.49 0.38 0.32CADsa series 0.57 0.30 0.20 0.16 0.13
H0 :I(1), H1: I(d)BDsa series 0.01 0.03 0.04 0.04 0.05CADsa series 0.14 0.12 0.11 0.10 0.10
aThe KPSS test is based on the following model:
yt 5 n t + rt + e t,
where t denotes the linear trend term e t is a stationary random error, and rt is a random walk:
rt 5 rt 2 1 + ut
The initial value (r0) is treated as ® xed and serves the role of an intercept. The stationary hypothesis isthat the variance of the residuals in the random walk component (ut) is zero.
The critical values are 0.12, 0.15, 0.18 and 0.22 at the 10%, 5%, 2.5% and 1% signi® cance level,respectively.
Table 2. Test for unit roots using the Perron test.a
H0: I(1), H1 :I(0) H0: I(2), H1 :I(1)
BDsa series 2 2.03 (1) 2 18.70 (0)CADsa series 2 1.90 (5) 2 9.17 (3)
aThe Perron regression is of the following form:
yt 5 c + b t + dDTB t + h DUMt + a yt 2 1 + +n
i 5 1
bi D yt 2 i + vt
where t 5 linear trend term, DTB 5 1 if t 5 TB + 1 (TB 5 time break 5 1990:01) and DTB 5 0 otherwise, DUM 5 0 if t< 5 TB and DUM 5 1 if t> TB, andD denotes the ® rst diþ erence. This regression allows for a structural break in boththe mean value and the deterministic trend of the variable under investigation.The null hypothesis of a unit root is a 5 1. The appropriate number of laggeddiþ erences (n) is determined by adding lags until the Ljung-Box test fails to rejectno serial correlation of vt at the 5% signi® cance level.
The critical values are 2 3.69, 2 4.04, 2 4.31 and 2 4.70 at the 10%, 5%,2.5% and 1% signi® cance level, respectively. Note that the lambda (de® ned aspre-break sample size per after-break sample size) is around 0.8 in our case.
the results indicated some slight departure from normality. This will not aþ ect thebootstrap based causality test however, since it is based on the true distribution ofthe underlying data, which does not necessarily have to be normally distributed.
4 Multivariate Causality Tests
By causality we mean causality in the Granger (1969) sense. That is, we wouldlike to know if one variable precedes the other variable or if they are contempora-neous. The Granger approach to whether CAD causes BD is to see how much ofthe current value of the second variable can be explained by the passed values ofthe ® rst variable. BD is said to Granger cause CAD if CAD helps in the predictionof BD, or equivalently, if the coeý cients of the lagged values of CAD are statisticallysigni® cant in a regression of BD on the lagged values of CAD.
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820 Hatemi-J. & G. Shukur
Shukur & Mantalos (2000) have considered the size and power of variousgeneralizations of tests for Granger-causality in integrated- cointegrated VARsystems. The authors used Monte Carlo methods to investigate the properties ofeight versions of the test in two diþ erent forms, the standard form and a modi® edform of the Wald test by Dolado & LuÈ tkepohl (1996). In both studies, the standardand the modi® ed Wald tests have been shown to perform badly, especially in smallsamples. In Shukur & Mantalos (2000), however, the authors found that the small-sample corrected LR-tests, and especially the Rao’s multivariate F-test, exhibit bestperformances regarding both size and power, even in small samples. In the casewhen we use the standard test and when there is no cointegration, however, all thetests have been shown to perform poorly, especially in small samples. Mantalos(2000) studied the properties of Wald, corrected-LR and Bootstrap tests for thesame purpose and found that the Bootstrap test exhibits the best performance inalmost all situations, regarding both size and power. Hatemi & Shukur (1999) haveapplied these test methods when investigating the ® scal policy in Finland, andfound that the methods almost indicated the same results. Note that in all thepreviously mentioned studies, the authors use the Ordinary Least Squares (OLS)method in the test regression, while we in this study use Zellner’s (1962) IterativeSeemingly Unrelated Regression (ISUR) method. The ISUR technique providesparameter estimates that converge to the maximum likelihood parameter estimates,which are unique.
4.1 The Systemwise Rao’s F-Test
Here, we present the Granger-causality test by using the multivariate Rao’s F-test(Rao, 1973). Consider the following VAR(p) process:
yt 5 v + A1yt 2 1 + . . . + Apyt 2 p + e t (1)
where e t 5 ( e 1t , . . . , e kt) ¢ is a zero mean independent white noise process with non-singular covariance matrix R e and, for j 5 1, . . . , k, E ½ e jt ½ 2 + s < ` for some s > 0.The order p of the process is assumed to be known. Now, by portioned yt in (m)and (k 2 m) dimensional subvectors y1
t and y2t and Ai matrices portioned conform-
ably then y2t does not Granger-cause the y1
t if the following hypothesis:
H0 :A12, i 5 0 for i 5 1, . . . , p (2)
is true. Since we only have two equations in our model, i.e. k 5 2, the nullhypothesis will be tested in the following system of equations:
yt 5 f y1t
y2t g 5 f v1
v2 g + f A11,1 A12,1
A21,1 A22,1 g 3 f y1t 2 1
y2t 2 1 g + . . . + f A11,p A12,p
A21,p A22,p g 3 f y1t 2 p
y2t 2 p g + f e 1t
e 2t g(3)
LuÈ tkepohl (1993) suggests the following notations when de® ning a general VARmodel:
Y: 5 (y1 , . . . , yT ) (k 3 T ) matrix,
B: 5 (v, A1 , . . . , Ap) (k 3 (kp + 1)) matrix,
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Multivariate based causality tests of twin de® cits 821
Zt : 5 f 1
yt
:
yt 2 p + 1g ((kp + 1) 3 1) matrix,
Z: 5 (Z0 , . . . , ZT 2 1) ((kp + 1) 3 T ) matrix, and
d : 5 ( e 1 , . . . , e T ) (k 3 T ) matrix.
By using these notations, for t 5 1, . . . , T, the VAR(p) model, including a constantterm (v), can be written compactly as:
Y 5 BZ + d . (4)
We ® rst estimate model (4), equation by equation, using the OLS method. Thewhole VAR system is then estimated using Zellner’s (1962) Iterative SeeminglyUnrelated Regression (ISUR) method. As we previously mentioned, the ISURtechnique provides parameter estimates that converge to the maximum likelihoodparameter estimates, which are unique.
Let us denote by d à U the (k 3 T ) matrix of estimated residuals from the unrestrictedregression (4) and by d à R the equivalent matrix of residuals from the restrictedregression with H0 imposed. The matrix of cross-products of these residuals willbe de® ned as SU 5 d à ¢
U d à U and SR 5 d à ¢R d à R respectively. The Rao test can be then
written as:
RAO 5 ( u /q)(U 1/s 2 1) (5)
where,
s 5 ! q2 2 4
k2(G2 + 1) 2 5,
r 5 q/2 2 1, u 5 D s 2 r, D 5 T 2 (k(kp + 1) 2 Gm) + 12[G 2 1) 2 1], U 5 detSR /
detSU´q 5 Gm2 is the number of restrictions imposed by H0 , where G is the prestriction in (4) and m is the dimension of the subvector y1
t . RAO is approximatelydistributed as F(q, u ) under the null hypothesis, and reduces to the standard Fstatistic when k 5 1.
4.2 The Bootstrap testing approach
In this subsection we present the Bootstrap testing procedure (Efron, 1979).Generally, the distributions of the test statistics we use are known only asympto-tically, which means that the tests may not have the correct size, and inferentialcomparisons and judgements based on them could be misleading.
From regression (4), a direct residual resampling gives:
Y* 5 BÃ Z* + d * (4a)
where d * are i.i.d. observations d *1 , . . . , d *T , drawn from the empirical distributions(Fà d ), putting mass 1/T into the adjusted OLS residuals ( d à i 2 d Š), i 5 1, . . . , T. Thebasic principle of Bootstrap testing is to draw a number of Bootstrap samples fromthe model under the null hypothesis, calculate the Bootstrap test statistic (RAO*).
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822 Hatemi-J. & G. Shukur
The Bootstrap test statistic (RAO*) can then be calculated by repeating this stepNb times. We then take the (a )th quintile of the bootstrap distribution of RAO*and obtain the a -level `bootstrap critical values’ (c*t a ). We then calculate the teststatistic (RAO), which is the estimated test statistic using the actual data set.Finally, we reject the null hypothesis if RAO < c*t a .
As regards Nb , the number of the bootstrap samples used to estimate bootstrapcritical value, we estimate the P-value for the test using Nb 5 1000.
5 Results and conclusions
In this study, we investigate the direction of causality relation between budgetde® cits and trade de® cits in the US economy, which has been termed as the twinde® cits phenomena. This issue is important from a policy-making point of view inorder to remedy twin de® cits, which is assumed to be a condition for the economyto thrive. For this purpose, quarterly data for the period 1975Q1- 1998Q2, fromInternational Financial Statistics, have been used. Note that, in all cases, the variableshave been shown to integrate the ® rst order I(1). Moreover, the VAR(2) model hasbeen chosen throughout in this study.
When looking at the entire sample period, all these test methods lead us to drawthe inference that these variables do not Granger cause each other (see Table 3).However, during the analysed period of this study, especially in the early 1990s,several events occurred (among others, the oil crisis, the Gulf war and the collapseof the Soviet Union), which may have caused structural breaks. This is likely tohave a substantial eþ ect on analysing the causality nature between those twovariables. Therefore, tests for parameter stability have been conducted by applyingrecursive estimates and CUSUMSQR tests. Based on the plots of the recursiveestimates of CUSUMSQR tests for each equation in the VAR model, we canconclude that the parameters are not stable during the entire sample period.Applying one-step-ahead systemwise ANOVA tests, for parameter stability anddetection of break points, show that structural change could have happened after1989.3 Hence, we decided to split the data into two sub-periods and made twoseparate estimations for the two subperiods. We used the same previously men-tioned criteria to select the order of the suitable VAR model, and found thatVAR(2) still had to be chosen in both sub-periods.
When using the same methods to test for causality, the results indicated that,during the ® rst period, i.e. 1975 to 1989, only BDsa Granger causes CADsa (seeTable 4). On the other hand, when analysing the second sub-period, i.e. 1990 to1998, we ® nd that the causality nature has almost changed direction from CADsato BDsa (see Table 5). This means that, during the second sub-period, i.e. 1990to 1998, the causality nexus between these two variables has a one-directional formin the opposite direction from the ® rst sub-period. The policy implication of thisresult is that reducing trade de® cits will result in decreasing budget de® cits in the
Table 3. Diþ erent test results for Granger-causality, for the period 1975:1 to 1998:4.
P-values
Null hypothesis Bootstrap test Rao’ s F-test
CADsa does not Granger cause Bdsa 0.6940 0.6009BDsa does not Granger cause CADsa 0.9740 0.9768
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Multivariate based causality tests of twin de® cits 823
Table 4. Diþ erent test results for Granger-causality, for the period 1975:1 to 1989:4.
P-values
Null hypothesis Bootstrap test Rao’ s F-test
CADsa does not Granger cause BDsa 0.6160 0.5811BDsa does not Granger cause CADsa 0.0100 0.0062
Table 5. Diþ erent test results for Granger-causality, for the period 1990:1 to 1998:4.
P-values
Null hypothesis Bootstrap test Rao’ s F-test
CADsa does not Granger cause BDsa 0.0240 0.0412BDsa does not Granger cause CADsa 0.5930 0.5831
US economy. Reducing imports, increasing exports, or a combination of bothmeasures can achieve decreasing trade de® cits. Which alternative is the appropriateone can only be answered by another study that explicitly ® nds the direction ofcausality between imports and the exports in the US during the period 1990-1998.
It is important to mention that, if tests for parameter stability had not been used,the implausible results from Table 3, i.e. results from the whole sample period,could be used without question. This, of course, stresses the importance of usingthe diagnostic checking of the model and the test for parameter stability. In muchcontemporary applied econometrics there is all-too-little attention given to thepossibility of changes in the economic process.
Notes
1. See Kearney & Monadjemi (1990) and references therein. Kasa (1994) reports a positive relationshipbetween twin de® cits in the US, Japan and Germany. Islam (1998) ® nds a positive relationshipbetween budget de® cits and trade de® cits for Brazil. McNelis & Siddiqui (1994) cannot ® nd anyempirical evidence that the twin de® cits establish a long-run equilibrium in New Zealand. Normandin(1999) indicates that there is a positive co-movement between the external and internal budgetde® cits in Canada and USA, in particular since the 1980s.
2. For more information regarding the selection of the VAR order see Hatemi (1999).3. The results of ANOVA tests and the plots of CUSUMSQR are not presented here but are available
from the authors on request.
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