budget deficits and exchange rates: further evidence from cointegration and causality tests

Budget deficitsand exchange

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Budget deficits and exchangerates: further evidence fromcointegration and causality

testsNicholas Apergis

University of Macedonia, Thessaloniki, Greece

IntroductionIn many countries large budget deficits are among the most serious problems oftheir economies. Theory argues that large budget deficits tend to have harmfuleffects on many macroeconomic variables, such as domestic interest rates,investments, and trade deficits. In particular, massive budget deficits result inhigh interest rates as the government’s demand for funds conflict with privatefinancing requirements; eventually, high interest rates discourage privateinvestment. The implication of high interest rates would be that residentialconstruction, business investment in plant and equipment and consumerspending on durable goods could be hard hit by the implementation of such afiscal policy, especially, if monetary policy is non-accommodative. In addition,budget deficits may affect interest rates via the channel of reduced savings andthereby saving ratios. Barro (1987), Evans (1985, 1987a, 1987b) and Hoelscher(1983) found no relation between budget deficits and interest rates. By contrast,Al-Saji (1992), Barth et al. (1985), Cebula (1988, 1993), Cebula and Koch (1989),Hoelscher (1986), Miller and Russek (1991) and Zahid (1988) found that federalbudget deficits have contributed to higher levels of interest-rate yields. Knoesterand Mak (1994) showed that only in Germany (among eight OECD economies)the government budget deficit contributes significantly to the explanation ofhigher interest rates.

Moreover, under the Ricardian equivalence view, deficit policy is a matter ofindifference, since an increase in government debt leads to a future increase intaxes and thus it is not an addition to private sector wealth. This fact has noeffect on consumption, interest rates, and aggregate demand. Bernheim (1989),Brunner (1986), Hoelscher (1986) and Tobin and Buiter (1980) presenttheoretical and empirical arguments against the Ricardian equivalence, whileEvans (1985, 1987b) and Fackler and McMillin (1989) provide evidence in favourof the hypothesis.

Journal of Economic Studies,Vol. 25 No. 3, 1998, pp. 161-178,

© MCB University Press, 0144-3585

The author would like to thank, without implicating, an anonymous referee from the journal forhelpful comments and suggestions.

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The economic reality, however, demonstrated that a component of economicactivity has been unfavourably hit by the presence of large budget deficits,especially in the USA. Large budget deficits contributed to a worseperformance by the trade deficit. Several researchers have examined theFeldstein hypothesis of the “twin deficits” (Feldstein, 1985, 1987). According tothis hypothesis, the current account deficit was caused by large public deficits.The explanation lies in the story behind budget deficits. Higher interest ratescomparative to their foreign counterparts, drive up the value of the domesticcurrency internationally, since they attract capital from the rest of the world,and, through this channel, they contribute to the deterioration in trade. Alse andBahmani-Oskooee (1992), Darrat (1988), Miller and Russek (1989) and havedemonstrated this perverse relation via empirical analysis. Cebula and Hung(1992) and Wijnbergen (1987) have shown that in Canada higher budget deficitshave led to higher interest rates and, therefore, to an appreciation of theCanadian dollar.

While many researchers have presented models to describe the relationshipbetween current and government deficits (Abell, 1990; Bernheim, 1988; Zietzand Pemberton, 1990), not many studies have examined explicitly the impact ofbudget deficits on the value of the domestic currency. A rise in budget deficit –associated with lower savings – tends to appreciate the exchange rate as aresult of capital inflows. Evans (1986) has found no evidence of the presence ofany relationship between the two variables concerned. By contrast, Feldstein(1986), Melvin et al. (1989) and Oskooee and Payesteh (1993) showed that higherbudget deficits have been followed by an appreciation of the dollar and viceversa. Evans (1986) argues that higher budget deficits tend to raise domesticconsumption. Higher consumption falls on both domestic and imported goods,which in turn leads to higher domestic interest rates with respect to theircounterparts abroad. Then, capital inflows are induced, which tend to beprevented by an appreciation in the exchange rate sufficient to motivate tradersto hold the existing stock of assets.

However, if the budget deficit contributes to aggregate demand, this mightlead to higher price levels and, therefore, to a depreciated currency (Evans,1985, 1987b). At the same time, other researchers have focused on the impact ofbudget deficits on different macroeconomic variables, such as inflation andmoney supply. Hamburger and Zwick (1981), Miller (1983), McMillin (1986) andGrier and Neiman (1987) have concluded that budget deficits seem to causeinflation, while Dwyer (1985), King and Plosser (1985), Barnhart and Darrat(1988, 1989), Landon and Reid (1990), and Karras (1994) have reported resultsthat demonstrate that deficits do not seem to contribute significantly to higherinflation. Sargent and Wallace (1981) have argued that budget deficits will forcethe central bank to monetise the deficit either in the current period or in futureperiods, depending on the degree of independence between monetary and fiscalauthorities. Finally, Turnovsky and Wohar (1987) have argued that theempirical results depend on the exchange rate regime examined. In terms nowof the relationship between budget deficits and money supply, some studies


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have found evidence in favour of the debt-monetisation hypothesis (Allen andSmith, 1983), while others have reached the opposite results (Niskanen, 1978).Inflationary conditions could be made worse through:

(1) monetary accommodation;

(2) crowding out, which tends to reduce the real capital stock in theeconomy, resulting in a lower growth rate of output, and thus, with agiven money supply to higher prices; and

(3) excessive issues of government bonds, since they constitute a substantialpart of money supply.

Therefore, higher budget deficits could aggravate the inflationary conditions inthe economy, contributing to the presence of a depreciated domestic currency.

Almost all of the relevant literature has focused on the impact of the USbudget deficit on certain macroeconomic variables including the exchange rate.The aim of this study is to investigate the effects of budget deficits on exchangerates within a multi-country sample and by making use of the cointegration andcausality approaches. The rest of the paper is organised as follows. Section twopresents methodological issues, while section three presents the empiricalresults. Finally, section four provides some concluding remarks.

Methodological issuesThe cointegration approachThe presence of a (long-run) relationship between real budget deficits (orsurpluses) and exchange rates is examined through the methodology ofcointegration as it was developed by Engle and Granger (1987) and Johansenand Juselius (1990). For the purposes of this paper use will be made of thetechnique by Johansen and Juselius (1990), who developed a method to estimatewhether two or more variables are cointegrated, via a multivariate maximum-likelihood procedure that overcomes many of the limitations of the bivariatetests of Engle and Granger (1987). These limitations require that one of the twovariables is considered exogenous, while these tests do not have well-definedlimiting distributions and, therefore, their critical values are sensitive to samplesize.

The Johansen maximum likelihood procedure begins by expressing aprocess of NI(1) variables in an Nx1 vector x as an unrestricted autoregression:

(1)

with t = 1, 2, …, T and ut being the random error term. The long-run staticequilibrium is given by Πx = 0, where the long run coefficient matrix Π isdefined as:

(2)


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where I is the identity matrix and Π is an nxn matrix whose rank determinesthe number of distinct cointegrating vectors which exist between the variablesin x. Define two nxr matrices α and β, such that:

(3)

with the rows of β′ to form the r distinct cointegrating vectors. The likelihoodratio statistic (LR) or trace test for the hypothesis that there are at most rcointegrating vectors is:

(4)

where λr + 1, …, λn are n-r the smallest squared canonical correlations betweenthe residuals of xt–k and ∆xt series, corrected for the effect of the laggeddifferences of the x process. Additionally, the likelihood ratio statistic for testingat most r cointegrating vectors against the alternative of r + 1 cointegratingvectors, namely, the maximum eigenvalue statistic, is given as:

(5)

Both statistics have non-standard distributions under the null hypothesis,although approximate critical values have been generated by Monte Carlomethods and tabulated by Johansen and Juselius (1990). If exchange rates arefound to be cointegrated with budget deficits, among other macroeconomicvariables, the next step is to examine the associated causality tests, since if twoor more variables are cointegrated causality in at least one direction must beimplied (Hall and Milne, 1994).

The long-run causality approachLong-run causality was first used by MacDonald and Kearney (1987) and Simset al. (1990) who showed that the presence of a cointegrating relationshipbetween certain variables under examination implies that causality tests couldbe applied and that these tests were asymptotically standard distributed.Therefore, the common practice implies the following tests:

(1) testing for cointegration; and

(2) under the presence of cointegrated variables, going back to the originalVAR model in levels and without imposing any cointegration restriction,to implement usual causality tests.

Furthermore, Mosconi and Giannini (1992) have provided a framework fortesting for causality by explicitly imposing certain cointegration restrictions.For the purposes of this study the approach followed imposes the restrictionthat a certain variable in the VAR model is zero in the cointegrating vector. Ahighly professional analysis of the long-run causality is given in Mosconi and


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Giannini (1992) as well as in Hall and Milne (1994). The empirical analysissection provides more details on the issue.

The Granger (short-run) causality approachCausality in the sense of Granger can be defined by stating that a time series Xcauses a time series Y if the present value of Y can be better predicted usingpast values of X in addition to all other relevant information. Needless to say,the correct estimation procedure would be to include all independent variablesindicated by the relevant economic theory. Excluding appropriate variablesmay yield irrelevant and useless results. Granger considers a system of thegeneral form:

(6)and

(7)

where X and Y are stationary series and u1 and u2 are white noise processes.Testing the hypothesis that M does not cause Y is equivalent to testing the jointrestriction that gi = 0 for i = 1, …, q2, while testing that Y does not cause Ximplies mi = 0 for i = 1, …, q3.

With more than two variables (X, Y, Z) the model may be written as:

(8)

where A, B, and C are polynomial lag operators of finite order.

Empirical resultsDataThe quarterly time series data on nominal budget deficits (D), exchange rates(E) defined as nominal effective exchange rates, real GDP (Y) at 1990 prices,prices (P) measured by the consumer price index, and money supply (M)measured as M1, for eight OECD economies have been collected from theInternational Financial Statistics tape. The effective exchange rate is measuredby the effective exchange rate index which represents the ratio (on base 1990 =100) of an index of the period average exchange rate of the currency in questionto a weighted geometric average of exchange rates for the currencies of selectedpartner countries, thus, an increase in the index reflects an appreciation.


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The countries involved are: Germany, the UK, Switzerland, Belgium, TheNetherlands, Italy, France, and Canada. The sample period runs from 1980 to1995. Lower case letters denote variables expressed in logarithms, except forthe case of the deficit. Finally, three types of software were employed for thepurposes of the empirical analysis, namely, RATS, MicroFit, and CATS inRATS.

Integration and cointegration analysisIt is crucial that the series are differenced the correct number of times. Table Ipresents the results of Phillips-Perron tests, proposed by Phillips (1987) andPhillips and Perron (1988). The results support the presence of a unit root in thelevels of all variables involved and the absence of any unit root when allvariables have been differenced once; in other words, all variables are I(1).

In addition, cointegration tests were performed and they are reported inTable II. As a first step the optimal number of lags of the VAR system has to becalculated. The strategy specifying the number of lags in the VAR model wasbased on Sims’ (1980) methodology. In particular, we started with a lag lengthof six and conducted likelihood ratio tests (with Sims’ degrees of freedomcorrection) of lag length from 6 v. 5 to 2 v. 1. These tests indicated a lag lengthof six for France, a lag length of five for The Netherlands, a lag length of fourfor the UK, a lag length of three for Germany and Canada, and a lag length oftwo for Italy, Belgium, and Switzerland. According to the results, the nullhypothesis of no cointegration is rejected only in the cases of Switzerland,Canada, the UK, and France. In cases where more than one cointegrating vectorhave been suggested, visual inspection of the residuals from the cointegratingvectors selected the appropriate cointegrating vector.

Furthermore, Hansen-Johansen (1993) recursive analysis stability tests werealso performed to test for temporal instability in Johansen’s results andconcerning the UK participation in the Exchange Rate Mechanism (ERM) aswell as the impact of the two ERM crises (occurred in September 1992 and inAugust 1993) on the relationship under examination and for the cases of the UKand France. The results (Figures 1-5) suggested that there was no break in thecointegration equations.

In other words, no evidence of temporal instability was present and theempirical findings reinforced the conclusions about the presence of arelationship between the exchange rate, the budget deficit, output, money, andprices

Causality testsLong-run causality. For the cases of Switzerland, Canada, the UK and Francehaving established that et, Dt, yt, mt, and pt are cointegrated, we can model thedata generating process for ∆et, ∆Dt, ∆yt, ∆mt, and ∆pt as an error correctionVAR (ECVAR).


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Variation PP1 PP2 PP3(X) Levels Differences Levels Differences Levels Differences

SwitzerlandD –1.73 –9.77* –1.95 –11.95* 0.31 69.48*

e –2.87 –6.72* –2.28 –7.52* 1.27 27.58*

m –1.04 –8.53* –0.99 –9.40* 1.31 43.14*

y –2.26 –10.20* –2.66 –12.10* 1.50 71.39*

p –1.10 –4.47* –1.37 –5.47* 0.95 14.63*

United KingdomD –1.36 –10.77* –1.86 –13.69* 1.15 91.27*

e –1.63 –8.10* –2.15 –9.00* 1.95 39.50*

m –1.87 –8.67* –1.77 –9.63* 1.52 45.23*

y –2.11 –8.93* –2.78 –10.17* 1.99 50.58*

p –1.65 –6.02* –1.11 –7.86* 1.87 30.53*

The NetherlandsD –1.68 –9.63* –1.35 –11.82* 1.64 68.00*

e –1.72 –7.45* –2.14 –8.30* 1.61 33.64*

m –1.32 –11.37* –2.08 –13.64* 1.27 91.01*

y –1.77 –10.39* –2.22 –12.49* 1.02 76.06*

p –0.40 –5.80* –1.37 –7.24* 2.32 25.58*

ItalyD –1.99 –9.05* –2.29 –10.56* 1.45 54.28*

e –1.76 –11.68* –1.40 –16.04* 1.34 12.52*

m –0.41 –9.47* –0.38 –10.87* –1.25 57.93*

y –1.44 –4.39* –1.47 –4.57* 1.66 6.49*

p –0.20 –4.88* –0.28 –6.28* 1.36 19.23*

GermanyD –1.80 –14.35* –1.22 –14.40* 0.74 10.20*

e –1.83 –7.05* –1.92 –7.98* 1.43 30.98*

m –1.72 –7.92* –1.49 –8.83* 1.17 38.02*

y –1.69 –9.74* –2.26 –11.05* 1.51 59.49*

p –2.56 –4.81* –1.33 –5.86* 1.29 16.71*

FranceD –1.25 –14.34* –1.51 –25.58* 1.11 31.90*

e –2.05 –5.90* –0.79 –7.15* 1.47 25.15*

m –2.21 –8.80* –1.55 –9.38* 0.98 43.02*

y –0.39 –6.38* –0.61 –7.37* 0.57 26.46*

p –0.01 –4.32* –0.02 –4.68* 0.42 10.64*

(Continued)Table I.

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Consider the following ECVAR model:

(9)

where x = [∆e ∆D ∆y ∆m ∆p] ′ is a 5 × 1 vector of endogenous variables; A(L) =[A∆e(L) A∆d(L) A∆y(L) A∆m(L) A∆p(L)]′ is a 5 × 5 polynomial matrix in the lagoperator of order q, with A∆e(L) = [γ(L) δ(L) ε(L)]′ , A∆D(L) = [ζ(L) η(L) θ(L)]′ ,A∆y(L) = [κ(L) µ(L) ϕ(L)]′ A∆m(L) = [ν(L) ξ(L) ρ(L)] and A∆p(L) = [σ(L) τ(L) υ(L)];Π = αβ′ and α and β are 5 × 1 matrices of loading factors and cointegratingcoefficients, respectively; finally, Ωt = [w1t w2t w3t w4t w5t]′ is a 5 × 1 vector ofwhite noise errors with properties: E(wt) = 0, E(wt, wt–s) = Ω when t = s andzero otherwise, with Ω denoting the variance-covariance matrix of residuals.The hypothesis that the EC term has incremental power in predictingmovements in exchange rates was examined by testing the restriction that theloading factor in the relevant equation is statistically significant from zero.

The results of the LR test on loading factors reported in Table III show thatthe budget deficit does cause exchange rates in the long run and for all fourcountries in which cointegration has been found. In other words, theinformation from the cointegrating vector does affect the exchange rate. Thesame holds for income and prices. One implication of this finding is that policymakers in these economies could stabilise their exchange rate in the long run bycontrolling fiscal (as well as income and prices) aggregates (Figures 1-5). The

Variation PP1 PP2 PP3(X) Levels Differences Levels Differences Levels Differences

CanadaD –2.35 –11.70* –2.43 –15.17* 1.99 11.22*

e –1.29 –5.02* –1.61 –6.08* 1.29 18.06*

m –1.90 –8.11* –1.96 –8.97* 1.89 39.23*

y –0.45 –4.43* –0.50 –4.89* 2.69 11.57*

p –0.09 –4.10* –0.10 –5.31* 0.30 13.75*

BelgiumD –1.79 –11.41* –1.86 –15.74* 1.36 12.06*

e –1.60 –7.05* –1.93 –7.86* 1.87 30.13*

m –2.32 –10.83* –2.25 –13.64* 1.39 9.06*

y –1.21 –9.25* –2.53 –10.98* 1.16 58.95*

p –0.85 –4.57* –0.88 –5.85* 1.65 16.63*

Notes: PP1 is the Perron test defined as: ∆x(t) = c + (a–1) x(t–1) + ε(t), while the nullhypothesis is a = 1 and it is tested with the statistic τµ. The PP2 is the Perron test defined as:∆x(t) = c* + d* T + (a* – 1) + ε(t) with the null hypothesis being a* = 1 and it is tested with thestatistic ττ. Finally, PP3 is the Perron test defined as ∆x(t) = c* +d* T + (a* – 1) x (t – 1) + ε(t)with the null hypothesis being d* = 0 and a* = 1 and it is tested with the statistic Φ3

*indicates significance at 5 per centTable I.


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r n-r m.λ 95% Tr 95%

Switzerlandr = 0 r = 1 65.4647 34.4000 135.7659 76.0690r < = 1 r = 2 41.1901 28.1380 70.3013 53.1160r < = 2 r = 3 14.8539 22.0020 29.1112 34.9100r < = 3 r = 4 8.3330 15.6720 14.2573 19.9640r < = 4 r = 5 5.9243 9.2430 5.9243 9.2430

United Kingdomr = 0 r = 1 39.5297 34.4000 115.7985 76.0690r < = 1 r = 2 38.3127 28.1380 76.2688 53.1160r < = 2 r = 3 29.0170 22.0020 37.9561 34.9100r < = 3 r = 4 15.6603 15.6720 18.9390 19.9640r < = 4 r = 5 3.2787 9.2430 3.2787 9.2430

The Netherlandsr = 0 r = 1 34.0436 34.4000 72.7567 76.0690r < = 1 r = 2 24.1079 28.1380 48.7131 53.1160r < = 2 r = 3 21.6581 22.0020 24.6052 34.9100r < = 3 r = 4 14.0884 15.6720 12.9470 19.9640r < = 4 r = 5 8.8586 9.2430 8.8586 9.2430

Italyr = 0 r = 1 28.6361 34.4000 58.0366 76.0690r < = 1 r = 2 23.0842 28.1380 49.4005 53.1160r < = 2 r = 3 19.1091 22.0020 26.3163 34.9100r < = 3 r = 4 5.4364 15.6720 7.2072 19.9640r < = 4 r = 5 1.7708 9.2430 1.7708 9.2430

Germanyr = 0 r = 1 26.2438 34.4000 73.3384 76.0690r < = 1 r = 2 21.4426 28.1380 57.0957 53.1160r < = 2 r = 3 19.1871 22.0020 25.6520 34.9100r < = 3 r = 4 11.8187 15.6720 16.4650 19.9640r < = 4 r = 5 4.6463 9.2430 4.6463 9.2430

Francer = 0 r = 1 41.5311 34.4000 105.4555 76.0690r < = 1 r = 2 37.7220 28.1380 63.9244 53.1160r < = 2 r = 3 29.2975 22.0020 36.2024 34.9100r < = 3 r = 4 10.1867 15.6720 16.9049 19.9640r < = 4 r = 5 6.7182 9.2430 6.7182 9.2430

Canadar = 0 r = 1 44.8462 34.4000 96.4434 76.0690r < = 1 r = 2 36.1230 28.1380 61.5972 53.1160r < = 2 r = 3 29.3355 22.0020 35.4742 34.9100r < = 3 r = 4 10.7663 15.6720 16.1388 19.9640r < = 4 r = 5 5.3725 9.2430 5.3725 9.2430

(Continued)

Table II.Johansen-Juselius

maximum likelihoodtests for cointegration


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consequences for the future behaviour for the two European economies, i.e. theUK and France, within a European Union (EU) framework are obvious.

Short-run causality. The results of the short-run causality tests reported inTable IV suggest that movements in the budget deficit have incrementalpredictive content for movements in exchange rates in all eight countries underexamination.

Table IV also reveals that in all countries concerned causality runs from thebudget deficit to the exchange rate (no feedback effects were detected). In termsof the sum of the coefficients of the budget deficit, the following empiricalfindings were obtained (Table IV): for the cases of The Netherlands, Germany,Canada, the UK, and Switzerland the sum is shown to be positive andstatistically significant, implying that deficit increases lead to domesticcurrency appreciation. The findings for Germany are in accordance to theKnoester and Mak (1994) results, since higher deficits lead to higher interest

r n-r m.λ 95% Tr 95%

Belgiumr = 0 r = 1 31.9490 34.4000 75.3790 76.0690r < = 1 r = 2 24.5856 28.1380 43.4300 53.1160r < = 2 r = 3 16.9368 22.0020 28.8444 34.9100r < = 3 r = 4 9.5167 15.6720 11.9076 19.9640r < = 4 r = 5 2.3909 9.2430 2.3909 9.2430

Notes: r = number of cointegrating vectors; n-r = number of common trends; m.λ = maximumeigenvalue statistics; Tr = trace statisticTable II.

Figure 1.Stability tests UK (ERMparticipation)

2

1,8

1,6

1,4

1,2

1

0,8

0,6

0,4

0,2

0

1990

4

1991 2 3 4

1992 2 3 4

1993 2 3 4

1994 2 3 4

1995 2 3 4

Critical value x 2(6) = 12,59 Quarters


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rates and, therefore, to a currency appreciation. They are also consistent withthose of Cebula and Hung (1992) for the case of Canada.

By contrast, in Italy, Belgium, and France, the sum of the coefficients ofpublic deficits becomes negative and statistically significant, implying thathigher deficits lead to the depreciation of the domestic currency. For the case ofItaly, Al-Saji (1991) and Cebula (1992) have shown that higher budget deficits

Figure 2.Stability tests, UK (1992

crisis)1995

2

1,8

1,6

1,4

1,2

1

0,8

0,6

0,4

0,2

0


1993 2 3 4 1994 2 3 4 2 3 4

Figure 3.Stability tests, UK

(1993 crisis)1995

2

1,8

1,6

1,4

1,2

1

0,8

0,6

0,4

0,2

0


1993 1994 2 3 4 2 3 4


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lead to higher interest rates, therefore, to a currency appreciation. However, thefindings of this study show that this does not occur in Italy.

The results in Table IV also demonstrate that for the cases of Italy, Belgium,and France budget deficits not only seem to cause money and prices, but alsothe total effect has a positive sign. In other words, in these countries higherdeficits tend to deteriorate inflationary conditions in the economy, thus, leadingto the depreciation of the domestic currency. By contrast, in the remainingcountries in the sample such conditions do not appear to hold, since the policymakers there tended to implement a very tight anti-inflationary policy, mainly,through restrictive monetary policy.

Figure 4.Stability tests, France (1992 crisis)

1995

3

2,5

2

1,5

1

0,5

0


1993 2 3 4 2 3 41994 4 2 3

Figure 5.Stability tests, France (1993 crisis)

21995

3

2,5

2

1,5

1

0,5

0


1993 2 3 4 41994 3


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Concluding remarksThis paper has attempted to examine empirically the relationship betweenbudget deficits and exchange rates within a multi-country sample over theperiod 1980-1995. The countries under examination were the UK, Germany,Switzerland, Belgium, France, The Netherlands, Italy, and Canada. Theempirical analysis employed the cointegration as well as the causality approachand it demonstrated that in the long-run only the UK, Switzerland, France, andCanada are characterised by a relationship between budget deficits andexchange rates. In addition, long-run causality was detected, indicating thatbudget deficits tend to cause exchange rates. In the short run, in countrieswhere an anti-inflationary policy was not followed in a strict manner, i.e. Italy,Belgium, and France, higher budget deficits seem to suggest the presence of adepreciating exchange rate. For the remaining countries, higher budget deficitssuggest that the domestic currency appreciates.

Restrictions LR tests p-values

Switzerlandα∆e = 0 χ2(1) = 65.63 0.00α∆D = 0 χ2(1) = 0.72 0.58α∆y = 0 χ2(1) = 15.98 0.02α∆m = 0 χ2(1) = 1.01 0.24α∆p = 0 χ2(1) = 28.03 0.00

United Kingdomα∆e = 0 χ2(1) = 26.83 0.00α∆D = 0 χ2(1) = 0.68 0.53α∆y = 0 χ2(1) = 11.27 0.02α∆m = 0 χ2(1) = 1.09 0.22α∆p = 0 χ2(1) = 33.47 0.00

Franceα∆e = 0 χ2(1) = 25.94 0.00α∆D = 0 χ2(1) = 0.27 0.64α∆y = 0 χ2(1) = 19.88 0.00α∆m = 0 χ2(1) = 1.30 0.11α∆p = 0 χ2(1) = 25.04 0.00

Canadaα∆e = 0 χ2(1) = 19.39 0.00α∆D = 0 χ2(1) = 1.12 0.47α∆y = 0 χ2(1) = 11.19 0.01α∆m = 0 χ2(1) = 1.24 0.13α∆p = 0 χ2(1) = 19.92 0.00

Table III.Long-run causality tests.

Zero loading factors


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Dependent variable Short-run causality t-values

Switzerland∆e ∆D (–1) → ∆e 2.998*

∆p ∆D (–1) →/ ∆p 1.393∆m ∆D (–1) →/ ∆m 0.922

United Kingdom∆e ∆D (–1) → ∆e –5.597*

∆D (–2) → ∆e –4.954*

∆D (–3) → ∆e –7.158*

∆D→∆e: F-test = 4.46, p-value = 0.02Sum of ∆D: 2.81 [2.79]*

∆p ∆D (–1) →/ ∆p 1.058∆D (–2) →/ ∆p 1.262∆D (–3) →/ ∆p 1.573

∆D→∆p: F-test = 1.06, p-value = 0.34Sum of ∆D: 0.36 [1.53]

∆m ∆D (–1) →/ ∆m 0.742∆D (–2) →/ ∆m 1.387∆D (–3) →/ ∆m 0.886

∆D→∆m: F-test = 1.61, p-value = 0.65Sum of ∆D: 0.38 [1.47]

The Netherlands∆e ∆D (–1) → ∆e –2.513*

∆D (–2) → ∆e –4.176*

∆D (–3) →∆e –3.875*

∆D (–4) →∆e –2.658*


∆p ∆D (–1) →/ ∆p 1.542∆D (–2) →/ ∆p 1.309∆D (–3) →/ ∆p 0.100∆D (–4) →/ ∆p 1.139

∆D→∆p: F-test = 1.84, p-value = 0.17Sum of ∆D: –0.002 [– 0.9]

∆m ∆D (–1) →/ ∆m 1.739∆D (–2) →/ ∆m 0.793∆D (–3) →/ ∆m –1.376∆D (–4) →/ ∆m –0.259

∆D→∆m: F-test = 1.31, p-value = 0.27Sum of ∆D: –0.003 [–0.55]

Italy∆e ∆D (–1) → ∆e –2.152*

∆p ∆D (–2) → ∆p 4.645*

∆m ∆D (–3) →∆m 2.265*

(Continued)

Table IV.Short-run (Granger) causality tests


rates

175


Germany∆e ∆D (–1) → ∆e –2.021*

∆D (–2) → ∆e –2.959*


∆p ∆D (–1) →/ ∆p 1.728∆D (–2) →/ ∆p 0.501

∆D→∆p: F-test = 0.11, p-value = 0.95Sum of ∆D: –0.18 [–0.48]

∆m ∆D (–1) →/ ∆m –0.016∆D (–2) →/ ∆m 0.247


France∆e ∆D (–1) → ∆e –2.759*

∆D (–2) → ∆e –2.539*

∆D (–3) → ∆e –2.713*

∆D (–4) → ∆e –2.688*

∆D (–5) → ∆e –2.899*

∆D→∆e: F-test = 4.93, p-value = 0.02Sum of ∆D: –0.65 [–5.88]*

∆p ∆D (–1) → ∆p 3.065*

∆D (–2) → ∆p 3.344*

∆D (–3) →∆p 2.512*

∆D (–4) →∆p 2.728*

∆D (–5) →∆p 3.821*

∆D→∆p: F-test = 3.13, p-value = 0.04Sum of ∆D: 0.24 [4.83]*

∆m ∆D (–1) →∆m 4.361*

∆D (–2) →∆m 2.507*

∆D (–3) →∆m 2.557*

∆D (–4) →∆m 2.549*

∆D (–5) →∆m 2.818*

∆D→∆m: F-test = 0.7, p-value = 0.65Sum of ∆D: –0.13 [0.08]

Canada∆e ∆D (–1) →∆e –3.361*

∆D (–2) →∆e –2.857*


(Continued) Table IV.


176

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budget deficits and exchange rates: further evidence from cointegration and causality tests

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