Testing the Buchanan-Wagner hypothesis: European evidencefrom panel unit root and cointegration tests
DIMITRIS K. CHRISTOPOULOS1∗ & EFTHYMIOS G. TSIONAS2
1Department of Economic and Regional Development, Panteion University, Athens, Greece;e-mail: [email protected]; 2Department of Economics, Athens University of Economicsand Business, Athens, Greece
Accepted 14 August 2002
Abstract. According to the Buchanan-Wagner hypothesis, public deficits reduce the per-ceived price of public goods to the current generation of voters who, in turn, increase thedemands for such social services. Several recent studies have attempted to test this proposition.In this paper, we apply modern time series techniques organized around panel unit root andpanel cointegration to draw sharper conclusions from the short time series that are typicallyavailable. We find that there is a long run positive relationship between government spendingand government deficits for each country individually, as well as for the panel as a whole.This provides support for the BW hypothesis. We also analyze the implications for the relativeproductivity performance of the public and private sector, the existence of scale economies inthe provision of public services, as well as the extent of crowding out effects.
1. Introduction
Public deficits and government expenditure growth are central to the conductof both monetary and fiscal policy. In this context, Buchanan and Wagner(1977) (henceforth BW) have suggested a theory to explain the existence oflarge budgetary deficits. According to the BW proposition, high deficits pro-duce higher levels of public spending. This happens because “public deficitsreduce the perceived price of publicly provided goods and services to thecurrent generation of voters who, in response increase the demands for suchsocial services”, see Craigwell, 1991: 373.
Several recent studies, for example Niskanen (1978), Provopoulos (1982),Khan (1988), Craigwell (1991), Tridimas (1992), Ashworth (1995) andHondroyiannis and Papapetrou (2001), have investigated empirically the rela-tionship between budget deficits and government spending. The conclusion inall these studies is that there exists a positive and statistically significant cor-relation between the budget deficit and government spending, leading thesestudies to conclude that the BW prediction cannot be rejected by the data.
∗ We wish to thank an anonymous referee for useful comments, George Hondroyiannis foruseful discussions, and Peter Pedroni for providing us with his code.
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The BW hypothesis is important in view of fiscal discipline in the EMU.The Maastricht Treaty sets explicit rules on public finances as condition forentry into the monetary union, and member states are advised to avoid ex-cessive deficits. Whether national governments can raise sufficient funds inthe financial markets to cover potential deficits is an open question in the eraof loss of complete fiscal autonomy. Some authors (Demopoulos and Pro-dromidis, 1994) state that this is not necessarily the end of the world becausealthough capital is freely mobile, the same cannot be said for labor, so gov-ernments could have some leverage in changing income tax rates without thefear that labor could migrate to a lower-tax country. At any rate, fiscal discip-line within the EMU is an important policy cornerstone for macroeconomicstability and long run growth.
We find some points worth mentioning in the approaches presented sofar in the literature. (a) Although cointegration modeling is the proper wayof testing the BW hypothesis, in view of the fact that many economic timeseries contain unit roots, this has not acknowledged in empirical research,with the exceptions of Ashworth (1995) and Hondroyiannis and Papapetrou(2001). (b) The time span of the data is usually quite small for robust longrun inferences, and all efforts must be made to utilize the data in the mostefficient manner in order to draw sharp conclusions. This is true for both theunit root and cointegration inferences.
The article draws upon advances in econometric time series and panel datamodeling to test the BW hypothesis in a sample of eleven E.U. countriesnamely, Belgium, Denmark, France, Italy, Netherlands, Portugal, the UK,Austria, Norway, Sweden and Finland over the period 1970–1999. Our mo-tivation for the particular data set has been the celebrated Maastricht Treatyaccording to which E.U. countries must achieve a high degree of convergence.This procedure involves convergence in inflation rates, long term interestrates, exchange rates and budget deficits. It is well known that nearly bal-anced budgets reinforce the credibility of prevailing economic policies, andcreate the conditions for monetary stability and stable long-run growth. Largebudget deficits are crowding out private investment, and depending on themoney supply conditions, they may produce inflation and push interest ratesupwards, thus endangering a country’s relative standing in the EMU. To avoidhigher interest rates at the Union level, it is apparent that fiscal and monetarydiscipline is the essential cornerstone of any feasible economic policy.
In this paper:1. We use time series unit root tests along with panel unit root tests to exam-
ine the stationarity properties of the data. The use of panel data statisticsis necessary because the power of standard time-series unit root tests may
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be quite low given the sample sizes and time spans typically available ineconomics.
2. The cointegration framework of Johansen (1988) is applied to test formultivariate cointegrating relationships. Additionally, panel cointegra-tion tests are conducted to make sure that problems of power in finitesamples do not distort the conclusions derived from Johansen’s tests.
3. Cointegrating vectors are estimated following the fully modified OLSestimation technique for heterogeneous cointegrated panels (Pedroni,2000). This methodology allows consistent and efficient estimation ofcointegrating vectors. It is known that OLS estimation is biased due tothe endogeneity of the integrated (i.e., I(1)) regressors.
The paper is organized as follows. The model is presented in Section2. The econometric methodology and the empirical results are discussed inSection 3. Also, various implications and comparisons with previous studiesare reported. The final section concludes the paper.
2. Theoretical model
The first step in the empirical analysis of the public choice theory of govern-ment expenditure growth is to consider Niskanen’s (1978) specification. Thisapproach resembles closely that of Bergstrom and Goodman (1973). It relatesthe quantity of government services consumed by the average voter taxpayerto the perceived price paid and to the level of real per capita income.
GSQ = f(P, Y) (1)
where GSQ is the quantity of government services, P is the price of gov-ernment services and Y represents a measure of income. The log-linearfunctional form for this specification is given by:
lnGRQ = α0 + α1ln(C × F) + α2ln Y (2)
where C is the unit cost of the bundle of cost services and F is the perceivedshare of the unit cost of government services paid by the average taxpayer,where C × F = P. The problem with the above formulation, is that GSQand C are unobserved. Thus, we consider an alternative specification of thegovernment services demand based on Ashworth (1995) and Hondroyiannisand Papapetrou (2001). This is given by the following.
where GEXP is total government spending, TEXP = TGEXP is the ratio of
total tax revenues (T) to total government spending (GEXP), and VOT is thenumber of voter-taxpayers.
We assume that the unmeasured variable C is a function of variablessuch as the average wage rate in the private sector (PW) and the totalnumber of voter-taxpayers (VOT), following Niskanen (1978), Ashworth(1995), Craigwell (1991) and Provopoulos (1982). Therefore, we obtain thefollowing.
lnC = µ + λlnPW + ϑ lnVOT (4)
Equation (4) has several features, which deserve comment: (a) If the coeffi-cient λ is greater (less) than zero, the private sector increases (decreases) itsproductivity more than the public sector. (b) If λ = 1, there is no increase inpublic sector productivity, (c) if ϑ = 0, then public services are “pure publicgoods”. In this case, unit cost is invariant to the number of taxpayers to whomthese services are supplied. Economies of scale emerge in the provision ofgovernment services when θ is less than zero, and (d) if ϑ = 1, then the costis proportional to the number of population while if ϑ > 1, a “crowding out”effect is implied.
This version of the model (Equations (3) and (4)) is difficult to estimatebecause the unmeasured variable C appears in both equations. However, thisproblem is readily handled by substituting Equation (4) in (3). After somemanipulation, we obtain:
(6)Equation (5) represents the basic model, based on which we can provideformal statistical tests of the BW hypothesis. The BW hypothesis would becorrect if Z1 < 0 in which case deficits would be positively related to theprovision of government services.
The problem with estimating Equation (5) from time series data, is that ifwe proceed without testing for cointegration when the time series involvedcontain unit roots, the results would be misleading. For this reason, we haveto check whether the variables contain unit roots, and if they do to ensurethat (5) represents a valid long-run relationship. This is not an easy task, andwe have to consider problems of small samples, homogeneity of parametersacross countries etc in order to be able to provide sharp inferences.
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3. Data, econometric methodology and empirical results
In this section, we present the econometric methodology and empirical resultsrelated to the BW hypothesis. All data required for this study were extrac-ted from the European Union’s AMECO database (Annual Macro EconomicData Base DG2) from 1970 through 1999. The data are as follows: GEXPis total public spending divided by consumer price index. TEXP is the ratioof total public tax revenues over total government expenditures. Y is real peradult gross domestic product. PW is measured by the average real wage inthe private sector (industry and services) while VOT is the total population 20years of age and older. All variables, with the exception of VOT, are expressedin ECU.
3.1. Unit root tests
Time series approachUnit root inference is an important step in the analysis of data. We test for thepresence of unit roots using the augmented Dickey-Fuller (ADF) statistics inwhich the null hypothesis is non-stationarity, as well as the KPSS test (Kwi-atkowski et al., 1992) in which the null hypothesis is stationarity. Table 1(a)reports the unit root statistics for each series. It is evident that we cannot rejectthe presence of a unit root in all variables at conventional levels of statisticalsignificance. One exception is the average wage (PW) in the private sectorfor Denmark where the ADF statistic indicates that this series is I(0). Thetests are performed again in first differences. From the results in Table 1(b),all series appear stationary in first differences with the exception of GEXPfor Belgium, Sweden and Finland, TEXP series for Belgium and Denmark,Y series for Belgium, VOT series for Belgium, Italy and Netherlands and PWseries for Belgium and Netherlands. However, the KPSS statistic indicatesthat these series are all stationary at the 10% level of significance. Since theADF and KPSS statistics yield different results, one cannot reach a definiteconclusion: It is well known that ADF and KPSS tests must be used jointly todetermine the presence of unit roots. However, as a working hypothesis, wecan accept the presence of a unit root or examine a more powerful test basedon panel data. We consider this possibility in what follows.
Panel data approachGiven the relatively short span of our time series (T = 29) all unit root testswe applied on a per country basis can have low power, see for example Pierseand Shell (1995). Thus, our results could be seriously misguided. An increasein power of individual unit root tests can be achieved by pooling individualtime series and performing panel unit root tests.
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Table 1. (a) ADF and KPSS unit root tests (levels)
ADF is the augmented Dickey-Fuller t-test for a unit root in the model (constant/trend). TheKPSS test statistic is associated with a null hypothesis that the variable in question is trendstationary. The 5% and 10% critical values are 0.15 and 0.12 respectively. Boldface valuesdenote sampling evidence in favour of unit roots. (∗∗∗) (∗∗) and (∗) signify rejection of theunit root hypothesis at the 1%, 5% and 10% level respectively.
Table 1. (b): ADF and KPSS unit root tests (first differences)
ADF is the augmented Dickey-Fuller t-test for a unit root in the model (constant/trend).. TheKPSS test statistic is associated with a null hypothesis that the variable in question is trendstationary. The 5% and 10% critical values are 0.15 and 0.12 respectively. Boldface values denotesampling evidence in favour of unit roots. (∗∗∗) (∗∗) and (∗) signify rejection of the unit roothypothesis at the 1%, 5% and 10% level respectively.
IPS is the Im, Pesarasn and Shin t-test for a unit root in the panel. Boldface values denotesampling evidence in favour of unit roots. (∗∗∗) denotes rejection of the unit root hypothesisat the 1% level.
To test for the existence of a unit root in a panel data setting, we have usedtests due to Im, Pesaran and Shin (IPS) (1997). These tests are based on theapplication of the ADF test to panel data, and allow heterogeneity in boththe constant and slope terms of the ADF regression. Results of the IPS arereported in Table 2. None of the variables is stationary in levels, and the testis performed again in first differences. As indicated, all series are stationary infirst differences. Therefore, we can accept that the series are I(1) based on theresults of panel unit root tests. The next step is to ensure that (5) represents avalid long-run relationship given that previous tests indicate the presence ofunit roots.
3.2. Cointegration tests
Johansen maximum likelihood testsEngle and Granger (1987) argue that, even though a set of economic series isnot stationary, there may exist some linear combinations of the variables thatis stationary. If the separate series are stationary only after differencing buta linear combination of their levels is stationary, the series are cointegrated.The proper way to test for co-integration is the maximum likelihood approachdeveloped by Johansen (1988). See also Johansen and Juselius (1991). Fromthe results in Table 3, the null hypothesis of no co-integration (r = 0) canbe decisively rejected at the 5% level for all countries. The null hypothesisthat we have one cointegrating vector (r ≤ 1 given that r ≤ 0 was rejected)cannot be rejected, and this is true except for Belgium, Denmark, France, theUK and Austria. However, the computed statistics are very close to criticalvalues. Indeed the hypothesis r ≤ 2 can be rejected for all countries with theexception of Belgium. Therefore, we have relatively strong evidence againstthe hypothesis of one cointegrating vector only for Belgium. For this country,
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Table 3. Johansen cointegration tests
Max eigenvalue statistics for H0: rank = r
Country r = 0 (87.31, 96.68) r ≤ 1 (62.99, 70.05) r ≤ 2 (42.44, 48.45)
r: Number of cointegrating vectors. The optimal lag structure for the VAR was selected byminimising the Schwarz criterion. (∗∗) and (∗) indicate rejection of the null hypothesis at 1%and 5% level respectively. Numbers in parentheses next to r = 0, r ≤ 1, and r ≤ 2 representthe 5% (first number) and 1% (second number) critical values of the test statistic.
we can take the results with some skepticism but for the remaining countriesa unique cointegrating vector seems to be a data-congruent hypothesis.
Panel cointegration testsPanel cointegration tests are used in order to draw sharper inferences sincetime spans of economic time series are typically short. However, whendealing with panel data the question of homogeneity arises, i.e., whetherparameters are the same across units. First, we use Pedroni’s (1997) panelversion of the ADF statistic. Second, we use a test due to Levin and Lin(1992) (LL) in the context of panel unit roots, which we apply to estimatedresiduals from (supposedly) long run relations. Third, we use the unit roottests developed by Harris and Tzavalis (1999) (HT). LL and HT tests involvethe computation of conventional ADF regressions to panel data accountingfor heterogeneity only in the intercept. Pedroni’s panel ADF test allows forheterogeneity in all parameters, so on a priori grounds we would be willing toplace more emphasis on results of Pedroni’s test. It must be noted that LL testsmay have substantially size distortion if there is cross-sectional dependence(O’Connell, 1998). Also, small T results in LL tests that are substantiallyundersized and have low power (Harris and Tzavalis, 1999). In addition Breit-ung (1999) finds that Levin and Lin test suffers a dramatic loss of power whenindividual trends are included, and the test is sensitive to the specification of
Notes: ∗∗ signifies rejection of the null hypothesis of no-cointegration at 5% significance level.Figures in italics indicate evidence in favour of the null hypothesis of no-cointegration atconventional levels of significance.
deterministic trends. The deficiency of both LL or HT tests is that they do notallow for heterogeneity in the autoregressive coefficient ρ.
Fortunately, all tests provide evidence in favor of cointegration (Table 4),and confirm the existence of a long-run relationship among government ex-penditure (GEXP) and TEXP, PW, Y, and VOT. Further, to ensure that onlyone cointegrating vector exists we perform Pedroni’s test under the assump-tion of alternative dependent variables. The results in Table 4 clearly indicatethat in the panel as a whole only one cointegrating vector exists. In otherwords having TEXP, PW, Y, and VOT as dependent variable, shows absenceof cointegration so such relations can be considered as spurious: The onlyvalid relation that can be derived is the one that has GEXP as the dependentvariable, and defines the unique cointegrating vector. This result is potentiallyimportant because it shows that the Buchanan-Wagner hypothesis could haveconsiderable support from the data: Equation (5) would represent a long-runrelation between government expenses, deficits and the other covariates, andit would make sense to test whether Z1 (or equivalently α1) is negative. Ifwe failed to establish cointegration, we would dismiss the BW hypothesisimmediately as it would be at odds with the data. The finding of existence ofpanel cointegration is important from the economic viewpoint as it impliesthat the basic model leading to (5) is a reasonable description of the data, inthe sense that voters do look at the cost of providing public goods to determinetheir demand for these goods. Of course, we need the additional restrictionthat Z1 < 0 to ensure that the way they look at the cost is consistent with theBW hypothesis.
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Fully modified OLS estimationIn this section we take up estimation of the long run equation given thatwe have established cointegration. In other words, given that (5) representsa structural and not spurious long-run relation, we proceed to estimate theparameters and test whether Z1 < 0, as the BW hypothesis implies. To drawsharp inferences, we will need to pool the data, and use estimating techniquesappropriate for panel data.
One method for estimation of cointegrating vectors in panels is the fullymodified OLS (FMOLS) technique. In our case, we estimate Equation (5)using FMOLS and use Equations (6) to recover estimates of the structuralparameters. Consider the following cointegrated system for panel data
yit = α1 + x′itβ + uit
xit = xi,t−1 + eit
where ξit = [uit, e′it] is stationary with covariance matrix �i. Following Phil-
lips and Hansen (1990) a semi-parametric correction can be made to the OLSestimator that eliminates the second order bias caused by the fact that theregressors are endogenous. Pedroni (2000) follows the same principle in thepanel data context, and allows for the heterogeneity in the short run dynamicsand the fixed effects.
FMOLS estimates of Equation (5) are reported in Table 5, and the resultsfor structural Equations (3) and (4) are presented in Table 6.1 The resultsshow the following:
1. There is a long run positive relationship between government spendingand government deficits for each country individually, as well as for thepanel as a whole (see Table 6). The estimated coefficient (α1) varies from–1.23 for Belgium to –0.40 for Norway, and all estimates are statisticallysignificant. Therefore, the Buchanan-Wagner (BW) proposition is con-firmed for all countries we examine as well as for the panel as a whole.We consider this to be very important empirical evidence in favor of theBW hypothesis, especially in view of the fact that the BW hypothesisholds for a relatively large number of countries. The BW prediction wasalso confirmed by Ashworth (1995) for the UK, Craigwell (1991) for Bar-bados, as well as Hondroyiannis and Papapetrou (2001) and Provopoulos(1982) for Greece. These authors have provided more or less scatteredevidence in favor of the BW hypothesis. Our results have a greater coun-try coverage, and they are based on econometric analysis that providessharper inferences.
2. All long run income elasticities of demand for government services arepositive and highly statistically significant. The income elasticities of de-mand for government services exceed unity for Netherlands, Portugal,
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Austria, Sweden, Norway and Finland, reflecting the strong impact ofthe growth of income on the public sector’s expansion in these countries.On the contrary, in Italy and the UK, the growth of income has not af-fected considerably the size of the public sector: The estimated elasticitywas found much lower than unity. However, for all eleven countries theresults show that that government spending is highly dependent on out-put growth. In addition, these results support Wagner’s view that outputgrowth affects materially the expansion of the public sector. It should benoted that Wagner’s law could not be documented for Greece (Hondroyi-annis and Papapetrou, 1995, 2001; Courakis et al., 1993), for Barbados(Craigwell, 1991), for UK (Ashworth, 1995) and for Portugal (Courakiset al., 1993).
3. Coefficients λ on PW indicate that for Italy and Portugal as well as for thepanel as a whole, private sector’s productivity has increased more rapidlythan the productivity in the public sector. On the contrary, for France,Netherlands and Norway, the public sector seems to be more productivecompared to the private sector. For the remaining countries no differenceseems to exist in sectoral productivity performance.
4. Finally, according to the size of ϑ a “crowding out effect” (ϑ > 1) isestablished in Denmark, France, Italy and Netherlands. For Belgium andSweden public services are “public goods” (the relevant coefficient isstatistically zero). This means that unit cost is invariant to the numberof taxpayers whom social services are supplied. Finally, for the panelas a whole and for Portugal, the UK, Austria and Finland an increasein the adult population reduces the unit cost of supplied public services,(ϑ < 0). In other words scale economies exist in the provision of publicservices.
4. Conclusions
The purpose of this paper was to test the Buchanan and Wagner (BW) pro-position for eleven E.U. countries, namely Belgium, Denmark, France, Italy,Netherlands, Portugal, UK, Austria, Norway, Sweden and Finland over theperiod 1970–1999. The study breaks new ground in the empirical analysisof the BW hypothesis in several respects: (a) We analyze the stationarityproperties of the data using individual along with panel unit root tests. (b)We employ multivariate Johansen cointegration tests along with panel coin-tegration tests to make sure that problems of power in finite samples do notdistort Johansen’s tests, and (c) we estimate the cointegrating vectors by thefully modified OLS procedure appropriate for panel data. We believe thatthis is a reasonable way to proceed if we need sharp inferences and parameter
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Table 5. Fully modified OLS estimates
Country Z1 Z2 Z3 Z4
Belgium –1.23∗∗∗ 0.95∗∗∗ 1.79 –0.004
[7.36] [2.60] [1.12] [0.23]
Denmark –0.55∗∗∗ 0.93∗∗∗ 2.56∗∗∗ 0.06
[5.27] [3.83] [2.50] [0.64]
France –1.09∗∗∗ 0.86∗∗∗ 0.96∗∗∗ 0.40∗∗∗[6.69] [8.27] [57.50] [4.98]
Notes: Figures in brackets are t-statistics. (∗∗∗) indicates statistical significance at 1% level.
estimates in light of the small time-series samples typically available in publicfinance studies. We find that that there is a long run negative relationshipbetween government spending and government deficits for each country indi-vidually, as well as for the panel as a whole, which provides strong support forthe BW hypothesis. For several countries, the income elasticities of demandfor government services exceed unity, and for all eleven countries the resultsshow that government spending is highly dependent on output growth. Witha few exceptions, the empirical results do not show a significant differencebetween the productivity of the private and public sector. Moreover, for thepanel as a whole, an increase in the adult population reduces the unit cost of
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Table 6. Estimates of structural Equations (3) and (4)
Country α1 α2 λ ϑ
Belgium –1.23∗∗∗ 0.95∗∗∗ 0.17 1.91
[7.36] [2.60]
Denmark –0.55∗∗∗ 0.93∗∗∗ 0.13 2.24
[5.27] [3.83]
France –1.09∗∗∗ 0.86∗∗∗ –4.44 12.55
[6.69] [8.27]
Italy –0.84∗∗∗ 0.71∗∗∗ 0.94 8.50
[5.45] [2.33]
Netherlands –1.50∗∗∗ 1.20∗∗∗ –0.68 3.14
[11.91] [10.94]
Portugal –0.77∗∗∗ 1.25∗∗∗ 0.22 –3.17
[4.41] [8.01]
UK –0.84∗∗∗ 0.59 1.12 –0.81
[3.34] [1.39]
Austria –0.69∗∗∗ 1.20∗∗∗ –0.48 –3.16
[6.52] [19.95]
Norway –0.40∗∗ 1.01∗∗∗ –0.52 0.03
[2.12] [13.49]
Sweden –1.07∗∗∗ 1.92∗∗∗ –1.14 57.42
[7.75] [3.81]
Finland –0.84 1.39∗∗∗ –0.32 –2.68
[3.37] [8.30]
Panel –0.89∗∗∗ 1.09∗∗∗ 0.82 –5.82
[19.47] [25.14]
Notes: Figures in brackets are t-statistics. (∗∗∗) indicates statistical significance at 1%level.
supplied public services. In other words scale economies exist in the provisionof public services.
Notes
1. The estimates in Table 6 are derived from FMOLS results and (6). Standard errors arenot reported for the parameters that are related in a nonlinear way with the parameters Zestimated from FMOLS.
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