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Yardstick competition in intergovernmental relationships: theory and empirical predictions
Economics Letters 83 (2004) 325 – 333 www.elsevier.com/locate/econbase
Yardstick competition in intergovernmental relationships: theory and empirical predictions Massimo Bordignon a,b,*, Floriana Cerniglia c, Federico Revelli d a
Facolta` Economia, Universita` Cattolica del Sacro Cuore, L.go Gemelli 1, 20123 Milan, Italy b CESifo, Mu¨nchen, Germany c Facolta` di Scienze Politiche, Universita` Cattolica del Sacro Cuore, L.go Gemelli 1, 20123 Milan, Italy d Facolta` di Scienze Politiche, Universita` di Torino, Via Po 53, 10124 Turin, Italy Received 22 April 2003; received in revised form 9 October 2003; accepted 3 November 2003
Abstract We review yardstick competition theory as applied to fiscal choices in the intergovernmental context. We show that the theory is consistent with opposite results concerning neighbouring governments’ fiscal behaviour, and discuss some empirical implications. D 2004 Elsevier B.V. All rights reserved. Keywords: Local property tax; Yardstick competition JEL classification: D72; H71
1. Introduction A long tradition in fiscal federalism theory suggests that the organisation of the public sector in different layers of government may help overcome a number of ‘‘failures’’ of the political system (e.g. Brennan and Buchanan, 1980; Oates, 1972; Tiebout, 1956). Starting from the seminal work of Salmon (1987); Besley and Case (1995a); a new argument has been recently proposed. Voters are ‘‘rationally ignorant’’ as it is costly for them to acquire information about politics, and self-interested politicians may exploit this informational advantage to the detriment of voters’ interests. A decentralised structure may help ease this problem, as voters may then engage * Corresponding author. Tel.: +39-02-7234-2694; fax: +39-02-7234-2781. E-mail addresses: [email protected] (M. Bordignon), [email protected] (F. Cerniglia), [email protected] (F. Revelli). 0165-1765/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2003.11.014
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in comparative performance evaluation between different local governments, and this may allow them to better distinguish between ‘‘bad’’ and ‘‘good’’ politicians. This argument in favour of decentralisation is particularly interesting because it does not rely upon either costless mobility of citizens or large difference in local preferences, assumptions which are both questionable in a number of countries. But of course the important question on policy grounds is if this argument is empirically founded. Following the seminal work of Besley and Case (1995a), a large amount of research has been devoted to this issue (e.g. Bivand and Szymanski, 1997; Heyndels and Vuchelen, 1998; Schaltegger and Kuttel, 2002; Sole´ Olle´, 2001)1. In most cases, this literature contents itself with showing that there is some mimicking behaviour going on among local governments, and takes this as conclusive evidence of the existence of yardstick competition phenomena (comparative performance evaluation). In this paper, we argue that this conclusion is unwarranted. Yardstick competition theory is too ‘‘weak’’ to produce welldefined empirical predictions concerning the fiscal choices of neighbouring jurisdictions, and some of the possible theoretical solutions do not involve mimicking behaviour at all. In order to test the theory, then, a much subtler work of linking the predictions of the theory with the institutional characteristics of the political system under analysis needs to be done.
2. The model Yardstick competition theory in the intergovernmental context predicts the existence of informational spillovers among voters of neighbouring jurisdictions. For empirical testing, one needs to consider the strategic reaction of politicians to citizens’ behaviour. Politicians are rational agents and know the kind of calculations citizens make. Hence, they might attempt to modify their fiscal choices to influence voters’ inference. On this point, following the seminal paper of Besley and Case (1995a), most of the empirical literature seems to have taken for granted that, in the presence of comparative performance evaluation on the part of voters, bad or incompetent governments may be forced to set fiscal variables in line with those chosen by neighbouring governments, in order to avoid being unseated. Hence, ‘copycatting’ or mimicking behaviour in local fiscal choices will be the expected result. However, this is only one possibility. Another possibility—that is explored in this paper—is that, by improving voters’ information set, yardstick competition increases the cost for bad or incompetent governments to imitate good ones, so inducing no or little mimicking behaviour. To show this point formally, consider the following version of Besley and Case (1995a) original model. The economy has three agents: an incumbent politician, an opposing politician and a voter. The economy lasts two periods and at the end of the first period an election takes place. In both periods, the incumbent politician chooses taxes and public good supply. Governments come in two types: they can be either ‘‘good’’ or ‘‘bad’’. Good politicians only want to provide the public good at the lowest possible cost; bad governments like instead to tax citizens more heavily in order to accumulate rents. Govern-
1
Brueckner (2003) reviews the recent empirical literature on strategic interaction among local governments and discusses the main econometric issues involved.
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ments know their type, while citizens have only some a-priori on the type of governments. More specifically, we assume that:
the citizen expects both the incumbent and the opposing government to be good with probability h, ha(0, 1); the production function of the public good is subjected to random shocks. Producing public good level g* costs t* if the shock is positive, and t*+ D, D > 0, if the shock is negative; negative shocks occur with probability q < 1; all agents in the economy discount future at rate d < 1.
The sequence of events is as follows. In period 1, nature moves first and chooses both the type of the incumbent and the realisation of the shock. The incumbent government observes those moves of nature, and then decides the tax rate and public good supply in the first period. The citizen does not observe the moves of nature, but observes the fiscal choices of the government and knows the stochastic structure of the economy. She thus uses these observations to revise her beliefs on the type of the incumbent. Let l(h, t, g) indicate the posterior beliefs of the citizen. An election then takes place, and the citizen votes for the politician who expects to be good with higher probability at the time of voting. When indifferent, she votes for the incumbent2. That is, the incumbent is re-elected if l(h, t, g) z h. Whichever government is in charge in period 2, it chooses again a level of the tax rate and of public good supply. The world ends here. 2.1. The equilibrium with one jurisdiction To solve this dynamic incomplete information game between voter and politicians, we look for perfect Bayesian Nash equilibria (PBE) of the game. For simplicity, we only focus on pure strategies equilibria of this game. Again for simplicity, suppose that governments of both types have to supply a fixed amount of public good, g*, in both periods3. Also suppose that good governments do not play strategically; they just do what is best for the citizen in the two possible cases; i.e. they impose a tax equal to t* if the shock is positive and t* + D if the shock is negative. Consider next the bad government. Suppose that there is a maximal tax rate it can impose on citizens (an upper bound on politically sustainable expropriation), and let us write this upper tax rate as t* + kD, where k>1. The maximal rent the bad type can earn in each period is either (k 1)D or kD depending on the realisation of the shock. In the second period, a bad government chooses the highest possible tax rate, t* + kD, as this tax rate maximises its utility. In the first period, however, it faces a trade off. It could still choose t* + kD, earning immediately the maximal rent, but then the citizen would immediately understand that it is of the bad type and throw it out of office at the ensuing election. Alternatively, it could try to mimic the good type and then be reelected with some positive probability. Let us suppose that the out-ofequilibrium beliefs of the voter are such that she assigns zero probability to a government being of a good type upon observing a tax rate different from one of the two rates a good government could possibly
2
This assumption effectively rules out mixed strategy equilibria. See Bordignon and Minelli (2001). As long as the quality of the public good supplied is observable by citizens, this assumption is of no consequence and only simplifies the analysis. 3
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choose; i.e. l( g*, h, t) = 0 for t p t* + D, and t p t*. Then it is clear that if the shock happens to be negative, the bad type would prefer to choose t* + kD in the first period, even if that implies losing the election. This is so because the maximum tax rate the bad type can impose without being discovered in period 1 is t* + D; but if the shock is negative, this means that the bad type earns zero rent in period 1. And even under the optimistic beliefs that it would be elected for sure if it followed that strategy, it would prefer to separate immediately, since waiting is costly: (k 1)D>y(k 1)D. What if the shock is positive? Repeating the argument just given, the bad type would never play t*. But could it play t* + D? Proposition 1. Suppose d z dj u (k 1)/k and q z 1/2. Then there exists a PBE in pure strategies where the bad type’s first period choice is t*+ D and any incumbent who selects t*+ D is re-elected for sure. Proof 1. By Bayes’ rule, at the proposed governments strategies, the citizen’s posterior beliefs upon observing t*+ D is l(h, t*+ D) = qh/(qh+(1 q)(1 h)). It follows l(h, t*+ D) z h if q z 1/2. Assuming this to hold, the bad type would play t = t*+ D when the shock is positive if this gives it an higher expected utility than playing its favourite strategy in the first period, i.e. if D + dkD z kD, which holds true for y z (k 1)/k. 5 2.2. Yardstick competition: two jurisdictions Suppose now we double our simple economy, introducing another jurisdiction which has exactly the same characteristics as the economy we just studied. A potential advantage for the citizen of having two economies instead of one is that she can now try to learn something about her incumbent in the first period, by looking at what is happening in the other jurisdiction. That is, the voter’s posterior beliefs in region i may now be written as a function of the fiscal choices of both jurisdictions: li(h, ti, tj), where the suffix indexes the jurisdiction, i = 1, 2, and t refers to first period choices4. For comparative performance evaluation to be meaningful, it is necessary that the two economies be somehow related. Besley and Case (1995a) assume perfect correlation among regional technological shocks in their theoretical model. However, this is implausible for most empirical applications of the model5, and it also hides some of the possible results of the model, which we want to emphasise. We take instead the following approach. Let r be the parameter, which measures the degree of correlation between the two economies. Denoting by Prob(X, Y) the joint probability that region i is hit by a shock X, while region j by shock Y, where X and Y indicate the nature of the shock, we have: ProbðN ; N Þ ¼ rq;
ProbðP; N Þ ¼ ProbðN; PÞ ¼ ð1 rÞq;
ProbðP; PÞ ¼ 1 qð2 rÞ;
ð1Þ
where N and P stand, respectively, for negative and positive shock. For r = q the two technological shocks are independent, for r = 1 they are perfectly correlated, while for q < r < 1 they are positively but 4
We suppress g from the argument of the revised beliefs’ function because public good supply is assumed to be fixed. While the fiscal policies of local jurisdictions often tend to be affected by correlated shocks (most frequently tax base shocks), the existing empirical literature shows that such a correlation is far from perfect. It generally declines over distance, with a spatial auto-regressive coefficient consistently below 0.5 (see for instance Bordignon et al., 2003). Moreover, the same empirical analysis of Besley and Case (1995a) on US state data uncovers no correlation in the shocks received by neighbouring states. 5
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imperfectly correlated. We assume instead the draws by nature of the type of government to be independently made in the two regions. Local governments make their tax choices simultaneously. Each incumbent only observes the realisation of the shock in its own jurisdiction and only knows the distribution over government types of the other jurisdiction. The central question to address is what effect comparative performance evaluation has on the equilibria of the game and therefore on the empirical predictions of the model. In particular, we want to know if pooling behaviour—bad types imitating the tax choices of the good types in the first period—is more or less likely under yardstick competition. To this aim, note first, by using the same dominance argument we used before, that if the shock is negative, bad governments will again prefer to separate in the first period by choosing the maximum tax rate and being defeated at the election. By the same token, if the shock is positive, they would never play t*. Would they play t* + D? To answer the question, note that at an equilibrium where all agents expect the bad types to play t* + D in the first period when the shock is positive, the expected probability of being reelected for a bad type in region i if it follows this strategy, let us call it G(t* + D), is:
Gðt* þ DÞ ¼ Probðej ¼ N Aei ¼ PÞðhRðti ¼ t* þ D; tj ¼ t* þ DÞ þ ð1 hÞRðti ¼ t* þ D; tj ¼ t* þ kDÞÞ þ Probðej ¼ PAei ¼ PÞðhRðti ¼ t* þ D; tj ¼ t*Þ þ ð1 hÞRðti ¼ t* þ D; tj ¼ t* þ DÞÞ: ¼ fð1 rÞqðhRðti ¼ t* þ D; tj ¼ t* þ DÞÞ þ ð1 hÞRðti ¼ t* þ D; tj ¼ t* þ kDÞÞ þ ð1 qð2 rÞÞðhRðti ¼ t* þ D; tj ¼ t*Þ þ ð1 hÞRðti ¼ t* þ D; tj ¼ t* þ DÞÞg=ð1 qÞ
ð2Þ
where R(ti = t* + D, tj = t) is the probability of being reelected by the bad type in region i if it plays t* + D and government j plays t, t = t*, t* + D, t* + kD. Clearly, by our previous assumption, R(ti = t* +D, tj = t) = 1 if l(h, ti = t* + D, tj = t) z h and R(ti = t* + D, tj = t) = 0 otherwise. By applying Bayes’ rule: lðh; ti ¼ t* þ D; tj ¼ t* þ DÞ ¼frqh2 þ hð1 hÞð1 rÞqÞg = fðrqh2 þ 2hð1 hÞð1 rÞq þ ð1 hÞ2 ð1 qð2 rÞÞg: lðh; ti ¼ t* þ D; tj ¼ t* þ kDÞ ¼ rh=frh þ ð1 hÞð1 rÞg: lðh; ti ¼ t* þ D; tj ¼ t*Þ ¼ sh=fsh þ ð1 hÞð1 sÞg:
where s ¼ ð1 rÞq=ð1 qÞ:
ð3Þ
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It follows:
Rðti ¼ t* þ D; tj ¼ t* þ DÞ ¼ 1 if h þ 2ð1 2hÞð1 rÞqzð1 qÞ; Rðti ¼ t* þ D; tj ¼ t* þ DÞ ¼ 0 otherwise;
Rðti ¼ t* þ D; tj ¼ t* þ kDÞ ¼ 1 if rz1=2;
ð4:1Þ
Rðti ¼ t* þ D; tj ¼ t* þ kDÞ ¼ 0 otherwise; ð4:2Þ
Rðti ¼ t* þ D; tj ¼ t*Þ ¼ 1 if ð1 rÞzð1 qÞ=2q;
Rðti ¼ t* þ D; tj ¼ t*Þ ¼ 0 otherwise; ð4:3Þ
Using (4), we can answer the question raised above. We begin by establishing: Proposition 2. Suppose q < 1/2, r>1/2. Then, there exist h*< 1, y*< 1 and k* such that there exists a PBE in pure strategies where bad type’s first period choices in both economies upon observing a positive shock are t*+ D. Proof 2. Invoking (4), under the conditions stated in the proposition, at the proposed equilibrium strategies for the two types, voter’s revised beliefs in region i, i = 1, 2, j = 1, 2, i p j, are such that R(ti = t*+ D, tj = t*+ kD) = 1 and R(ti = t*+ D, tj = t*) = 0. R(ti = t*+ D, tj = t*+ D) = 1 if h z h*u ((1 q(3 2r))/((1 4(1 r)q)) < 1 as r>1/2. Invoking Eq. (2), G(t*+ D)={(1 h)(1 q) + hq(1 r)}/(1 q). The expected utility of the bad type when playing his equilibrium strategy is then D + dkD{(1 h)(1 q) + hq(1 r)}/(1 q). This dominates its best deviation, playing t*+ kD and not be reelected in the second period, if y z y*=(k 1)(1 q)/k{(1 h)(1 q) + hq(1 r)}. In turn y*< 1 if k < k*u (1 q)/h(1 q(2 r)). 5 A comparison between Propositions 1 and 2 makes it clear that it is in principle possible to find values of the parameters that support a pooling equilibrium under yardstick competition when this would not be possible otherwise (as q < 1/2). Vindicating the empirical literature mentioned above, in this case the ex ante probability of finding the two regions selecting similar tax rates (in the first period) would be higher under yardstick competition than without it, so that a high correlation among the tax rates of neighbouring regions could be interpreted as a signal of the presence of comparative performance evaluation among governments by voters. This is not the only possibility, however, as the next proposition illustrates. Proposition 3. Suppose q z 1/2 and (1 q)>h. Then, there exist q V r1 < r2 < 1 such that the bad type’s first period equilibrium choices in both economies upon observing a positive shock are t*+ D if the following (sufficient) conditions are satisfied: (i) r>r2, d z d** and k < k**; (ii) r2 z r>r1, d z d* and k < k*; (iii) r1 z r, d z dj, where dj < d*< d**< 1 and 1 < k**< k*.
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Proof. At the proposed strategies for the two types, voter’s posterior beliefs are such that (1) R(ti = t*+ D, tj = t*+ kD) = 1 br, as r z q and q z 1/2 by assumption; (2) R(ti = t*+ D, tj = t*) = 1 if r V r1 u (3q 1)/2q. (3) R(ti = t*+ D, tj = t*+ D) = 1 if r V r2 u {(3q 1) + h(1 4q)}/2q(1 2h). Note that q z 1/2 and (1 q)>h implies h < 1/2 so that r2>0. Furthermore, q z 1/2 also implies r1 V r2. Using (1)-(2)-(3), it is clear that in case (iii), the expected probability to be elected for the bad type when playing t*+ D in the first period upon observing a positive shock is just one, so that the condition on y for the existence of a pooling equilibrium coincides with those in Proposition 1, y z yj; in case (ii), this probability is {(1 h)(1 q) + hq(1 r)}/(1 q), so that the conditions on y and k for the existence of a pooling equilibrium coincides with those of Proposition 2, y z y* and k < k*. In case (i), finally, G(t*+ D)={(1 h)q(1 r)}/(1 q), giving an expected utility to the bad type when playing t*+ D in the first period of D + dkD{(1 h)q(1 r)}/(1 q). This dominates playing t*+ kD in the first period if y z y**=(k 1)(1 q)/k{(1 h)q(1 r)}. In turn y**< 1 if k < k**u (1 q)/(1 q(2 r(1 h) h). 5 Clearly, in this second example, supporting a pooling equilibrium becomes unambiguously more difficult under yardstick competition than without it, in the sense that stricter restrictions on the parameters must be imposed to get pooling behaviour. Furthermore, these restrictions increase with the degree of correlation between the two economies. When this correlation is very low, r V r1, a pooling equilibrium can be supported under the same conditions as in the case with a single jurisdiction. As r increases, y must also increase to support a pooling equilibrium, and, under the conditions on q and h stated in the proposition, this equilibrium simply disappears when the two economies become perfectly correlated. Empirically, in this second example, one should expect to find less correlation in tax rates among neighbouring jurisdictions (in the first period) and more politicians being unseated at elections as a result of yardstick competition. The contradictory results of Propositions 2 and 3 can be readily explained. For r = q, the two economies are effectively separated, and the equilibrium with two jurisdictions coincides with that with one jurisdiction. As r increases, there are two effects in this economy. On the one hand, the larger is r, the more the citizen learns by observing the fiscal choices in the other jurisdiction, and the more difficult it is for the bad politician to escape detection when cheating. This effect, by increasing the cost of mimicking, pushes toward more separation and less pooling in the first period. On the other hand, a larger r may also have the opposite effect of making it easier to fool the voter. In Proposition 2, for example, as r is large (r>1/2), observing t* + D or t* + kD in region j reassures the voter in region i that effectively a bad shock occurred in her region and that therefore the incumbent playing t* + D in her region is indeed a good government. This supports more pooling and less separation with respect to the case with a single jurisdiction. Which of the two effects prevails at the equilibrium, in turn, depends on the other parameters of the problem, that is, on q and h.
3. Concluding remarks The main message of this paper is on the negative side. As the two examples in Propositions 2 and 3 prove, yardstick competition may induce either more pooling or more separating behaviour among
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different types of government, depending on the model parameters6. This theoretical indeterminacy raises serious doubts on all the attempts made to test the theory by focusing only on the fiscal choices of neighbouring jurisdictions. A sheer evidence of spatial auto-correlation in local fiscal policies may have other explanations (for instance, fiscal externalities arising from tax competition, or even unobserved spatially correlated shocks) which have nothing to do with yardstick competition. On more positive grounds, our results should also be interpreted as a strong suggestion to look more carefully into the institutional characteristics of the economy being studied in order to isolate yardstick competition effects. In fact, while spatial correlation in local fiscal policies is not a necessary implication of yardstick competition theory, still it is consistent with some of the equilibria illustrated above. Hence, if one did find correlation among the fiscal variables of neighbouring jurisdictions and could convincingly exclude other competing theories as possible explanations, the result could be taken as evidence of the existence of yardstick competition effects7. Moreover, if yardstick competition induces more separation among types, there is then a natural test to be attempted. Incumbents setting fiscal choices differently from neighbouring jurisdictions should be more easily punished by voters. Consequently, whether electoral results are affected by comparative performance evaluation on fiscal issues may represent a further complementary test of yardstick competition theory8. Indeed, the crucial point about testing yardstick competition theory is not about local tax setting behaviour as such, but in tax setting as linked to the incentives and constraints that are generated by the local electoral system.
References Besley, T., Case, A., 1995a. Incumbent behaviour: vote seeking, tax setting and yardstick competition. American Economic Review 85, 25 – 45. Besley, T., Case, A., 1995b. Does electoral accountability affect economic policy choices? Evidence from gubernatorial term limits. Quarterly Journal of Economics 110, 769 – 798. Bivand, R., Szymanski, S., 1997. Spatial dependence through local yardstick competition: theory and testing. Economics Letters 55, 257 – 265. Bordignon, M., Minelli, E., 2001. Rules transparency and political accountability. Journal of Public Economics 80, 73 – 98. Bordignon, M., Cerniglia, F., Revelli, F., 2003. In search of yardstick competition: a spatial analysis of Italian municipality property tax setting. Journal of Urban Economics 54, 199 – 217. Brennan, G., Buchanan, J.M., 1980. The Power to Tax. Analytical Foundations of a Fiscal Constitution Cambridge. University Press, Cambridge.
6
In principle, of course, if one knew the exact values of the relevant parameters, it could still be possible to derive from the theory precise implications on the tax setting behaviour of neighbouring jurisdictions, implications which could then be directly tested. In practice, however, this is likely to be extremely difficult. 7 For instance, in our own attempt to test the theory among Italian local governments (Bordignon et al., 2003), we exploit the peculiar features of the Italian political system (term limits and double electoral turn) to derive identifying restrictions on the parameters to be tested, by arguing that only mayors who may run again and face a serious electoral context should worry about comparative performance evaluation effects and behave consequently. As it does turn out that only these majors set local taxes in line with neighbours’, we conclude that there is evidence of yardstick competition effects in Italy. For a more general analysis of the impact of term limits on policies see also Besley and Case (1995b) on US states. 8 Besley and Case (1995a) found that the probability of defeat of US state governors is positively affected by own tax increases and negatively affected by tax increases in neighbouring states. For a similar test using UK local election results and local property tax data see Revelli (2002).
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Brueckner, J., 2003. Strategic interaction among governments: an overview of empirical studies. International Regional Science Review 26, 175 – 188. Heyndels, B., Vuchelen, J., 1998. Tax mimicking among Belgian municipalities. National Tax Journal 60, 89 – 101. Oates, W.E., 1972. Fiscal Federalism. Harcourt Brace Jovanovich, New York. Revelli, F., 2002. Local taxes, national politics and spatial interactions in English district election results. European Journal of Political Economy 18, 281 – 299. Salmon, P., 1987. Decentralization as an incentive scheme. Oxford Review of Economic Policy 3, 24 – 43. Schaltegger, C., Kuttel, D., 2002. Exit, voice, and mimicking behaviour: evidence from Swiss cantons. Public Choice 113, 1 – 23. Sole´ Olle´, A., 2001. Tax Mimicking and Electoral Control: An Empirical Analysis of Local Tax Setting in Spain. Universitat de Barcelona. Mimeo. Tiebout, C., 1956. A pure theory of local expenditures. Journal of Political Economy 64, 416 – 424.
Yardstick competition in intergovernmental relationships: theory and empirical predictions Massimo Bordignon a,b,*, Floriana Cerniglia c, Federico Revelli d a
Facolta` Economia, Universita` Cattolica del Sacro Cuore, L.go Gemelli 1, 20123 Milan, Italy b CESifo, Mu¨nchen, Germany c Facolta` di Scienze Politiche, Universita` Cattolica del Sacro Cuore, L.go Gemelli 1, 20123 Milan, Italy d Facolta` di Scienze Politiche, Universita` di Torino, Via Po 53, 10124 Turin, Italy Received 22 April 2003; received in revised form 9 October 2003; accepted 3 November 2003
Abstract We review yardstick competition theory as applied to fiscal choices in the intergovernmental context. We show that the theory is consistent with opposite results concerning neighbouring governments’ fiscal behaviour, and discuss some empirical implications. D 2004 Elsevier B.V. All rights reserved. Keywords: Local property tax; Yardstick competition JEL classification: D72; H71
1. Introduction A long tradition in fiscal federalism theory suggests that the organisation of the public sector in different layers of government may help overcome a number of ‘‘failures’’ of the political system (e.g. Brennan and Buchanan, 1980; Oates, 1972; Tiebout, 1956). Starting from the seminal work of Salmon (1987); Besley and Case (1995a); a new argument has been recently proposed. Voters are ‘‘rationally ignorant’’ as it is costly for them to acquire information about politics, and self-interested politicians may exploit this informational advantage to the detriment of voters’ interests. A decentralised structure may help ease this problem, as voters may then engage * Corresponding author. Tel.: +39-02-7234-2694; fax: +39-02-7234-2781. E-mail addresses: [email protected] (M. Bordignon), [email protected] (F. Cerniglia), [email protected] (F. Revelli). 0165-1765/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2003.11.014
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in comparative performance evaluation between different local governments, and this may allow them to better distinguish between ‘‘bad’’ and ‘‘good’’ politicians. This argument in favour of decentralisation is particularly interesting because it does not rely upon either costless mobility of citizens or large difference in local preferences, assumptions which are both questionable in a number of countries. But of course the important question on policy grounds is if this argument is empirically founded. Following the seminal work of Besley and Case (1995a), a large amount of research has been devoted to this issue (e.g. Bivand and Szymanski, 1997; Heyndels and Vuchelen, 1998; Schaltegger and Kuttel, 2002; Sole´ Olle´, 2001)1. In most cases, this literature contents itself with showing that there is some mimicking behaviour going on among local governments, and takes this as conclusive evidence of the existence of yardstick competition phenomena (comparative performance evaluation). In this paper, we argue that this conclusion is unwarranted. Yardstick competition theory is too ‘‘weak’’ to produce welldefined empirical predictions concerning the fiscal choices of neighbouring jurisdictions, and some of the possible theoretical solutions do not involve mimicking behaviour at all. In order to test the theory, then, a much subtler work of linking the predictions of the theory with the institutional characteristics of the political system under analysis needs to be done.
2. The model Yardstick competition theory in the intergovernmental context predicts the existence of informational spillovers among voters of neighbouring jurisdictions. For empirical testing, one needs to consider the strategic reaction of politicians to citizens’ behaviour. Politicians are rational agents and know the kind of calculations citizens make. Hence, they might attempt to modify their fiscal choices to influence voters’ inference. On this point, following the seminal paper of Besley and Case (1995a), most of the empirical literature seems to have taken for granted that, in the presence of comparative performance evaluation on the part of voters, bad or incompetent governments may be forced to set fiscal variables in line with those chosen by neighbouring governments, in order to avoid being unseated. Hence, ‘copycatting’ or mimicking behaviour in local fiscal choices will be the expected result. However, this is only one possibility. Another possibility—that is explored in this paper—is that, by improving voters’ information set, yardstick competition increases the cost for bad or incompetent governments to imitate good ones, so inducing no or little mimicking behaviour. To show this point formally, consider the following version of Besley and Case (1995a) original model. The economy has three agents: an incumbent politician, an opposing politician and a voter. The economy lasts two periods and at the end of the first period an election takes place. In both periods, the incumbent politician chooses taxes and public good supply. Governments come in two types: they can be either ‘‘good’’ or ‘‘bad’’. Good politicians only want to provide the public good at the lowest possible cost; bad governments like instead to tax citizens more heavily in order to accumulate rents. Govern-
1
Brueckner (2003) reviews the recent empirical literature on strategic interaction among local governments and discusses the main econometric issues involved.
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ments know their type, while citizens have only some a-priori on the type of governments. More specifically, we assume that:
the citizen expects both the incumbent and the opposing government to be good with probability h, ha(0, 1); the production function of the public good is subjected to random shocks. Producing public good level g* costs t* if the shock is positive, and t*+ D, D > 0, if the shock is negative; negative shocks occur with probability q < 1; all agents in the economy discount future at rate d < 1.
The sequence of events is as follows. In period 1, nature moves first and chooses both the type of the incumbent and the realisation of the shock. The incumbent government observes those moves of nature, and then decides the tax rate and public good supply in the first period. The citizen does not observe the moves of nature, but observes the fiscal choices of the government and knows the stochastic structure of the economy. She thus uses these observations to revise her beliefs on the type of the incumbent. Let l(h, t, g) indicate the posterior beliefs of the citizen. An election then takes place, and the citizen votes for the politician who expects to be good with higher probability at the time of voting. When indifferent, she votes for the incumbent2. That is, the incumbent is re-elected if l(h, t, g) z h. Whichever government is in charge in period 2, it chooses again a level of the tax rate and of public good supply. The world ends here. 2.1. The equilibrium with one jurisdiction To solve this dynamic incomplete information game between voter and politicians, we look for perfect Bayesian Nash equilibria (PBE) of the game. For simplicity, we only focus on pure strategies equilibria of this game. Again for simplicity, suppose that governments of both types have to supply a fixed amount of public good, g*, in both periods3. Also suppose that good governments do not play strategically; they just do what is best for the citizen in the two possible cases; i.e. they impose a tax equal to t* if the shock is positive and t* + D if the shock is negative. Consider next the bad government. Suppose that there is a maximal tax rate it can impose on citizens (an upper bound on politically sustainable expropriation), and let us write this upper tax rate as t* + kD, where k>1. The maximal rent the bad type can earn in each period is either (k 1)D or kD depending on the realisation of the shock. In the second period, a bad government chooses the highest possible tax rate, t* + kD, as this tax rate maximises its utility. In the first period, however, it faces a trade off. It could still choose t* + kD, earning immediately the maximal rent, but then the citizen would immediately understand that it is of the bad type and throw it out of office at the ensuing election. Alternatively, it could try to mimic the good type and then be reelected with some positive probability. Let us suppose that the out-ofequilibrium beliefs of the voter are such that she assigns zero probability to a government being of a good type upon observing a tax rate different from one of the two rates a good government could possibly
2
This assumption effectively rules out mixed strategy equilibria. See Bordignon and Minelli (2001). As long as the quality of the public good supplied is observable by citizens, this assumption is of no consequence and only simplifies the analysis. 3
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choose; i.e. l( g*, h, t) = 0 for t p t* + D, and t p t*. Then it is clear that if the shock happens to be negative, the bad type would prefer to choose t* + kD in the first period, even if that implies losing the election. This is so because the maximum tax rate the bad type can impose without being discovered in period 1 is t* + D; but if the shock is negative, this means that the bad type earns zero rent in period 1. And even under the optimistic beliefs that it would be elected for sure if it followed that strategy, it would prefer to separate immediately, since waiting is costly: (k 1)D>y(k 1)D. What if the shock is positive? Repeating the argument just given, the bad type would never play t*. But could it play t* + D? Proposition 1. Suppose d z dj u (k 1)/k and q z 1/2. Then there exists a PBE in pure strategies where the bad type’s first period choice is t*+ D and any incumbent who selects t*+ D is re-elected for sure. Proof 1. By Bayes’ rule, at the proposed governments strategies, the citizen’s posterior beliefs upon observing t*+ D is l(h, t*+ D) = qh/(qh+(1 q)(1 h)). It follows l(h, t*+ D) z h if q z 1/2. Assuming this to hold, the bad type would play t = t*+ D when the shock is positive if this gives it an higher expected utility than playing its favourite strategy in the first period, i.e. if D + dkD z kD, which holds true for y z (k 1)/k. 5 2.2. Yardstick competition: two jurisdictions Suppose now we double our simple economy, introducing another jurisdiction which has exactly the same characteristics as the economy we just studied. A potential advantage for the citizen of having two economies instead of one is that she can now try to learn something about her incumbent in the first period, by looking at what is happening in the other jurisdiction. That is, the voter’s posterior beliefs in region i may now be written as a function of the fiscal choices of both jurisdictions: li(h, ti, tj), where the suffix indexes the jurisdiction, i = 1, 2, and t refers to first period choices4. For comparative performance evaluation to be meaningful, it is necessary that the two economies be somehow related. Besley and Case (1995a) assume perfect correlation among regional technological shocks in their theoretical model. However, this is implausible for most empirical applications of the model5, and it also hides some of the possible results of the model, which we want to emphasise. We take instead the following approach. Let r be the parameter, which measures the degree of correlation between the two economies. Denoting by Prob(X, Y) the joint probability that region i is hit by a shock X, while region j by shock Y, where X and Y indicate the nature of the shock, we have: ProbðN ; N Þ ¼ rq;
ProbðP; N Þ ¼ ProbðN; PÞ ¼ ð1 rÞq;
ProbðP; PÞ ¼ 1 qð2 rÞ;
ð1Þ
where N and P stand, respectively, for negative and positive shock. For r = q the two technological shocks are independent, for r = 1 they are perfectly correlated, while for q < r < 1 they are positively but 4
We suppress g from the argument of the revised beliefs’ function because public good supply is assumed to be fixed. While the fiscal policies of local jurisdictions often tend to be affected by correlated shocks (most frequently tax base shocks), the existing empirical literature shows that such a correlation is far from perfect. It generally declines over distance, with a spatial auto-regressive coefficient consistently below 0.5 (see for instance Bordignon et al., 2003). Moreover, the same empirical analysis of Besley and Case (1995a) on US state data uncovers no correlation in the shocks received by neighbouring states. 5
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imperfectly correlated. We assume instead the draws by nature of the type of government to be independently made in the two regions. Local governments make their tax choices simultaneously. Each incumbent only observes the realisation of the shock in its own jurisdiction and only knows the distribution over government types of the other jurisdiction. The central question to address is what effect comparative performance evaluation has on the equilibria of the game and therefore on the empirical predictions of the model. In particular, we want to know if pooling behaviour—bad types imitating the tax choices of the good types in the first period—is more or less likely under yardstick competition. To this aim, note first, by using the same dominance argument we used before, that if the shock is negative, bad governments will again prefer to separate in the first period by choosing the maximum tax rate and being defeated at the election. By the same token, if the shock is positive, they would never play t*. Would they play t* + D? To answer the question, note that at an equilibrium where all agents expect the bad types to play t* + D in the first period when the shock is positive, the expected probability of being reelected for a bad type in region i if it follows this strategy, let us call it G(t* + D), is:
Gðt* þ DÞ ¼ Probðej ¼ N Aei ¼ PÞðhRðti ¼ t* þ D; tj ¼ t* þ DÞ þ ð1 hÞRðti ¼ t* þ D; tj ¼ t* þ kDÞÞ þ Probðej ¼ PAei ¼ PÞðhRðti ¼ t* þ D; tj ¼ t*Þ þ ð1 hÞRðti ¼ t* þ D; tj ¼ t* þ DÞÞ: ¼ fð1 rÞqðhRðti ¼ t* þ D; tj ¼ t* þ DÞÞ þ ð1 hÞRðti ¼ t* þ D; tj ¼ t* þ kDÞÞ þ ð1 qð2 rÞÞðhRðti ¼ t* þ D; tj ¼ t*Þ þ ð1 hÞRðti ¼ t* þ D; tj ¼ t* þ DÞÞg=ð1 qÞ
ð2Þ
where R(ti = t* + D, tj = t) is the probability of being reelected by the bad type in region i if it plays t* + D and government j plays t, t = t*, t* + D, t* + kD. Clearly, by our previous assumption, R(ti = t* +D, tj = t) = 1 if l(h, ti = t* + D, tj = t) z h and R(ti = t* + D, tj = t) = 0 otherwise. By applying Bayes’ rule: lðh; ti ¼ t* þ D; tj ¼ t* þ DÞ ¼frqh2 þ hð1 hÞð1 rÞqÞg = fðrqh2 þ 2hð1 hÞð1 rÞq þ ð1 hÞ2 ð1 qð2 rÞÞg: lðh; ti ¼ t* þ D; tj ¼ t* þ kDÞ ¼ rh=frh þ ð1 hÞð1 rÞg: lðh; ti ¼ t* þ D; tj ¼ t*Þ ¼ sh=fsh þ ð1 hÞð1 sÞg:
where s ¼ ð1 rÞq=ð1 qÞ:
ð3Þ
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It follows:
Rðti ¼ t* þ D; tj ¼ t* þ DÞ ¼ 1 if h þ 2ð1 2hÞð1 rÞqzð1 qÞ; Rðti ¼ t* þ D; tj ¼ t* þ DÞ ¼ 0 otherwise;
Rðti ¼ t* þ D; tj ¼ t* þ kDÞ ¼ 1 if rz1=2;
ð4:1Þ
Rðti ¼ t* þ D; tj ¼ t* þ kDÞ ¼ 0 otherwise; ð4:2Þ
Rðti ¼ t* þ D; tj ¼ t*Þ ¼ 1 if ð1 rÞzð1 qÞ=2q;
Rðti ¼ t* þ D; tj ¼ t*Þ ¼ 0 otherwise; ð4:3Þ
Using (4), we can answer the question raised above. We begin by establishing: Proposition 2. Suppose q < 1/2, r>1/2. Then, there exist h*< 1, y*< 1 and k* such that there exists a PBE in pure strategies where bad type’s first period choices in both economies upon observing a positive shock are t*+ D. Proof 2. Invoking (4), under the conditions stated in the proposition, at the proposed equilibrium strategies for the two types, voter’s revised beliefs in region i, i = 1, 2, j = 1, 2, i p j, are such that R(ti = t*+ D, tj = t*+ kD) = 1 and R(ti = t*+ D, tj = t*) = 0. R(ti = t*+ D, tj = t*+ D) = 1 if h z h*u ((1 q(3 2r))/((1 4(1 r)q)) < 1 as r>1/2. Invoking Eq. (2), G(t*+ D)={(1 h)(1 q) + hq(1 r)}/(1 q). The expected utility of the bad type when playing his equilibrium strategy is then D + dkD{(1 h)(1 q) + hq(1 r)}/(1 q). This dominates its best deviation, playing t*+ kD and not be reelected in the second period, if y z y*=(k 1)(1 q)/k{(1 h)(1 q) + hq(1 r)}. In turn y*< 1 if k < k*u (1 q)/h(1 q(2 r)). 5 A comparison between Propositions 1 and 2 makes it clear that it is in principle possible to find values of the parameters that support a pooling equilibrium under yardstick competition when this would not be possible otherwise (as q < 1/2). Vindicating the empirical literature mentioned above, in this case the ex ante probability of finding the two regions selecting similar tax rates (in the first period) would be higher under yardstick competition than without it, so that a high correlation among the tax rates of neighbouring regions could be interpreted as a signal of the presence of comparative performance evaluation among governments by voters. This is not the only possibility, however, as the next proposition illustrates. Proposition 3. Suppose q z 1/2 and (1 q)>h. Then, there exist q V r1 < r2 < 1 such that the bad type’s first period equilibrium choices in both economies upon observing a positive shock are t*+ D if the following (sufficient) conditions are satisfied: (i) r>r2, d z d** and k < k**; (ii) r2 z r>r1, d z d* and k < k*; (iii) r1 z r, d z dj, where dj < d*< d**< 1 and 1 < k**< k*.
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Proof. At the proposed strategies for the two types, voter’s posterior beliefs are such that (1) R(ti = t*+ D, tj = t*+ kD) = 1 br, as r z q and q z 1/2 by assumption; (2) R(ti = t*+ D, tj = t*) = 1 if r V r1 u (3q 1)/2q. (3) R(ti = t*+ D, tj = t*+ D) = 1 if r V r2 u {(3q 1) + h(1 4q)}/2q(1 2h). Note that q z 1/2 and (1 q)>h implies h < 1/2 so that r2>0. Furthermore, q z 1/2 also implies r1 V r2. Using (1)-(2)-(3), it is clear that in case (iii), the expected probability to be elected for the bad type when playing t*+ D in the first period upon observing a positive shock is just one, so that the condition on y for the existence of a pooling equilibrium coincides with those in Proposition 1, y z yj; in case (ii), this probability is {(1 h)(1 q) + hq(1 r)}/(1 q), so that the conditions on y and k for the existence of a pooling equilibrium coincides with those of Proposition 2, y z y* and k < k*. In case (i), finally, G(t*+ D)={(1 h)q(1 r)}/(1 q), giving an expected utility to the bad type when playing t*+ D in the first period of D + dkD{(1 h)q(1 r)}/(1 q). This dominates playing t*+ kD in the first period if y z y**=(k 1)(1 q)/k{(1 h)q(1 r)}. In turn y**< 1 if k < k**u (1 q)/(1 q(2 r(1 h) h). 5 Clearly, in this second example, supporting a pooling equilibrium becomes unambiguously more difficult under yardstick competition than without it, in the sense that stricter restrictions on the parameters must be imposed to get pooling behaviour. Furthermore, these restrictions increase with the degree of correlation between the two economies. When this correlation is very low, r V r1, a pooling equilibrium can be supported under the same conditions as in the case with a single jurisdiction. As r increases, y must also increase to support a pooling equilibrium, and, under the conditions on q and h stated in the proposition, this equilibrium simply disappears when the two economies become perfectly correlated. Empirically, in this second example, one should expect to find less correlation in tax rates among neighbouring jurisdictions (in the first period) and more politicians being unseated at elections as a result of yardstick competition. The contradictory results of Propositions 2 and 3 can be readily explained. For r = q, the two economies are effectively separated, and the equilibrium with two jurisdictions coincides with that with one jurisdiction. As r increases, there are two effects in this economy. On the one hand, the larger is r, the more the citizen learns by observing the fiscal choices in the other jurisdiction, and the more difficult it is for the bad politician to escape detection when cheating. This effect, by increasing the cost of mimicking, pushes toward more separation and less pooling in the first period. On the other hand, a larger r may also have the opposite effect of making it easier to fool the voter. In Proposition 2, for example, as r is large (r>1/2), observing t* + D or t* + kD in region j reassures the voter in region i that effectively a bad shock occurred in her region and that therefore the incumbent playing t* + D in her region is indeed a good government. This supports more pooling and less separation with respect to the case with a single jurisdiction. Which of the two effects prevails at the equilibrium, in turn, depends on the other parameters of the problem, that is, on q and h.
3. Concluding remarks The main message of this paper is on the negative side. As the two examples in Propositions 2 and 3 prove, yardstick competition may induce either more pooling or more separating behaviour among
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different types of government, depending on the model parameters6. This theoretical indeterminacy raises serious doubts on all the attempts made to test the theory by focusing only on the fiscal choices of neighbouring jurisdictions. A sheer evidence of spatial auto-correlation in local fiscal policies may have other explanations (for instance, fiscal externalities arising from tax competition, or even unobserved spatially correlated shocks) which have nothing to do with yardstick competition. On more positive grounds, our results should also be interpreted as a strong suggestion to look more carefully into the institutional characteristics of the economy being studied in order to isolate yardstick competition effects. In fact, while spatial correlation in local fiscal policies is not a necessary implication of yardstick competition theory, still it is consistent with some of the equilibria illustrated above. Hence, if one did find correlation among the fiscal variables of neighbouring jurisdictions and could convincingly exclude other competing theories as possible explanations, the result could be taken as evidence of the existence of yardstick competition effects7. Moreover, if yardstick competition induces more separation among types, there is then a natural test to be attempted. Incumbents setting fiscal choices differently from neighbouring jurisdictions should be more easily punished by voters. Consequently, whether electoral results are affected by comparative performance evaluation on fiscal issues may represent a further complementary test of yardstick competition theory8. Indeed, the crucial point about testing yardstick competition theory is not about local tax setting behaviour as such, but in tax setting as linked to the incentives and constraints that are generated by the local electoral system.
References Besley, T., Case, A., 1995a. Incumbent behaviour: vote seeking, tax setting and yardstick competition. American Economic Review 85, 25 – 45. Besley, T., Case, A., 1995b. Does electoral accountability affect economic policy choices? Evidence from gubernatorial term limits. Quarterly Journal of Economics 110, 769 – 798. Bivand, R., Szymanski, S., 1997. Spatial dependence through local yardstick competition: theory and testing. Economics Letters 55, 257 – 265. Bordignon, M., Minelli, E., 2001. Rules transparency and political accountability. Journal of Public Economics 80, 73 – 98. Bordignon, M., Cerniglia, F., Revelli, F., 2003. In search of yardstick competition: a spatial analysis of Italian municipality property tax setting. Journal of Urban Economics 54, 199 – 217. Brennan, G., Buchanan, J.M., 1980. The Power to Tax. Analytical Foundations of a Fiscal Constitution Cambridge. University Press, Cambridge.
6
In principle, of course, if one knew the exact values of the relevant parameters, it could still be possible to derive from the theory precise implications on the tax setting behaviour of neighbouring jurisdictions, implications which could then be directly tested. In practice, however, this is likely to be extremely difficult. 7 For instance, in our own attempt to test the theory among Italian local governments (Bordignon et al., 2003), we exploit the peculiar features of the Italian political system (term limits and double electoral turn) to derive identifying restrictions on the parameters to be tested, by arguing that only mayors who may run again and face a serious electoral context should worry about comparative performance evaluation effects and behave consequently. As it does turn out that only these majors set local taxes in line with neighbours’, we conclude that there is evidence of yardstick competition effects in Italy. For a more general analysis of the impact of term limits on policies see also Besley and Case (1995b) on US states. 8 Besley and Case (1995a) found that the probability of defeat of US state governors is positively affected by own tax increases and negatively affected by tax increases in neighbouring states. For a similar test using UK local election results and local property tax data see Revelli (2002).
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Brueckner, J., 2003. Strategic interaction among governments: an overview of empirical studies. International Regional Science Review 26, 175 – 188. Heyndels, B., Vuchelen, J., 1998. Tax mimicking among Belgian municipalities. National Tax Journal 60, 89 – 101. Oates, W.E., 1972. Fiscal Federalism. Harcourt Brace Jovanovich, New York. Revelli, F., 2002. Local taxes, national politics and spatial interactions in English district election results. European Journal of Political Economy 18, 281 – 299. Salmon, P., 1987. Decentralization as an incentive scheme. Oxford Review of Economic Policy 3, 24 – 43. Schaltegger, C., Kuttel, D., 2002. Exit, voice, and mimicking behaviour: evidence from Swiss cantons. Public Choice 113, 1 – 23. Sole´ Olle´, A., 2001. Tax Mimicking and Electoral Control: An Empirical Analysis of Local Tax Setting in Spain. Universitat de Barcelona. Mimeo. Tiebout, C., 1956. A pure theory of local expenditures. Journal of Political Economy 64, 416 – 424.