The political economy of publicly provided private goods

Transcription

1 Journal of Public Economics 73 (1999) The olitical economy of ublicly rovided rivate goods Soren Blomquist *, Vidar Christiansen a, b a Deartment of Economics, Usala University, Box 513, SE Usala, Sweden b Deartment of Economics, University of Oslo, P.O. Box 1095 Blindern, N-0317 Oslo, Norway Received 1 July 1998; received in revised form 1 November 1998; acceted 1 November 1998 Abstract This aer integrates two different aroaches to the analysis of ublic rovision of rivate goods (education, health care, day care, etc.). While normative ublic economics has established an efficiency case for such rovision, the commonly held olitical economy view has been that it is an economically inefficient henomenon generated by the olitical rocess. We establish a olitical economy framework which in general yields an efficient choice of distributional olicy. It follows that the central mechanism studied in the normative theory is equally relevant to voting models of decisions on ublic rovision. It is shown that under lausible information constraints economically efficient ublic rovision of rivate goods will be art of olitically rational decisions. The result is established both within a median voter rocess and a reresentative democracy of olitical arties Elsevier Science S.A. All rights reserved. Keywords: Political economy; Public rovision; Private goods; In-kind transfers JEL classification: D7; H1; H4; I38 1. Introduction Public rovision of rivate goods (education, health care, day care, etc.) is quantitatively imortant in all develoed countries, amounting to as much as *Corresonding author. address: Soren.Blomquist@nek.uu.se (S. Blomquist) / 99/ $ see front matter 1999 Elsevier Science S.A. All rights reserved. PII: S (99)0000-X

2 3 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) % of GNP in some countries. In several countries, like the Nordic ones, education and health care are almost exclusively ublicly rovided, whereas in other countries, like the U.S., there is a mix of rivate and ublic rovision. Public rovision of daycare for reschool children is also an imortant art of ublic exenditure in the Nordic countries. There is an ongoing ublic debate both in North America and Euroe to what extent the ublic sector should rovide rivate goods. Particularly in the U.S. there is also a debate on whether individuals should be allowed to sulement and/ or ugrade ublicly rovided goods with rivate urchases. Esecially with resect to education voucher systems have been discussed (Ele and Romano (1998)). Standard textbooks in ublic economics rovide no exlanation for this tye of ublic exenditure. However, there is an emerging, fast growing, literature attemting to exlain the role of ublic rovision of rivate goods. This literature consists of two quite disarate arts roviding very different views on what the function of ublicly rovided goods is in the economy. One strand of literature with normative theories shows how ublic rovision of rivate goods under certain conditions can be beneficial and imrove efficiency. These theories distinguish between two basic functions of ublic rovision of a rivate good. One is to mitigate an informational constraint that restricts the redistribution that can be accomlished by an otimal nonlinear income tax. Another function is to mitigate a time inconsistency roblem. In another strand of literature consisting of voting models there is no efficiency enhancing role for ublicly rovided goods. In the voting models ublicly rovided rivate goods is a means for some grous in the economy to redistribute resources to themselves. One conclusion of an influential article, Ele and 1 Romano (1996a), is that ublic rovision of health care leads to inefficiency. The two strands of literature model the economy in quite different ways. The voting models usually imose highly restrictive assumtions on the available tax and transfer instruments. Normative theories on the other hand frequently use models where a nonlinear income tax is available for redistribution. Our urose is to make a synthesis of the two strands of literature. Two stes are essential in our aroach. First, we construct a olitical economy framework which establishes a case for a choice of efficient olicy. Second, we construct a ositive theory of ublic rovision of rivate goods where we allow the tax instruments to be as flexible as ossible, and where as an essential art of the model we include one of the mechanisms for imroved efficiency that are described in the normative literature. It is shown that there will be a voting equilibrium with ublicly rovided rivate goods in models where ublicly rovided rivate goods do not serve as a substitute for tax instruments, and the equilibrium will be Pareto efficient. 1 Ele and Romano denote the ublicly rovided rivate good as health care. However, the good does not ossess any inherent roerties suggesting that it is in the caacity of health care that it should be ublicly rovided.

3 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) Meltzer and Richard (1985) is an early contribution to the literature on ublicly rovided rivate goods. One can see this aer as a forerunner both for later normative models and ositive voting models. Their article studies a voting rocess. However, in contrast to later articles on voting models, ublic rovision of a rivate good is in their model not driven by severe restrictions on the tax instruments but by a mechanism whereby the ublicly rovided good affects the size of the tax base. More recent articles like Ele and Romano (1996a), Gradstein and Justman (1996) and Gouveia (1997) are examles of voting models where the result that there is ublic rovision of a rivate good is driven by severe restrictions on the tax instruments. For examle, in Ele and Romano (1996a), where the ublicly rovided rivate good is financed by a roortional income tax, the raison detre ˆ for ublic rovision is that it serves as a substitute for a 3 demogrant. If the model allowed a linear tax, there would not exist a voting 4,5 equilibrium with ublic rovision. The normative models focus on the efficiency enhancing role of ublicly rovided rivate goods. Nichols and Zeckhauser (198) is a fascinating aer ointing to the role of in-kind transfers in imroving the efficiency of redistribution schemes. Public rovision schemes imly that some individuals will face quantity constraints. Guesnerie and Roberts (1984) show that if the economy initially is at a second-best osition it is in general ossible to achieve a Pareto imrovement by introducing a small quantity constraint. Besley and Coate (1991) make the observation that different grous of eole can value ublicly rovided 6 goods differently. Using a model with a head tax to finance the ublicly rovided good they show how ublic rovision can induce self-selection and achieve redistribution with lower efficiency costs than if cash transfers were used. Boadway and Marchand (1995) and Blomquist and Christiansen (1995) show that even if an otimal nonlinear income tax is available for redistribution there is a role for ublicly rovided rivate goods. 7 The roblem they study is how to Bergstrom and Blomquist (1996) study a similar mechanism. In their model the labor force articiation of mothers increases if day care is ublicly rovided. Under certain conditions this can lead to such a large increase in the tax base that the income tax can be lowered as the level of ublicly rovided day care increases. This means that all individuals would vote for some ublic rovision of day care. Lundholm and Ohlsson (1998) also study a tax base effect mechanism. However, in their model wages are endogenous and art of the benefits of ublicly rovided day care is due to wage effects. 3 Hence the scheme is basically the same as that of Roberts (1977) which rovides a olitical economy exlanation for the choice of income tax rate and a lum-sum transfer in cash. 4 This is also ointed out in footnote 15 in Ele and Romano (1996a). 5 Gouveia (1996) and Ele and Romano (1996b) are other articles with voting models. The focus of Besley and Coate (1997) is not on ublic rovision of rivate goods. However, one of their examles rovides a olitical economy model of ublic rovision of rivate goods. 6 Blackorby and Donaldson (1988) rovide a similar argument. 7 Bruce and Waldman (1991), Coate (1995), Cremer and Gahvari (1997) and Blomquist and Christiansen (1998a) are other examles of normative theories of ublicly rovided rivate goods.

4 34 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) achieve redistribution from high-skilled to low-skilled individuals when the identity of the two tyes of individuals is not observed by the government. Because of this asymmetric information the redistribution is hamered by a self-selection constraint. The otential role of ublic rovision is to alleviate the self-selection constraint by giving art of the transfer to the low-skilled ersons in the form of the ublicly rovided good. This is the mechanism we will build into our voting models. In Section we elaborate on the mechanism by which ublicly rovided rivate goods can imrove the efficiency of the economy. Even though the ublic rovision of rivate goods rovides the motivation for the resent study our olitical economy models will also yield results that are of interest beyond this articular issue. The central olitical economy considerations are valid more generally and in models with other olicy instruments affecting the distribution of welfare. In Section 3 we introduce a median voter model and characterize the voting equilibrium in general and in the articular case in which we embed the ublic rovision scheme of Section. Since olicy making rarely is decided through simle majority voting we study in Section 4 the more realistic case of reresentative democracy with two olitical arties cometing for votes. Section 5 concludes.. Publicly rovided rivate goods as a skill screening device A central urose of our study is to discuss from a olitical economy ersective the case for ublic rovision of rivate goods that has been established in the normative theory. As a background for the rest of the aer and for subsequent reference it is helful to summarize the main asects of the model which has been the vehicle of much of the normative analysis. The motivation for focusing on this articular model is not only that it has been central in the literature, but more imortantly it has a number of features that enables us to establish a more fundamental case for ublic rovision than does a number of alternative models. In articular the case rests on basic information asymmetries rather than on deficiencies of the tax design or ad hoc restrictions on the available tax instruments. In the olitical economy models we study below ublic rovision of rivate goods serves as a skill screening device, allowing redistribution to take lace with less distortions than if only taxes and cash transfers were used. This mechanism has been studied by, for examle, Blomquist and Christiansen (1995, 1998a), Boadway and Marchand (1995) and Cremer and Gahvari (1997). The model considers an economy with two tyes of individuals, one grou of low roductivity and one grou of high roductivity individuals. Skill levels are reflected in wage rates. Information about individual skills (wage rates) is rivate information not available to the government. Let h be hours of work, y 5 wh

5 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) before-tax labor income and B after-tax income. Let c denote a quantity of a good that is only available on the market and x be the quantity of a good that can be bought on the market, but also can be ublicly rovided. For convenience we normalize the roducer rices of c and x to one. Individual references are reresented by a strictly quasi concave utility function U(c, x, h). We define the conditional demand function x(b, h) bymaxu(c, x; h) w.r.t c and x s.t. c 1 x 5 B. We will assume the references are such that x(b, h)/ B $ 0 and x(b, h)/ h $ 0, i.e. x is a normal good and the demand for x increases in hours of work for a 8 fixed income. Blomquist and Christiansen (1998a,. 405) show that x(b, h)/ h $ 0 is equivalent to MRS cx / h $ 0, i.e. that the marginal valuation of x in terms of c increases in hours of work. Blomquist and Christiansen (1998a) also show that, rovided that x(b, h)/ h. 0, the best ublic rovision scheme is the one that allows the consumers to to u the ublic quantity at their own exense. The instruments available to the government are income taxes and ublic 9 rovision of x. We denote the ublicly rovided quantity by x. No restrictions are imosed directly on the shae of tax schedule that can be used. However, the asymmetric information imlies that the olicy must be designed subject to an information constraint. The income/ consumtion bundle assigned to a erson must be chosen subject to being unattractive to the other erson. Let V(x, B, Y/w)denote the indirect utility function conditional on the labour suly h 5 Y/w and the i ublic rovision x. We use a suerscrit to indicate tye of individual. N denotes the number of individuals of tye i[h1,j. The roblem of designing a Pareto otimal income tax and ublic rovision structure is then given by: Max V(x, B, Y /w ) (1) B 1,Y 1,B,Y,x s.t. V(x, B, Y /w ) $ V () 1 1 V(x, B, Y /w ) $V(x, B, Y /w ) (3) V(x, B, Y /w ) $V(x, B, Y /w ) (4) N (Y B ) 1 N (Y B ) (N 1 N )x $ 0 (5) The constraint () assigns a minimum utility level to erson. The constraint (3) 8 The conditional demand function x(b, h) has been used quite much in the theoretical study of otimal commodity taxes. However, it has not been emirically studied. For some goods we can make an informed guess about the sign of x/ h. For examle, if x is day care it seems likely that the demand for x increases in hours of work. 9 As discussed by Cremer and Gahvari (1997) the availability of commodity taxes makes little difference for the case for ublic rovision. However, as discussed in Blomquist and Christiansen (1998b) commodity taxes may be redundant rovided that an income tax and ublic rovision are both available.

6 36 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) Fig. 1. The Pareto frontier with and without ublic rovision. is the self-selection constraint imosing that the taxes must be set in such a way that erson does not gain by mimicking erson 1. Eq. (4) is the corresonding constraint that erson 1 does not gain by mimicking erson. One can show that at most one self-selection constraint is binding. The most studied case (often called the normal case) is the one where redistribution is from the high skill grou to the low skill grou to the extent that constraint (3) is binding. This constraint causes the otimal taxation to be such that a distortion is imosed on the low skill erson. He is induced to substitute leisure for market consumtion so that the before tax/after tax income is too low as comared with the first best. Inequality (5) is the government s budget constraint. When x is restricted to zero, the roblem above reduces to the standard otimal income tax roblem as formulated by Stiglitz (198) and Stern (198). The solid curve in Fig. 1 deicts the corresonding Pareto frontier. For levels of V sufficiently close to the laissez faire level, indicated by oint A, redistribution can take lace without the self-selection constraint being binding. However, for more ambitious redistribution the self-selection constraint will bind. As shown in detail in Blomquist and Christiansen (1995, 1998a), if leisure is nonsearable from goods, ublic rovision of a suitable rivate good can alleviate the self-selection 10 constraint and generate a Pareto imrovement. Fig. 1 illustrates how ublic 10 Given the assumtion that x/ h. 0 a commodity subsidy on can also be used to alleviate the self-selection constraint (see Edwards et al. (1994) and Blomquist and Christiansen (1998b)).

7 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) rovision can shift the frontier outwards. To the left of oint B and to the right of oint C ublic rovision is art of the Pareto efficient olicy. One can show that the ure tax otimization has a unique solution. This imlies 1 1 that to each oint on the Pareto frontier there exists a unique olicy oint hy, B, Y, B j. For x.0 there might exist multile solutions to the otimization roblem, i.e., there might be oints on the Pareto frontier that could be imlemented by alternative olicies. This does not create any roblems for the following analysis excet that it comlicates notation. For notational simlicity we therefore in the following write as if the solution to the roblem defined by Eqs. (1) (5) always is unique. We will briefly comment on this in Section 3. To get further intuition for the role of ublic rovision, consider the case in which there is redistribution from high-skill to low-skill individuals and constraint (3) is strictly binding. Note that if the high-skill tye mimics the low-skill tye, the former has more leisure as less work effort is required to obtain a given income when the wage rate is high. With the assumtion that has been made about the demand for x, the mimicker has a lower demand than erson 1. This means that it is ossible to give the low-skill erson a transfer in terms of x that is at the same time within the consumtion level desired by erson 1 and beyond the level desired by the mimicker. Then for the low-skill erson the transfer is equivalent to a transfer in cash, while from the ersective of the mimicker it is inferior. The advantage is that the transfer is achieved with less inducement for erson to mimic. The self-selection constraint is softened and it is ossible to achieve a more favorable otimum. Blomquist and Christiansen (1995) discuss how ublic rovision of education, day care and health care can be fitted into this framework. To be concrete we could exemlify with day care. If low skill women working full time require, say, 1800 h of day care and buy this in the market, then their situation would be unchanged if one introduced the same amount of ublicly rovided day care and at the same time added the cost of rovision to the tax bill. The situation for high skill women who work full time, requiring 1800 h of day care, would also be unchanged. However, high skill women thinking of working half time instead of full time will now find the former otion less attractive. This is because the after tax income earned by working half time has decreased with an amount equal to the cost of 1800 h of day care whereas the day care they need is only 900 h. Blomquist and Christiansen (1995) characterize goods suitable for ublic rovision: 1. The good should be such that it is imossible (or at least very hard) to resell the ublicly rovided quantity.. There should not be any close market substitutes to the good in question. 3. The demand for the ublicly rovided good should vary much as leisure varies. 4. Leisure should not be weakly searable from goods. The idea behind these characteristics is that it should be ossible to imose a

8 38 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) quantity constraint on erson when mimicking and that this quantity constraint should hurt. Clearly, if it were ossible to resell the ublicly rovided quantity the mimicker would not be hurt by ublic rovision. Likewise, if goods c and x were close market substitutes it would not hurt the mimicker much to have the comosition between c and x changed from the oint selected if he could choose c 11 and x freely given his after tax income. That the very same good as the one rovided can be urchased in the market when toing u is ossible, oses no roblems as the mimicker will not want to use this otion. Characteristic iii ensures that it is ossible to find a ublic rovision level that hurts the mimicker but is fairly harmless for the low skill erson. Characteristic iv is a necessary condition for the scheme to work. If leisure is weakly searable from goods the low skill erson and the mimicker would have the same demand for x and ublic rovision would hurt the low skill erson as much as the mimicker. The normative theory of taxation and ublic rovision described above derives a number of results. Confining our attention to the so-called normal case, we may draw attention to the following results: Result 1. Suose x/ h 5 0, then no Pareto-imrovement can be obtained by ublic rovision of x. See Blomquist and Christiansen (1995), (Proosition 1), Boadway and Marchand (1995), (Proosition 1), (Blomquist and Christiansen (1998a), (Proosition ) and Cremer and Gahvari (1997), (Proosition ). Result. Suose that x/ h. 0, and individuals are allowed to sulement the ublic rovision on the market, then a olicy with otimal taxation and otimal ublic rovision strictly Pareto dominates the ure tax otimum. See Blomquist and Christiansen (1998a, Lemma ). 3. A median voter model We shall study a voting equilibrium of a model where there are only two skill classes as in Section. However, we shall take a more general aroach to olicy making while still using the model above to infer imlications of the voting equilibrium for ublic rovision of rivate goods in articular. As discussed in the introduction the literature on this issue has rovided a major motivation for the resent study. A central assumtion in our voting model will be that individuals differ with resect to how much redistribution they want. To establish the building blocks of our model we shall discuss each of these elements in turn. 11 There could very well exist a nonmarket erfect substitute for the ublicly rovided rivate good. For day care this is clearly the case. Care of children at home is a very good substitute for day care bought in the market. This is the very reason why it is reasonable that the market demand for day care increases with hours of work (decreases with amount of leisure available.)

9 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) Policy instruments At the general level we let a vector of olicy instruments be denoted by z while Z is the olicy set such that z[z. By definition Z is the set of available and feasible olicies that catures all relevant restrictions. We shall interret the olicy as some kind of economic olicy with distributional imlications, but otherwise this is a very general olicy formulation. The tax and ublic rovision model above is a secial case in which a olicy z consists of a constellation of before and 1 1 after tax incomes intended for the high and low skill grous hy, B, Y, B j and a value of the ublic rovision. In this secial case Z is the set of combinations hx, 1 1 Y, B, Y, B j that achieve budget balance, and satisfy the self-selection constraints as stated by Eqs. (4) and (5) above. 3.. Political references In general each individual has references over consumtion bundles including leisure (or labour) that can be reresented by a (direct) utility function. We imose the standard assumtion from otimum tax theory that the basic utility function is the same for everybody. When deciding on his consumtion/ labour choice the individual is suosed to maximise his utility. Maximising behaviour in resonse to a given olicy then imlies a utility level indicated by an indirect utility i i i i function V (z), which in the secific model is given by V(x, B, Y /w ). When voting the individual will exress his reference for choice of olicy. This is a decision which is of a different nature than the choices made in the market lace. To vote is to exress an oinion also about distributional olicy. The voter can then adot three different attitudes. (i) He can take a urely selfish and myoic attitude voting for the olicy from which his own well-being will benefit more given his resent osition. (ii) The voter can be basically selfish, but may feel uncertain about his own future and erhas that of his children. He may then have an insurance motive for suorting transfers that will make him a net contributor in his resent osition, but from which he will benefit if in the future state he is derived of his resent skill. The ercetion of distributional olicy as a social insurance scheme is fairly common in the literature, see e.g. Barr (199), Sinn (1995, 1996). (iii) The voter may be genuinely altruistic and care about the welfare of other eole. In ractice it is hard to distinguish insurance and genuinely altruistic motivation, but in the resent context identifying the true motivation is of little interest. What we shall assume is that not everybody is myoically selfish even though it is erfectly ossible that there is such a category of eole in the model. There is a subgrou of individuals who care about the welfare of eole in the other skill class. The notion that eole are not entirely selfish is not a novel idea. Lindbeck and Weibull (1993) assume that a voter is motivated both by a arty identification and

10 40 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) the utility she derives from a articular olicy. With two arties A and B a voter who is a B-artisan may vote for arty B even though she would derive a somewhat higher utility from A s olicy. See also Fiorini (1981) for a discussion. Dixit and Londregan (1998) assume that in addition to caring about the imlications of income transfers for their own wellbeing, voters genuinely care about social issues: That voters equity concerns are not mere rhetorical masks for self-interest is clear; there are rich liberals who will vote for a leftist arty that romises a high tax rate, and oor libertarians who will suort a rightist arty even though they will ersonally benefit little from its tax and transfer olicies (o.cit.. 499). Our assumtions imly that when voting an individual attaches a weight to the utility of the own grou, but in general also to that of the other grou. It is still ossible that a number of voters assign a zero weight to the utility of the other skill grou, and that voters from one class tyically attach a greater weight to the utility of his/her own class. Let a be the weight given to the utility of the low-skill class and 1a the weight given to the high-skill class where 0#a #1. The value of a characterises the olitical references of each voter, and a has a continuous i i distribution with a class secific density f (a), i 5 1,. Let V denote the utility of i an individual in skill class i that is obtained at the olicy z, and recall that N is the number of individuals in that class. An individual s olitical references are then reresented by a olicy reference function: 1 1 W 5 an V 1 (1 a)n V (6) In the tax and ublic rovision model the olicy reference function will take the form W 5 an V(x, B, Y /w ) 1 (1 a)n V(x, B, Y /w ) (7) The erson will suort the olicy that yields the higher W for the value of a corresonding to his references. It is of interest to note that (6) is general enough to accommodate the class of mixed reference functions bv 1 gn V 1 (1 g )N V for a erson who is a 1 member of class 1 (and likewise for class ). We can interret bv as a selfish art with the arameter b measuring the degree of selfishness, whilst the 1 remaining arts constitute a social art. We assume that b $ 0, 0 # g # 1, and at least one of the arameters is strictly ositive. These references are equally well reresented by a function s(bv 1 gn V 1 (1 g )N V ) where s is an arbitrary ositive arameter. Let s and a be defined by the following equations: 1 1 s(b 1 gn ) 5 an and s(1 g ) 5 1 a, and we see that we are back to a reference function of tye (6). Solving with resect to s and a we get 1 Dixit and Londregan (1998) also introduce mixed references made u of a selfish art and a social art, but they use other secifications of the resective arts.

11 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) N b 1 N g s 5]] 1 and a 5 ]]] 1. N 1 b b 1 N We note that s.0 and 0#a #1 as should be the case. One might argue that truly social references should not be biased in favour of any class so that g Then we immediately see that any deviation of a from 0.5 reflects selfishness. Having assumed that everybody has the same basic references for own consumtion bundle, we do not cature the ossibility that reference for equality (or selfishness) and reference for leisure are interrelated. One might for instance susect that more hard-working eole would feel more entitled to kee the fruits of their work than the rich and lazy, and would be more oosed to give transfers to others. Otherwise it is hard to see convincing arguments in general why social attitudes should vary systematically with work reference Individuals voting behaviour How an individual ranks different olicies according to (6) only deends on 1 how the olicies affect V and V. When studying how an individual ranks different olicies we can therefore study how he ranks different combinations of 1 V and V. Since all individuals within a skill class are treated equally we can draw the Pareto frontier as in Fig. 1. Definition. We denote the median a as am and define the median voter as the voter characterized by a m The voting equilibrium The voting equilibrium can be characterised by the following roosition. 13 Proosition 1. The median voter s referred olicy will be a Condorcet winner. This olicy is Pareto efficient. Proof. Let us consider two olicies zm and z a, where the former is the olicy referred by the median voter and the latter is a feasible, but otherwise arbitrary 1 alternative olicy. The olicy zm imlies the utility levels V m and V m for the resective skill tyes. For simlicity, and without loss of generality, we now assume there is one erson of each tye Since the median voter assigns ositive weights to the utilities of both skill tyes his referred olicy is obviously Pareto 1 efficient. The utility levels corresonding to z are V and V. Let us define D(a) a a a 13 A Condorcet winning olicy is one that will win in majority voting against any other feasible olicy that may be roosed.

12 4 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) as the difference between the welfare level resulting from zm and the welfare level 1 obtained from za as erceived by a voter of tye a. D(a) 5 [av m1 (1 a)v m] [av a 1 (1 a)v a 5 a[(v mv a) 1 (V a V m)] 1V mv a and D9(a) 5 [(V m 1 1 V a) 1 (V a V m)]. There are three cases to consider. (i) Assume first that V m 1 V a, 0, V a V m, 0, i.e. the alternative olicy is more generous to tye one and less generous to tye two. Then D9(a m), 0. Since zm is the referred olicy of the median voter, obviously D(a). 0. It follows that all voters with a # a m (and some voters with a greater than but close to a m) will refer zm to z a. (ii) Assume 1 1 next that (V mv a). 0, (V a V m). 0, i.e. the alternative olicy is more generous to tye two and less generous to tye one. Then D9(a). 0. It follows that all voters with a $ a m (and some voters with a less than but close to a m) will refer zm to z a. We may note that in the cases considered so far za may or may not be a Pareto efficient olicy. The only assumtion is that this olicy is not Pareto 14 dominated by z m, which is the final case to be considered. (iii) Assume that 1 1 (V mv a). 0, (V a V m), 0. Since the alternative olicy is Pareto dominated by z m, everybody will refer zm to z a. QED Readers familiar with the median voter theorem know that the theorem is only alicable to voting over one dimensional issues. So why do we obtain a median voter result here? The reason is that the voting is de facto over oints on the Pareto frontier, which is one-dimensional since there are only two grous. The intuition for Proosition 1 is strong. When voting each individual s most referred oint is the one that maximizes the olicy reference function, which we recognize as a Bergson-Samuelson social welfare function. But we know from welfare economics that a maximum of such a social welfare function is necessarily a Pareto otimum. When all individuals have a referred olicy which is efficient, it would indeed be surrising if the voting equilibrium were not also efficient. Returning to the tax and ublic rovision model of Section, we can state : Corollary 1. At the voting equilibrium of the tax and ublic rovision model Results 1 and are valid. According to Proosition 1 the median voter s referred olicy will be a Condorcet winner, that is, it will win in majority voting against any other roosed olicy. Since the median voter s referred olicy is Pareto efficient, ublic rovision will be art of the olicy if the median voters referred olicy is in a certain range of the Pareto frontier. We note that in the resent setting otimal nonlinear income taxes are available. Still, the voting equilibrium will be such that ublic rovision is art of the olicy. The reason is that by using ublic rovision of a rivate good the efficiency of the income redistribution is increased. It also 14 Since z is Pareto efficient, there is of course no case where it is Pareto dominated by the m alternative olicy.

13 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) means that the characterization of rivate goods suitable for ublic rovision that is given in Blomquist and Christiansen (1995) and reroduced in Section above would be valid in the resent context. In Section we noted that the solution to Eqs. (1) (5) may fail to be unique. However, this does not create any serious difficulties. The reason for this is that what determines how individuals vote is the solution in utility sace. Suose, for examle, that the otimization roblem solved by the median voter has two 1 1 solutions zm and zm that both yield the utility allocation hv *, V * j. To obtain uniqueness in olicy sace we must add a mechanism whereby the median voter chooses one of the two olicies. The median voter, as all other voters, is indifferent between the two olicies. Hence adding a simle random mechanism would do. In the model above the electorate have been endowed with social references. In a comanion aer (Blomquist and Christiansen (1998c)) we have also analysed within a simle majority voting model the situation in which all voters are indeed entirely selfish. Assuming that the low-skill class is the larger it will exloit its majority osition to maximise the utility of the class members subject to the 15 relevant constraints. The referred olicy of the low-skill individuals will then be a Condorcet winner, and it is trivial that this olicy is Pareto efficient. Obviously Results 1 and are valid in the tax and ublic rovision version of the model. 4. Reresentative democracy with two olitical arties We shall consider a voting model of two olitical arties. The model is established by first making assumtions about the olitical arties and then about the voters. The cometition between the arties is erceived as a non-cooerative game which is shown to have a Nash equilibrium. The roerties of this equilibrium are examined in some detail The arties Our model is insired by Hansson and Stuart (1984), Lindbeck and Weibull (1993) and Dixit and Londregan (1998). There are two arties denoted by L (leftist arty) and R (rightist arty). The nature of the olicy set Z is the same as before. Prior to the election each arty chooses a olicy z [ Z; 5 L, R. We assume that the olicy that is actually imlemented is the olicy of the arty that wins the election. The underlying resumtion is that each arty is able to 15 The utility level of the high-skill class may be bounded from below by a subsistence level or a reservation utility in the case of mobility or it may be lowered to the oint where further taxation of the high-skilled fails to generate additional transfers to the low-skilled because of disincentives.

14 44 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) credibly commit to a certain olicy. Thus we rule out the ossibility that a arty 16 does not kee its romises from the election camaign. It is common in the literature to make some kind of assumtion to the effect that the arties imlement their romised olicies if winning. Sometimes it is just imosed as an assumtion that the arties imlement their romised olicies (e.g. Dixit and Londregan (1998)), sometimes the assumtion is imlicit (e.g. Lindbeck and Weibull (1987) or Hansson and Stuart (1984)), and sometimes there is an aeal to underlying assumtions. Lindbeck and Weibull (1993) assume that at least all voters believe that the winning arty will imlement its announced olicy. For a theory of what haens at the election this may be a sufficient assumtion. For a theory of actual olicy one obviously needs to know also how the arties actually behave. Lindbeck and Weibull also aeal to the existence of future elections (otherwise not aearing in the model) to suggest that cheating may be rohibitively costly in terms of future loss of credibility. Besley and Coate (1997) oint out that it is natural to assume that the citizen who wins the election imlements his referred olicy (i.e. the olicy he would choose as a dictator), while commitment to other 17 olicies is more roblematic due to lack of credibility. At the re-election stage the outcome of the election is erceived as random. Once the outcome of the election is known, each arty evaluates the winning olicy according to its social welfare function. We assume there is no benefit from winning the election as such. There is no so-called ego-rent. It follows that rior to the election the objective function of a arty is the exected welfare according to the references of the arty. For arty L the exected welfare is given by: L L L R L L R R (z, z )W (z ) 1 (1 (z, z ))W (z ) (8) where (z L, z R) is the robability that arty L will win the election. This robability deends on the olicy choices of the two arties. Below we describe L how this robability is determined. The social welfare function W (z ) is given by L 1 1 W (z ) 5 a NV (z ) 1 (1 a )N V (z ) 5 L, R. (9) L L The exected welfare from the ersective of arty R is defined in a symmetric way. We assume the leftist arty assigns a higher weight to the welfare of the low skill grou, a L. a R. Party L maximizes the exected welfare w.r.t. zl for a given z and vice versa. R 16 A comlication in ractice may be that at the time the olicy is designed the state of the world that will materialise in the eriod of office is not known with certainty. Since there is limited scoe for state contingent election manifestos, it may be a matter of interretation whether the actual olicy is according to the re-election latform when allowing for the need to adjust to the circumstances that arise. We abstract from uncertainty of this kind. 17 See Alesina (1988).

15 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) Individuals voting behavior The voters are assumed to have exactly the sort of references as in the median voter model above. They may be more or less myoically selfish, altruistic or concerned with social insurance. An individual s olitical references are reresented by a olicy reference function: 1 1 W 5 an V 1 (1 a)n V (10) which is identical to (6) above. In our model it is otimal to vote sincerely. To understand why this is so it is worthwhile to consider a number of the assumtions that have been made. First, a voter cannot influence a arty s choice of rogramme by threatening to vote for the other arty under certain contingencies. This is because there is no way a voter can credibly commit to do so. Everybody knows that when election day comes along it is in the interest of a citizen to cast his vote in favour of the olicy which is more in line with his references. Doing otherwise will only increase the robability that a olicy he likes less is going to win. Secondly, it is assumed that the olicy of the winning arty is fully imlemented. If the actual olicy were to be determined as some sort of weighted comromise between the olicies of the two arties with the weights affected by vote shares, strategic voting behaviour might cree in as a voter might then hoe to draw the actual olicy a bit closer to his referred olicy by voting for a olicy he would not like to see fully imlemented. (But even then sincere voting is not necessarily ruled out; see Dixit and Londregan, 1998). Thirdly, there is only one election eriod and thus no incentive to try and influence a arty s future choice of latform. Our assumtions imly that an individual votes for arty L if an V 1 (1 a)n V $ an V 1 (1 a)n V (11) L L R R We rewrite this as N (V RV L) L R R L a $ ]]]]]]]] 5a ˆ (1) N (V V ) 1 N (V V ) 1 Let a be distributed as f (a) and f (a), 0#a #1, for the low and high skill class, resectively. The number of individuals referring arty L s olicy is then given by m 5 m(z, z ) 5E Nf (a)da 1E Nf (a)da (13) L R ˆ a ˆ a If the voting behaviour is entirely deterministic each arty can calculate for any configuration of olicies whether it is going to win the election. The olicies will then converge as from the ersective of any arty a winning olicy is always better than a losing olicy as long as the winning olicy is considered at least

16 46 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) slightly referable to the olicy of the oonent. This scenario is not very realistic. In ractice there are numerous elements which are beyond the control of the arties and which they will treat as random. In the literature several aroaches 18 have been adoted to model random voting behaviour. But it seems that the exact way to model random voting behaviour is of less imortance. What is central is that the arties can only affect the robabilities of winning and the exected outcome in terms of olicy and welfare according to a arty s reference scale. Acceting this remise we may as well choose a simle random element. We know that in most elections not everyone will vote and that an imortant asect of winning an election is to motivate the individuals suorting the arty to actually vote. We do not intend to go into this in any deth, but use a quite stylized model to cature the fact that many eole do not vote. Without lack of generality we assume that individuals suorting arty R will always vote. However, only a 19 fraction of the individuals suorting arty L will actually vote. This fraction is a random variable u assumed to follow a uniform distribution with suort 0, a, 1 u, b, 1. Let N 5 N 1 N and g 5 (N m)/m. Ifg, a the robability that arty L will win is 1. If g $ b the robability that arty L will win is zero. For a, g, b the robability that art L will win is given by: Pr(arty L wins) 5 Pr(um(z, z ). N m(z, z )) L R L R b 1 5 Pr[u. (N m(z L, z R)) /m(z L, z R)] 5E ]] du b a b g 5 ]]. b a Rewriting this robability we obtain: 1 1 b N Pr(arty L wins) 5 (z L, z R) 5]] ]]]. b a m(b a) An imortant feature of this exression is that / m.0. g 18 Sometimes it is just ostulated that robabilities deend on olicy choices. Sometimes more secific assumtions are made. For instance Dixit and Londregan (1998) assume that there are grous of extremist voters suorting their resective arties irresective of election manifestos, but the size of each grou is unknown to and is treated as random by the arties. 19 The inclination to go and vote may deend on weather conditions, whether there is an influenza eidemic, the encouragement offered by the mass media, etc. One may argue that it is a bit secial to link voting roensity to arty adherence as such. The imortant assumtion is that the robability of voting differs between grous otherwise the stochastic element would just be similar to having an electorate of random size but with deterministic shares of arty suort. We have oted for the simlest way to model a systematic difference between classes. Our aroach may even have a claim for realism as it is known from several countries that conditions inducing a high turn-out tend to favour certain arties.

17 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) Nash equilibrium To study the Nash equilibria for this model we need to study the reaction functions z L(z R) and z R(z L). This is comlicated since zp is multidimensional. However, we can reduce the dimensionality of the roblem and instead study the reaction functions V L(V R) and V R(V L). The reason why it is sufficient to study these functions is that each arty will always resond with a Pareto efficient olicy. This means that we can summarize the olicy of arty P by a single 1 number V P. Since only Pareto efficient oints are relevant V P is then uniquely 0 determined. Let us establish that all chosen olicies are Pareto efficient. Proosition. The otimal strategy for a arty is to roose a Pareto efficient olicy. Proof. Recall that the exected welfare from the oint of view of a arty is (z, z o)[w (z ) W (z o)] 1 W (z o), where z is the arty s own olicy, zo is the olicy of the oonent and W is the welfare level according to the references of the arty. Also recall that the welfare function of any arty and voter is of the form 1 1 an V 1 (1 a)n V. We assume that for both arties 0,a,1, and there is a continuous distribution of voters from those with a 5 a o $ 0 to those with n a 5 a # 1. Assume that the arty is going to make a choice between a olicy z which is not Pareto efficient, and a Pareto suerior olicy z, while taking the olicy roosal of the oonent as fixed. The choice will have two effects. It will affect the welfare that the arty obtains if it wins, and it will affect the robability of winning. Since the arty adheres to the Pareto rincile (i.e., it always considers a Pareto imrovement to be desirable), the welfare it obtains if winning must increase if it icks the Pareto suerior olicy. Since the voters also adhere to the Pareto rincile, all voters will find the arty (at least weakly) more attractive if it 1 selects the Pareto suerior olicy. Becoming a more attractive arty to vote for the arty cannot lose suort. In fact, since there is a continuum of voters, some who would otherwise be marginal suorters of the oonent will now vote for the arty under consideration. Choosing a Pareto suerior olicy is the way to increase P 0 In Section we noted that there might exist multile solutions to Eqs. (1) (5). However, we have ursued the analysis as if the solutions were unique. This is not restrictive. Since arties and individuals evaluate olicies in terms of the utility imlications the analysis will remain unaffected if a certain utility allocation can be imlemented by more than one olicy. If one arty rooses a utility allocation that can be imlemented by two or more olicies one could add a mechanism whereby the arty chooses a unique olicy. Since it is of no consequence which olicy that is actually chosen a simle random mechanism would do. 1 The only caveat is that as a secial case the Pareto suerior olicy may only benefit one grou, and there may be voters who assign a zero weight to that grou. These voters will then be indifferent, while the others strictly refer the Pareto suerior olicy.

18 48 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) welfare if the arty wins and the way to increase the robability of winning. QED Recalling from Section the roerties of a Pareto otimum in the tax and ublic rovision model it is trivial to state: Corollary. At the olitical equilibrium of the tax and ublic rovision model Results 1 and are valid. When discussing further the olitical equilibrium it is useful to consider as benchmarks the (hyothetical) cases in which each arty is not exosed to olitical cometition. Definition. If the arties could act as dictators they would choose olicies that maximize their resective welfare functions, i.e., objective functions of tye (9). We will denote these olicies as the dictator olicies. We denote the corresonding values of V as V R and V L. The imlied oints on the Pareto frontier are indicated by R and L in Fig.. Deending on their value of a different individuals refer different oints on the Pareto frontier. For an individual with a 50 the referred oint will be the one where V achieves its maximum. We denote this V max. As a increases the referred oint will move down towards the right along the Pareto frontier. If Fig.. The Pareto frontier and dictator olicies.

19 S. Blomquist, V. Christiansen / Journal of Public Economics 73 (1999) a 51 the oint where V is maximized will be the referred one. We denote this oint V min. To guarantee that the voting roblem is non-degenerate, i.e. that no arty wins with certainty, we have to make assumtions on the distribution of a. We assume the distribution of a is such that more than 50% of the individuals refer a value of V that is less than V R. Otherwise the olicy corresonding to R would win with certainty. We also assume that more than a fraction (10.5/a) of the individuals refer a value of V that is larger than V L. Otherwise the olicy corresonding to L would win with certainty. Proosition 3. There exists a Nash equilibrium. R L L R We want to study crucial roerties of the reaction functions V (V ) and V (V ) and show that the resonse curves cross at least once. First, suose that one arty rooses to set V 5V max. Then there exists a value of V 5 V,V max which the oonent refers to V max, and which the oonent can adot and be sure of winning the election. To see this it suffices to note that by icking V arbitrarily close to V max the share of the electorate favouring the V max can be made infinitesimally small. It obviously follows that the best resonse of the oonent is also some value of V, V max. We can conclude that V R(V max), V max, and V L(V max),v max. By analogous reasoning we can show that V R(V min).v min and V L(V min).v min. These features of the resonse functions are reflected in Fig. 3. V L(V R)will start below the 458 line and end u above the 458 line on the horizontal axis indicating V max. V R(V L) will start above the 458 line and end u below the 458 line on the vertical line indicating V max. Hence the resonse curves will cross and there will be a Nash equilibrium. QED Corollary. A Nash equilibrium is Pareto efficient and the Results 1 and aly. Proof. The corollary follows from Proosition and the Results 1 and. QED The corollary imlies that there will be ublic rovision of a rivate good at a olitical equilibrium rovided that consumer references satisfy the assumtion in Result and the redistributional ambitions are sufficiently large. Definition. We denote a Nash equilibrium as V ˆ, V ˆ. Having established the existence of a Nash equilibrium we next roceed to characterize further such an equilibrium. In the lemma and roosition below we narrow down the set of ossible Nash equilibria. L R The Pareto frontier is the art of the curve in Fig. where the curve is downward sloing.