Online Appendix for the paper “New Parties and Policy Outcomes: Evidence from Colombian Local Governments” Hector Galindo-Silva∗ In this appendix, I present a simple career concerns model in which I apply the insights from the political agency literature to the context of Colombian municipalities.1 It also intends to provide an explanation for the empirical results in Sections 4 and 5.3 Consider a two-period economy. In each period t, a political party in power must decide public spending and the tax rate, denoted by gt and xt , respectively. Between periods there is an election in which voters choose between the party that was in power in period 1 and a challenger.2 Each period the winning party faces a balanced budget constraint xt y = gt + rt + t

(1)

where y denotes the taxable revenue assumed to be equal to one, rt is a parameter that measures the rents captured by the members the political party in power, which can loosely be interpreted as the honest of this party, and t is a productivity shock, assumed to be independent, identically distributed with mean zero.3 The important simplifying assumption of the career concerns models inspired by Holmstrom (1999), which I adopt here, is that there is symmetric information. I identify each political party by its honesty, which I assume is constant over time. Parties, as well as voters, are uncertain about this honesty. I assume that rt is drawn at random from a normal distribution with mean r and variance σr2 , with c.d.f. and p.d.f. denoted by F and f , respectively. A possible justification is that the rents that a party captures during its time in office depend on the qualities of the members of the government, or on demands from interest groups that helped the party get elected. It is reasonable to assume that the leader of the party does not have perfect information about this.4 Crucially, I assume that old and new parties have different σr2 . Specifically, I say that ∗

Barcelona Institute for Political Economy and Governance. Email: [email protected]. The literature contains many political agency models; see Besley (2006) for a review. Mine is built on Persson and Tabellini (2000, Ch. 4.5), but reintroducing some ideas originally in Holmstrom (1999). 2 Note that the use of career concerns allows us to apply the model to situations in which the periods considered are not successive, since what matters for voters are future policies eventually taken by parties that at some degree care about their political future. 3 It is reasonable to assume a balanced budget constraint for Colombian municipalities. Although some municipalities are allowed to run deficits, Colombian legislation (Law 358 of 1997) allows the central government to effectively limit the debt burden of municipalities according to their past performance, their own revenue, and to the implementation of a fiscal adjustment plan. These measures have proven to be very effective from 2000 onward (for instance, from 2000 to 2008, regional and local authorities averaged a fiscal surplus of 0.3% of GDP; see DAF, 2009). 4 This assumption also simplifies the analysis, as there is no possibility of signalling. As previously mentioned, in the model a party in power will choose a policy not to signal information about itself. Rather, it will “jam” or interfere with the inference problem faced by the voters. For more about these models, named by Fudenberg and Tirole (1986) as “signal jamming” models, see Holmstrom (1999), Persson and Tabellini (2000, Ch. 4.5), Prat (2005), Ashworth (2005) and Ashworth and Bueno de Mesquita (2008). 1

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Assumption 1. The precision of the information that the players have about rt (as captured by σr2 ) is lower when the government is led by a politician from a new party . A possible justification is as follows. By definition, new parties have never been in power. On the other hand, the political colleagues, bureaucracy and interest groups close to mayors from an old party are better known: these parties have been in power before, for many years, and these structures usually persist. Since governments’ honesty depends on these structures, then it is clear that when an old party is in power, relative to a new party, the players have more precise information about its level of honesty.5 Voters’ one-period utility is quasi-linear, with the per-period utility of voter i given by wi (gt , xt ) = (1 − xt ) + H(gt ) − D2i δ i

(2)

where H is a concave, increasing function representing the utility from consumption of local public goods, and δ i is an ideological bias against the party in power in period 1, uniformly distributed 1 1 on [− 2φ , 2φ ], and only relevant in period 2 when the party in power in period 1 is reappointed (in i this case D2 is one, in any other case it is equal to zero). The per-period utility of a typical member of a political party is given by v(gt , xt , Dtp ) = (1 − xt ) + H(gt ) + Dtp rt

(3)

where (1 − xt ) + H(gt ) is the utility of its members as citizens, Dtp is a dummy variable equal to one if his party leads the local government, and zero if a contender’s party is in power, and rt are the rents extracted when Dtp is one. The party in power maximizes its two-period utility, with a discount factor of β ∈ [0, 1]. The timing of the game is as follows: (1) the party in power at time t = 1 chooses a policy g1 ; (2) r1 and 1 are realized and observed by the party, and the taxes xt are residually determined so as to satisfy (1); (3) voters observe x1 and 1 , but neither r1 nor g1 ; (4) elections take place, and each voter either supports the party that was in power in period 1 or a contender; if the party in power in period 1 is not re-elected, an opponent is appointed, with honesty r20 drawn at random from a normal distribution with mean r0 ; (5) the party in power at time t = 2 chooses a policy g2 , and payoffs are realized. Analysis of the Model As a solution concept I focus on a subgame perfect equilibrium (SPE). I proceed by backward induction. At t = 2, the political party in power solves a static problem: by maximizing the expected value of its utility (3) subject to the budget constraint, it chooses g2∗ = Hg−1 (1). The tax rate, x∗2 , is residually determined so as to satisfy (1). I now move to period 1. In their decision about whether or not to reappoint the party in power in period 1, voters look at what they expect to get in each case. In both cases, given (1), they know that E[x∗2 ] = g2∗ + E[r2 ]. When the party is reappointed, they also know that E[r2 ] = E[r1 |x1 , 1 ] because honesty lasts over time, and in the case where a contender is elected, that E[r2 ] = r0 . Replacing these expressions in (2), and rearranging, it is easy to see that voter 5

This assumption is especially true in Colombia. There are three main reasons: (i) the shared control that Liberals and Conservatives had of almost all the elected positions and public offices for more than a century, (ii) the candidate selection mechanism employed by these parties, usually based on the number and strength of the candidates’ connections (see Pizarro, 2002, 2006), and (iii) their bureaucracy, usually composed of people from their own party (see Gutierrez and Ramirez, 2002).

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i prefers to reappoint the party in power in period 1, denoted by I, when δ i ≤ r0 − E[r1 |x1 , 1 ]. 1 1 Given that δ i is uniformed distributed on [− 2φ , 2φ ], I’s vote share is πI =

1 + φ[r0 − E[r1 |x1 , 1 ]] 2

(4)

From I’s point of view, voters use all the information they have to update their beliefs about the party. Voters know x1 and 1 , and that g1 and r1 must respect (1), so they make a conjecture about g1 , denoted by g˜1 , such that E[r1 |x1 , 1 ] = x1 − g˜1 − 1 , where x1 must also respect (1). Replacing this expression in (4), I’s probability of winning is h 1i pI = P r πI ≥ = F (r0 + g˜1 − g1 ) 2

(5)

In the first period, I chooses spending without knowing r1 nor 1 , in order to maximize its expected two-period utility:
max E[v(g1 , x1 , 1)] + β pI E[v(g2 , x2 , 1)] + (1 − pI )E[v(g2 , x2 , 0)] (6) g1 ≥0

where v(gt , xt , ·) is given by (3). Computing v(gt , xt , ·) using (3) and (1), replacing the result in (6), rearranging and differentiating, we have that the first-order condition of (6) is Hg (g1∗ ) − 1 = f (r0 )βr0

(7)

in which we have used the equilibrium condition g˜1 = g1∗ . This first result is stated in the following proposition. Proposition 1. In the unique SPE equilibrium of the game described above, spending in the first period is given by (7) and spending in the second period is given by g2∗ = Hg−1 (1). The following corollary relates the size of government chosen by the politician in the first period with his political party. Corollary 1. For r and r0 such that (r0 − r)2 < σr2 , an increase in σr2 increases the size of government chosen by the politician in the first period. Proof. In (7), note that the only term that depends on σr2 is f (r0 ). Given that H 00 (·) < 0, it is sufficient to show that if (r0 −r)2 < σr2 , an increase in σr2 decreases f (r0 ), implying a higher g1∗ . Since rt is 0 2 normally distributed with mean r and variance σr2 , we know that f (r0 ) = (2πσr2 )−0.5 exp( −(r2σ−r) ). 2 Differentiating f (r0 ) with respect to σr2 , and rearranging, we have that Thus,

∂f ∂σr2

∂f ∂σr2

=

f (r0 ) (r0 −r)2 [ σ2 2σr2 r

r

− 1].

< 0 if and only if (r0 − r)2 < σr2 .

Corollary 1 states that the newness of the parties, proxied by the information about the their qualities, is crucial. The mechanism is the following: less precise information (higher σr2 ) means that the actions of the party in power in period 1 are less informative, making it more difficult for the party to influence voters’ beliefs about its quality. This increases the uncertainty associated with the rents the party is able to extract, and reduces its effective time horizon. This results in greater levels of spending in the first period. The important point about this corollary is that it allows us to establish the impact of the presence of a politician from a new party in power: given that, by Assumption 1, for these politicians the information that voters have about their qualities

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is less precise, they choose in the first period higher levels of spending and taxes relative to what a politician from an old party would have chosen.6 Note that Corollary 1 includes the possibility that the prior beliefs for new parties are different than for established parties, insofar as r and r0 are not too different relative to σr2 . As I argued before, in Colombia new parties often have anti-corruption platforms, which suggests that when new and old parties are characterized by the parameters r and r0 , respectively, it is reasonable to expect that r0 ≥ r. In this context, and importantly, the condition (r0 −r)2 < σr2 can be interpreted as saying that the old parties do not have an extremely bad reputation. This additional condition allows us to establish an additional consequence of having a new party in power: these parties should have a lower probability of being reappointed. The corollary and proof are the following. Corollary 2. For r0 > r, an increase in σr2 decreases the probability that the party in power in period 1 is reappointed. Proof. By (5), note that in equilibrium, the probability that the party in power in period 1 is reappointed is equal to F (r0 ), where F is the c.d.f. of a random variable normally distributed with mean r and variance σr2 . It is possible to show (see Casella and Berger, 2001, p. 134) that for this distribution (in general for scale families), F is stochastically increasing in σr2 when r0 > r ≥ 0; thus, for all y > σr2 , F (r0 ; y) < F (r0 ; σr2 ) = F (r0 ).7 Parties ideologically distinct So far I have assumed that parties do not differ relative to their ideological preferences over fiscal policy. Now I show that Corollary 1 still holds for ideologically distinct new and old parties, insofar as their ideological differences are not very big. Let us use n to denote a new party, and o to denote 2 , where j denotes party j’s ideal policy. an old party. For j ∈ {n, o}, assume that H j (g) = −(g−j) 2 j Note that at t = 2, j chooses g2 = j − 1 if inpower. Let us assume that voters are all risk neutral, so H i (g) = g. Repeating the same steps as before, j’s optimal choice at t = 1 is g1j = 1 + j − f (rk )β rk +

(k − j)2
2

(8)

where k 6= j ∈ {n, o}. By (8), note that g1n > g1o iff (n − o)2 o n [f (r ) − f n (ro )] > 0 (9) 2 It is possible to show (see footnote 6) that for σr2n  σr2o , f o (rn )rn − f n (ro )ro > 0. It is also easy to see that f o (rn ) − f n (ro ) > 0. Thus in (9) it is crucial whether n ≶ o. First, note that for n > o, which may correspond to the case of new parties competing against the Conservatives (the traditional center-right party), (9) is satisfied, so we have g1n > g1o . For the case o > n, (9) can still be satisfied if o and n are ideologically not very different. (n − o) + β[f o (rn )rn − f n (ro )ro ] + β

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A formal proof of this statement is as follows. Let us denote the mean, variance and p.d.f. of a new party as rn , σr2n and f n , respectively, and denote rn , σr2o and f o as the corresponding parameters for an old party. By assumption, σr2n > σr2o . By (7) note that g1n > g1o if and only if f n (ro )ro < f o (rn )rn . I show that this last condition is satisfied when (ro − rn )2 < σr2n . Replacing the p.d.f. for each variable, and rearranging, we get  o −rn )2 σr2n   o n )2 1  f n (r o ) = σσrno exp (r 2σ ( σ2 − 1) > 0. Let us define the function g(x) = σ√rxo exp (r −r ( σ2 − x1 ) , with 2 f o (r n ) 2 r n

o

rn

ro

ro

(r ) 0 −1 g(σr2n ) = ff o (r ((ro − rn )2 x−1 − 1), so g 0 (x) < 0 iff (ro − rn )2 < x. Thus, for x = σr2n , n ) . Note that g (x) = g(x)(2x) 2 we have that g(σrn ) is monotonic decreasing iff (ro − rn )2 < σr2n . Finally, note that limσ2n →∞ g(σr2n ) = 0, so there r

n

exists a σ 2r defined by g(σ 2rn ) = rro such that g(σr2n ) < g(σ 2rn ) for all σr2n > σ 2r . 7 Sensu stricto, what is stated and proved in this corollary does not guarantee that new parties have a lower probability of being reappointed relative to old parties. A formal proof of this statement will require small modifications to the baseline model (for instance, an additional bias in favour of old parties). Since this result is not one of the main results of the paper, and unnecessarily complicates the model, I leave this development available upon request.

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References Ashworth, S., October 2005. Reputational dynamics and political careers. Journal of Law, Economics and Organization 21 (2), 441–466. Ashworth, S., Bueno de Mesquita, E., 2008. Electoral selection, strategic challenger entry, and the incumbency advantage. The Journal of Politics 70, 1006´ı1025. Besley, T., 2006. Principled Agents?: The Political Economy of Good Government. Oxford University Press. Casella, G., Berger, R., 2001. Statistical Inference. Brooks-Cole. DAF, 2009. 10 anos de transformacion fiscal territorial en colombia 1998-2008. Tech. rep., Direccion de Apoyo Fiscal, DAF, Minhacienda, Bogota. Fudenberg, D., Tirole, J., Autumn 1986. A “Signal-Jamming”; Theory of Predation. RAND Journal of Economics 17 (3), 366–376. URL http://ideas.repec.org/a/rje/randje/v17y1986iautumnp366-376.html Gutierrez, F., Ramirez, L., 2002. Familias, redes y facciones. Revista de Estudios Sociales 2. Holmstrom, B., 1999. Managerial incentive problems: A dynamic perspective. The Review of Economic Studies 66 (1), 169–182. URL http://restud.oxfordjournals.org/content/66/1/169.abstract Persson, T., Tabellini, G., 2000. Political Economics: Explaining Economic Policy. Vol. 1 of MIT Press Books. The MIT Press. Pizarro, E., 2002. La atomizaci´ on partidista en colombia: el fen´omeno de las micro-empresas electorales. Working papers 292-02, Kellogg Institute for International Studies. Pizarro, E., 2006. Giants with feet of clay: Political parties in colombia. In: Mainwaring, S., Bejarano, A., Pizarro, E. (Eds.), The crisis of democratic representation in the Andes. Stanford University Press, pp. 78–99. Prat, A., June 2005. The Wrong Kind of Transparency. American Economic Review 95 (3), 862– 877. URL http://ideas.repec.org/a/aea/aecrev/v95y2005i3p862-877.html

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