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Federal subsidization of state expenditure to reduce political budget cycles

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Abstract

In this note, we analyze whether a federal transfer system can be designed to increase welfare when state governments create political budget cycles. The results show how the federal government can counteract the welfare costs of these cycles, without hindering politicians from signaling their type, by announcing a transfer scheme to subsidize expenditures that voters do not consider when voting.

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Notes

  1. For example, Gonzalez (2002) and Shi and Svensson (2006) have found that politicians at the highest level of government use the budget to increase reelection chances. Similar results have been found for state governments (Schneider 2010; Mechtel and Potrafke 2013), regional governments (Blais and Nadeau 1992; Sjahrir et al. 2013) and municipal governments (Veiga and Veiga 2007; Sakurai and Menezes-Filho 2011).

  2. There is also a source of external uncertainty in the election outcome, which both politicians and voters observe just before the election. This can, for example, capture uncertainty in the candidates’ performance during the end of the election campaign. The external uncertainty means that the probability to become reelected will be in the interval (0, 1) for all incumbents, which allows the pooling equilibrium to be ruled out using the intuitive criterion by Cho and Kreps (1987). The equilibrium described below remains an equilibrium also with multiple elections, with the difference that the expected future benefits from being reelected become larger, since reelection opens the possibility of being reelected once more, etc. This tends to aggravate the political budget cycle. With repeated elections, there could also be a reputational equilibrium with little or no political budget cycle if \(\beta \) is close to one, the external uncertainty is sufficiently small, and the time between elections is short. We share Rogoff’s judgment that such an equilibrium is unlikely in reality.

  3. In models with vertical fiscal externalities and benevolent policy makers, Aronsson and Wikström (2001, (2003) show that intergovernmental transfer schemes can, in certain situations, be designed to induce correct incentives for the lower-level governments.

  4. In the present model, the federal government only decides on this transfer policy and associated revenue collection, i.e., we abstract from public consumption and investment directly decided on at the federal level. This simplification is not important for the social welfare consequences of curbing the political budget cycles at the lower level.

  5. We thank an anonymous reviewer for suggesting this case.

  6. That is, since \(\hbox {W}\) is concave and \(E_t \hbox {W}_t^O \left( N \right) =E_t \hbox {W}_t^L \left( {N+\rho \left( {\alpha ^{H}-\alpha ^{L}} \right) } \right) \), where O denotes the opposition candidate and N denotes net transfers, \(D\left( N \right) \equiv E_t \hbox {W}_t^O \left( N \right) -E_t \hbox {W}_t^L \left( N \right) \) is convex.

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Acknowledgments

Research grants from the Bank of Sweden Tercentenary Foundation, the Swedish Council for Working Life and Social Research, and the Swedish Tax Agency (all of them through project number RS10-1319:1) are gratefully acknowledged. The authors would also like to thank two anonymous reviewers for helpful comments and suggestions.

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Correspondence to David Granlund.

Appendix

Appendix

Proof of Proposition 3

Using Eqs. (5) and (6) we see that

$$\begin{aligned}&\rho \text{ min }\_\kappa _t^{LH} <\rho \left( {\rho \kappa _t^{HH} +\left( {1-\rho } \right) \kappa _t^{LH} } \right) ,\end{aligned}$$
(9)
$$\begin{aligned}&\left( {1-\rho } \right) \text{ min }\_\kappa _t^{LL} <\left( {1-\rho } \right) \left( {\rho \kappa _t^{HL} +\left( {1-\rho } \right) \kappa _t^{LL} } \right) . \end{aligned}$$
(10)

Adding (9) and (10) gives

$$\begin{aligned} \rho \hbox {min}\_\kappa _t^{LH} +\left( {1-\rho } \right) \hbox {min}\_\kappa _t^{LL}< & {} \rho ^{2}\kappa _t^{HH} +\rho \left( {1-\rho } \right) \left[ {\kappa _t^{HL} +\kappa _t^{LH} } \right] \nonumber \\&+\,\left( {1-\rho } \right) ^{2}\kappa _t^{LL} =\varGamma _{t+1} /r, \end{aligned}$$
(11)

which is the condition for that states where L mimics H would be net payer in the transfer system on average.

Since the utility function in Eq. (1) is concave, and L needs \(\alpha ^{H}-\alpha ^{L}\) more in net transfers to obtain the same utility as H, the expected utility difference of electing the opposition candidate, for whom \(\alpha _t^I =\alpha ^{H}\) with probability \(\rho \), instead or reelecting L is a convex function of the net transfer.Footnote 6 This, and that states where L mimics H would be net payer in the transfer system on average, imply that the transfer system will increase the average loss in expected utility for voters of reelecting L. Therefore, the transfer increases the average value of \(\hbox {min}\_\kappa _t^L .\)

To show that the median political budget cycle is reduced, we show that among states with \(\alpha _t^I =\alpha ^{L}\), the majority will get negative net transfers if the incumbent mimics H. Note that \(r \hbox {min}\_\kappa _t^{LL} -\varGamma _{t+1} <0\) if \(\hbox {min}\_\kappa _t^{LL} <\rho ^{2}\kappa _t^{HH} +\rho \left( {1-\rho } \right) \left[ {\kappa _t^{HL} +\kappa _t^{LH} } \right] +\left( {1-\rho } \right) ^{2}\kappa _t^{LL} .\) The following inequality

$$\begin{aligned} \hbox {min}\_\kappa _t^{LL} <\hbox {min}\_\kappa _t^{LH} , \end{aligned}$$
(12)

which is due to the assumption that k is a normal good, together with Eqs. (5) and (6), show that this is the case.

Note that \(r \hbox {min}\_\kappa _t^{LH} -\varGamma _{t+1} <0\) if

$$\begin{aligned} \hbox {min}\_\kappa _t^{LH} <\rho ^{2}\kappa _t^{HH} +\rho \left( {1-\rho } \right) \left[ {\kappa _t^{HL} +\kappa _t^{LH} } \right] +\left( {1-\rho } \right) ^{2}\kappa _t^{LL} . \end{aligned}$$
(13)

Since all goods are normal,

$$\begin{aligned} \hbox {min}\_\kappa _t^{LH} -\hbox {min}\_\kappa _t^{LL} <\alpha ^{H}-\alpha ^{L}. \end{aligned}$$
(14)

Inequalities (6) and (14) together imply \(\hbox {min}\_\kappa _t^{LH} <\kappa _t^{HL} \). Therefore, a sufficient condition for inequality (13) to hold is that \(\hbox {min}\_\kappa _t^{LH} <\kappa _t^{LL} \). Note that – since \(\kappa _t^{LH} -\kappa _t^{LL} <\alpha ^{H}-\alpha ^{L}\) – this condition holds if

$$\begin{aligned} \hbox {min}\_\kappa _t^{Lj} +\alpha ^{H}-\alpha ^{L}=\kappa _t^{Hj} <\kappa _t^{Lj} ; \qquad \hbox {j}=\hbox {L},\hbox { H}. \end{aligned}$$
(15)

Another sufficient condition for inequality (13) to hold is that

$$\begin{aligned} \left( {1-2\rho \left( {1-\rho } \right) } \right) \hbox {min}\_\kappa _t^{LH} \le \rho ^{2}\kappa _t^{HH} +\left( {1-\rho } \right) ^{2}\kappa _t^{LL}. \end{aligned}$$
(16)

This can be written as

$$\begin{aligned} \left( {1-\rho } \right) ^{2}\left( {\hbox {min}\_\kappa _t^{LH} -\kappa _t^{LL} } \right) \le \rho ^{2}\left( {\kappa _t^{HH} -\hbox {min}\_\kappa _t^{LH} } \right) . \end{aligned}$$
(17)

Since \(\hbox {min}\_\kappa _t^{LH} -\kappa _t^{LL}<\kappa _t^{LH} -\kappa _t^{LL} <\alpha ^{H}-\alpha ^{L} \) and \(\kappa _t^{HH} -\hbox {min}\_\kappa _t^{LH} =\alpha ^{H}-\alpha ^{L}\), a sufficient condition for this sufficient condition to hold is that \(\left( {1-\rho } \right) ^{2}\le \rho ^{2}\), i.e., that \(\rho \ge 1/2\). This means that \(r \hbox {min}\_\kappa _t^{LH} -\varGamma _{t+1} \), which is relevant for the fraction \(\rho \) of the states, only can be positive if \(\rho <1/2\). \(\square \)

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Aronsson, T., Granlund, D. Federal subsidization of state expenditure to reduce political budget cycles. Int Tax Public Finance 24, 536–545 (2017). https://doi.org/10.1007/s10797-016-9404-5

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