The model combines elements from Lohmann (
1998), Shi and Svensson (
2006) and Bohn and Veiga (
2017). It captures an economy with
n voters and two opportunistic candidates, an incumbent and a challenger, who compete for holding office every alternate period. Each agent’s expected utility depends on the discounted present value of expected per-period utilities which, in turn, consist of additively separable economic and political utilities (
\(\beta \) is the discount factor;
E is the expectations operator). In each period, voters derive utility from consumption
c (
\(u(c_{s}))\), which has the standard concavity properties, from local public goods
L and from political utility
\(\theta ^{i}z_{s}\) (with weight
\(\alpha \)). Voter
i’s ideological preference or personal sympathy,
\(\theta ^i\), is distributed uniformly over the interval [− 1,1];
z indicates who is in power (
\(z_{s}=-\frac{1}{2}\), if
a is in power;
\(z_{s}=\frac{1}{2}\), if
b is in power; without limiting the generality of the analysis we call
a the incumbent and
b the challenger). If her favorite candidate is in power, voter
i receives positive political utility; political utility is smaller for more moderate voters, i.e., voters with weaker views on the candidates’ competencies. Voters vote prospectively in that they choose the candidate who can deliver the highest expected utility in the future. More moderate voters might, therefore, vote for the “wrong” candidate, if they are compensated by higher economic utility. The voters’ utility function is:
$$\begin{aligned} U_{t}^{i}= \, \, \sum _{s=t}^{\infty } \, \, (\beta ^i)^{s-t} \, E_t[u(c_{s})+L_s+\alpha \theta ^{i}z_{s}]; \quad s=t, t+1, \ldots ; \quad i=1, \, \ldots , \, n. \end{aligned}$$
(1)
The candidates’ economic utility is the same as the voters’. However, candidates receive a political (dis-)utility only if they are in office: an ego rent and a potential reputation loss, if they also were responsible for missing pre-set debt target
\(B^{*}_{s-1}\) (see further down) in the previous year:
$$\begin{aligned} V_t^{j}= & {} \sum _{s=t}^{\infty }W_{s}^{j} =\, \, \sum _{s=t}^{\infty }(\beta ^j)^{s-t} \, \, E_t[u(c_{s})+L_s+ \mathbf{I }_s X_{s} - \mathbf{I }_{s-1}\mathbf{I }_s \xi _{s} (B^{*}_{s-1}-B_{s-1})^2 ]; \nonumber \\&s=t, t+1, \ldots ; \quad j=a,b; \quad \mathbf{I }_r = {\left\{ \begin{array}{ll} 1 &{}\quad {\hbox {if in power in period}} \; r; \\ 0 &{}\quad {\hbox {otherwise.}} \end{array}\right. } \end{aligned}$$
(2)
Everybody’s expected consumption depends on expected after-tax income:
$$\begin{aligned} E^k_t[c_{s}] \; = \; E^k_t[(1-\tau _s) \epsilon _s {\bar{y}}] \; = \; (1-\tau _s) \epsilon _s, \qquad k=j,i. \end{aligned}$$
(3)
where
\(\tau _s\) is the tax rate. Period-specific expected growth factor shock
\(\epsilon _s\) captures the deviation from trend (or previous period or potential) output
\({\bar{y}}\) which is normalized to 1;
\(\epsilon _s>1\) is an expected boom; and
\(\epsilon _s<1\) is an expected recession.
The government’s budget constraint relates primary deficit
\(D_s\) to the provision of (local) public goods
\(L_s\). It takes into account expected tax revenue
\(\tau _s \epsilon _s\) and the government’s competence
\(\eta _{s}^{j}\) (see further down):
$$\begin{aligned} L_{s}=\tau _s \epsilon _s + D_s +\eta _{s}^{j}. \end{aligned}$$
(4)
Excessive-debt municipalities are obliged to reduce their debts by a certain percentage every year and may have to impose a particularly high tax rate to do so. Low-debt municipalities do not face such requirements. In a continuous setting, we capture budget dynamics with two continuous functions. Every municipality’s yearly (period-specific) debt target
\(B^{*}_s\) (which depends on the initial level of debt
\(B_{t-1}\)) is
$$\begin{aligned} B^{*}_s= & {} \delta B^{*}_{s-1}, s=t, t+1, \ldots ; {\hbox { with }} B^{*}_{t-1} \equiv B_{t-1};\nonumber \\ \delta= & {} \delta (B^{*}_{t-1}); \, 0<\delta \le 1 {\hbox { for }} B^{*}_{t-1} \ge 0; \nonumber \\ \delta (0)= & {} 1 {\hbox { and }} \delta {\hbox { monotonously decreasing}}. \end{aligned}$$
(5)
We assume that the municipality’s tax rate
\(\tau _s\) is predetermined and—as argued before—also depends on the initial level of debt
\(B_{t-1}\), too:
$$\begin{aligned} \tau _s = \tau = \tau (B_{t-1}); \quad {\hbox {with }} \tau ^{\prime } > 0; \, \tau ^{\prime \prime } < 0. \end{aligned}$$
(6)
Given the interest payment on the inherited debt level
\(B_{s-1}\) from the previous period, and, possibly, debt reduction from
\(B_{s-1}\) to target level
\(B^{*}_s\) the government normally would be obliged to produce a primary surplus. Let’s call it the primary surplus requirement (component 1) which would imply
\(D_s<0\) and require spending cuts. However, the government may choose to disregard the rules, especially in an election year, and maximize with respect to the second component, the freely choosable deficit
\(D^{free}_s\).
$$\begin{aligned} D_{s}\equiv & {} \quad (B_s \quad - \quad B_{s-1}) \quad - \quad r B_{s-1}. \nonumber \\ D_{s}=\, & {} ((B^{*}_s+ D^{free}_s) - B_{s-1}) - r B_{s-1}; \nonumber \\= & {} \underbrace{(B^{*}_s - B_{s-1}) - r B_{s-1}}_{\text {primary surplus requirement}} + \underbrace{D^{free}_s}_{\text {freely choosable}};\nonumber \\= & {} \quad \delta B^{*}_{s-1} - (1+r) B_{s-1} \quad + \quad D^{free}_s. \end{aligned}$$
(7)
As in Rogoff (
1990), government competence is modelled as an MA(1) process. However, Shi and Svensson (
2006) suggested that there new tasks always arise that do not allow candidates to know their own competencies
\(\eta _{s}^{j}\) in advance:
$$\begin{aligned} \eta _{s}^{j}=\mu _{s}^{j}+\mu _{s-1}^{j}. \end{aligned}$$
(8)
Shocks
\(\mu _{t}^j\) are random variables with mean 0 and distribution function
\(F[\mu _{t}^j]=F[\bullet ]\). For simplicity, density function
\(f[\mu _{t}^j]=f[\bullet ]=F^{\prime }[\bullet ]\) is assumed to be bell-shaped, but more general specifications also would be possible. Inserting Eqs. (
6) to (
8) into budget constraint (
4) we obtain:
$$\begin{aligned} L_{s}=\, & {} \tau _s \epsilon _s + D_s +\mu _{s}^{j}+\mu _{s-1}^{j}; \end{aligned}$$
(9)
$$\begin{aligned}= & {} \tau (B_{t-1}) \epsilon _s + \delta B^{*}_{s-1} - (1+r) B_{s-1} + D^{free}_s +\mu _{s}^{j}+\mu _{s-1}^{j}. \end{aligned}$$
(10)
The timing of events is presented in Table
1. Elections take place in alternating periods. At the beginning of election period
t, voters and incumbent
a observe the realizations of last period’s skills shock
\(\mu _{t-1}^a\) and predetermined current period tax rate
\(\tau _t\). The incumbent also observes (period-specific) debt target
\(B_t^{*}\) and growth shock
\(\epsilon _t\) which allow her to decide on the optimal level of freely choosable deficit
\(D^{free}_t\).
4 On that basis, the government chooses the primary deficit level
\(D_t\), thereby providing quantity
\(L_t\) of local public goods. Voters observe
\(L_t\) and form expectations of skills shock,
\(\widehat{\mu _t^a}\), which is, however, affected by their expectations of the growth shock,
\(\widehat{\epsilon _t}\), and of the primary deficit,
\(\widehat{D_t}\). Voters base their decisions on whether to vote for the incumbent on
\(\widehat{\mu _t^a}\) because period
t skills affect the incumbent’s competence in providing local public goods in (
\(t+1\)). Note that voters’ expectations of the incumbent’s competence can be mistaken for two reasons: (1) they may not be able to fully anticipate the incumbent’s deficit policy; and (2) they may not be able to anticipate fully an imminent economic slump or boom.
Table 1
The timing of events
Period t | (1) Voters i and incumbent a observe: |
the incumbent’s last period skills \(\mu _{t-1}^a\); |
the predetermined tax rate \(\tau _t\). |
(2) Incumbent a observes: |
the temporary debt target \(B_t^{*}\); |
growth (estimate) \(\epsilon _t\). |
(3) Incumbent a: |
chooses primary deficit \(D_t\); |
thereby providing local public goods \(L_t\). |
(4) Voters i observe: |
local public goods \(L_t\). |
(5) Voters i: |
form expectations of the incumbent’s current period skills \(\widehat{\mu _t^a}\); |
and vote. |
Period t + 1 | The winner of the period t elections takes office, receives an ego rent and suffers a reputation loss, if she missed debt target \(B_t^{*}\) |
In period (
\(t+1\)), the winner of the election receives ego rent
X. Policy in (
\(t+1\)) no longer depends on voting, though; hence, either policymaker (
a or
b) will repay the costly debt to the extent possible, thereby cutting the provision of local public goods.
5 Voters anticipate that response, but can do nothing to prevent it. Note also that the voting decision in election period
t does not extend to considering expected utility in
\(t+2\) because the MA(1) nature of the competence process makes incumbent and challenger indistinguishable then. Policymakers likewise do not account for
\(t+2\) in solving their optimization problem when determining the optimal level of
\(D^{free}_t\) because they cannot influence their own utility or boost their reelection chances in
\(t+2\). Hence, the model can be split into cycles of two periods consisting of election period
t and off-election period (
\(t+1\)).