Hibbs (1977) introduced the partisan behavior of an incumbent and Alesina (1987, 1988) incorpo-rated rational expectations in the monetary approach of the political business cycle. Contrary to the opportunistic behavior, partisan incumbents have clear economic policy preferences or ideolo-gies, such as - left-wing parties may prefer higher employment and output growth even at the cost of tolerating higher inflation, while the right-wing parties might target lower inflation. We now model the the possibility of partisan behavior of the incumbent, assuming perfect information. By this, we imply that the voters know the ideological bent of the incumbent and the actions that she/
he would take. In this case, to contain the extent of opportunistic behavior, the relative weight δ assigned to the deficit,D(t)−D∗, is assumed to be close to 1 (in the specific case that we consider, δ = 1), as the partisan incumbent assigns almost equal weight to both voting support, M(t), and budgetary deficit, D(t)−D∗. In addition, the partisan behavior may also be captured by a lower intertemporal elasticity of substitution (as the behavior of a partisan incumbent is more predictable and, thus, less variable over time) implied by a higher value of ǫ (which may be close to 1). To begin with, we discuss some analytical results for the partisan case.
4.1 Partisan Incumbent in the Absence of Anti-incumbency
The analysis in this part is analogous to the case of the opportunist incumbent in the absence of an anti-incumbency factor. Here, the only parameters permanently changed are δ andǫ. We consider higher values of ǫ, even close to 1. We retain the assumption of 1−ǫ >0 for aggregate utility to be positive.
Proposition 11: When α > γ such that α > δγ, 0 < ρ < 1, δ = 1 and ǫ close to 1, the voting support, M(t), and the level of budgetary deficit of the incumbent, D(t)−D∗, are both positive and continuously increasing over time.
From an observation of the solutions in eqs. (9) and (11), and given the parametric restrictions for partisan behavior, the time paths of bothM(t) andD(t)−D∗are positive and increasing up to the election period. ForM(t), this can be explained as follows. In view ofM0 >0 and large, andα > γ,
e(α−δγ)δ t−1
>0. Thus, the first term in eq. (9), that is, Γ1e(α−δγδ )t, will dominate the second term, Γ2. In the partisan case, the numerator and denominator of the ratio in square brackets in the third term of Eq. (9), that is,
e−ρǫ t−eǫ−1δǫ (α−δγ)t (α−δγ)+ǫ−1δρ
, will have the same sign (each negative in this case) and the ratio will always be positive. However, despite δ = 1 and ǫ sufficiently large (even close to 1), the values of e−ρǫt and eǫ−1δǫ (α−δγ)t will tend to be very small as the the power of the exponential function is always negative, and the difference between the two exponential functions will also be rather small. Further, the value of ǫ−1δǫ will be smaller than in the case of opportunism.
However, using the same reasoning as in case of opportunism, Γ3 and e(α−δγδǫ )(t−T) will be very small, and although the latter term will be rising over time, it will only approach the value of 1 from below as t → T. Thus, the entire third term will be dominated by the sum of the first two terms, and M(t) will be positive in each time period. Moreover, following the reasoning for the opportunistic case and absent anti-incumbency,M(t) will be rising over time.
We next turn our attention to budgetary deficit in eq. (11). We focus on the third term.
From our earlier discussion, in the case of a partisan incumbent, we have h
e−ρǫt−eǫ−1δǫ (α−δγ)ti
0. Also, since the values of both δ and ǫ are higher in case of the partisan incumbent than in the opportunist case, the denominator of the third term, ǫ−1δǫ , in eq. (11) will be small and negative.
However, e(α−δγδǫ )(t−T) will be small albeit increasing only to approach the value 1 from below as t→ T. Consequently, the third term of eq.(11) is small and will dominated by the first term. In fact, the first term will dominate both the second and the third terms. Thus, the D(t)−D∗ will be positive. Moreover, similar to the opportunistic case, this will also be rising over time.
The results of numerical simulations in Figure 5(a) and 5(b) support this claim. One can observe a continuous increase in voting support associated with an increase in the budgetary deficit over time in Proposition 12(s),
Proposition 12(s): For a wide range of parametric configurations, all of which satisfy the re-strictions stated in Proposition 11, voting support, M(t), and budgetary deficit, D(t)−D∗, of an incumbent will be continuously increasing over time.
Table 3 contains the parameter values that have been used to simulate the time path of voting support and deficit paths, where fixed values have been assigned to some parameters, whereas other are changed to capture the comparative dynamics. The fixed parameters are the same as in the opportunistic case, namely,M0 = 30,D∗ = 5 andKM = 20. It is found that, for a high enough initial level of voting support, M0, the time path of voting support and budgetary deficit will be positive and increasing over time. The five simulations capture the change with respect to change in the following parameters: α,γ,δ,ǫ, andρ, respectively. Figure 5(a) captures this whenα changes fromα= 0.05 toα= 0.08,0.12,0.15, and 0.20, while the values of the other parameters are assumed to be fixed at γ = 0.03, δ = 1, ǫ= 0.90 and ρ = 0.02. In Figure 5(b), the value of γ is changing according to γ = 0.001,0.004,0.008,0.01,0.03, with fixed values of α = 0.05, δ = 1, ǫ= 0.90 and ρ= 0.02. Similarly, Figures 5(c) and 5(d) capture the time path of voting support and deficit path with the respective change in the parameters δ from δ = 0.80,0.85,0.90,0.95 and δ = 1 and ǫas ǫ= 0.85,0.88,0.92,0.96 andǫ= 0.99. Corresponding to the change inδandǫ, the fixed parametric values are α = 0.05, γ = 0.03, ǫ= 0.90 and ρ = 0.02 in the former and α = 0.05, γ = 0.03, δ = 1 and ρ = 0.02 in the latter case. Figure 5(e) captures the time path of voting support and deficit when the time preference parameterρis changing fromρ= 0.02,0.03,0.05,0.08 andρ= 0.10, while keeping the remaining parameters fixed asα= 0.05, γ = 0.03, δ= 1 andǫ= 0.90.
Table 3 summarizes these.
Table 3: Parametric Configurations in Case of Partisan Incumbent and No Anti-incumbency
Name of the Parameters Parameters Change in Parameters Values Fixed Parameters
Minimum Voting Support M0 - 30
Benchmark Deficit D∗ - 5
Constant part of Shadow Value KM - 20
Sensitivity of Deficit to Voting Support α 0.05, 0.08, 0.12, 0.15, 0.25 γ= 0.03,δ= 1.00,ǫ= 0.9,ρ= 0.02 Friction Parameter Gamma γ 0.001, 0.004, 0.008, 0.01, 0.03 α= 0.05,δ= 1.00,ǫ= 0.9,ρ= 0.02 Weight toD(t)−D∗versesM(t) δ 0.80, 0.85, 0.90, 1.00 α= 0.05,γ= 0.03,ǫ= 0.9,ρ= 0.02 Marginal Elasticity of Substitution ǫ 0.85, 0.88, 0.92, 0.96, 0.99 α= 0.05,γ= 0.03,δ= 1.00,ρ= 0.02 Discount Factor ρ 0.02, 0.03, 0.05, 0.08, 0.12 α= 0.05,γ= 0.03,δ= 1.00,ǫ= 0.9
29
(c) Voting Support and Deficit path whenδ changes (d) Voting Support and Deficit path whenǫchanges (e) Voting Support and Deficit path whenρchanges
Source: Authors’ Calculation
In case of all the five simulations, the positive and rising trend in M(t) andη(t) holds. However, unlike the opportunistic case, now the path of the budgetary deficit, η(t), lies below the path of voting support,M(t). This follows from the assumed value ofδ being different in this case, and is explained as follows.
Proposition 13: To garner an additional unit of voting supportM(t), the change in the deviation of budgetary deficit from the benchmark will be equal to δ.
From eq. (A13) in the appendix A, we have the equation D(t)−D∗ = 1
δM(t)−δ1−ǫǫ (αZm)−1ǫe−ρǫt+(α−δγ)δǫ (t−T) (25) The above equation can be re-expressed as M(t) = δ[D(t)−D∗] +δ1ǫ(αZm)−1ǫe−ρǫt+(α−δγ)δǫ (t−T). We find that the marginal change, ∂[D(t)−D∂M(t) ∗] =δ.
Since, in the opportunistic case, the value ofδis small (even close to zero), it implies that additional voting support garnered due to an incremental increase in the deviation of budgetary spending from the benchmark (D∗) is very small (or even close to zero). Contrary to this,δ is large (even close to 1) in case of a partisan incumbent, and hence the incumbent is able to derive a much larger voting support (even 1:1) with an additional unit increase of current deficit above the benchmark level, D∗. Thus, notably, the incumbent will have to manipulate the deficit much more to get an unit of additional voting support in the opportunistic case than in case of a partisan incumbent. Hence, the opportunist incumbent may end up running a huge deficit close enough to the election.
Finally, given our modeling structure, and the definition of incumbency, the case of anti-incumbency is not found consistent with the regularity condition for a partisan incumbent. Recall that, the regularity condition for the partisan incumbent is 1−ǫ < α−δγρδ (see eq. (16)). To characterize a partisan incumbent with anti-incumbency, we need to haveα < γ such thatα < δγ, ǫ < 1 (close to 1). This violates the regularity condition, 1−ǫ < α−δγρδ , since (1−ǫ) > 0 and
ρδ α−δγ <0.
5 Conclusion
In an optimal control method, under the assumption of an iso-elastic kind of the net utility function from voting support vis-a-vis budgetary deficit, the citizen voters provide support to an opportunist as well as a partisan incumbent, but reject the same when there is very strong anti-incumbency factor in the opportunistic case. Given a large enough initial level of voting support (that is plausible for an incumbent politician in office), the path of both voting support and deficit is found to be positive and rising in the case of absence of anti-incumbency. Moreover, to garner additional voting support, the opportunist incumbent has to incur an incrementally higher level of deficit as compared to the partisan incumbent. Thus, an opportunist incumbent is able to mobilize votes at the much higher cost of budgetary deficit to the economy, whereas voting support is positive and increasing even in partisan case but will entail lower cost in terms of budgetary deficit. However, the time path of both voting support and deficit will be falling when anti-incumbency exists.
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Appendix A
Proof of Proposition 1: The Hamiltonian function is,
H = [[M(t)−δ(D(t)−D∗)]1−ǫ
(1−ǫ) ]e−ρt+λM(t)[αD(t)−γM(t)] (A1)
∂H
∂D(t) = [M(t)−δ(D(t)−D∗)]−ǫe−ρt(−δ) +αλM(t) = 0
⇔δ[M(t)−δ(D(t)−D∗)]−ǫe−ρt=αλM(t) (A2)
λ˙M(t) = − ∂H
∂M(t) ⇔λ˙M(t) =−[M(t)−δ(D(t)−D∗)]1−ǫe−ρt+γλM(t)
⇔λ˙M(t)−γλM(t) =−[M(t)−δ(D(t)−D∗)]1−ǫe−ρt (A3)
and
M˙(t) =αD(t)−γM(t) (A4)
Substituting eq.(A2) in eq. (A3)
λ˙M(t) + (α
δ −γ)λM(t) = 0⇔λM(t) =KMe−(αδ−γ)t (A5) at t=T and assumingλM(T) =Zm>0
λM(T) =KMe−(αδ−γ)T ⇔KM =Zme−(αδ−γ)(t−T)
⇔λM(t) =Zme−(αδ−γ)(t−T) (A6)
The transversality condition is; λM(T) ≥ 0 ⇒ [M(T)−Mmin]λM(T) = 0. Since λM(T) = Zm > 0 ⇒
M(T) =Mmin. Substituting eq(A6) in eq(A2)gives, We find solution forM(t) and the values of constant of integration (CM) att= 0 gives,
M(t) = [M0+ αδD∗
substituting eq.(A12) in eq.(A7)
(i)The path of voting support and deficit att= 0 is as follows,
M(t) =M0 (A16)
D(t)−D∗=M0−δ1−ǫǫ (αZm)−1ǫe−(α−δγ)δǫ T (A17)
(ii)The path of voting support and deficit att=T is as follows,
M(T) = [M0+ αδD∗