The influence of direct democracy on the shadow economy

Abstract

We analyze, both theoretically and empirically, the influence of direct democratic institutions on the size and development of shadow economies. Our model suggests that, as the extent of direct democracy increases, implemented fiscal policies more nearly reflect the preferences of citizens and so reduce their incentives to operate in the informal sector. This theory implies a negative relationship between the extent of direct democracy and the size of the country’s shadow economy. We also theorize that direct democracy has a greater effect in reducing the informal sector when the former is at low or intermediate values and when the electoral system is characterized by a larger district magnitude. An empirical investigation of a sample of 57 democracies confirms our model’s predictions.

Appendix

Proof of Proposition 1

Corollary 1 establishes a negative relationship between the maximized net income of the representative agent and the size of the shadow economy. Under prevention (δ>δ ^∗), higher levels of δ do not change the reformed policy or the maximized net income of the agents; therefore, the size of the shadow economy becomes independent of δ and is related to the level of income under the status quo policy. That is, it’s size is $x(\hat{y}(t_{0},\gamma_{0}))$ for all δ>δ ^∗ because $\hat{y}(t_{0},\gamma_{0}) = \hat{y}(t_{P},\gamma_{P})$ (see Lemma 3). Under nonprevention (δ≤δ ^∗), the policy implemented is the status quo (t ₀,γ ₀) with probability P(δ) and the reformed policy (t _N ,γ _N )=(t _m ,γ _m ) with probability 1−P(δ). Therefore, the expected size of the shadow economy is ${E}x(t_{N},\gamma {}_{N},\delta ) = P(\delta )x(\hat{y}(t_{0},\gamma_{0})) + [1 - P(\delta )]x(\hat{y}(t_{m},\gamma_{m}))$. From $\hat{y}(t_{0},\gamma_{0}) > \hat{y}(t_{m},\gamma_{m})$ and Corollary 1 it follows that $x(\hat{y}(t_{0},\gamma_{0})) < x(\hat{y}(t_{m},\gamma_{m}))$. Since dP(δ)/dδ>0, the expected size of the shadow economy will be decreasing in δ; that is, dEx(t _N ,γ _N ,δ)/dδ<0. It is also immediate that Ex(t _N ,γ _N ,δ)>x(t _P ,γ _P ) irrespective of the value of δ. □

Proof of Proposition 2

The threshold δ ^∗ is implicitly defined (when it is interior) by ${E}V(t_{N},\gamma_{N},\phi ) | _{\delta = \delta^{*}} - V(t_{P},\gamma_{P}) = 0$, where the first term is given by (10) and the second term by (9). Applying the implicit function theorem to this expression yields

$$\frac{\partial \delta^*}{\partial m} = - \frac{\partial {E}V(t_{N},\gamma_{N},\phi ) / \partial \delta}{\partial {E}V(t_{N},\gamma_{N},\phi ) / \partial m}, $$

where ∂EV(t _N ,γ _N ,ϕ)/∂δ<0 by Lemma 4. Hence, from

$$\frac{\partial {E}V(t_{N},\gamma_{N},\phi )}{\partial m} = W\frac{\partial \phi}{\partial m} > 0 $$

it follows that ∂δ ^∗/∂m>0. The second part of the lemma is a consequence of higher levels of direct democracy having a greater effect under the nonprevention than under the prevention strategy—that is, when δ≤δ ^∗ (see Proposition 1). □