Size versus scope: on the trade-off facing economic unions

Abstract

This paper analyzes the relationship between the size of an economic union and the degree of policy centralization. We consider a political economy setting in which elected representatives bargain over the degree of centralization within the union. In our model, strategic delegation affects the identity of the representatives, and hence the equilibrium policy outcome. We show that the relationship between the extensive and the intensive margin of centralization may be non-monotonic: Up to a certain threshold a larger size implies deeper integration, whereas beyond that threshold centralization declines with further increases in size. We also show that freezing the level of centralization and associate memberships can mitigate this trade-off.

Appendices

Appendix A

This appendix derives the marginal effects of $\alpha_{i}^{\mathrm{rep}}$ on $Z_{i}^{e}$ and $\tilde{\beta}^{e}$ holding all $\alpha_{j}^{\mathrm{rep}}$ ($j \not=i$) constant. As we depart from the symmetric equilibrium, we can summarize all countries $j \not= i$ by a representative country −i.

With $s_{i}=s (\alpha^{\mathrm{rep}}_{i},\beta)$ and $s_{-i}=s (\alpha^{\mathrm{rep}}_{-i},\beta)$, the first-order conditions for Z _i and Z _−i can be written as

From these two equations, we can eliminate λ:

$$ \bigl(1+\gamma Z_i^e \bigr)\cdot\biggl( \int _{\tilde{\beta}^e}^1 s_i\,d\beta+ Z_{i}^e \biggr) = \bigl(1+\gamma Z_{-i}^e \bigr)\cdot\biggl(\int_{\tilde{\beta}^e}^1 s_{-i}\,d \beta+ Z_{-i}^e \biggr). $$

(14)

Defining $\tilde{s}^{e}_{i}=s (\alpha^{\mathrm{rep}}_{i},\tilde{\beta}^{e} )$ and $\tilde{s}^{e}_{-i}=s (\alpha^{\mathrm{rep}}_{-i},\tilde{\beta}^{e} )$, we can write the first-order condition for $\tilde{\beta}^{e}$ as

This yields:

$$ -\tilde{s}_i^e\cdot\biggl( \int_{\tilde{\beta}^e}^1 s_{-i} \,d\beta+ Z_{-i}^e \biggr)= (n-1 ) \tilde{s}_{-i}^e\cdot\biggl(\int_{\tilde{\beta}^e}^1 s_i\,d\beta+ Z_{i}^e \biggr). $$

(15)

Combining (14) with (15) leads to:

$$ \bigl(1+\gamma Z_i^e \bigr)\cdot\tilde{s}_i^e + (n-1 ) \cdot\bigl( 1+\gamma Z_{-i}^e \bigr)\cdot\tilde{s}_{-i}^e=0 . $$

(16)

In addition, the budget constraint has to be satisfied:

$$ Z_i^e+ (n-1 )Z_{-i}^e = - \frac{\gamma}{2} \bigl(Z_i^e \bigr)^2- \frac{\gamma(n-1 )}{2} \bigl(Z_{-i}^e \bigr)^2. $$

(17)

Equations (14), (16), and (17) determine the three unknowns, $Z_{i}^{e}$, $Z_{-i}^{e}$, and $\tilde{\beta}^{e}$. Totally differentiating these three equations, setting $d\alpha_{-i}^{\mathrm{rep}}=0$, and employing the symmetry properties $Z_{i}^{e}=Z_{-i}^{e}=0$, $\alpha _{i}^{\mathrm{rep}}=\alpha_{-i}^{\mathrm{rep}}$, and $\tilde{s}_{i}^{e}=\tilde{s}_{-i}^{e}$ yields

(18)

(19)

(20)

From (19)–(20), we can derive

(21)

(22)

Appendix B

This appendix determines the centralization surplus for a setting in which elected policymakers also decide on the public good levels. In this case, the supplied public good levels in the third stage of the model depend on the identity of the representatives according to $g_{i}^{d}=\alpha _{i}^{\mathrm{rep}}$ and $g_{i}^{c}=\alpha_{i}^{\mathrm{rep}}+\sum_{j\not=i} \alpha_{j}^{\mathrm{rep}} \beta$. The centralization surplus of a citizen in country i with preference α is given by

(23)

Taking the derivative of (23) at $\bar{\alpha}= \alpha^{\mathrm{rep}}$ implies

$$ \frac{\partial s_i(\alpha,\alpha^{\mathrm{rep}},\beta)}{\partial\alpha_i^{\mathrm{rep}}} \bigg|_{\bar{\alpha}=\alpha^{\mathrm{rep}}}= \frac{ (n-1)\beta(\beta-1)}{1+(n-1)\beta} < 0. $$

(24)

An increase in the preference of the domestic representative for public spending therefore lowers the surplus from the view of the voters.

In the first stage of the model, the median voter in country i maximizes

The first-order condition is given by

$$ \frac{\partial Z_i^e}{\partial\alpha_i^{\mathrm{rep}}} - s_i(\cdot)\frac {\partial\tilde{\beta}^e}{\partial\alpha_i^{\mathrm{rep}}} + \frac{\bar{\alpha}}{\alpha_i^{\mathrm{rep}}} -1 + \int_{\tilde{\beta}^e}^1 \frac{\partial s_i}{\partial\alpha_i^{\mathrm{rep}}}\,d\beta= 0. $$

(25)

As in the baseline model (Eq. (11)), the sum of the first two terms of (25) is negative (as $\partial Z_{i}^{e}/\partial\alpha_{i}^{\mathrm{rep}}<0$ and s _i (⋅)=0) for $\alpha ^{\mathrm{rep}}=\bar{\alpha}$. According to (24), the last term of (25) is also negative. Therefore, we can conclude that the first order condition implies $\alpha_{i}^{\mathrm{rep}}<\bar{\alpha}$ similar to our baseline model.