Protection for sale: evidence from around the world

Abstract

The “protection-for-sale” motive introduced by Grossman and Helpman (Am Econ Rev 84: 833–850, 1994) has been adopted widely in the literature, but only a few papers test the theory empirically. To provide empirical evidence for the protection-for-sale theory, we proceed in three steps. First, we argue that among all existing theories, only the mechanism in the protection-for-sale theory depends on the government’s political strength. Second, we develop a theoretical model to rationalize the connection between political strength and import tariffs. Our extended protection-for-sale model predicts that a government with greater political power generally imposes higher tariffs. Third, we propose that political strength can be proxied by the share of legislative seats held by the governing party or coalition. We test the model prediction using panel data covering 95 product categories and 105 countries, from 1996 to 2014. Our estimates provide support the protection-for-sale theory. The estimated effects of political strength on tariffs are larger in small and democratic countries.

Appendices

Appendix A: Proofs

1.1 Proof of Proposition 1

Proposition 1

Equilibrium tariffs are increasing in political strength.

Proof

To simplify the notation, we define $\Omega \left({\uptau }_{\mathrm{i}}\right)={\Pi }_{\mathrm{i}}\left({\uptau }_{-\mathrm{i}},{\uptau }_{\mathrm{i}}\right)+\mathrm{aW}\left({\uptau }_{-\mathrm{i}},{\uptau }_{\mathrm{i}}\right)$.

Equation (4) is simplified to

$$\frac{{\partial \left( {\rho \left( {\theta ,\tau_{i} } \right)} \right)}}{{\partial \tau_{i} }}\Omega \left( {\tau_{i} } \right) + \rho \left( {\theta ,\tau_{i} } \right)\frac{{\partial \Omega \left( {\tau_{i} } \right)}}{{\partial \tau_{i} }} = 0,$$

(10)

which gives

$$\frac{{\partial \Omega \left( {\tau_{i} } \right)}}{{\partial \tau_{i} }} = - \underbrace {{\frac{{\partial \left( {\rho \left( {\theta ,\tau_{i} } \right)} \right)}}{{\partial \tau_{i} }}}}_{ - }\underbrace {{\frac{{\Omega \left( {\tau_{i} } \right)}}{{\rho \left( {\theta ,\tau_{i} } \right)}}}}_{ + } > 0,$$

(11)

From the implicit function theorem, Eq. (10) leads to

$$\underbrace {{\frac{\partial }{\partial \theta }\left[ {\frac{{\partial \left( {\rho \left( {\theta ,\tau_{i} } \right)} \right)}}{{\partial \tau_{i} }}\Omega \left( {\tau_{i} } \right) + \rho \left( {\theta ,\tau_{i} } \right)\frac{{\partial \Omega \left( {\tau_{i} } \right)}}{{\partial \tau_{i} }}} \right]}}_{*} + \underbrace {{\frac{\partial }{{\partial \tau_{i} }}\left[ {\frac{{\partial \left( {\rho \left( {\theta ,\tau_{i} } \right)} \right)}}{{\partial \tau_{i} }}\Omega \left( {\tau_{i} } \right) + \rho \left( {\theta ,\tau_{i} } \right)\frac{{\partial \Omega \left( {\tau_{i} } \right)}}{{\partial \tau_{i} }}} \right]\frac{{{\text{d}}\tau_{i} }}{{{\text{d}}\theta }}}}_{**} = 0.$$

(12)

The first term, denoted by (*), can be reduced as follows:

$$\frac{\partial }{\partial \theta }\left[ {\frac{{\partial \left( {\rho \left( {\theta ,\tau_{i} } \right)} \right)}}{{\partial \tau_{i} }}\Omega \left( {\tau_{i} } \right) + \rho \left( {\theta ,\tau_{i} } \right)\frac{{\partial \Omega \left( {\tau_{i} } \right)}}{{\partial \tau_{i} }}} \right] = \underbrace {{\frac{{\partial^{2} \left( {\rho \left( {\theta ,\tau_{i} } \right)} \right)}}{{\partial \tau_{i} \partial \theta }}}}_{ + }\underbrace {{\Omega \left( {\tau_{i} } \right)}}_{ + } + \underbrace {{\frac{{\partial \rho \left( {\theta ,\tau_{i} } \right)}}{\partial \theta }}}_{ + }\underbrace {{\frac{{\partial \Omega \left( {\tau_{i} } \right)}}{{\partial \tau_{i} }}}}_{ + } > 0,$$

where the last line is from Eq. (11). Thus, we can conclude that the derivative in the first term denoted by (*) must be positive.

In addition, because $\rho \left(\theta ,{\tau }_{i}\right)\Omega \left({\tau }_{i}\right)$ is strictly concave in ${\tau }_{i}$, its second derivative, $\frac{{\partial }^{2}}{\partial {\tau }_{i}^{2}}\left(\rho \left(\theta ,{\tau }_{i}\right)\Omega \left({\tau }_{i}\right)\right)=\frac{\partial }{\partial {\tau }_{i}}\left[\frac{\partial \left(\rho \left(\theta ,{\tau }_{i}\right)\right)}{\partial {\tau }_{i}}\Omega \left({\tau }_{i}\right)+\rho \left(\theta ,{\tau }_{i}\right)\frac{\partial \Omega \left({\tau }_{i}\right)}{\partial {\tau }_{i}}\right]$, must be negative. Thus, the second term, denoted by (**), is negative.

Therefore, Eq. (12) concludes that

$$\frac{{{\text{d}}\tau_{i} }}{{{\text{d}}\theta }} = - \frac{{\underbrace {{\frac{\partial }{\partial \theta }\left[ {\frac{{\partial \left( {\rho \left( {\theta ,\tau_{i} } \right)} \right)}}{{\partial \tau_{i} }}\Omega \left( {\tau_{i} } \right) + \rho \left( {\theta ,\tau_{i} } \right)\frac{{\partial \Omega \left( {\tau_{i} } \right)}}{{\partial \tau_{i} }}} \right]}}_{ + }}}{{\underbrace {{\frac{\partial }{{\partial \tau_{i} }}\left[ {\frac{{\partial \left( {\rho \left( {\theta ,\tau_{i} } \right)} \right)}}{{\partial \tau_{i} }}\Omega \left( {\tau_{i} } \right) + \rho \left( {\theta ,\tau_{i} } \right)\frac{{\partial \Omega \left( {\tau_{i} } \right)}}{{\partial \tau_{i} }}} \right]}}_{ - }}} > 0.$$

$\square$

1.2 Proof of Corollary 1

Corollary 1

Political contributions are increasing in political strength.

Proof

To simplify the notation, we define $\Omega \left({\uptau }_{\mathrm{i}}\right)={\Pi }_{\mathrm{i}}\left({{\varvec{\uptau}}}_{-\mathrm{i}},{\uptau }_{\mathrm{i}}\right)+\mathrm{aW}\left({{\varvec{\uptau}}}_{-\mathrm{i}},{\uptau }_{\mathrm{i}}\right)$.

According to the Nash bargaining problem, political contribution in sector ${\text{i}}$ is equal to

$$\begin{aligned} c_{i} = & \left( {1 - \sigma } \right)\rho \left( {\theta ,\tau_{i} } \right)\left( {\Pi_{i} \left( {{\varvec{\tau}}_{ - i} ,\tau_{i} } \right) - \Pi_{i} \left( {{\varvec{\tau}}_{ - i} ,0} \right)} \right) + \sigma \rho \left( {\theta ,\tau_{i} } \right)\left( {aW\left( {{\varvec{\tau}}_{ - i} ,0} \right) - aW\left( {{\varvec{\tau}}_{ - i} ,\tau_{i} } \right)} \right) \\ = & \left( {1 - \sigma } \right)\rho \left( {\theta ,\tau_{i} } \right)\left( {\Omega \left( {\tau_{i} } \right) - \Omega \left( 0 \right)} \right) + \left( {aW\left( {{\varvec{\tau}}_{ - i} ,0} \right) - aW\left( {{\varvec{\tau}}_{ - i} ,\tau_{i} } \right)} \right). \\ \end{aligned}$$

The derivative of ${\mathrm{c}}_{\mathrm{i}}$ with respect to political strength $\uptheta$ is

$$\begin{aligned} \frac{{{\text{d}}c_{i} }}{{{\text{d}}\theta }} = & \frac{{\partial c_{i} }}{\partial \theta } + \frac{{\partial c_{i} }}{{\partial \tau_{i} }}\frac{{{\text{d}}\tau_{i} }}{{{\text{d}}\theta }} \\ = & \left( {1 - \sigma } \right)\frac{{\partial \rho \left( {\theta ,\tau_{i} } \right)}}{\partial \theta }\left( {\Omega \left( {\tau_{i} } \right) - \Omega \left( 0 \right)} \right) \\ & + \left[ {\left( {1 - \sigma } \right)\frac{{\partial \rho \left( {\theta ,\tau_{i} } \right)}}{{\partial \tau_{i} }}\left( {\Omega \left( {\tau_{i} } \right) - \Omega \left( 0 \right)} \right) + \left( {1 - \sigma } \right)\rho \left( {\theta ,\tau_{i} } \right)\frac{{\partial \Omega \left( {\tau_{i} } \right)}}{{\partial \tau_{i} }} - a\frac{{\partial W\left( {{\varvec{\tau}}_{ - i} ,\tau_{i} } \right)}}{{\partial \tau_{i} }}} \right]\frac{{{\text{d}}\tau_{i} }}{{{\text{d}}\theta }} \\ = & \underbrace {{\left( {1 - \sigma } \right)\underbrace {{\frac{{\partial \rho \left( {\theta ,\tau_{i} } \right)}}{\partial \theta }}}_{ + }\underbrace {{\left( {\Omega \left( {\tau_{i} } \right) - \Omega \left( 0 \right)} \right)}}_{ + }}}_{ + } + \left[ { - \underbrace {{\underbrace {{\frac{{\partial \rho \left( {\theta ,\tau_{i} } \right)}}{{\partial \tau_{i} }}}}_{ - } \underbrace {{\left( {1 - \sigma } \right)\left( {\Omega \left( 0 \right)} \right)}}_{ + }}}_{ + }\underbrace {{ - a\underbrace {{\frac{{\partial W\left( {{\varvec{\tau}}_{ - i} ,\tau_{i} } \right)}}{{\partial \tau_{i} }}}}_{ - }}}_{ + }} \right]\underbrace {{\frac{{{\text{d}}\tau_{i} }}{{{\text{d}}\theta }}}}_{ + } \\ & > 0, \\ \end{aligned}$$

where the last simplification uses the condition in Eq. (11). Therefore, political contributions are increasing in political strength.$\square$

Appendix B: empirical analysis

2.1 List of countries

Albania, Algeria, Angola, Argentina, Australia, Austria, Bahrain, Bangladesh, Belarus, Belgium, Bolivia, Botswana, Brazil, Brunei, Burundi, C. Verde Is., Cambodia, Cameroon, Canada, Cent. Af. Rep. Chad, Chile, Colombia, Congo, Costa Rica, Cote d’Ivoire, Cyprus, Czech Rep., Denmark, Djibouti Dom. Rep., Ecuador, Egypt, El Salvador Eq., Guinea, Estonia, FRG/Germany, Finland, France, Gabon, Greece, Guatemala, Guinea, Guinea-Bissau, Honduras, Hungary, India, Indonesia, Ireland, Israel, Italy, Japan, Jordan, Kenya, Kuwait, Latvia, Lebanon, Lesotho, Lithuania, Luxembourg, Madagascar, Malawi, Malaysia, Maldives, Mali, Malta, Mauritius, Mongolia, Morocco, Mozambique, Myanmar, Namibia, Nepal, Netherlands, New Zealand, Nicaragua, Niger, Nigeria, Norway, Oman, Pakistan, Panama, Paraguay, Peru, Philippines, Poland, Portugal, Qatar, Romania, Russia, S. Africa, Saudi Arabia, Senegal, Sierra, Leone, Slovakia, Slovenia, Spain, Sri Lanka, St. Lucia, Swaziland, Sweden, Switzerland, Togo, Turkey, UAE, UK, Uganda, Uruguay, Venezuela, Vietnam, Zambia, Zimbabwe.

See Tables 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.