Heterogeneity and Colonial Governance

Some existing studies argue that indirect colonial rule adversely affects postcolonial development. To analyze the situation under which a colonial power adopts indirect rule to govern a colony, we analyze a delegation model wherein the colonial power decides whether to delegate policy choice to an agent who has an information advantage but has different policy preferences from that of the colonial power. The colonial power decides whether to delegate policy choice in multiple districts, and can acquire information by paying a cost in each district. We show that colonial powers are prone to adopt indirect rule when the heterogeneity among districts is high. The results are a possible explanation for why colonial powers utilized indirect rule in Africa, a region with high levels of ethnic diversity.


Introduction
Developing countries experienced divergent economic development paths during the last half of the twentieth century: while some Asian countries experienced rapid growth, the economies in most Sub-Saharan African countries stagnated.Recent research has revealed that colonial experience is a critical factor in such divergent development experiences.In particular, direct and indirect colonial rules have entirely different effects on postcolonial development.While direct rule, under which colonial powers build centralized governing structures to dominate entire region of colonies, favors postcolonial development by leaving effective state capacity, indirect colonial rule, under which autonomous governing power is delegated to indigenous rural elites, harms state building and growth after independence [1]- [4].This raises a natural question: what is the source of such divergent forms of colonial governance? 1ub-Saharan Africa has two notable features.The first feature is that most African colonies were ruled through indirect rule [6].The second feature is its high level of ethnic diversity [7].Thus, countries in Sub-Saharan Africa comprise heterogeneous ethnic groups with varying norms, cultures, and rules to solve disputes.This paper provides a simple theoretical logic that links a colony's heterogeneity and the form of governance by colonial powers.We incorporate two features into a standard delegation model in which a principal decides whether to delegate policy choice to an agent who has information advantage but has different policy preferences from that of the principal (See [8] for a review of the delegation models of this type.Bendor and Meirowitz [9] provide both general treatment and many extensions of this type of delegation models.).First, a principal (a colonial power) decides whether to delegate policy choice in multiple districts.Second, the principal can acquire information on the realized value of unobservable policy shock in each district.Homogeneity of a colony is modeled by correlation among policy shocks in the districts.When the degree of heterogeneity is large, the information acquired in a district is less useful to govern another district.In this situation, if the uncertainty about policy outcomes is considerably large, directly governing the colony is costly for the colonial power, and thus indirect rule is adopted.

The Model
Consider a colony with two districts: districts 1 and 2. Indigenous agents implement policies in each district.We call the indigenous agent in district i agent i , where . In direct rule, a colonial power chooses policies to be implemented in each district and instructs each indigenous agent to implement the policies.In indirect rule, the colonial power delegates policy choice in district i to agent i .
In district i , policy outcome i x ∈  depends on the policy choice i p ∈  and a random shock i  .2We assume that i i i x p = +  .In this environment, observation of the realized value of i  enables the policy maker to achieve his/her ideal point.The possible realized value of i . Furthermore, the two random variables correlate with each other.We assume that . The parameter q represents the degree of homogeneity between the two districts.As q becomes larger, the two districts are more likely to have similar policy environments, and are more homogeneous with each other.Hence, a small value of q means that the two districts are heterogeneous.Indigenous agent i can observe the realization of i  .The colonial power can observe the realization of i  by paying the cost of information acquisition 0 c > .The payoff that the colonial power obtains in district i is ci i i u x I c = − − , where i I equals one if the co- lonial power acquires information in district i and equals zero otherwise.The total payoff of the colonial power is 1 2 c c u u + .The payoff of the indigenous agent i is ( ) . We assume that 0 A x > .Decision making in district 1 precedes that in district 2. The timing of events in each district is as follows: 1) The colonial power decides whether to delegate policy choice to agent i .
2) The value of i  is realized.3) If no delegation occurs, then the colonial power decides whether to acquire the information on the realized value of i  .4) Either the colonial power or agent i chooses policy i p .We derive the subgame perfect equilibrium of this game.In the following, we assume that the cost of information acquisition is sufficiently large.Under this assumption, the colonial power never chooses to acquire information in district 2. Assumption

Policy Choice in District 2
First consider the case where the colonial power delegates the policy choice to indigenous agent 2. Because the indigenous agent can observe the realized value of 2  , agent 2 can realize his/her ideal point A x by choosing 2 2 A p x = −  .In this case, the colonial power obtains Next, consider the case where the colonial power does not delegate the policy choice and acquires information on the realized value of 2  .In this case, the colonial power can realize its ideal point 0 by choosing 2 2 p = − ; however, it incurs the cost of information acquisition c − .Thus, the payoff that the colonial power obtains in district 2 is c − .When the colonial power neither delegates the policy choice nor acquires information, its payoff in district 2 depends on whether the colonial power has acquired information on 1  in district 1.If the colonial power does not have information on the realized value of 1  , then any policy in [ ] , −  is optimal, and the colonial power obtains − from district 2.
In the case where the colonial power knows that 1 =   , ( ) . Thus, the colonial power's payoff from 2 p can be written as 3 Hence, the colonial power chooses 2 p = − and obtains Similarly, the colonial power who obtains information that 1 = −   chooses 2 p =  and obtains ( )

Delegation Choice in District 2
From the results in the previous section, in the case where the colonial power does not know the realized value of 1  , the colonial power delegates the policy choice if and only if A x − > − . 4In the case where the colonial power knows the realized value of 1  , the colonial power delegates the policy choice if and only if ( )

Policy Choice in District 1
The policy choice in district 1 is similar to that in district 2. If the colonial power delegates the policy choice, then it obtains A x − .If the colonial power directly chooses a policy without acquiring information on 1  , then it obtains − .If the colonial power directly chooses a policy with information, then it obtains c − .

Equilibrium
To derive the equilibrium, we first show the following preliminary results.Lemma 1 If the colonial power delegates policy choice in district 1, then it delegates policy choice in district 2.
Proof.See Appendix.Lemma 2 If the colonial power directly chooses a policy without acquiring information in district 1, then it does so in district 2.
Proof.See Appendix.Lemma 3 If the colonial power acquires information in district 1, it directly chooses a policy without acquiring information in district 2.
Proof.See Appendix.
From the above results, depending on the values of parameters, three equilibrium-governance patterns are possible: 1) The colonial power delegates the policy choice in both districts.
2) The colonial power directly chooses policies without acquiring information in both districts.
3) The colonial power acquires information in district 1 and directly chooses policies in both districts.Case 1 can be interpreted as indirect rule, and cases 2 and 3 are direct rules.The colonial power chooses a governance strategy that provides the maximum payoff.The colonial power obtains 2 A x − in case 1, 2 −  in case 2, and ( ) Thus, the colonial power chooses indirect rule if and only if which can be rewritten as 3 Since choosing 2 p >  and choosing 2 p < − are suboptimal for the colonial power, the equilibrium policy satisfies [ ] ( ) The degree of homogeneity q affects the form of governance when the degree of policy uncertainty is suf- ficiently high: ( ) . Thus, we can derive the following proposition.Proposition 1 Assume that the degree of policy uncertainty  is greater than ( ) 2 1 c q+ .Then, the colonial power is prone to choose indirect rule in the following situations: • The cost of information acquisition c is large.
• The policy preferences of indigenous agents are close to that of the colonial power ( A x is small).• The policy uncertainty  is large.
• The degree of homogeneity between districts q is small.
When the degree of heterogeneity is larger (i.e., q is smaller), information acquired in district 1 is less useful to govern district 2. In this situation, if the uncertainty about policy outcomes  is large, then directly governing the colony is costly for the colonial power, and indirect rule is adopted.

Conclusion
To analyze the situation under which the colonial power adopts indirect rule to govern a colony, we analyze a delegation model wherein the colonial power decides whether to delegate policy choice to an agent who has an information advantage but has different policy preferences from that of the colonial power.The colonial power decides whether to delegate policy choice in multiple districts, and can acquire information by paying a cost in each district.We show that colonial powers are prone to adopt indirect rule when the heterogeneity among districts is high.The results are a possible explanation for why colonial powers utilized indirect rule in Africa, a region with high level of ethnic diversity.