Ting (2009) - Organizational Capacity

• This page is referenced in BPP Field Exam Papers

Reference(s)

Ting, Michael (2009), "Organizational Capacity", forthcoming JLEO, available on his website pdf (Class Slides: Set1 Set2, © Adrienne Hosek)

Abstract

Organizational capacity is critical to the effective implementation of policy. Consequently, strategic legislators and bureaucrats must take capacity into account in designing programs. This paper develops a theory of endogenous organizational capacity. Capacity is modeled as an investment that effects a policy's subsequent quality or implementation level. The agency has an advantage in providing capacity investments, and may therefore constrain the legislature's policy choices. A key variable is whether investments can be targeted" toward speciffc policies. If it cannot, then implementation levels decrease with the divergence in the players' ideal points, and policy-making authority may be delegated to encourage investment. If investment can be targeted, then implementation levels increase with the divergence of ideal points if the agency is suffciently professionalized, and no delegation occurs. In this case, the agency captures more benefits from its investment, and capacity is higher. The agency therefore prefers policy-specific technology.

Summary

This is a principal-agent model where the agent can make an investment in either general capacity or capacity specific to a policy. The principal can choose policy and 'use' the capacity of the agent. The model is one of complete and perfect information, and has two stages. The solution concept is SPNE and the game is solved by backwards induction. In later section the choice of type of specialization is endogenized, as is whether the principal would rather delegate the choice of policy to the agent.

Key concepts:

• Fungible: Two investment are fungible if they can be mutually substituted. This leads to the notion of general capacity that can be used to support any policy.

The Model

There is a:

• Principal - [math]P\,[/math]
• An Agent - [math]A\,[/math]

The variables are:

• Policy set by the principal is [math]x_t \in X, for \lt math\gt t=\{1,2\}\,[/math].
• Agents have ideal points of [math]x^A\,[/math] and [math]x^P\,[/math].
• Agents can invest in capacity [math]c\,[/math], at a cost [math]k(c)\,[/math] which is continuous, increasing and convex
  • [math]c\,[/math] is assumed to be a vector, with [math]k(c)\,[/math] having weakly-negative cross-partials to allow for cost efficiencies, but this doesn't seem crucial to the model.
• The implementation level, or production function, or capacity 'realization' function, [math]z(c,\cdots)\,[/math] is weakly concave and increasing in [math]c\,[/math].
  • [math]z\,[/math] is assumed to be [math]z(x,y,c)\,[/math], though it is hard to see why this full generality matters.
  • [math]z(c)\,[/math] is assumed to have positive cross-partials to allow for complementary investments, though this doesn't seem crucial to the model.
• WLOG the model assumes that [math]x^P \lt x^A\,[/math]

The utility functions are:

[math]u_t^P = u^P(x_t,z; x^P)\,[/math]

[math]u_t^A = u^A(x_t,z; x^A) - k(c_t)\,[/math]

The utility functions are assumed to meet:

• [math]\frac{\partial u^i}{\partial z} \gt 0\,[/math] : Utility is increasing in the effect of capacity
• [math]\frac{\partial^2 u^i}{\partial z^2} \le 0\,[/math] : Utility is concave in the effect of capacity
• [math]\frac{\partial^2 u^i}{\partial z \partial x} \gt 0 \mbox { for } x \lt x^i\,[/math]: Utility is increasing in policy if policy is below the ideal point, holding capacity fixed
• [math]\frac{\partial^2 u^i}{\partial z \partial x} \lt 0 \mbox { for } x \gt x^i\,[/math]: Utility is decreasing in policy if policy is above the ideal point, holding capacity fixed
• [math]\frac{\partial^2 u^A}{\partial z \partial x} = p \pi(x)\,[/math]: where [math]p\,[/math] represents the politization of the agent
  • For low politization the agent is largely indifferent to the policy
  • For high politization the agent wants lower implementation ([math]z\,[/math]) if the policy is far from [math]x^A\,[/math]
• There are various assumptions on the utility and cost functions to avoid corner solutions
• There exists some [math]z\,[/math] such that [math]u^P(x^P,0) = u^P(x,z)\,[/math], that is the principal can be made indifferent to her ideal point by some capacity implementation.
• The total utility across both periods is additive with a discount factor: [math]u^i = u_1^i+\delta u_2^i\,[/math]

The sequence of the game is:

1. [math]A\,[/math] chooses [math]c_1\,[/math] and [math]y\,[/math] (period 1a)
2. [math]P\,[/math] chooses [math]x_1\,[/math] (period 1b)
3. [math]P\,[/math] chooses [math]x_2\,[/math] and [math]c_2 \in \{c | 0 \le c \le c_1\}\,[/math] (period 2)

An equilibrium is characterized by: [math]y^*, x_t^*, c_t^*, z_t^*\,[/math]

There are two tie-break rules (it isn't clear when they are used):

1. [math]P\,[/math] breaks ties in favour of lower levels of investment
2. [math]A\,[/math] breaks ties by choosing the [math]x\,[/math] closest to [math]x_A\,[/math]

There are two basic versions of the game: Generalized (GC) and Specific Capacity (SC), then several variables are endogenized.

Generalized Capacity (GC)

This version of the model assumes that [math]z(c)\,[/math] alone - that is [math]z(\cdot)\,[/math] is independent of [math]x_t\,[/math] and [math]y\,[/math]. Thus the agent invests in generalized capacity that is not targeted at any specific purpose and the principal can use it in any fashion.

In both the GC and SC games:

[math]c^o(x;x^A) = \mbox{arg} \max_c u^A(x, z(x,y,c); x^A) - k(c)\,[/math]

In the GC game the unique SPNE is:

• [math]x_1^*=x_2^*=x^P\,[/math]
• [math]c_1=c_2=c^0(x^p)\,[/math]
• [math]c_1^*\,[/math] and [math]z_1^*\,[/math] are strictly decreasing in [math]x^A\,[/math]

In the second period, the principal can choose any policy and so chooses [math]x^P\,[/math] to maximise her utility. Further, utility is increasing in [math]z\,[/math] and [math]z\,[/math] is increasing in [math]c\,[/math], so [math]P\,[/math] also wants to maximize [math]c_2\,[/math] and does this by setting it to [math]c_1\,[/math].

In the first period, [math]P\,[/math]'s best response to any [math]c\,[/math] is [math]x^P\,[/math]. [math]A\,[/math] then maximizes utility by choosing [math]c_1\,[/math] subject to this. However, as [math]z\,[/math] is independent of [math]x\,[/math] (and [math]y\,[/math]), and as [math]A\,[/math]'s utility is concave in [math]c\,[/math], but costs are convex, [math]A\,[/math] chooses the interior maximum irrespective of [math]P\,[/math]'s choice to maximize [math]z\,[/math] and hence [math]u\,[/math] (subject to the constraint that [math]x=x^p\,[/math]). Any [math]y\,[/math] can be choosen as it will have no effect.

Specialized Capacity (SC)

In this version of the model we assume that:

[math] z(x_t,y,c_t) = \begin{cases} z(c_t) & \mbox{ if } x_t = y \\ 0 & \mbox { otherwise} \end{cases} \,[/math]

That is if the principal enacts policy [math]x_2 = y\,[/math], then the production function kicks in and the benefits to specialization are realized. Otherwise, there are no benefits to the agent's investment in capacity.

Solving backwards we note that [math]P\,[/math] can implement one of two policies:

• if [math]x_2 \ne y\,[/math], then [math]x_2 = x^P\,[/math] is optimal, and [math]c_2=0\,[/math] results
• otherwise [math]y\,[/math] is optimal and [math]c_2 = c_1\,[/math] is optimal

Supposing that [math]x_2 = x^P\,[/math] is choosen, then [math]c_2 = 0\,[/math] and [math]z=0\,[/math] as [math]z(x_2,y,0)=0\,[/math]. Otherwise if [math]x_2 = y\,[/math] then [math]P\,[/math] wants the full benefit of specialization and implements [math]c_2=c_1\,[/math] as this maximises her utility.

The choice as to whether [math]x_2=y\,[/math] is therefore:

[math]u^P(x^P,0) \le u^P(y,z(c_1))\,[/math]