class: left, middle, inverse, title-slide # Evolution, Uncertainty, and the Asymptotic Efficiency of Policy ### <br>Brian C. Albrecht <span style="font-size: 50%;"> University of Minnesota</span><br><br> Joshua R. Hendrickson<span style="font-size: 50%;"> University of Mississippi</span><br><br> Alexander William Salter<span style="font-size: 50%;"> Texas Tech University</span><br><br> ### February 15, 2019<br><br> Paper <i class="fas fa-link "></i> <a href="http://bit.ly/bca-evolution">bit.ly/bca-evolution</a> <br><i class="fab fa-twitter "></i> <a href="https://twitter.com/briancalbrecht">briancalbrecht</a> --- Views of Politics ==================================== Government failure theory: - Political decision makers have power and can extract from citizens - Politics involves concentrated benefits and dispersed costs (Olson 1965) - Politics as social conflict (Acemoglu 2003) -- - Douglass North (1995): ###.center[Institutions are **not** necessarily or even] ###.center[usually created to be **socially efficient**] --- Can Democratic Politics Be Efficient? ==================================== ###Yes, if 1. Define away inefficiency - Cheung (1998): "The Pareto condition is always satisfied" -- 2. No transaction costs (Coase 1960) - Wittman (1989): "Democratic political markets are structured to reduce these costs" -- 3. Democracy **selects** for efficient policies - Today's presentation --- Our Evolutionary Middle-ground ==================================== - Alchian (1950): profit mechanism selects for firms who have made relatively better choices concerning profit-making - In markets, selection replaces explicit choice of firm managers `\(\Rightarrow\)` In the long-run, production is efficient -- - **Our paper**: develop model of politics as dynamic, evolutionary process - In politics, interest group formation replaces explicit choice of politicians `\(\Rightarrow\)` In the long-run, policy is efficient --- A Selection Mechanism ==================================== - At any point in time, interest groups may want to leave gains from trade on the table - Once possible gains are large enough: - Interest groups pay cost to form, - Enter politics, and - Overturn policies - Interest group entry is a democratic selection mechanism --- Preview of Results ==================================== - ### Proposition 1: - Policy inefficiencies are eliminated in the long run -- - ### Proposition 2: - The level of inefficiency is bounded in the short run -- - ### Proposition 3: - Policies remain in the dynamic problem that do not in the static --- Building On ==================================== - Interest group models of politics - Stigler (1971), Peltzman (1976), Posner (1974), Becker (1983), Tollison (1988) - Focus on dynamic **selection mechanisms** -- - Evolutionary perspective of institutions - Markets: Alchian (1950), Smith (2007), Todd and Gigerenzer (2012) - Common law: Rubin (1977), Priest (1977), Gennaioli and Shleifer (2007) - Focus on **legislative institutions** --- Road Map for Talk ==================================== 1. Simple Coasean Example a. Static Bargaining b. Dynamic Bargaining 2. Formal Real Option Model 3. Model Results a. Formal Propositions b. Broader Implications --- Static Political "Coase" Theorem ==================================== - Suppose competing interest groups bargain over policy - e.g. steel producers vs. steel consumers - Steel producers want to enact tariffs with benefit `\(B\)` to them - Consumers would incur a cost `\(C\)` - Without transaction costs, new policy is enacted if `\(B > C\)` --- Static Political "Coase" Theorem ==================================== - In a competitive model, tariffs are inefficient: `\(B < C\)` - Consumers can organize into their own interest group and block tariff - Consumers can offer to pay producers an amount `\(B + \epsilon < C\)` - Without transaction costs, the no tariff policy is efficient and enacted -- - Yet we see many tariffs: why? - As Coase taught us, there must be relevant transaction costs --- Adding Organizational Costs ==================================== - Cost of organizing an interest `\(~O_i\)` for `\(i \in \{P,C\}\)` - Producers want to organize and enact tariff if `\(B - O_P > 0\)` - If `\(B<C\)`, to prevent inefficient tariff, consumers must form and pay a bribe, costing them: `$$\underbrace{B - O_P + \epsilon}_{\textrm{Bribe/Transfer}} + \underbrace{O_C}_{\textrm{Organizational Cost}}$$` -- - If `\(B < C\)`, but `\(B + \epsilon + (O_C - O_P) > C\)`, then bribe will never materialize - Consumers are better off living with `\(C\)` than working to prevent - `\(O_C - O_P\)` creates friction that prevents efficient bargains (Olson 1965) --- Moving to Dynamics ==================================== - These examples can't speak to long-lasting vs. temporary policies - No distinction in Becker (1983), Wittman (1989), Peltzman (1990), etc - These examples are like a one time, eternal vote on policy - A policy passed last week is just as likely to be inefficient as long-lasting and widespread policies -- - We argue there is an important difference - Long-lasting policies have survived an (imperfectly) competitive selection mechanism --- Adding Uncertainty ==================================== - If steel productivity in foreign countries follows a random walk, then cost of tariff `\(C\)` will follow a random walk - Once `\(C\)` crosses some threshold, the consumer group will enter and **select the efficient** policy -- - The longer a policy survives, the less likely it is inefficient - Eventually all inefficient policies will cross the threshold --- class:center,middle #A Real Option Model --- Model ==================================== - Time is continuous, lasts forever - Current policy generates: - Flow benefits to current interest group: `\(B\)` - Flow cost to rest of society: `\(C\)` - Cost to organize an interest group: `\(O\)` --- class:middle - Entering politics to overturn current policy: `$$\textrm{Entry benefit} = \underbrace{E \int_t^{\infty} e^{-\rho t} C(t)dt}_{\textrm{Expected Cost Saving}} - \underbrace{\bigg(E \int_t^{\infty} e^{-\rho t} B(t)dt + \epsilon\bigg)}_\textrm{Expected Bribe} - \underbrace{O}_{\textrm{Entry Cost}}$$` - Alternatively, `$$\textrm{Entry benefit} = \underbrace{E \int_t^{\infty} e^{-\rho t}[C(t) - B(t)]dt - \epsilon}_{\textrm{Expected Net Cost Saving}} - \underbrace{O}_{\textrm{Entry Cost}}$$` --- Beyond Political "Coase" Theorem ==================================== - `\(N = C - B\)`: net social cost of the current policy - If `\(N\)` is positive, current policy is **inefficient** - Current policy fails standard cost/benefit - In a Coasean world with no transaction costs, the policy will be overturned -- - We have two frictions: 1. Organizational costs 2. Uncertainty about future cost of policy --- Policy Uncertainty ==================================== - Suppose net social cost of the policy varies randomly and exogenously - Outside control of any interest group - Geometric Brownian motion `$$\frac{dN(t)}{N(t)} = \mu dt + \sigma dz$$` - `\(\mu \geq 0\)`: expected rate of change in the net cost - `\(\sigma\)`: conditional standard deviation - `\(dz\)`: increment of a Wiener process - `\(dz = \epsilon \sqrt{dt}\)`, where `\(\epsilon\)` is drawn from a standard normal distribution --- Real Option to Enter ==================================== - The interest group always has the option to enter the political market and end the costly policy - Option to enter is like a financial option - Can derive the value of this option as a function of the net cost of existing legislation - Can determine the precise value for the net cost at which the prospective interest group will decide to enter the market --- name:option_value Option Value ==================================== - Let `\(V(N)\)` be the option value to enter the political market - Recursive Bellman representation: `$$V(N, t) = \frac{1}{1 + \rho \Delta t} E V(N', t + \Delta t)$$` - `\(\rho\)`: rate of time preference - `\(E\)`: expectations operator - `\(N'\)`: net cost of the policy after a time interval of length `\(\Delta t\)` - [In continuous time](#continuous_time) `$$\rho V(N) = \frac{1}{dt} E dV$$` --- name:diffeq_solution Solution ==================================== - `\(\rho V(N) = 1/dt E dV\)` has [known solution](#diffeq_solving) `$$V(N) = \alpha_1 N^{\beta^+} + \alpha_2 N^{\beta^-}$$` - Simplify using economic intuition - First, option becomes worthless when net cost goes to zero `$$\lim_{N \rightarrow 0} V(N) = 0$$` - Only holds if `\(\alpha_2=0\)` `$$V(N) = \alpha_1 N^{\beta^+}$$` --- class:middle - Second, let `\(N^*\)` be the net cost when the interest group enters - At `\(N^*\)` the interest group must be indifferent between holding and exercising option `$$V(N^*) = \alpha_1 (N^*)^{\beta^+} = \frac{N^*}{\rho - \mu} - O$$` - We assume that `\(\epsilon \approx 0\)` - Solving this expression for `\(\alpha_1\)` yields: `$$\alpha_1 = (N^*)^{-\beta^+} \bigg(\frac{N^*}{\rho - \mu} - O\bigg)$$` --- Full Solution ==================================== `$$V(N) = \underbrace{\bigg(\frac{N}{N^*}\bigg)^{\beta^+}}_{\textrm{Stochastic Discount Factor}} \times \underbrace{\bigg(\frac{N^*}{\rho - \mu} - O\bigg)}_{\textrm{Value at the Exercise Point}}$$` -- - High `\(N^*\)` raises yields greater benefit when option is exercised - Do not pay `\(O\)` on low `\(N\)` policies - However, high `\(N^*\)` means longer wait times on policies -- - The optimal `\(N^*\)` trades these off to maximize option value `$$N^* = \bigg(\frac{\beta}{\beta - 1}\bigg) (\rho - \mu) O$$` --- Stochastic Time ==================================== - `\(N^*\)` is proportional to organizational cost, `\(O\)` - If `\(N \geq N^*\)`, the interest group will enter the political market and bribe the existing interest group to overturn the inefficient policy - `\(N\)` is stochastic, the amount of time that an inefficient policy will last is also stochastic - Let `\(\tilde{T}\)` denote the time period when the interest group enters, `$$\tilde{T} = \inf \{t \geq 0 | N \geq N^* \}$$` --- Selection Mechanism ==================================== - Consider a particular policy `\(j\)` - Prospective interest groups will enter whenever `\(N_j \geq N^*_j\)` - Interest group entry is a **selection mechanism** that eliminates inefficient policies - Inefficient policies will tend to be eliminated faster as `\(N^*_j\)` declines, such as when `\(O\)` declines --- Asymptotic Efficiency ==================================== ### Proposition 1: The probability that any inefficient policy `\(j\)` survives goes to zero as time goes to infinity. -- Idea: - Equivalent to stating that the stopping time is finite, or `\(P(\tilde{T} < \infty) = 1\)`. - Known result for Brownian motion with a constant barrier - See Stokey (2009, Theorem 5.1) --- class: middle, center ##"Every durable social institution or practice is efficient, <br> or it would not persist over time." .right[George Stigler (1992)] --- Bounded Inefficiency ==================================== ### Proposition 2: For any parameters `\(\rho, \mu_j, \sigma_j\)` there is an upper bound on the level of inefficiency. -- Proof: If a policy is still in place at time `\(t\)`, this implies that the net cost to society `\(N_j(t)\)` is below `\(N_j^*\)`. `$$\frac{N_j(t)}{\rho - \mu_j} \leq %\frac{N_j^*}{\rho - \mu_j} = \bigg(\frac{\beta_j}{\beta_j - 1}\bigg) O_j.$$` -- - Corollary: The bound is increasing in the organizational costs, `\(O_j\)`. - Similar result to static example with `\(O_C - O_P\)` --- Dynamic vs. Static ==================================== ### Proposition 3: Policies remain in the dynamic problem that do not in the static problem. - Proof: In a static environment, interest groups have not entered if `$$E\int_0^{\infty} e^{-\rho t} [C_j(t) - B_j(t)] dt = E\int_0^{\infty} e^{-\rho t} N_j(t) dt = \frac{N_j}{\rho - \mu_j} \leq O_j$$` In the dynamic model, it is `$$\frac{N_j(t)}{\rho - \mu_j} \leq \frac{\beta_j}{\beta_j - 1}O_j$$` --- The Role of Uncertainty ==================================== - People prefer to wait and see if the net costs are moderate before paying the organizational costs - If costs remain moderate, people will be willing to tolerate them --- background-image: url(images/evolution/tikz_A.png) background-size: contain --- background-image: url(images/evolution/tikz_B.png) background-size: contain --- Model Implications ==================================== 1. Losers must be compensated 2. Durable legislation improves efficiency 3. Lowering political organizational costs improves efficiency --- Just Compensation (Cutsinger 2018) ==================================== - In 2010, the House of Representatives changed significantly - They eliminated a housing counseling assistance program - Program had given $88 million to non-profit organization - Justice Department's settlement authority restored half of funding - $30 million came from large banks based on their conduct in the mortgage backed securities market --- Durability of Legislation ==================================== - Settlement authority makes policy effectively **more durable**: even if overturned, must be paid value of rents - Durability raises `\(E\int_0^{\infty} e^{-\rho t} C_j(t) dt\)` and encourages entry - If legislation is likely to be overturned later legislatures, willingness to pay `\(O_j\)` drops -- - Similar result to principal-agent models of politicians: - Future benefits encourage efficient action today - `\(\Rightarrow\)` Institutions that enhance durability improve efficiency --- Independent Judiciary ==================================== - If durability has value, then legislatures will have an incentive to make it difficult to overturn legislation - Landes and Posner (1975): independent judiciary can favor original interpretations and need not be subservient to current legislatures - Anderson, Shughart, and Tollison (1989): legislatures reward judges who display independence with higher salaries - Implication: judicial independence could explain variation in interest group formation and the efficiency of policy --- Free Speech ==================================== - Our most direct implication: lower `\(O_j\)` improves efficiency - U.S. Supreme Court upheld freedom of speech for corporations, unions, and non-profits making explicit reference to interest groups - Justice Kennedy argued in favor of the **informational role** of interest groups, not just constitutional rights - Speech restrictions increase the organizational costs - If our theory is correct, the ruling is efficiency enhancing --- Re-framing Political Economy ==================================== Normative Implications: - Propositions 1 and 2 lead to a *pre*sumption of efficiency (Breton 1993) - However, policies are **not efficient by assumption** - Avoid "whatever is, is efficient" tautologies -- - Between government failure theory and "efficiency always" - Long last policies likely have a hidden efficiency justification - Hendrickson, Salter, and Albrecht (2018): capital taxation helps for national defense --- Implication for Political Economy ==================================== - Political economists who want to argue that a particular long-lasting policy is inefficient must 1. Reconsider the magnitude of the cost of the policy, or 2. Explain why the organizational costs are so high - Otherwise, political economists can go around claiming there are $10 trillion bills on the sidewalk --- Re-framing Political Economy ==================================== Positive Implications: - Role of political economist is to identify the relevant organizational costs - Retain efficiency as a tool for positive economics - Mirrors Steven Cheung's (1998) approach to study of markets: .center["whenever the Pareto condition fails to hold we would] .center[immediately know that some constraints are missing."] -- Downside - Only applies to long-lasting policies --- class: center, middle ###<i class="fas fa-link "></i> Paper: [bit.ly/bca-evolution](http://bit.ly/bca-evolution) <br> ###<i class="fas fa-link "></i> Slides: [bit.ly/bca-clemson](https://bit.ly/bca-clemson) <br> ###<i class="fab fa-twitter "></i> [@briancalbrecht](https://twitter.com/briancalbrecht) --- name:continuous_time Continuous Time ==================================== `$$V(N, t) = \frac{1}{1 + \rho \Delta t} E V(N', t + \Delta t)$$` - Multiplying both side of by `\(1 + \rho \Delta t\)` and re-arranging yields `$$\rho V(N) = \frac{1}{\Delta t} E dV$$` where `\(EdV := E V(N', t + \Delta t) - V(N, t)\)`. - Taking the limit as `\(\Delta t\)` goes to zero. `$$\rho V(N) = \frac{1}{dt} E dV$$` - [Return](#option_value) --- name:diffeq_solving Solving Differential Equation ==================================== Using Ito's Lemma option formula can be written as `$$\rho V(N) = \frac{1}{dt} E\bigg[ V'(N) dN + \frac{1}{2} V''(N) (dN)^2\bigg]$$` Substituting and simplifying yields: `$$\frac{1}{2} \sigma^2 N^2 V''(N) + \mu N V'(N) - \rho V(N) = 0$$` Second-order differential equation has a known solution of the form: `$$V(N) = \alpha_1 N^{\beta^+} + \alpha_2 N^{\beta^-}$$` --- Solving Differential Equation ==================================== `$$V(N) = \alpha_1 N^{\beta^+} + \alpha_2 N^{\beta^-}$$` where `\(\alpha_1\)` and `\(\alpha_2\)` are positive constants and `\(\beta^+\)` and `\(\beta^-\)` are the positive and negative solutions, respectively, to the quadratic equation: `$$\frac{1}{2} \beta^2 + \bigg(\mu - \frac{1}{2} \sigma^2\bigg) \beta - \rho = 0$$` - [Return](#diffeq_solution)