In many democratic countries, the timing of elections is flexible. We explore this potentially valuable option using insights from option pricing in finance.
The paper offers three main contributions on this problem. First, we derive a rationally-based mean-reverting political support process for the parties, assuming that politically heterogeneous voters continuously learn over time about evolving party fortunes. We solve for the long-run density for this process and derive the polling process from it by adding polling noise.
Second, we explore optimal timing using the political support process. The incumbent sees its poll support, and must call an election within five years of the last election to maximize its expected total time in office. This resembles the optimal exercise rule for an American financial option. This option is recursive, and the waiting and stopping values subtly interact. We prove the existence of the optimal exercise rule in this setting, and show that the expected longevity is a convex-then concave function of the political support. Our model is tractable enough that we can analytically derive how the exercise rule responds to parametric shifts.
We calibrate our model to the Labour-Tory rivalry in the U.K., with polling data from 1943-2005 and the 16 elections after 1945. Excluding three elections essentially forced by weak governments, our maximizing story quite well explains when the elections were called, and beats simple linear regressions. We also measure the value of election options, finding that over the long run they should more than double the expected time in power of a fixed term electoral cycle.
JEL Classification No.: D83, D72, G1
Keywords: American option, European option, Brownian motion, Electoral timing
This paper produces a comprehensive theory of the value of Bayesian information and its static demand. Our key insight is to assume ‘natural units’ corresponding to the sample size of conditionally i.i.d. signals – focusing on the smooth nearby model of the precision of an observation of a Brownian motion with uncertain drift. In a two state world, this produces the heat equation from physics, and leads to a tractable theory. We derive explicit formulas that harmonize the known small and large sample properties of information, and reveal some fundamental properties of demand: (a) Value ‘non-concavity’: The marginal value of information is initially zero; (b) The marginal value is convex/rising, concave/peaking, then convex/falling; (c) ‘Lumpiness’: As prices rise, demand suddenly chokes off (drops to 0); (d) The minimum information costs on average exceed 2.5% of the payoff stakes; (e) Information demand is hill-shaped in beliefs, highest when most uncertain; (f) Information demand is initially elastic at interior beliefs; (g) Demand elasticity is globally falling in price, and approaches 0 as prices vanish; and (h) The marginal value vanishes exponentially fast in price, yielding log demand. Our results are exact for the Brownian case, and approximately true for weak discrete informative signals. We prove this with a new Bayesian approximation result.
Keywords: Value of information, Non-concavity, Heat equation, Demand, Bayesian analysis