This month’s *Quarterly Journal of Economics* features an article by Snowberg, Wolfers, and Zitzewitz:

Analyzing high frequency financial fluctuations on November 2 and 3 in 2004, we find that markets anticipated higher equity prices, interest rates and oil prices and a stronger dollar under a Bush presidency than under Kerry. … analyses of all Presidential elections since 1880 … [suggests] electing a Republican President raises equity valuations by 2-3 percent, and that since Reagan, Republican Presidents have tended to raise bond yields.

Their method can show how speculators expect a Republican president to effect any outcome X, but it suffers from three key limitations:

the election, and the relevant outcome X, must both be forecast by markets whose prices change many times on election day,

you must believe other important influences on X have been controlled in the statistical regression analysis, and

it is not available in time to usefully advise voters on how to vote in that election.

For many years I have suggested that organizations use "decision markets" (decision conditional market forecasts) to advise key choices. Such markets can in principle suffer from "decision selection bias", but this is not a problem when decision makers know no more than market speculators. This can be achieved by putting the market directly in control of the decision, or, when the decision-making group is small and well motivated, by letting that group trade in the markets. But elections, with a huge poorly-motivated decision making group, are more of a problem.

To avoid decision selection bias in elections, while also avoiding the three problems above, let me propose a variation on the Snowberg et al. approach: *Shock Response Futures*. As in the Snowberg et al. approach, we require two other markets, one in who wins the election and the other in some outcome X. Unlike their approach, however, we only need two election day prices from each market.

The "shock" DP is the change over election day in the market’s chance the Republican wins, while the "response" DX is the change over election day in the market estimate of X. The "shock response" is then SR = DX/DP, which can of course be positive or negative. A binary "shock response future" could pay if SR were greater than some threshold T, while a linear future could pay proportional to how much SR exceeded some minimum value.

Shock response futures could trade long before the election, giving voters early non-partisan estimates of how large a change in outcome X would be *caused *by electing a candidate. This estimate would not need to be corrected for other influences on X; speculators would average over other influences in producing their shock response market estimate. Pick your favorite outcome: unemployment, war casualties, GDP, infant mortality, Roe v. Wade reversal, whatever, shock response futures could cut through the bull to tell voters clearly which candidates would cause which outcomes.

## Shock Response Futures

Eric, you are right, the shock due to a debate could also be a reasonable basis, and could give advice well before the election. I also agree that the method can be applied when there is just one price jump; I was just concerned about whether that would give enough statistical power.

I like the shock futures idea. At some point I think I pitched something similar to Intrade. I think it was your idea but without the denominator, i.e. "Election Day returns conditional on GDP wins" (trades unwound otherwise) and a similar contract for the Dems.

Unfortunately they (probably correctly) thought it would be too complicated for most people to want to trade. That's the frustration with a lot of otherwise cool contracts, but hopefully that'll change as the concept matures.

A couple other thoughts:

1. I completely agree on your limitation #2. One point we make in the paper is that if you regress the S&P on Prob(Bush) during the pre-election time period (i.e. a time period in which the state of the economy is affecting both), you can get very biased results.

2. Re limitation #1: I think our method would work fine if the results were announced exactly at midnight, and the probability jumped from P to 1. In that case, our regression would just yield the standard event study result, scaled appropriately by 1/(1-P) using the prediction market price. Obviously, the incremental power of the method over a traditional event study is greater when news doesn't come all at once (or can't be timed precisely).

3. Re limitation #3: if you have a setting or time period in which you are confident about the direction of causality, then you are fine. For example, we don't talk about it in the paper, but in talks I mention that we did a Wald estimator for one of the 2004 debates of dS&P/dProb(Bush). You do get results that are much less precise, (I think we got a Bush effect of 3% +/- 6%) but you can at least reject the naive pre-election estimates.

And of course, another counter example is our pre-war paper on Iraq.