TABLE A-1. Economic Variables Observations Variable Description 3 Month Maturity

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1 WEB APPENDIX for Fowler, James H. Elections and Markets: The Effect of Partisan Orientation, Policy isk, and Electoral Margins on the Economy, Journal of Politics Tables A-1 and A-2 explain how data are derived from futures prices. Panels are based on the following periods: 6/10/88-11/9/88, 1/22/92-11/4/92, 6/21/94-11/9/94, 1/2/96-11/6/96, 2/3/98-11/4/98, 1/3/00-11/10/00, 7/20/02-11/6/02. These periods start on the first day in which at least one bond futures price and one election futures contract price are observed within the year of the election and they end the day the election outcome is known. IEM records daily historical data prices at midnight after the market has absorbed all the prime-time news. This contrasts with financial markets that close in the afternoon before critical campaign information is released. Therefore electoral probabilities are lagged by one day relative to interest rates to make sure that today's financial markets know about yesterday evening's political news. This should also address concerns about possible endogeneity. A maor difficulty with aroaches based on monthly data (such as Cohen 1993 is that they assume a one-month lag in economic variables because the market gets data for the prior month. However, based on release dates published in the Bureau of Labor Statistics, CPI data has been TABLE A-1. Economic iables Observations iable Description 3 Month Maturity 2 Year Maturity 5 Year Maturity 10 Year Maturity 30 Year Maturity Change in future 3 month Treasury bill yield in percent. Calculated as (100 futures price Change in future 2 year Treasury note yield in percent. Calculated as the effective yield at the current futures price of a 2 year bond with a biennial coupon of 8 percent Change in 5 year Treasury note future yield in percent. Calculated as the effective yield at the current futures price of a 5 year bond with a biennial coupon of 8 percent for and 6 percent for Change in 10 year Treasury note future yield in percent. Calculated as the effective yield at the current futures price of a 10 year bond with a biennial coupon of 8 percent for and 6 percent for Change in 30 year Treasury note future yield in percent. Calculated as the effective yield at the current futures price of a 30 year bond with a biennial coupon of 8 percent for and 6 percent for M Most recent one week rate of growth in the M1 money suly as reported by the Federal eserve Board. Inflation Most recent one month rate of growth in the consumer price index as reported by the Bureau of Labor Statistics. Unemployment Industrial Production Most recent unemployment rate as reported by the Bureau of Labor Statistics Most recent one month rate of growth in the industrial production index as reported by the Federal eserve Board.

2 Table A-2. Election Futures iables iables Panels Obs. Description Probability Left Wins House (p C Probability Left Wins Presidency (p P Democratic Presidential Vote Share [HM.DEM + (1 - HM.EP] / [H.lose + (1- (H.hold + H.gain + (NhNs + Nhs + (1 - (hs + hns] / [P.CL + (1 - (P.BU + P.PE] / [(CLIN + OTDEM + (1 - (EP + OF96] / [Dem + (1 - (ep + eform] / [(Dukakis + Jackson / (Dukakis + Jackson + Bush] [(D.B + D.CL + D.HA + D.KE + D.F + D.TS + (1 -.BU] / [V.CLIN + (1 V.DOLE] / 2 (µ [DemVS / (DemVS + epvs] Note: Negative implied values and implied values greater than one are set to zero and one, respectively. Abbreviations in calculations for probabilities and vote shares based on election futures contracts are taken directly from Iowa Electronic Markets ( released as late as eight weeks after-the-fact. Therefore, these models probably give the market more prescience than it actually has. To solve this problem, unrevised control data are matched with release dates to specify precisely when the market receives the information. This is especially important since the tests here are based on daily data. Incumbent probabilities are not observed but they can be derived given partisan probabilities and information about the incumbent parties. Let IP, IC {0,1} denote the current party in the Presidency and the Congress (0 for epublicans and 1 for Democrats. The probability of the challenger party winning the Presidency is h, P = ((1 IP pp + IP (1 pp and the probability of the challenger party winning the Congress is h, C = ((1 IC pc + IC (1 pc. The number of observations for each panel varies depending on trading volume, contract availability, and rules regarding the first date a contract may be traded. As a result, if we use listwise deletion for the analysis, missingness in the data forces us to eliminate most of the observations in the data set. One possible solution is to eliminate some of the independent variables from consideration. However, missingness in the dependent variable is correlated with several of the independent variables, suggesting that listwise deletion may cause omitted variable bias. Thus I follow the advice of King, et al (2001 who recommend multiple imputation as a superior alternative to listwise deletion. The imputation model is based on the EM algorithm with importance sampling and includes all of the variables used in the analysis model. Specifically, this means I include variables for the yields implied by two and five year treasury futures, variables related to electoral probabilities and vote share ( pp, pc, pppc, pp(1 pp, 2 pc(1 pc, cov( pp, pc, ((1 IP pp + IP(1 pp, ((1 IC pc + IC(1 pc, IP, I C, µ, µ, and economic controls (M1, CPI, UE, IP. To improve estimation, the imputation model also includes variables for yields implied by 3 month, 10 year, and 30 year treasury futures.

3 Table A-3. Impact of Electoral Outcomes on Interest ates Dependent iable: Expected Post-Electoral Nominal Interest ates Two Year Maturity Five Year Maturity MLE 95% Conf. Int. MLE 95% Conf. Int. Model Coefficients α Change Lagged Level π Change D π Lagged Level S Change Lagged Level Change D Lagged Level Change Lagged Level Change S Lagged Level Change ch, P Lagged Level Change ch, H Lagged Level Economic Controls M1 Inflation Unemployment Industrial Production Change Lagged Level Change Lagged Level Change Lagged Level Change Lagged Level Technical Parameters Lagged Dependent Change iable Level Constant Y η Mean Log Likelihood LaGrange Multiplier Test (effect of εt 1 on ε t Note: Maximum likelihood estimates of coefficients in equation (7 using an error correction model and restricting attention to the elections. Confidence intervals calculated from profile likelihood.

4 To deal with serial correlation, the imputation model assumes an ADL(1,1 structure to the data. Lagrange Multiplier Tests in the unimputed data suggest that one lag of each of the variables is sufficient to reduce serial correlation to insignificance. Note that there is only one observation (the election outcome for p C in 1988 and 1992 so all these data are imputed. However, Table A-3 shows that model results are not substantively different when these two elections are excluded. Election Day changes in electoral probabilities are much larger than typical changes prior to Election Day, but Table A-4 shows that when these outliers are excluded the substantive results remain the same. Table A-4. Impact of Electoral Outcomes on Interest ates (WITHOUT OUTLIES Dependent iable: Expected Post-Electoral Nominal Interest ates Two Year Maturity Five Year Maturity Symbol MLE 95% Conf. Int. MLE 95% Conf. Int. Model coefficients elative influence of α Change Presidency Lagged Level Partisan difference in π D π Change inflation Lagged Level Partisan difference in D Change inflation risk Lagged Level epublican inflation risk c D Change minus partisan covariance Lagged Level Effect of challenger party ch,p Change in Presidency Lagged Level Effect of challenger party ch,h Change in House Lagged Level Effect of mandate on s Change inflation Lagged Level Effect of mandate on S Change inflation risk Lagged Level Economic Controls M1 Inflation Unemployment Industrial Production β M1 Change Lagged Level Β CPI Change Lagged Level Β UE Change Lagged Level Β IP Change Lagged Level Technical Parameters Lagged Dependent Change iable Level Constant Y η Mean Log Likelihood Lagrange Multiplier Test (effect of εt 1 on ε t

5 It may not be clear how covariance in the model relates to observed electoral outcomes, so I elaborate here. Let X and Y be random variables such that 1 if a Democrat is elected President 1 if Democrats win the Congress X = and Y = 0 if a epublican is elected President 0 if epublicans win the Congress The th realization of X is x Bernoulli( p P, a draw from a Bernoulli random variable with mean p P, which is itself a random variable with mean p P. The th realization of Y is y Bernoulli( p C, a draw from a Bernoulli random variable with mean p C, which is itself a random variable with mean p C. The probability of a Democratic President and Congress is thus ust the expected value of the product of the probabilities of observing each outcome: pdd Pr ( x = 1, y = 1 = E( x y = E( pp pc Similarly, the expected values of the other three possible outcomes are p Pr x = 1, y = 0 = E x (1 y = E p (1 p ( ( ( ( ( ( ( ( ( D P C p Pr x = 0, y = 1 = E (1 x y = E (1 p p D P C p Pr x = 0, y = 0 = E (1 x (1 y = E (1 p (1 p P C As mentioned in the text we have reason to believe that p P and p C may covary positively or negatively. Theorem in Casella and Berger (2002, 170 shows that Cov( X, Y = EXY µ Xµ Y, where EXY is the oint probability of X and Y and µ X, µ Y are the mean of X and Y. earranging, EXY = µ µ + Cov( X, Y. Thus, in our model ( ( ( (, (, P C P C P C P C P C E p p = E p E p + Cov p p = p p + Cov p p. This allows us to rewrite the oint probabilities to take the covariance into account: p = E p p = p p + Cov p, p X Y DD ( P C P C ( P C p ( (1 (1 (,(1 (1 (, D = E pp pc = pp pc + Cov pp pc = pp pc Cov pp pc p ((1 (1 ((1, (1 (, D = E pp pc = pp pc + Cov pp pc = pp pc Cov pp pc pd = E( (1 pp (1 pc = (1 pp (1 pc + Cov( (1 pp, (1 pc = (1 pp (1 pc + Cov( pp, pc Note that ( Cov pp, p C is not observed, but we can estimate it from n observations since ( = = = (, ( ( ( ( ( ( ( (, E Cov p p E E p p E p E p E p p E p E p Cov p p n P C n P C P C P C P C P C where p P and p C are vectors of n observations of p P and p C, respectively. If we assume the covariance remains fixed for all observations prior to a given election, then: E Cov p, p = Cov p, p n ( ( P C ( P C and the best estimate for the covariance will thus be C Cov( p, p =. For simplicity I drop PC P C the subscripts in the article text since there are already a number of relevant subscripts to keep track of.

6 It may not be obvious that E( x y E( pp pc =. However, it is important to remember that p P and p C are themselves random variables. Each day we have one draw from the p P distribution and one draw from the p C distribution, and these draws determine the probabilities that X~Bernoulli(p P =1 and Y~Bernoulli(p C =1. Since we have already accounted for the covariance of the election outcomes within the probability distributions p P and p C, the oint probability of X and Y will ust be the expectation of the product of these two probability distributions, not their means. Whenever one is in doubt on a basic point like this, one can always use simulation to check the math. Below is a program in that generates probability distributions for p P and p C with some fixed covariance cov(p P,p C. I use observations from these distributions to generate X and Y distributions of election outcomes. I then generate both E(XY and E(p P p C. I run the program 1000 times with randomly drawn values for the means, variances, and covariance of p P and p C. This data aears on the last pages below. Notice that E(XY = E (p P p C for all 1000 combinations, even when the covariance is close to its maximum possible value. Thus, the simulations confirm that the equality holds. To estimate the covariance cov( pp, p C in the model, I use the product moment of the two probability estimates at each time point during the election period measured under the assumption that it remains fixed for each election. Although we can estimate the difference in inflation risk for the two parties D, neither the absolute level of inflation risk nor the covariance in inflation risk between the two parties c can be estimated separately. These two D parameters always aear together as the term c in equation (5, which causes the model D to become unidentified if we estimate them separately. The same technical difficulty also prevents us from estimating separate variances for each party by chamber. While it is possible for serial correlation to affect the estimates, analysis of the cross-correlations at several lags suggests that it does not they do not differ significantly from the zero-lag estimates. obust covariance estimation with nearest neighbor variance (Wang and aftery 2002 also yields similar results. Under all of these procedures, the range of the covariances across all elections is very close to zero [-0.02,0.01] and does not change significantly for different subsets of each election time series (e.g. the last 20 days before the election. This evidence suggests that covariance should not have much impact on the estimation since there is no evidence that it changes significantly over time. In other words, fixed covariance aears to be a reasonable assumption. The bottom line here is that the substantive findings would probably not change even if we knew the time-varying covariance with certainty. Finally, it is important to note that one might have an ecological inference problem if we did not assume that the covariance remains fixed for a given election. However, if we do assume it is fixed then we can use all of the individual daily observations of the electoral probabilities to estimate the covariance for the two series. If we did not impose this constraint, then there would be no way to go from the marginal probabilities p P and p C to the oint probability p DD. By assuming the covariance is fixed we essentially lock in the relationship between the marginal probabilities and the oint probabilities. In a more perfect world we would observe the oint probabilities directly, but given that the estimated covariance does not aear to change much over time it is doubtful that such observations would significantly change the results.

7 # Program to simulate E(XY and compare it to E( # define suort for random component of probabilities so they stay between 0 and 1.suort <- c(0,1.suort <- c(0,1 # draw 100 million observations from a uniform distribution with suort ".suort" # for the probability Dems win the Presidency <-runif( ,.suort[1],.suort[2] # let the probability Dems win the Congress be a function of the # probabilty Dems win President, depending on convex combination # of President's probability and an independent probability alpha <- 0.5 # [0,1] parameter that determines how closely probabilities covary # alpha = 0 = independent, alpha = 1 = perfectly correlated <- alpha * + (1 - alpha * runif( ,.suort[1],.suort[2] # use each randomly generated probability to draw a random election outcome for Pres, # TUE = 1 = Dem, FALSE = 0 = ep x <- ( > runif( ,0,1 # use each randomly generated probability to draw a random election outcome for Cong, # TUE = 1 = Dem, FALSE = 0 = ep y <- ( > runif( ,0,1 # use random election draws to calculate expectation that # both branches are Dems E.xy <- mean( x * y # calculate means of the randomly generated probabilities that Dems win Pres, House mean. <- mean( mean. <- mean( # calculate convariance of these two distributions cov. <- cov(, # calculate oint probability that Dems win House, Pres E.. <- mean. * mean. + cov. # report results print(c(mean.,mean.,cov.,e..,e.xy

8 mean mean cov E E XY mean mean cov E E XY mean mean cov E E XY

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