Stock Market for Dummies

Three dummies and the stock market Brian Doyle (202) 785-6011 brian.m.doyle@frb.gov http://www.geocities.com/brian m doyle Jon Faust (202) 452-2328 faustj@frb.gov http://patriot.net/∼ faustj International Finance Division Federal Reserve Board Washington, DC 20551 December 2001 (revised June 7, 2002) Abstract: There are large literatures about the role of three dummy variables in explaining economic activity: Republican elections, oil shocks, and Romer dates, which mark monetary tightening. Many have argued that one or more of the three is not a cause of recessions. This paper parallels those literatures in examining equity returns and the three dummies. Given that equity returns vary with the business cycle, it seems likely that the dummies will predict asset returns, and they do. The losses that predictably follow the dummy events, however, do not come when the dummy events happen, but later when the business cycle peak actually occurs. Based on this, we argue that the markets, at least, are also suspicious of the evidence that the dummies signal recession. Keywords: equity returns, Romer dates, oil shocks, Political business cycles While Jonathan Wright has helped us a great deal on this paper, given the title we hesitated to add him as a third author. We also would like to thank Robert Barsky, Jim Hamilton, and participants at the International Finance Workshop, the 2002 North American Econometric Society Meetings, and 2002 Canadian Economics Association Meetings for helpful comments. NOTE: The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or other members of its staff. Post-war U.S. recessions have reliably been preceded by three zero-one, dummy, variables marking the election of Republican presidents, oil price shocks, and monetary policy tightenings (Figure 1). As the Fed tightened policy and oil prices again spiked before the 2000 election, followers of these dummies began to suppose a recession was in the offing. When the Supreme Court completed the trifecta by putting a Republican in office, we simply had to wait for the NBER to make it official. With that complete, we add one more case to the striking empirical regularity regarding the three dummies. Many papers, reviewed below, have examined whether the link between any of these dummies and economic activity demonstrates causality between the item measured by the dummy and recessions. Obvious alternatives are that the striking associations in Fig. 1 are simply due to luck (good or bad, depending on your perspective), or that only one of the three is the real culprit. It is well known that stock market returns also vary with the business cycle. The simplest motivation for this paper is to see whether these dummy variables also systematically precede movements in equity returns. While the core of the paper is simply data summary complementing the work done on output measures, this study could shed light on which if any of these dummies is important in causing recessions. The economic activity variables already studied move slowly into recession after the events measured by the dummies. Since the dummies all signal at similar times, it is difficult to distinguish their effects on output. The stock market moves more sharply when the onset of recession becomes apparent as lower dividend expecta- 1 tions and higher risk lead to capital losses at the moment the onset of recession is recognized. Thus, studying the behavior of the market around the times these dummies signal could help reveal whether the market believes they signal recession. For much the same reason, taking these dummies from the macro literature may shed some new light on the business cycle variation of equity returns. These dummy variables move much more sharply than the financial ratios and spreads and traditional macro variables often used to capture business cycle variation of equity returns. These sharply moving variables have been shown be very significant in explaining real activity, and it seems likely that they could play even a larger role in accounting for financial market variation. The essence of the paper is first to measure the movement of equity returns around business cycle peaks and to test whether this movement is associated with any of the dummies. We find, that the months surrounding NBER peaks are associated on average with losses on the stock market. This has been observed before, of course. The traditional variables used to explain business cycle variation of returns essentially explain none of this sharp movement at peaks. Thus, the market seems to recognize the onset of recession in about same month that the NBER chooses as the peak. As for the dummies, they are followed by losses in the stock market. These losses do not, however, occurs at the time the dummies signal. They come months later, at approximately the time of the NBER peak date. We take this as evidence that the market, at least, does not see any of these as strong signals of recession. Two 2 of the dummies are publicly observed (oil shocks and Republican elections). The monetary tightening dummy (the Romer dates) is not, necessarily known by the public when they happen. These dates were chosen by reading Fed material that was not public at the time. Arguably, however, in most cases the public knew that the Fed was tightening in these periods. In section 1 we provide some background; section 2 provides some background on the dummies and the stock market; section 3 has more formal results; and section 4 concludes. 1 1.1 Background Three dummies and the economy There are large (and to some extent separate) literatures on each of the dummies. In discussing oil shocks, Hamilton (1983) concisely laid out the possible explanations for the associations: 1) mere luck, 2) some third factor (perhaps one of the other dummies) causing both the dummy and the recession, 3) causality. We briefly review some of the literature on these possibilities for each dummy. As a frame of reference for later figures, figure 2 gives the average unemployment rate in the U.S. in the months surrounding business cycle peaks. Thus, for the zeroth month, the main line gives the average rate in the month of 9 post-war peaks, and the vertical bar is a 1 standard deviation bar, where the standard deviation is measured over these same 9 items. The unemployment rate, on average rises sharply beginning 3 at the peak and continuing for about 9 months. Republicans. There are large theoretical and empirical literatures on political business cycles.1 It is an amazing regularity that recessions happen early in Republican administrations (every post-War Republican administration but Reagan II follows this rule). Figure 2 is analogous to Figure 1 but is now centered on the month of election of a Republican; the zero month is now an election November. About 9 months after the election, the unemployment rate mirrors the upward movement of figure 2. It is easy to imagine that some of this could be luck: a few accidental Buchanan voters could have changed the recent election.2 It is certain that from an econometric perspective there are some unfortunate small sample associations among arguably exogenous variables. For example, Hamilton (2000) has identified 5 dates of oil shocks associated with Mideast wars and made a convincing case that the timing is exogenous to the U.S. economy. Two of five are within one month of a Republican election, one follows shortly after a Republican election (the relevant dates are noted in the data Appendix). With relatively few post-war recessions, such coincidences— if those they be—greatly complicate sorting out various theories. Various authors have taken up the argument that a third factor is causing both the Republican elections and recessions. For example, (Faust and Irons, 1999) provides some evidence that one cannot reject the hypothesis that the association comes from reverse causation from the economy to the election outcome. 1 Alesina and Rosenthal (1995) provide a good summary of theories and evidence focusing on aggregate demand management. Faust and Irons (1999) critique this evidence. 2 Just as a few less dead Illinois voters might have put Nixon in office in 1960. 4 Oil shocks. In a series papers, Hamilton (1983, 1985, 1996, 2000) has demonstrated a close relation between oil price shocks and recessions. Hamilton has measured the oil shock variable in various ways including a zero-one dummy indicating major oil supply disruptions and monthly oil price increases relative to the previous 12 month peak in the oil price. Hamilton shows that both of these variables strongly predict output declines. The relation is apparent in Figure 4 which gives the average unemployment rate centered on 10 oil shock dates from Hoover and Perez (1994). The civilian unemployment gradually rises about two percentage points over the 24 months following the shock. There have been various challenges to the robustness of this statistical relationship (e.g., Mork (1989), Hooker (1996)), but Hamilton (2000) shows strong evidence for this relationship. Bernanke, Gertler and Watson (1997) argue that it is not oil per se, but the reaction of monetary policy around the time of oil shocks that causes the recession. One still might view oil as the original impulse leading to recession in this view. Barsky and Kilian (2001) claim that stop-go monetary policy can explain stagflation over the 1970s and early 1980s, and that oil shocks themselves can be explained by a combination of monetary fluctuations, and cartel theory. Monetary shocks—Romer dates. Romer and Romer’s (1989, 1994) narrative approach chooses zero-one dummies to indicate “exogenous” monetary policy tightenings, which by their description are times when the Federal Reserve tightens policy in response to inflationary pressures rather than real phenomena. The Romers find these dates to be strongly associated with subsequent recessions, consistent with 5 figure 1. In figure 5, like the previous two figures, we see that the unemployment rises almost two percentage points on average after the Romer dates. In this case, it was Leeper (1997), Shapiro (1994), Hoover and Perez (1994) who took up the argument that the dummy is endogenous. Even if the dummies were exogenous, Hoover and Perez (1994) further contend that the Romers’ narrative approach would not be able to distinguish between oil shocks and monetary policy as having caused recessions. 1.2 Stock Market and Business Cycles It is well known that stock returns vary with the business cycle. Indeed, Siegel (1991) shows that although the stock market does fall at other times, one can significantly increase ones returns by switching from stocks to bonds around the time of NBER business cycle peaks. This is apparent in Figures 6 and 7, which show the CRSP value-weighted 1month and 3-month excess returns over the T-bill rate centered on business cycle peaks. Note that all returns in the paper are at 1-month rates (not annualized).3 Further, the timing convention is that the three month return plotted, e.g., at time zero is for time zero to zero plus three: the returns are forward looking. The pattern is especially clear in the 3-month returns, which are sharply negative in the months surrounding the peak and sharply positive 12 to 15 months later. The one standard deviation bands fall entirely below and above zero in these two periods, respectively. 3 For details on the data, see the data appendix. 6 This systematic movement of rates around peaks does not necessarily imply that these returns are predictable since peaks are themselves hard to predict. Peaks are quite predictable contemporaneously or with a short lag, however. At least in recent years the NBER announces peak dates with an average lag of about 9 months.4 Thus, the positive average returns more than a year after the peak are in principle predictable. Of course, required stock returns should vary with the business cycle. It is well known that the volatility of the stock market rises during recessions. After NBER business cycle peaks monthly volatility of the S&P 500, calculated using daily squared returns, rises by about 50% then declines over the course of the recession (Figure 8). We know that business cycle peaks are associated with a fall in the market value of wealth, a rise in uncertainty about other sources of income (salaries, bonuses, etc.), and a rise in stock market volatility. All of these suggest that required returns should covary with business cycles. As French, Schwert and Stambaugh (1987) outline, positive shocks to required returns at business cycle peaks should cause actual returns to fall, consistent with figures 6 and 7. What we rely on heavily below is that this conclusion holds so long as the business cycle peak is a surprise. If any of the three dummies is a significant causal factor in recessions, one might also expected negative returns around the time of the dummies. Previous studies have found that a variety of macroeconomic variables have had 4 The announcement lag is reported on the NBER web site at http://www.nber.org. 7 success predicting stock returns. In keeping with theory, Lettau and Ludvigson (2001) find that the consumption to wealth ratio has predictive power for stock returns. Other studies examine other measures of economic activity. Jagnathan and Wang (1996) and Reyfman (1997) examine labour income; Chen, Roll and Ross (1986) use industrial production and inflation; and Cochrane (1996) looks at investment growth. Various leading indicators of recessions have also been studied. Keim and Stambaugh (1986), Fama and French (1989), Fama (1990), Schwert (1990), Chen (1991), and Estrella and Hardourelis (1991) demonstrated that variables such as at the short-term-long-term interest rate spread, and default spreads (such as the different between a market portfolio of corporate bonds and the yield on Aaa bonds), the dividend-price ratio and the dividend-payout ratio predict stock returns. Fama and French (1989) emphasized the role of such variables in accounting for business cycle variation of stock returns. The best predictors tend to account for 5 to 10 percent of the variation of stock returns at most (Campbell, Lo, and MacKinlay 1997 provide a nice summary of this evidence). While these variables are cyclical and do account for some of the business cycle variation in stock returns, the basic pattern in figure 7 is unchanged after removing the component of returns predicted by such variables. For example, Figure 9 takes the residual from a regression of the three-month value weighted excess return on the log dividend-price ratio and the stochastically detrended short rate (the one-month rate minus the 12-month lagging average of the one-month rate). These are two of 8 the star performers in predicting returns; the adjusted R2 is 0.09 similar to results reported in, e.g., Campbell, Lo, and MacKinlay (1997).5 The systematic variation in this residual return over the business cycle peak is nearly identical to the return without the “predictable” component removed. Indeed, the negative returns are somewhat sharper and more protracted. The positive returns a year after the peak are somewhat attenuated. These results are not altered by considering other standard predictors such as the term spread. The essential points from this brief survey are that business cycle peaks appear are accompanied by negative returns and perhaps by significantly positive returns a year or so later. This variation is not accounted for or predicted by standard business cycle measures. 2 A preliminary look at three dummies and the stock market We are aware of very little prior work examining the role of the three dummies in business cycle variation of stock returns. Recently, Santa-Clara and Valkanov (SCV) (2001) examined average returns under Republicans and Democrats, finding significantly lower returns under Republicans. Among other things, SCV measure average returns under each party controlling for standard business cycle variables such as those mentioned above and including a dummy variable that is one in NBER expansions and zero otherwise. We do similar calculations below for each dummy. 5 For details on the data, see the data Appendix. The sample period is 1947:12 to 2000:10. 9 Our work is very much complementary to SCV, but with two differences. First, we recognize that the business cycle variables included to control for the effect of recessions may leave in the data most of the losses associated with business cycle peaks. Second, we are most concerned with the dynamic response of returns to elections or the other dummies as opposed to the average returns over long periods such as presidential terms or business cycle phases. As is clear in Figure 10, the average return over the presidential term has a distinct shape, with average returns becoming quite negative near the end of the first year in office—just as the unemployment rate begins to take off. (Remember that all but one Republican administration has a recession in the first two years.) Returns rise sharply at the time of the mid-term election, when the economy is beginning to come out of recession. A basic idea motivating the inference we do more formally in the next section is that if the Republicans cause recessions and the market knows it, the negative returns associated with the positive required return shock should happen immediately and not eight months later. Goto (2001) has looked at the effect of oil and other commodity prices on the stock market, and Goto and Valkanov (2001) have looked at the effect of identified monetary policy shocks on returns. This work is also complementary to our own focus on the dynamics of return in response to these discrete dummies. Figures 11 and 12 show the response of the 3-month excess return to the HooverPerez oil shock dummy variable and to the Romer dates. Similar to the Republican 10 dummy, there is no real sign of negative returns immediately around the time of the shock. Returns turn negative about half a year later and then quickly bounce back. For the Romer dummy, however, there is some weak evidence of negative returns in the 5 months around the date as well as negative returns over a year later. 3 3.1 Formal results The approach Our basic approach is to combine the standard approach in equity returns regressions with a standard approach to studying the influence of these dummies. This suggests running a regression excess returns over some horizon, h, on standard variables, xt , as well as a distributed lag of one or more dummy variables: L rh,t = α + β xt + i=0 γi dt−i + . . . + t (1) where the ellipses indicate that more than one dummy variable term may be included. There are many well-known pitfalls with such regressions (e.g., Campbell, Lo, and MacKinlay, 1997). We focus on the 1-month and 3-month return horizons, and will not suffer from the worst of the problems with long horizon regressions, but we must be aware of the issues raised by overlapping returns. Further, we know there is heteroskedasticity in returns that is correlated with our business cycle indicators. A standard approach is to use Newey-West (1987) heteroskedasticity and autocorrelation consistent standard errors in forming test statistics. Unfortunately, 11 preliminary simulations showed that these are exceedingly badly behaved with our dummy variables: comparing Newey-West-based F statistics to standard F critical values led to vast over rejection of the null. Thus, we choose to use a nested bootstrap approach. We bootstrap our F test statistics in standard manner, but also estimate the variance-covariance matrix of the coefficients upon which the test statistics are based using a second bootstrap nested in the first. More specifically, to test the hypothesis that the γs are jointly equal to zero, we calculate the conventional F statistic based on the OLS estimate, γ , and its ˆ bootstrap variance-covariance matrix, Σboot . Then we repeatedly create pseudosamples using weighted bootstrap proposed by Wu (1986), studied by Cribari-Neto and Zarkos (1999) and used in the context of returns by Malliaropulos and Priestley (1999). The basic idea of the bootstrap is to resample from the estimated residuals, ˆ, in the regression in a way that preserves the heteroskedasticity properties. In ∗ ˆ ∗ ˆ ˆ particular, each draw ε∗ = εt zt , where zt is a random draw from εt /σε and σε is ˆ t the standard error of ε. Details are in the Appendix. ˆ There remains the question of how to pick the number of parameters in estimating γ. The figures make it appear that there may be some interesting dynamics over extended periods, so longer lag lengths may be preferred. On the other hand, we may sacrifice power in rejecting the null hypothesis of all γs being zero if too many lags are included. 12 We choose a combination approach. We estimate with lag lengths of L ∈ {6, 12, 18, 24}. We also try economizing on degrees of freedom by making the γ lie in a lower dimensional space parameterized by harmonic functions (see, e.g. Judge, et al., 1980). In this parametrization, each additional harmonic term adds two parameters; thus, choosing q terms where q < L/2 conserves on parameters. We consider q ∈ 3, 4, 6, 9. Each q is paired with each L (when q ≤ L/2) to give 12 combinations. As with polynomial distributed lags, the parameters can be estimated by OLS on variables that are linear combinations of the original variables. We experimented with various x variables, but ultimately settled on reporting results with just two: the dividend price ratio and the stochastically detrended short rate. We also report results with no x variables. The sample for all of these regressions goes from 1948:2 to 2000:10. 3.2 The results We first provide a Santa-Clara-Valkanov-style summary of the association of the dummies with returns (Table 1). For each of the dummies except the Romer dates, returns are about 1 percentage point lower in the 12 months following the dummy than in other months. This difference is measured in a regression including the dividend price ratio and the stochastically detrended short rate. The difference is significant at near the 10 percent level in each case. Given that mean monthly returns are far less than 1 (about 0.04), these mean differences imply that over the sample period one made significant losses in the stock market for the 12 months after 13 these events and would have been better off with money in the risk free asset. The similar magnitude and significance of these differences is, of course, due to the fact that the events happen at the same time and, thus, we are measuring approximately the same thing. As is evident from Fig. 1, the Romer dates are not as tightly aligned with recessions as the other variables. Generally when we move to the 18 month horizon the results are weaker, as the negative returns around the peak are mixed with the positive returns that follow. Obviously we cannot distinguish among the causal roles of these dummies in this way. We move now to more carefully studying the dynamics around the time of the peaks and the dummies. We begin by considering whether significant losses are registered at the time any of the three dummy variables signal. We consider a regression of the one month excess return and including the peak dummy and each other dummy in succession. For both dummies in the regression we include the dummy at one lead, contemporaneously and at one lag. We consider two versions of these regressions, including and excluding our x variables, the dividend-price ratio and the stochastically detrended short rate. We include a lead and a lag of the dummy to all the regressions to account for the possibility that the information hits a month before or after the time picked in generating the dummy. In the vast majority of the regressions (Table 2), the peak dummy is significant contemporaneously and at one lag. The coefficient is quite large indicating negative excess returns of over 3 percent per month in the month of the peak and month following. Of the other dummies, only the contemporaneous Romer dummy is sig- 14 nificant at the 10 percent level. The sign of the other dummies’ effects is also quite erratic. If the signal of the dummy were strong evidence of oncoming recession with the associated heavy losses in the stock market, one might expect losses at the time the dummy signals. This does not appear to happen. Next we consider the dynamic pattern and statistical significance lags of the dummy variables as well as the NBER peak dates (Table 3). These regressions involve adding lags of each dummy separately to a base regression including only the two x variables. We report the smallest (across the 12 lag specifications) marginal p-value for the F -test that all the γs are jointly zero. The table also reports the ¯ corresponding R2 and in the final column is the percentage of the 12 specifications in which the p-value was less than 10 percent. The peak variable is significant in most specifications. It approximately doubles ¯ the R2 of the base regression (0.03 at the 1-month horizon; 0.09 at the 3-month horizon). The Republican dummy variable is also often significant and has an ap¯ preciable affect on the R2 . The oil and Romer date variables are never significant at the 10 percent level. For reference purposes, we also show Table 4, which has analogous results when the x variables are removed so that the base regression contains only a constant. The p-values fall, and in some cases the oil and Romer variables become significant at the 10 percent level. The coefficients on the lag variables are of some interest. To conserve space, we report very few of these. When the dummy variables come in significantly, their 15 patterns match the patterns depicted in figures 10–12. The coefficients from the specifications in the second panel of Table 3 are reported in figures 13–16. Except for the peak dummy variable, there are very few individual coefficients that appear statistically significant. The most significant coefficients suggest negative returns at lags of more than half a year, at about the time when the business cycle peak occurs. This suggests that if one included the peak dummy in the base regression that the economic and statistical significance of the other dummies might fall even further. The individual coefficients at lags zero and one are never significant indicating no significant impact effect. This is confirmed in tables 5 and 6. We add the three dummies separately to a base specification including the peak variable. The same 12 lag specifications are run and the lag specifications for the peak dummy and other dummy are the same in each case. In Table 5 the base specification includes the x variables, in Table 6 it does not. The last two columns indicate the proportion of specifications in which the peak variable and other dummy are significant at the 10 percent level. The result in both tables is that the peak variables are often significant in these specifications, while the other dummy variable are in only one case. 4 Conclusions The main object of this exercise is to provide data summary regarding equity returns that parallels the work that has been done regressing output measures on the three dummy variables. As equity returns vary with the business cycle, and the dummies 16 explain business cycle variation of output, we might expect them to be significant. They are (e.g. Table 1). If you had abandoned the market for a year when these dummy events happen, you would have avoided losses (relative to normal times) of about 1 percent per month for 12 months. The question of interest to us in this paper is whether this association is dumb luck or something more significant. Defenders of each dummy might argue that their dummy (or what it measures) is causally affecting the economy and hence, the market, and that the other two are dumb luck.6 Such a position requires belief that at least two dummies might line up with post-War recessions simply by luck. Faced with such a claim, we are inclined to wonder, “Why not three?” NBER peaks are much studied, and there are arbitrarily many dummy-like variables earnest economists might search over. When trying to explain 9 or 10 events, we are likely to stir up some remarkable associations. We attempt to shed light on this issue by documenting that equity returns are abnormally low at the time of NBER peaks. While losses on the stock market follow the dummy events, they seem to follow at significant lags and only really materialize when the peak happens. We do not find losses immediately around the time the dummy signals, which would be expected if the market believes that the dummy is reliably followed by recession. We emphasize that any of the three stories behind the dummies could be correct or all could be part of the story. We have very few post-War recessions and there are 6 They also argue that their dummy causes both the economy and the other two dummies. 17 some very unfortunate (from an econometric point of view) associations between, e.g., oil shocks and Republican elections. It is very difficult to definitively sort this out and the current recession has only made the situation worse. In future work, we intend to more formally measure returns that might come from exploiting the dummy variables. That is, we will use the dummies and other public variables to model the probability of an NBER peak in real time with real time data. Then we will see what returns one could make by exploiting the resulting estimates. 18 Data Appendix The one-month value weighted return at in month t is taken from CRSP and the excess return is the one-month return minus the one-month rate from the FamaBliss risk-free rates file. The three month excess return at t is the average of the one-month return at t, t + 1 and t + 2. The dividend-price ratio at t is constructed as the log of the dividends from t−11 to t over the price at t. The variable in the regressions is the log of this variable and it is always lagged one period relative to the returns being explained. The stochastically detrended short rate at t is the one-month rate mentioned above minus the average of the same rate from t − 11 to t. The business cycle peak dummy is 1 in the months reported as peaks by the NBER. The Republican dummy is one in the November of any year of a Republican presidential election victory. The Hamilton dummy is explained in Hamilton (2000) and is one in November 1956, November 1973, December 1978, October 1980, August 1990. The Hoover-Perez dummy is explained in Hoover and Perez (1994), and is one in December 1947, June 1953, June 1956, February 1957, March 1969, December 1970, January 1974, March 1978, September 1979, and February 1981. Bernanke, Gertler and Watson (1997) add August 1990. The Romer dummy is explained in Romer and Romer (1989, 1994) and is one in October 1947, September 1955, December 1968, April 1974, August 1978, October 19 1979, and December 1988. Technical Appendix: the bootstrap The steps in the bootstrap are as follows. 0. Estimate the unrestricted model, estimate the variance-covariance matrix of α, beta, and γ, and calculate the F statistics of interest. 1. Estimate the model under the null hypothesis that all γs are zero. ∗ 2. Calculate the residuals for this model, εt , and the normalized residuals zt ˆ which are simply the original residuals divided by their standard errors. 3. Generate bootstrap samples r ∗ of r using the coefficients of the model esti∗ ∗ ˆ mated in (1) and with residuals generated as ε∗ = εt ∗ zt , where zt is a random t draw (with replacement) from the zs. 4. Estimate the unrestricted model, and the variance-covariance matrix of its parameters, and calculate the F statistics of interest. Repeat steps 3 and 4 500 times and report where the F statistics in step 0 fall in the empirical distribution build up in 3 and 4. In steps 0 and 4, however, estimate the variance-covariance matrix by this same bootstrap. In particular, same bootstrap based on the estimation data used in 0 or 4. In this case, in the nested steps 0 and 4, only estimate the slope parameters not the variance-covariance matrix. Collect 100 estimates of these parameters and use their empirical variance-covariance matrix in calculating the F statistics in the original steps 0 and 4. 20 References [1] Alesina, A. and H. Rosenthal, 1995, Partisan Politics, Divided Government and the Economy (Cambridge University Press, New York). [2] Barsky, Robert B., and Lutz Kilian (2001), “A Monetary Explanation of the Great Stagflation of the 1970s,” forthcoming in the NBER Macroeconomics Annual 2001. [3] Bernanke, Ben, Mark Gertler, and Mark Watson (1997), “Systematic Monetary Policy and the Effects of Oil Shocks,” Brookings Papers on Economic Activity, 1, 91-142. [4] Campbell, John Y., Andrew Lo, and Craig MacKinlay (1997), The Econometrics of Financial Markets, Princeton University Press, Princeton, NJ. [5] Chen, Nai-Fu (1991), “Financial Investment Opportunities and the Macroeconomy,” Journal of Finance, 46, 2, 529-554. [6] Chen, Nai-Fu, Richard Roll, ans Stephen Ross (1986), “Economic forces and the stock market,” Journal of Business, 59, 3(July): 383-403. [7] Cochrane, John (1996), “A Cross-sectional Test of an Investment-based Asset Pricing Model,” Journal of Political Economy, 104, 3:(June) 463-485. [8] Cochrane, John (1999), “New Facts in Finance,” Economic Perspectives, Federal Reserve Bank of Chicago, 23, 3:(3rd Quarter) 36-58. [9] Cribari-Neto, F. and S.G. Zarkos (1999), “Bootstrap methods for heteroskedastic regression models: Evidence on estimation and testing,” Econometric Reviews, 18, 2:(May), 211-28 [10] Estrella, A. and G. A. Hardouvelis (1991), “The Term Structure as a Predictor of Real Economic Activity,” Journal of Finance, 46, 555-576. [11] Fama, Eugene F. (1990), “Stock Returns, Expected Returns, and Real Activity,” Journal of Finance, 45, 4(September): 1089-1108. [12] Fama, Eugene F., and Kenneth R. French (1989), “Business Conditions and Expected Returns on Stocks and Bonds,” Journal of Financial Economics, 25, 23-49. [13] Faust, Jon and John Irons (1999), “Money, Politics, and the Post-War Business Cycle, Journal of Monetary Economics, 43 61-89. [14] French, Kenneth R., G. William Schwert and Robert Stambaugh (1987), “Expected Stock Returns and Volatility,” Journal of Financial Economics, 19, 3-29. 21 [15] Goto, Shingo (2001), Crude Materials Prices and the Stock Market,” University of California at Los Angeles, mimeo. [16] Goto, Shingo (2001), “Time-Varying Mark-ups and Expected Stock Returns,” University of California at Los Angeles, mimeo, (November). [17] Goto, Shingo and Rossen Valkanov (2001), “The Fed’s Effect on Excess Returns and Inflation is Much Bigger Than You Think,” University of California at Los Angeles, mimeo. [18] Hamilton, James D. (1983), “Oil and the macroeconomy since World War II,” Journal of Political Economy, 91, 228-248. [19] Hamilton, James D. (1985), “Historical Causes of Postwar Oil Shocks and Recessions,” Energy Journal, 6, 97-116. [20] Hamilton, James D. (1996), “This is What Happened to the Oil PriceMacroeconomy Relationship,” Journal of Monetary Economics, 38, 215-220. [21] Hamilton, James D. (2000), “What is an Oil Shock?” mimeo, University of California, San Diego. [22] Hooker, Mark A. (1996), “What Happened to the Oil Price-Macroeconomy Relationship?,” Journal of Monetary Economics, 38, 195-213. [23] Hoover, Kevin D. and Stephen J. Perez (1994), “Post hoc ergo propter once more: An evaluation of ‘Does monetary policy matter?’ in the spirit of James Tobin,” Journal of Monetary Economics, 34, 47-73. [24] Jagannathan, Ravi and Zhenyu Wang (1996), “Than conditional CAPM and the cross-section of expected returns,” Journal of Finance, 51, 1:(March) 3-53. [25] Judge, George G., W.E. Griffiths, R. Carter Hill, Helmut Lutkepohl, and Tsoung-Chao Lee (1980), The Theory and Practice of Econometrics, John Wiley and Sons, New York, NY. [26] Keim, Donald B. and Robert F. Stambaugh (1986), “Predicting returns in the stock and bond markets,” Journal of Financial Economics, 17, 357-390. [27] Kling, John L. (1985), “Oil Price Shocks and Stock Market Behavior,” Journal of Portfolio Managemenent, 12, 34-39. [28] Leeper, Eric (1997), “Narrative and VAR approaches to monetary policy: Common identification problems,” Journal of Monetary Economics, 40, 641-657. [29] Lettau, Martin and Sydney Ludvigson (2001), “Consumption, Aggregate Wealth and Expected Stock Returns,” Journal of Finance, 56, 815-849. 22 [30] Malliaropulos, Dimitrios and Richard Priestley (1999), “Mean Reversion in Southeast Asian Stock Markets,” Journal of Empirical Finance, 6, 4:(October) 355-84. [31] Mork, Knut (1989), “Oil and the Macroeconomy When Prices Go Up and Down: An Extension of Hamilton’s Results,” Journal of Political Economy, 91, 740-744. [32] Newey, Whitney, and Kenneth West (1987), “A Simple Positive Semi-Definite, Heteroscedasticity and Autocorrelation Consistent Covariance Matrix,” Econometrica, 55, 703-708. [33] Reyfman, Alexander (1997), “Labor Market Risk and Expected Asset Returns,” University of Chicago, Ph.D. Thesis. [34] Romer, Christina and David Romer (1989), “Does monetary policy matter? A new test in the spirit of Friedman and Schwartz,” in Olivier Blanchard and Stanley Fischer (editors), NBER Macroeconomics Annual, 4, MIT Press, Cambridge, MA. [35] Romer, Christina and David Romer (1994), “Monetary policy matters,” Journal of Monetary Economics, 34, 75-88. [36] Santa-Clara, Pedro and Rossen Valkanov (2001), “Political Cycles and the Stock Market,” University of California at Los Angeles, [37] Schwert, G. William (1990), “Stock Returns and Real Activity: A Century of Evidence,” Journal of Finance, 45, 4:(September), 1237-1257. [38] Shapiro, Matthew (1994), “Federal Reserve: Cause and Effect,” in Gregory Mankiw (editor), Monetary Policy, University of Chicago Press, Chicago, IL, 307-334. [39] Siegel, Jeremy J. (1991), “Does It Pay Stock Investors to Forecast the Business Cycle?” Journal of Portfolio Management, 18, 1:(Fall) 27-34. [40] Wu, C.F.J. (1986), “Jackknife, bootstrap and other resampling methods in regression analysis,” Annals of Statistics’ 14, 1261-1295. 23 Table 1: Average returns following dummy diff. 12 months peak -0.014 Romer -0.001 Hoover-Perez -0.009 Hamilton -0.009 Republican -0.009 18 months Peak -0.003 Romer -0.004 Hoover-Perez -0.006 Hamilton -0.008 Republican -0.013 the dummy events p-val 0.01 0.88 0.09 0.12 0.04 0.46 0.35 0.09 0.09 0.01 Notes: The column “diff” gives the estimated difference in mean returns between 1 month after the dummy event and h months after (where h is 12 or 18) and all other months. The p-val is for a bootstapped t-test that this difference is zero as described in the text. 24 Table 2: Impact effect of the dummy variables on excess returns Peak dummy e−1 e e+1 Other dummy e−1 e e+1 ratio -0.010 0.009 0.029 -0.003 0.30 0.66 0.75 0.42 Dummy Romer date Hoover-Perez Dummy Hamilton Oil Dummy Republican President Romer date Hoover-Perez Dummy Hamilton Oil Dummy Republican President including short rate and dividend-price coefficient -0.011 -0.036 -0.039 0.009 -0.029 -0.011 -0.036 -0.037 -0.011 -0.001 -0.012 -0.033 -0.038 0.010 -0.030 -0.010 -0.035 -0.038 -0.003 0.026 p-value 0.11 0.06 0.05 0.72 0.10 0.11 0.04 0.01 0.26 0.47 0.14 0.07 0.02 0.80 0.27 0.11 0.04 0.05 0.34 0.90 Romer date Hoover-Perez Dummy Hamilton Oil Dummy Republican President Romer date Hoover-Perez Dummy Hamilton Oil Dummy Republican President not including short rate and dividend-price ratio coefficient -0.011 -0.038 -0.041 0.005 -0.036 -0.014 -0.010 -0.037 -0.039 -0.012 -0.003 0.008 -0.011 -0.035 -0.040 0.007 -0.033 0.021 -0.011 -0.038 -0.041 -0.005 0.023 -0.006 p-value 0.15 0.02 0.03 0.59 0.07 0.19 0.16 0.06 0.02 0.23 0.42 0.68 0.16 0.02 0.04 0.81 0.34 0.72 0.14 0.03 0.04 0.11 0.88 0.31 Notes: The equation is estimated by OLS with a constant and the specified other righthand side variables. Each regression includes the peak dummy and one other dummy at one lead, contemporaneously, and one lag, labelled e − 1, e, e + 1, respectively, where e stands for “event.” The p-values are for a one-tailed t-test that the dummy coefficient is zero versus a negative value and come from the bootstrap described in the text. 25 Table 3: Comparison of Best Dummy P-values, including detrended short rate and Dividend/Price in regression 2 Dummy Dummy’s P-value R Lags Terms % signif. at 10% For 1 month returns: Business Cycle Peaks 0.00 0.06 18 3 83% Republican President 0.01 0.05 24 3 17% Hamilton Oil Dummy 0.18 0.07 18 9 0% Hoover-Perez Dummy 0.19 0.04 24 6 0% Romer Date 0.44 0.03 24 4 0% For 3 month returns: 0.01 0.15 18 0.02 0.15 24 0.19 0.13 24 0.14 0.12 24 0.62 0.09 12 Business Cycle Peaks Republican President Hamilton Oil Dummy Hoover-Perez Dummy Romer Date 4 3 4 6 4 50% 8% 0% 0% 0% Table 4: Comparison of Best Dummy P-values, not including detrended short rate and Dividend/Price in regression, 2 Lags Terms % signif. at 10% Dummy Dummy’s P-value R For 1 month returns: Business Cycle Peaks 0.00 0.04 18 4 67% Republican President 0.01 0.01 24 3 8% Hamilton Oil Dummy 0.08 0.02 24 4 8% Hoover-Perez Dummy 0.17 0.02 24 6 0% Romer Date 0.31 0.01 12 3 0% For 3 month returns: 0.00 0.08 18 0.09 0.07 24 0.03 0.06 24 0.10 0.04 24 0.33 0.01 12 Business Cycle Peaks Republican President Hamilton Oil Dummy Hoover-Perez Dummy Romer Date 4 4 4 9 4 58% 8% 8% 0% 0% 26 Table 5: Comparison of Best Dummy P-values, including detrended short rate and Dividend/Price in regression and Peak Dummy Dummy’s % Peaks % Dummies 2 Dummy P-value R Lags Terms signif. at 10% signif. at 10% For 1 month returns: Republican President 0.22 0.19 6 3 50% 0% Hamilton Oil Dummy 0.18 0.07 6 3 58% 0% Hoover-Perez Dummy 0.34 0.06 24 9 58% 0% Romer Date 0.67 0.15 24 4 50% 0% For 3 month returns: 0.07 24 3 0.17 12 6 0.15 24 9 0.06 18 9 Republican President Hamilton Oil Dummy Hoover-Perez Dummy Romer Date 0.22 0.02 0.29 0.28 42% 50% 33% 50% 0% 8% 0% 0% Table 6: Comparison of Best Dummy P-values, including Peak Dummy but not detrended short rate and Dividend/Price in regression, Dummy’s % Peaks % Dummies 2 R Lags Terms signif. at 10% signif. at 10% Dummy P-value For 1 month returns: Republican President 0.21 0.04 24 4 33% 0% Hamilton Oil Dummy 0.22 0.04 18 3 42% 0% Hoover-Perez Dummy 0.29 0.09 12 3 33% 0% Romer Date 0.40 0.03 24 3 33% 0% For 3 month returns: 0.13 24 4 0.09 12 4 0.04 24 9 0.06 12 4 Republican President Hamilton Oil Dummy Hoover-Perez Dummy Romer Date 0.15 0.07 0.28 0.34 42% 42% 42% 33% 0% 8% 0% 0% 27 Figure 1: US Business Cycle Peaks and 3 Dummies -- Oil Shocks (O), Romer Dates (M), and Election of Republicans (R) M R O O M R O O M R OO R M MM R OOO R M R O M* R O* O 45 50 55 60 65 70 75 80 85 90 95 00 Oil Shocks are from Hoover and Perez (1994) adding April 1999. Romer dates are Monetary Policy tightenings from Romer and Romer (1989) adding January 2000. Elections are U.S. Presidential Elections. Figure 2: Civilian Unemployment Rate centered on 9 US Business Cycle Peaks, 1948-2000 (Mean and 1 Standard Deviation band) 10 8 6 4 2 -24 -21 -18 -15 -12 -9 -6 -3 0 3 6 months from event 9 12 15 18 21 24 Figure 3: Civilian Unemployment Rate centered on 7 Elections of a Republican President, 1948-1999 (Mean and 1 Standard Deviation band) 10 8 6 4 2 -24 -21 -18 -15 -12 -9 -6 -3 0 3 6 months from event 9 12 15 18 21 24 Figure 4: Civilian Unemployment Rate centered on 10 Hoover and Perez (1994) Oil Shock Dummies, 1948-2000 (Mean and 1 Standard Deviation band) 10 8 6 4 2 -24 -21 -18 -15 -12 -9 -6 -3 0 3 6 months from event 9 12 15 18 21 24 Figure 5: Civilian Unemployment Rate centered on 6 Romer Dates for Monetary Policy tightenings, 1948-2000 (Mean and 1 Standard Deviation band) 8 6 4 -24 -21 -18 -15 -12 -9 -6 -3 0 3 6 months from event 9 12 15 18 21 24 Figure 6: 1 Month Value Weighted Excess Returns centered on 9 US Business Cycle Peaks, 1945-2000 (Mean and 1 Standard Deviation band) .1 .05 0 -.05 -.1 -24 -21 -18 -15 -12 -9 -6 -3 0 3 6 months from event 9 12 15 18 21 24 Figure 7: 3 Month Value Weighted Excess Returns centered on 9 US Business Cycle Peaks, 1945-2000 (Mean and 1 Standard Deviation band) .05 0 -.05 -24 -21 -18 -15 -12 -9 -6 -3 0 3 6 months from event 9 12 15 18 21 24 Figure 8: Monthly Volatility of the S&P 500 from squared daily returns centered on 8 US Business Cycle Peaks, 1953-2000 (Mean and 1 Standard Deviation band) .015 .01 .005 0 -24 -21 -18 -15 -12 -9 -6 -3 0 3 6 months from event 9 12 15 18 21 24 Figure 9: Residual Excess Returns centered on 9 US Business Cycle Peaks, 1945-2000 (Mean and 1 Standard Deviation band) .05 0 -.05 -24 -21 -18 -15 -12 -9 -6 -3 0 3 6 months from event 9 12 15 18 21 24 Residual excess returns are the residual from regression of 3 month value weighted returns on the log dividend price ratio and the stochastically detrended short rate. Figure 10: 3 Month Value Weighted Excess Returns centered on 7 Elections of a Republican President, 1945-1999 (Mean and 1 Standard Deviation band) .05 0 -.05 -24 -21 -18 -15 -12 -9 -6 -3 0 3 6 months from event 9 12 15 18 21 24 Figure 11: 3 Month Value Weighted Excess Returns centered on 10 Hoover and Perez (1994) Oil Shock Dummies, 1945-2000 (Mean and 1 Standard Deviation band) .05 0 -.05 -24 -21 -18 -15 -12 -9 -6 -3 0 3 6 months from event 9 12 15 18 21 24 Figure 12: 3 Month Value Weighted Excess Returns centered on 7 Romer Dates for Monetary Policy tightenings, 1945-2000 (Mean and 1 Standard Deviation band) .05 0 -.05 -.1 -24 -21 -18 -15 -12 -9 -6 -3 0 3 6 months from event 9 12 15 18 21 24 Figure 13: Lag coefficients on peak and 2 standard error bands from best 3-month rate regression in Table 3. .04 .02 0 -.02 -.04 0 5 10 lag 15 20 Figure 14: Lag coefficients on Republican dummy and 2 standard error bands from best 3-month rate regression in Table 3. .05 0 -.05 0 12 lag 24 Figure 15: Lag coefficients on Hamilton dummy and 2 standard error bands from best 3-month rate regression in Table 3. .05 0 -.05 -.1 0 12 lag 24 Figure 16: Lag coefficients on Hoover-Perez dummy and 2 standard error bands from best 3-month rate regression in Table 3. .04 .02 0 -.02 -.04 0 12 lag 24 Figure 17: Lag coefficients on Romer dummy and 2 standard error bands from best 3-month rate regression in Table 3. .04 .02 0 -.02 -.04 0 6 lag 12