Stock Prices, Output and the Monetary Regime. Robert Flood and Nancy Marion. September 22, 2004

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1 Draft Comments Welcome Stock Prices, Output and the Monetary Regime By Robert Flood and Nancy Marion September 22, 2004 Abstract: Should monetary policy react to stock prices? The answer depends on whether stock prices are good predictors of future economic activity. To provide empirical background, we use long annual time-series data for the G-7 countries to examine whether the predictive power of stock prices varies over time by monetary regime. We also investigate a potential nonlinear relationship between stock prices and output by examining the linkage between extreme movements in stock prices and the volatility of future output growth. We find that the monetary regime has no systematic effect on the predictive power of stock prices for output growth. We also find no evidence in annual data that stock price booms or busts predict greater output growth volatility in the post- Bretton Woods era or under Bretton Woods, but they did have predictive power during the gold standard. Robert Flood Research Department IMF rflood@imf.org Nancy Marion Department of Economics Dartmouth College nancy.marion@dartmouth.edu We thank Michael Bordo for helpful discussions, and Nicholas Emiliano Amoroso Plaza for research assistance.

2 I. Introduction In this paper we study the relationship between stock prices and output growth in the G-7 countries. Our intent is to provide empirical background for policy discussions on whether monetary policy should react to asset prices. We are not the first to explore the relationship between stock prices and output, but we extend the exploration in two directions. We use a much longer time series--- annual data going back over 150 years for some countries--- to investigate whether stock prices predict output growth. The long time span, extending through a variety of monetary regimes, allows us to study how the predictive power of stock prices varies across regimes. We also investigate a potential nonlinear relationship between stock prices and output. We do so by examining the linkage between extreme changes in stock prices booms and busts-- and the volatility of output growth. Our focus on output growth volatility comes from the popular concern that strong upward or downward trends in stock prices may be driven by market fundamentals or by extraneous factors. Suppose, for example, that a fundamentals-based stock price boom reflects disperse information about increased future profits that are production linked. The stock-price boom then is a leading indicator of increased output growth. If the stock price boom reflects instead some temporary market-wide over-enthusiasm, then the nonfundamentals-based price boom is likely a harbinger of an eventual price crash. Crashing stock prices can be associated with strong downturns in economic activity. Recall the great crashes in , the 1990 crash in Japan, and the crashes in East Asia. A stock price boom, therefore, may predict either high or low output growth. If both fundamentals and extraneous factors are present in the data, we would not expect a 1

3 strong linear relationship in either direction. We might, however, expect that the price boom would be associated with increased volatility in the future growth rate. Although the price boom could be a weak linear predictor of output growth, it might signal increased heteroscedasticity volatility in the residuals from a linear output growth regression. The mirror image story holds when the stock market valuations are low. The low valuation could reflect a forecast of low future profits and output or it could reflect excessive pessimism. Regardless, while a large stock price bust may not lead in a linear fashion to a future growth slump or to a correcting price boom and growth upturn, it may well generate large residuals in a linear growth regression. We therefore search the data for evidence of a predictive link between measures of stock-market over-and under-valuation and volatility of output growth residuals from linear growth regressions. Do stock market extremes predict high output growth volatility? Our investigation is motivated by an ongoing policy debate. Most modern dynamic macroeconomic models assume stock prices are based only on market fundamentals. But popular and press discussions and a branch of academic research entertain the possibility that asset prices can diverge from fundamentals at times. 1 It is natural to ask: How should policy makers respond to asset booms and busts? Should they ignore asset-price movements even if they seem unjustified by fundamentals? If 1 For academic examples, see Allen and Gale (2000), Cogley (1999), and Hunter, Kaufman and Pomerleano (2003). 2

4 stock price booms are a leading indicator of greater output volatility, is there a stronger case for preemptive monetary restrictions when stock prices appear over-valued? 2 We will not resolve these policy issues here. Our goal is to inform the debate by providing some empirical background with the help of long-horizon, cross-country data. These data allow us to characterize aspects of the joint distribution of output growth and stock-price growth as well as the joint distribution of output volatility and various measures of stock price over-and under-valuation. We also have interest in learning whether the predictive power of stock prices varies across monetary regimes. It might be the case, for example, that stock prices are more significantly correlated with output growth or output volatility under a noninterventionist gold standard than under the more policy-active post-bretton Woods system. Of course, such a finding would not mean that the monetary regime in operation caused the difference in correlations between stock prices and output. Indeed, the adoption of a particular monetary regime may be the endogenous outcome of economic conditions. Suppose, for example, that the gold standard is the optimal regime choice when productivity growth is stable and extraneous stock-market noise is minimal. It is likely then that under the gold standard stock prices and output would be both stable and positively correlated. In the example, the gold standard policy itself causes neither the stability nor the correlation we would see in data. All observed changes result from 2 Bernanke and Gertler (2000) believe monetary policy should not respond to changes in asset prices except insofar as they signal changes in expected inflation. Cecchetti, Genberg, Lipsky and Wadhwani (2000) argue that monetary policy should act to minimize the likelihood of macroeconomic instability arising from extreme changes in asset prices. They believe the monetary authority should try to distinguish between a rise in asset prices driven by higher productivity growth and one driven by bubbles or some other sort of misalignment. 3

5 changes in the stochastic environment. We must, therefore, refrain from inferring regime causality in this study. 3 The rest of the paper is organized as follows. Section 2 describes the literature on asset prices and output that motivates our study. Section 3 lays out the methodology and data. Section 4 reports the results of our investigation. Section 5 concludes. II. The Relationship Between Stock Prices and Output Two lines of research, one by Bernanke and Gertler (1989), the other by Bordo and Jeanne (2002a, 2002b), have influenced our thinking. Bernanke and Gertler (BG) develop a model where the borrower s net worth affects the costs of financing capital investments. Business upturns improve net worth, lower borrowing costs, and increase real investment, amplifying the upturn. Business downturns work in the opposite way. If the firm s own stock helps collateralize its investment loans, then a high stock valuation leads to a real investment boom and subsequent output growth. Low stock valuation leads to collateralization difficulties, a drop in real investment, and a reduction in output growth. The BG flexible accelerator allows stock prices to anticipate future output growth for two reasons they reflect information about future productivity and they signal reduced borrowing costs. The BG work leads us to look for a linear association between stock-price growth and output growth. Stock and Watson (2003) review the large literature on asset prices as linear predictors of output growth and then undertake their own empirical assessment using quarterly data on many different asset prices for each of the G-7 countries over the 3 Making inferences about the effects of policy regime changes would require us to model the regime changes. 4

6 last forty years. Their findings are consistent with the earlier literature. They show that while some asset prices predict output growth in some countries in some periods, their predictive power is not reliable. The second line of research influencing us is by Bordo and Jeanne (BJ). They develop a model in which credit is based on the collateral of productive capital, and the expected level of productivity in the long run drives the price of collateral. If the longrun level of productivity turns out to be higher than expected, the price of the asset rises, increasing the collateral basis for new borrowing and increasing real activity. The opposite occurs if the long-run productivity is lower than expected. If the price of collateral falls below a certain threshold, there can be a widespread credit crunch that depresses economic activity. Their model suggests an essentially nonlinear relationship between asset prices and output growth. 4 In our work, we study both the linear relation between stock prices and output growth and the nonlinear relation between stock prices and output growth volatility. III. Methodology and Data Stock and Watson (2003) review the vast literature on predicting output growth using asset prices. They observe that the most common method of assessing the predictive content of asset prices is to examine significance tests or marginal R 2 s in output growth regressions. These regressions are usually bivariate, meaning that real 4 BJ (2002a, p.6) say: The linkages between asset prices, financial instability and monetary policy are complex because they are inherently non-linear and involve extreme (tail probability) events. The possible importance of events in the tails of distributions leads us to look for asset-price conditional residual heteroskedasticity in the linear residuals. 5

7 output growth is regressed only on lagged real asset price growth. Sometimes lagged output growth is included as a regressor, and sometimes additional predictors, such as money growth, are included also. Researchers commonly use a full sample rather than a rolling sample to estimate output growth and they rely on post-world War II data of high frequency, such as quarterly data. A number of asset prices have been tested for their predictive power. Stock and Watson (2003) test the predictive content of almost forty different asset prices and other indicators, including stock prices, exchange rates, housing prices, gold and silver prices, oil prices, aggregate commodity prices, interest-rate spreads, term spreads, and default spreads. The logic of testing the predictive content of stock prices is straightforward. Economic models show that stock prices equal the discounted expected value of future earnings. Thus stock prices (or returns) should help forecast earnings or, more broadly, output growth. The evidence is disappointing, however. As Stock and Watson write, Stock returns generally do not have substantial in-sample predictive content for future output, even in bivariate regressions with no lagged dependent variables (e.g. Fama [1981], Harvey [1989]), and any predictive content is reduced by including lagged output growth. (Stock and Watson, 2003, p.797) 5 5 Campbell (1999) used a log-linear representative agent model to show the log stock price-dividend ratio is the rational discounted forecast of dividend growth rates and stock returns, making it an appropriate forecasting variable. But he found the variable to have little predictive content in fifteen countries over the 1970s and 1980s. 6

8 For our test of a linear relation between stock prices and output, we use a version of the benchmark regression model in Stock and Watson (2003). Their regression is of the form: h y t +h h = β 0 + β 1 (L)y t + β 2 (L)x t + β 3 (L)Z t +ε t +h (1) where y is the growth of real output, 6 to be forecast h periods ahead, x is the growth rate of the real asset price, Z represents other predictors, and the β i (L)are lag polynomials. Stock and Watson always include the lagged dependent variable along with a single asset price indicator in their forecasting regressions, but they do not always include additional predictors. They use quarterly data, set h = 4 (quarters), and also choose four quarterly lags for the β i (L), noting that it is natural to use data-dependent lag lengths but crosscountry and cross-series comparisons make fixed lag lengths more appropriate. Our historical time-series data are available only on an annual basis. We therefore set h = 1 (year) and experiment with several lag lengths before settling on one annual lag for the dependent variable and two annual lags for the stock price variable. We do not include additional predictors that are standard in the literature, such as money growth, but we do consider the role of the monetary regime. We let Z be a vector of monetary regime dummy variables. We also interact the regime dummies with stock price growth to see if stocks influence growth differently across regimes. Our forecasting model takes the form: 6 Implementing (1) requires taking a stand on the order of integration of the dependent variable. Stock and Watson (2003) treat the logarithm of real output as integrated of order one, so y is the growth rate of output. 7

9 y t = µ + ay t 1 + β 1 (L)s t + b i Z it + β 2 (L)[s t * Z it ]+ ε t (2) where s is real stock price growth and two annual lags are used for β i (L). The squared residuals ( ε ) from the output growth regression in (2) are our 2 t measure of output growth volatility. We test whether this volatility is predicted by stock price booms and busts. The nonlinearity we investigate is conditional heteroscedasticity of the residuals from equation (2). Do stock-price booms and busts predict high volatility in the residuals from output growth regressions? If so, when we regress squared residuals on lagged boom/bust measures, we should get positive coefficients. We should find negative coefficients if booms/busts predict quiescence of output growth residuals. 7 Our forecasting model for volatility is: ε t 2 =δ +γ 1 (L)boom t + γ 2 (L)bust t + γ 3 (L)[boom t * Z it ] + γ 4 (L)[bust t * Z it ] +ν t (3) where the γ i (L) are lag polynomials. We include monetary regime dummies to check whether our measures of stock price over- or under-valuation influence volatility differently across regimes. We experiment with different methods of constructing the boom and bust measures. We first define a boom (bust) as a year in which the annual growth rate of real stock prices exceeds (falls short of) the country s historical average rate by at least one standard deviation. Table 1 illustrates the booms/busts obtained for each of the G-7 countries using this technique. As robustness checks, we alter the threshold needed to 7 In the appendix we produce a brief example to help fix ideas. 8

10 qualify as a boom or bust by varying the number of standard deviations from the historical average. 8 As additional robustness tests, we redefine a boom (bust) as in BJ (2002a), identifying a boom (bust) in years t, t-1 and t-2 when in year t the three-year moving average of the growth rate in real stock prices exceeds (falls short of) the average rate by x standard deviations of the average, where x can vary. 9 We also experiment with different ways of measuring volatility. In addition to specifying volatility as the contemporaneous squared residuals from the output growth regression, we also try measuring it either as a three-year or a five-year moving average of the squared residuals. We also compute residuals from an output growth regression that excludes all monetary regime dummies and a regression that includes regime dummies but excludes observations from two periods, wars and the transition off Bretton Woods. Our historical time-series data for stock prices, national income, and price indices come from Bryan Taylor s Global Financial Data. Our monetary regime classifications 8 With annual data, applying as much as two standard deviations from the average considerably reduces the number of identified booms and busts. 9 Using the first method for categorizing booms/busts in stock prices and setting x=1, we find in U.S. data that a boom year is one where the annual growth of real stock prices exceeds 19.46%, while a bust year is one where the growth of real stock prices is less than %. (See Table 1.) This definition of booms/busts picks up the busts in 1884, , and 2002, among others, as well as the booms in and in the second half of the 1990s. Using the second method for categorizing booms and busts, the one in BJ (2002a), we find that that the three-year average growth rate in stock prices in the U.S. has to exceed 11.45% to be designated a boom and fall below 8.41% to be a bust. While this second method of computing booms/busts does not pick up the bust in 1884 (where the three-year average fall in stock prices was 7.88%), it does capture many other episodes in a sensible way. 9

11 are standard in the literature. 10 We identify six regimes the gold standard, wars, the transition period around wars, Bretton Woods, the transition off Bretton Woods, and the post-bretton Woods era. The gold standard (including bimetallism) spans the pre-1913 period. The war regime covers (World War I), (World War II), and, for the United States, (the Civil War). The transition regime captures the interwar war period of , and, for the United States, the period after the U.S. Civil War from The Bretton Woods regime is , the transition off Bretton Woods is the period , and the post-bretton Woods regime is the period 1973-present. We plot the data in Figure 1, showing how real output growth, real stock price growth, and the monetary regime vary over time for each of the G-7 countries. IV. Results Results for the G-7 countries are reported in Table 2 and Table 3. These are representative results that probably make the strongest case for a significant relationship between output growth and stock price growth in the first stage and between output growth volatility and booms/ busts in stock prices in the second stage See, for example, Eichengreen and Leblang (2003) and Bordo (1999). 11 The results from all regressions are too numerous to be included here, but are available from the authors. We ran three versions of the output growth regression. The first excluded the monetary regime dummies, the second included them, and the third version included them but omitted data from wars and transition off Bretton Woods. We used residuals from each of these output-growth regressions to construct volatility measures. We measured volatility in three different ways, as the contemporaneous squared residuals, or as the three-year or five-year moving average of the squared residuals. We thus have nine different volatility measures. Each volatility measure was regressed on lagged measures of booms and busts. We tried six different measures of booms and busts. 10

12 Table 2 reports results from an output growth regression that includes regime dummies for pre-1914 ( gold ), the aftermath of war ( after ), and Bretton Woods ( bw ). The post-bretton Woods period is the omitted dummy regime, and observations during wars and the Bretton Woods transition period are excluded from the regression. Table 3 reports results when volatility is measured by the contemporaneous squared residuals from the Table 2 output-growth regression and a boom (bust) in stock prices is defined as a year in which the annual growth rate of real stock prices exceeds (falls short of) the country s historical average rate by at least one standard deviation. Table 2 shows that the monetary regime does not have a systematic effect on the predictive power of stock prices for output growth. For example, stock prices predict higher future output growth in the post-bretton Woods era in the United States, Canada and Japan, but not in the other G-7 countries. 12 They predict higher output growth during We first defined a boom (bust) as a year in which the annual growth rate of real stock prices exceeded (fell short of) the country s historical average rate by at least 0.75, 1.0 or 1.25 standard deviations. We also defined a boom (bust) as in BJ (2002a), identifying a boom (bust) in years t, t-1 and t-2 when in year t the three-year moving average of the growth rate in real stock prices exceeded (fell short of) the average rate by 0.75, 1.0, or 1.25 standard deviations of the average. We also experimented with different lag structures for the boom/bust variables. In Table 2, we report results from the third version of the output growth regression, the one that includes monetary regime dummies but excludes data from the war period and the transition off Bretton Woods. We take the contemporaneous squared residuals from this output growth regression as our measure of volatility and we report in Table 3 results where this volatility measure is regressed on once-lagged booms and busts, defined as years in which the annual growth rate of real stock prices exceeded (for booms) or fell short of (for busts) the country s historical average rate by at least one standard deviation. For Germany, the historical average was computed excluding the hyperinflation period. 12 The post-bretton Woods era is the omitted regime, so we examine the significance of the coefficients attached to sl1 and sl2 in Table 2 to determine the predictive power of stock prices during this regime. At least one of the coefficients is significant at the 95 percent confidence level for the U.S., Canada and Japan. Also observe that the p-value associated with the F test (sl1+sl2=0) at the bottom of Table 2 is less than 0.05 for 11

13 Bretton Woods in the United States, Canada, Germany and Italy, but not in the United Kingdom, France, or Japan. 13 These results are consistent with Stock and Watson (2003) and others who find stock prices are a leading indictor of output growth in the post-1958 period, but their predictive power varies by country and by period. Interestingly, stock price growth is a significant positive predictor of future output growth for the United States across all monetary regimes. The p-values from F- tests indicate that stock price growth is a good predictor of future output growth (at the 99 percent confidence level) under the bimetallism/gold standard, in the aftermath of the Civil War and World War I, during the Bretton Woods era and in the post-bretton Woods period. For the other G-7 countries, the predictive power of stock prices varies across monetary regimes. Indeed, the four European members of the G-7 have little in common except in the recent post-bretton Woods period. In this period, stock price growth fails to predict the subsequent year s output growth in all European countries. Table 3 shows that the relationship between stock price extremes and output growth volatility is more systematic by monetary regime. In the current post-bretton Woods era as well as under Bretton Woods, booms/busts are never a significant predictor of output growth volatility in any country. Since the post-bretton Woods regime is the omitted regime in Table 3, the insignificant coefficients attached to booml1 and bustl1 across all countries mean there is no predictive relationship between stock price extremes these three countries, so we can reject the null that lagged stock prices have no effect in the post-bretton Woods period. 13 The p-values associated with the F tests (sl1+(s*bw)l1=0) and (sl2+(s*bw)l2=0) are less than 0.05 only for the U.S., Canada, Germany and Italy. 12

14 and output growth volatility in the post-1973 period. The high p-values from F-tests on [booml1+(boom*bw)l1=0] and [bustl1+(bust*bw)l1=0] across all countries indicate no significant relationship at standard confidence levels between stock price extremes and output growth volatility during Bretton Woods. In contrast, booms are a significant predictor of greater volatility under the gold standard in all countries for which we have both stock price data and identified booms and busts (U.S., U.K. and Germany). 14 It is notable that the gold standard is the only regime in which stock price booms have predictive power in the U.K. Busts also predict greater volatility under the gold standard in the United States. In the interwar period, the predictive power of booms and busts is not systematic; only Canada and Italy show a significant link between stock price extremes and volatility. It is possible that booms and busts in stock prices predict future output growth volatility during some monetary regimes in some countries but the linkage is not discernable in annual data. As a robustness test, we apply our methodology to quarterly data. We use the Stock and Watson (2003) data on stock prices, output and deflators available for the period 1959:1 1999:4 to compute output growth residuals. 15 Table 4 displays results from regressing the contemporaneous squared residuals on thrice-lagged boom and bust measures. In the quarterly data, we find no systematic 14 Global Financial Data reports no stock price data for Japan and Canada in the pre gold-standard period, while France and Italy have no identified booms/busts in stock prices in the pre-1914 period for which stock price data are available. 15 The residuals are obtained from a growth regression that employs four lags of the dependent variable, four lags of real stock price growth, monetary regime dummies, and four lags of stock price growth interacted with the regime dummies. Real output is seasonally adjusted. Quarterly data are unavailable before 1959, so robustness tests apply only to the Bretton Woods and post-bretton Woods periods. 13

15 evidence that booms and busts predict output growth volatility in the Bretton Woods or post-bretton Woods periods. However, we do find that booms and busts occasionally predict volatility one, two or three quarters in the future. For example, in the post- Bretton Woods period, booms predict lessened volatility next quarter in the United Kingdom. Busts predict greater volatility two or three quarters in the future in four countries (the U.S., U.K., France and Japan). These results suggest that the inability to uncover in annual data a relationship between extreme changes in stock prices and output growth volatility during the Bretton Woods and post-bretton Woods periods may be due, in part, to the low frequency of the data. Even so, results using higher-frequency quarterly data do not suggest that this nonlinear relationship is significant in all G-7 countries under any particular regime. V. Conclusion Using historical time-series annual data for the G-7 industrial countries, we found that stock prices are a significant leading indictor of output growth, but their predictive power varies by country and monetary regime. This matches and extends the findings of Stock and Watson (2003) who used only post-world War II data. Only in the United States do stock prices positively and significantly predict output growth across all monetary regimes, from the pre-1914 gold standard to the post-bretton Woods operating since We also found that booms and busts in stock prices fail to predict greater output growth volatility in any G-7 country during the post-bretton Woods period or during the earlier Bretton Woods system. We do, however, find evidence that extremes 14

16 in stock prices are correlated with greater output growth volatility under the gold standard in the countries for which we have data. While our results do not directly answer the important policy questions we set out in the introduction, they do help formulate the set of questions policy modelers will need to confront. Why is it that stock prices linearly predict output growth across all monetary regimes in the U.S. but not elsewhere in the G-7? Is it because of different shocks hitting the U.S.? Is it because of different policy-operating characteristics across countries within regimes that leave the U.S. with significant stock-price effects but remove the effects for other countries? What types of shocks lead countries to change their policy regimes? If we think of the gold standard period as being the least activist monetary regime in the sample, then our findings are consistent with the Bordo-Jeanne (2002a) idea that when policy makers are unresponsive to stock prices, the stock-price output-growth relation is nonlinear. Extreme movements in stock prices then become a leading indicator of greater output growth volatility. 15

17 References Allen, Franklin and Douglas Gale, Bubbles and Crises, The Economic Journal, Vol Bernanke, Ben and Mark Gertler, Should Central Banks Respond to Movements in Asset Prices? American Economic Review, Vol. 91(2) May, pp , Monetary Policy and Asset Price Volatility, NBER Working Paper 7559, February. Bordo, Michael and Olivier Jeanne, 2002a. Monetary Policy and Asset Prices: Does Benign Neglect Make Sense? IMF Working Paper 02/225., 2002b. Boom-Busts in Asset Prices, Economic Instability, and Monetary Policy, NBER Working Paper No. 8966, June. Bordo, Michael and Anna Schwartz, 1999 The Operation of the Specie Standard; Evidence for Core and Peripheral Countries, , in Michael Bordo (ed.), The Gold Standard and Related Regimes, Cambridge, U.K.: Cambridge University Press. Cogley, T., Should the Fed Take Deliberate Steps to Deflate Asset Prices? Federal Reserve Bank of San Francisco Economic Review 1, Campbell, John, Asset Prices, Consumption and the Business Cycle, in J.B. Taylor and M. Woodford (eds.), Handbook of Macroeconomics, Vol. 1, Amsterdam: Elsevier, Cecchetti, Stephen, Hans Genberg, John Lipsky, and Sushil Wadhwani, Asset Prices and Central Bank Policy, Geneva Reports on the World Economy, No. 2, International Center for Monetary and Banking Studies and Centre for Economic Policy Research. Eichengreen, Barry and David Leblang, Capital Account Liberalization and Growth: Was Mr. Mahathir Right? NBER Working Paper No. 9427, January. Fama, E. F., Stock Returns, Real Activity, Inflation and Money, American Economic Review 71, Harvey, C.R., Forecasts of Economic Growth from the Bond and Stock Markets, Financial Analysts Journal 45 (5),

18 Hunter, William, George Kaufman and Michael Pomerleano, Asset Price Bubbles: The Implications for Monetary, Regulatory and International Policies, Cambridge: MIT Press. Stock, James and Mark Watson, Forecasting Output and Inflation: The Role of Asset Prices, Journal of Economic Literature, Volume 41, Issue 3, September. 17

19 Appendix Suppose there are 3 states, A, B, and C. Each state occurs with equal probability 1/3. In state A at time t, there is no information about what will happen to output next period. In state B at time t, there is a positive stock-pricing error that indicates low output at t+1. In C, agents learn good news at t about next period s output. The t+1 outputs are: A) y t +1 (A) = y + z t +1, error is mean zero with variance σ 2. B) y t +1 (B) = y h, h>0. There is a post-bubble bust. C) y t +1 (C) = y + h. There is a post-information boom. Asset prices are given by: p t = E t ρ i y t +i + D(S)b(t), where D(S) is a dummy i=1 variable equal to 0 in states A and C and D(B) =1. The pricing error is b(t) = 2ρh. If we regress: y t +1 =α + βp t +ε t +1, then β = cov(y, p ) t +1 t = 0, α = y. There is no linear var( p t ) prediction from stock price to future output. 2 When we regress ε t +1 on p t, the regression coefficient will be cov(ε 2 t +1, p) and its var(p) sign is determined by cov(ε 2, p) = ( σ 2ρh + h 2 2ρh ) = 2h (h 2 σ 2 ). Since h > 0, this is positive as long as h >σ. In this example, if asset booms today predict relatively big output shocks next period, this translates to h >σ and should produce a positive 2 regression coefficient on p t when ε t +1 is regressed on p t.. 18

20 Figure 1: History of Stock Prices, Output and the Monetary Regime in the G-7 United States: gold/bimeta w t gold w t w BW t post-bw w=war year BW=Bretton Woods t=transition after war or after BW output growth stock price growth US: year output growth stock price growth 19

21 US: year real output growth real stock price growth 20

22 UK: gold w t w BW t post-bw w=war year BW=Bretton Woods t=transition after war or after BW real output growth real stock price growth UNITED KINGDOM: Crimean War year Anglo-Persian War Boxer Rebellion 1900 real output growth real stock price growth 21

23 UK: year real output growth real stock price growth 22

24 France: gold w t w BW t post-bw w=war year BW=Bretton Woods t=transition after war or after BW real output growth real stock price growth France: year real output growth real stock price growth 23

25 Germany: gold w t w BW t post-bw w=war BW=Bretton Woods year t=transition after war or after BW real output growth real stock price growth Germany: year real output growth real stock price growth 24

26 Germany: year real output growth reqal stock price growth 25

27 Italy: gold w t w BW t post-bw w=war year BW=Bretton Woods t=transition after war or after BW real output growth real stock price growth ITALY: year real output growth real stock price growth 26

28 CANADA: t w BW t post-bw w=war year BW=Bretton Woods t=transition after war or after BW real output growth real stock price growth CANADA: year real output growth real stock price growth 27

29 JAPAN: w t w BW t post-bw w=war year BW=Bretton Woods t=transition after war or after BW real output growth real stock price growth JAPAN: year real output growth real stock price growth 28

30 TABLE 1: Booms and Busts in Stock Prices Booms (in boldface) are at least one standard deviation above the average growth of real stock prices. Busts (in shaded italics) are at least one standard deviation below the average growth of real stock prices. United States United Kingdom France Germany Italy Canada Japan boom threshold bust threshold Year Growth Rate Growth Rate Growth Rate Growth Rate Growth Rate Growth Rate Growth Rate 29

31 United States United Kingdom France Germany Italy Canada Japan

32 United States United Kingdom France Germany Italy Canada Japan

33 United United France Germany Italy Canada Japan States Kingdom

34 33

35 34

36 35