NRG WORKING PAPER SERIES
STOCK MARKET VOLATILITY AND MACROECONOMIC
                               UNCERTAINTY
            ...
NRG WORKING PAPER SERIES

                   Stock Market Volatility and Macroeconomic
                                   ...
Abstract
This paper provides empirical evidence on the link between stock market volatility and macroeconomic
uncertainty....
1. Introduction
The link between the macroeconomy and the stock market has intuitive appeal, as
macroeconomic variables af...
In examining which factors drive systematic stock return covariation, Chan, Karceski and
Lakonishok (1998) even conclude (...
estimates leading to different empirical outcomes. The fourth and, we believe, most
important limitation is that time-seri...
Figure 1 shows the gist of our paper for one of our macroeconomic variables. It combines
SPF-based unemployment uncertaint...
Schwert (1989), we adjust the critical values from regressions of stock market volatility on
macroeconomic volatility and ...
Monday, 9 on Tuesday, 7 on Wednesday, 5 on Thursday and 16 on Friday. By the same
token, I tJAN is an indicator variable e...
3. Data and methodology
3.1 Measuring macroeconomic uncertainty
The SPF is our sole source of macroeconomic forecasts. It ...
definition was not uniform across forecasters prior to 1990Q4. This leaves us with the ten
variables listed in Table 2.


...
3.2 Measuring stock market volatility
We follow the approach of Schwert (1989) in calculating the standard deviation of qu...
nineties. The effects of the Internet bubble at the turn of the Millennium are also clear from
Figure 2.


3.3 Measuring m...
4. The relation between macroeconomic uncertainty and macro-
        economic volatility
As discussed above, Schwert’s (19...
coefficients between volatility and uncertainty of the deflator and corporate profits, all
correlations coefficients in pa...
bootstrap experiment to determine the finite sample properties of the Newey and West
(1987) t-statistics, R-squares and li...
median first order autocorrelation of the long time-series is 0.66, compared to 0.07 for the
volatility series. When we ge...
has nothing to say about causality running either from the stock market to the
macroeconomy or vice versa. In section 6 be...
(8)     σ SP500,t = α + β uncert.σ tY ,uncert. + β vol.σ tY ,vol. + ε t

(9)     σ SP 500,t = α + β uncert.σ tY ,uncert. +...
contrast, our calendar time measure would take returns between April 1st and June 30th.
From 1990Q2 onwards, when the Phil...
earlier work showing that stock market volatility increases during recessions.
Macroeconomic uncertainty measures also hav...
Appendix: Bootstrapping critical values
In order to provide evidence on the finite sample properties of the t-values and R...
The 10,000 observations of t ( β i ) and R 2,i form the bootstrap distribution for the t-value and
                       ...
References
Andersen, T.G., T. Bollerslev and F.X. Diebold (2002), Parametric and Non-Parametric
Volatility Measurement, wo...
Engle, R.F. (1982), Autoregressive Conditional Heteroskedasticity with Estimates of the
Variance of United Kingdom Inflati...
Poon, S., Taylor, S.J. (1991) Macroeconomic factors and the UK stock market, Journal of
Finance and Accounting, 18, p. 619...
Figure 1: Macroeconomic uncertainty versus macroeconomic volatility
Unemployment uncertainty as measured by the cross-sect...
Table 1: The impact of SPF releases on the stock market
The table provides Gaussian maximum likelihood estimates of the pa...
Table 3: Relationships between uncertainty, volatility and recessions
Panel A shows betas and Newey and West (1987) correc...
Table 4: Stock market volatility and macroeconomic uncertainty and volatility: before 1997
The regression model σ SP 500,t...
Table 5: Stock market volatility and macroeconomic uncertainty and volatility: from 1997
The regression model σ SP 500,t =...
Table 6: Incremental effects
The regression model σ SP 500, t = α + βσ tY + γσ SP 500 ,t −1 + ε t contains a constant, lag...
Table 7: Incremental and additional effects
Panel A reports beta-coefficients and Newey and West (1987) t-values for the r...
Table 8: Forecasting stock market volatility
Panel A (B) reports beta-coefficients and Newey and West (1987) t-values for ...
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Stock Market Volatility and Macroeconomic Uncertainty ...

  1. 1. NRG WORKING PAPER SERIES STOCK MARKET VOLATILITY AND MACROECONOMIC UNCERTAINTY EVIDENCE FROM SURVEY DATA Ivo J.M. Arnold, Evert B. Vrugt Nyenrode Research Group March 2006 no. 06-08
  2. 2. NRG WORKING PAPER SERIES Stock Market Volatility and Macroeconomic Uncertainty Evidence from Survey Data Ivo J.M. Arnold Evert B. Vrugt March 2006 NRG Working Paper no. 06-08 NRG The Nyenrode Research Group (NRG) is a research institute consisting of researchers from Nyenrode Business Universiteit and Hogeschool INHOLLAND, within the domain of Management and Business Administration. Straatweg 25, 3621 BG Breukelen P.O. Box 130, 3620 AC Breukelen The Netherlands Tel: +31 (0) 346 - 291 696 Fax: +31 (0) 346 - 291 250 E-mail: nrg@nyenrode.nl NRG working papers can be downloaded at http://www.nyenrode.nl/research/publications
  3. 3. Abstract This paper provides empirical evidence on the link between stock market volatility and macroeconomic uncertainty. We show that US stock market volatility is significantly related to the dispersion in economic forecasts from SPF survey participants over the period from 1969 to 1996. This link is much stronger than that between stock market volatility and the more traditional time-series measures of macroeconomic volatility, but disappears after 1996. Keywords Stock market volatility, macro-economic factors, survey data JEL codes E44, G12 Address for correspondence Ivo J.M. Arnold (corresponding author) Universiteit Nyenrode, Straatweg 25, 3621 BG, The Netherlands E-mail: i.arnold@nyenrode.nl Evert B. Vrugt ABP Investments, Amsterdam, The Netherlands E-mail: evert.vrugt@abpinvestments.nl The views expressed in this paper do not necessarily reflect the views of ABP Investments. 2
  4. 4. 1. Introduction The link between the macroeconomy and the stock market has intuitive appeal, as macroeconomic variables affect both expected cash flows accruing to stockholders and discount rates. A common theoretical framework connecting stock prices to fundamentals is the dividend discount model. According to this model, new macroeconomic information will affect stock prices if it impacts on either expectations about future dividends, discount rates, or both. Empirically, the evidence linking macroeconomic factors to the stock market is mixed at best. Chen, Roll, and Ross (1986) were one of the first to explore the link between macroeconomic variables and stock prices. Using a multifactor model, they found evidence that macroeconomic factors are priced. Pearce and Roley (1985), Hardouvelis (1987) and Cutler, Potterba and Summers (1989) also conclude that stock prices respond to macroeconomic news. Subsequent studies have produced more mixed results. While some studies confirmed Chen, Roll and Ross’s (1986) findings (see e.g McElroy and Burmeister, 1988, Hamao, 1988), others have been less successful (see e.g Poon and Taylor, 1991, Shanken, 1992). Moving from first to second moments, Veronesi (1999) presents a theoretical model that formalizes the link between economic uncertainty and stock market volatility. He shows that investors are more sensitive to news during periods of high uncertainty, which in turn increases asset price volatility. Yet establishing the empirical link between the second moments of stock returns and macroeconomic variables has proven to be even more challenging than that between their first moments. Based on US data, Schwert (1989) concludes that there is a volatility puzzle (p. 1146): “The puzzle highlighted by the results in this paper is that stock volatility is not more closely related to other measures of economic volatility.”
  5. 5. In examining which factors drive systematic stock return covariation, Chan, Karceski and Lakonishok (1998) even conclude (p. 182): “... the macroeconomic factors do a poor job in explaining return covariation. In terms of understanding the return covariation across stocks, widely used factors such as industrial production growth and unanticipated inflation do not seem to be more useful than a randomly generated series of numbers.” There are a few exceptions to this negative finding, mainly for countries or periods where macroeconomic volatility has been higher than in the US. For Europe, Errunza and Hogan (1998) find a significant influence of monetary and real macroeconomic volatility on stock market volatility for the seven largest European countries. Bittlingmayer (1998) finds significant effects of economic and political uncertainty on German stock market volatility for the period 1880–1940, yet this period includes rather dramatic economic and politicial circumstances and may thus not be representative for more stable times. Given the poor results in explaining stock market volatility, at least for the US, a more recent branch of the literature focuses on identifying the effect of macroeconomic announcements on asset volatility using high frequency data, see e.g. Jones, Lamont and Lumsdaine (1998) for fixed income, Andersen et al. (2003) for foreign exchange and Flannery and Protopapadakis (2002) for equities. Using dummies to account for days with macroeconomic announcements, this approach is more successful in linking macroeconomic news to asset volatility. It has been difficult, however, to establish this link beyond the daily-frequency domain. Starting with Schwert (1989), the most common way to extract macroeconomic volatility is by means of a time-series model. The absolute residuals from autoregressive models fitted on stock returns and macroeconomic growth rates are typically used as volatility estimates. But there are some limitations to this approach, see also Giordani and Söderlind (2003). First, a major concern is that time-series models are backward looking, whereas most applications are about ex-ante uncertainty. Second, time-series measures present problems when time-series are subject to structural breaks. Third, there is no universal time-series model to extract expectations. Different models will thus yield different uncertainty 4
  6. 6. estimates leading to different empirical outcomes. The fourth and, we believe, most important limitation is that time-series volatility captures the volatility in just one single ex- post realization of macroeconomic developments out of many possible ex-ante scenarios. One realized path of macroeconomic growth rates may appear smooth ex-post, notwithstanding significant ex-ante uncertainty as to which path would occur. The time- series dimension of the data will not capture this notion of uncertainty adequately. In this context, Robert Merton has interpreted the Great Depression as an example of the “Peso problem” (see Schwert (1989). At that time, there was significant uncertainty whether the economic system as a whole would survive, which is not apparent by looking at the ex-post data. A similar reasoning has been applied by Kleidon (1986) on the excess volatility puzzle, where actual stock prices appear to be much too volatile compared to the smooth patterns in ex-post dividends which we observe. In this paper, we provide new empirical evidence on the link between stock market volatility and macroeconomic uncertainty. We show that stock market volatility is significantly related to the dispersion in economic forecasts from participants in the Survey of Professional Forecasters (SPF) over the period 1969–1996, rather than to macroeconomic time-series volatility. This finding adds to a literature favouring dispersion-based measures of uncertainty over times-series volatility. Also using the SPF, Giordani and Söderlind (2003) show that disagreement among forecasters is a reasonable proxy for uncertainty. Commonly applied time-series models, on the other hand, have difficulties in capturing macroeconomic uncertainty. Driver, Trapani and Urga (2004) develop a theoretical framework relating time- series based measures of volatility to dispersion-based measures of uncertainty. They state that (p. 12-13): “The general pattern of the results suggests that time series measures are not related in any simple way to the dispersion of expectations. ... care should be used when representing time-series volatility measures as indices of uncertainty, given that the dispersion across agents have been found in previous literature to be good proxy for subjective uncertainty.” 5
  7. 7. Figure 1 shows the gist of our paper for one of our macroeconomic variables. It combines SPF-based unemployment uncertainty, time-series based unemployment volatility and stock market volatility. [Insert Figure 1 here] The following observations can be made from Figure 1. First, there seems to be more variation in unemployment uncertainty than in unemployment volatility. Second, on the face of it, there seems to be a much stronger link between unemployment uncertainty and stock market volatility than between unemployment volatility and stock market volatility. Third, recession periods are associated with large spikes in unemployment uncertainty. This is compatible with Merton’s Peso problem interpretation and with Veronesi’s (1999) theoretical model. Unemployment volatility seems to be much less strongly associated with recessions. Finally, from the mid-1990s onwards, stock market volatility is trending upward with no clear link with either unemployment uncertainty or unemployment volatility. The behavior of stock market volatility cannot be explained by macro factors during this period. This comes to us as a puzzle. If these results stand up to formal testing, as we will see below, Schwert’s (1989) volatility puzzle can be narrowed down to a specific sample period. This corresponds to a more recent paper by Schwert (2002), in which he observes that in the stock market data since 1997 “the most unusual behavior has occurred” (p. 4) and documents the importance of the technology sector in explaining stock market volatility during the late 1990s. This paper is organized as follows. As our first contribution to the literature, the next section documents the impact of SPF releases on stock volatility within a GARCH-framework. A significant impact of SPF releases on the stock market would increase our confidence in the relevance of this source of data for the stock market. Section 3 describes the construction of our data. Next, in section 4 we provide evidence on whether macroeconomic uncertainty and macroeconomic volatility are closely related or distinct pieces of information. The main results of the contemporaneous link between macroeconomy uncertainty and stock market volatility are presented in section 5. Section 6 reports evidence on predictability of stock market volatility. In contrast to Bittlingmayer (1998), Errunza and Hogan (1998) and 6
  8. 8. Schwert (1989), we adjust the critical values from regressions of stock market volatility on macroeconomic volatility and uncertainty for small sample biases and the fact that macroeconomic volatility is measured rather than observed. This turns out to be important, as adjusted critical values are considerably higher than their asymptotic counterparts. We do so using a bootstrap experiment that is explained in the appendix. 2. Does the release of the SPF matter to the stock market? In order to establish whether the stock market reacts to the actual release of the SPF, we collect daily values of the S&P 500 index from January 1990 to January 2005 as well as the release dates for the survey. If the release of the SPF contains a substantial piece of new information to the stock market, its announcement should have an impact on daily stock returns. Ideally, we would like to construct a measure that captures the unexpected component op the SPF contents, containing only information new to the market. This is the route taken by Andersen, Bollerslev, Diebold and Vega (2003) using high-frequency exchange-rate data and market participant expectations for series to be announced during the subsequent week. For the SPF, that contains eighteen different economic indicators, no such measure of expectations is available. We therefore follow the analytical framework employed by Jones, Lamont and Lumsdaine (1998) and Flannery and Protopapadakis (2002) and analyze the behavior of conditional stock market risk on days when the SPF is released. A GARCH (1,1) model is estimated adding a set of calendar dummies: 5 (1) Rt , S & P = μ + δ 1 I tSPF + ∑ δ i I tday i + δ 6 I tJAN + ε t i=2 5 (2) σ t2 = ω + αε t2−1 + βσ t2−1 + γ 1 I tSPF + ∑ γ j I tday j + γ 6 I tJAN , j =2 where Rt , S & P is the continuously compounded daily return on the S&P 500, I tSPF is an indicator variable equaling one on days when the SPF is released and zero otherwise, I tday i are dummies for the days of the week to take into account possible interactions between the release of the SPF and well-documented effects of the day-of-the-week on stock returns and volatility. Of the total number of 59 SPF releases since January 1990, 22 occurred on 7
  9. 9. Monday, 9 on Tuesday, 7 on Wednesday, 5 on Thursday and 16 on Friday. By the same token, I tJAN is an indicator variable equaling one in January and zero otherwise to account for the January-effect. All parameters are estimated using maximum likelihood assuming normally distributed errors. Table 1 summarizes the results. [Insert Table 1 here] The analysis reveals significant announcement effects of the SPF on both the stock market mean and its conditional variance. While the stock market return is significantly higher on days when the SPF is released, risk is significantly lower. The January indicator is insignificant in both the mean and the variance equation. Though none of the individual day- of-the-week dummies is significant, joint significance cannot be rejected for the conditional variance equation using a Wald test. The release of the SPF may reveal new information (either positive or negative) to market participants not previously incorporated into the stock market. Absorbing the new information may increase stock market volatility and hence we would expect a positive link between the SPF release and stock market volatility. The evidence in Table 1 points in the opposite direction and presents a puzzle. However, Flannery and Protopapadakis (2002) also find that the announcements of some macroeconomic variables are associated with lower (rather than higher) conditional volatilities, most notably for the consumer price index, new home sales, industrial production, leading indicators, producer price index and real GNP/GDP. Except for the leading indicators, these variables are also part of the SPF. Furthermore, out of three series for which Flannery and Protopapadakis (2002) find a statistically significant positive effect, only one (employment) is included in the SPF. Therefore, although our finding of a negative effect on conditional variance may appear puzzling, it is consistent with the findings of Flannery and Protopapadakis (2002) and indicates that the SPF is a relevant source of information for the stock market with an impact on stock market risk that seems consistent with the evidence in Flannery and Protopapadakis (2002) on the release of individual series. 8
  10. 10. 3. Data and methodology 3.1 Measuring macroeconomic uncertainty The SPF is our sole source of macroeconomic forecasts. It was started in 1968 by the American Statistical Association and the National Bureau of Economic Research. The Federal Reserve Bank of Philadelphia took over the SPF in June 1990. Participants in the survey are professional forecasters mainly from the business world and Wall Street. They submit their forecasts anonymously to “... encourage people to provide their best forecasts, without fearing the consequences of making forecast errors. In this way, an economist can feel comfortable in forecasting what she really believes will happen to interest rates, even if it contradicts her firm’s official position.” (Croushore, 1993, p. 8) From the SPF, we take ten economic variables that are currently included in the survey. Some of the variables have been in the survey since inception (1968Q4), whereas others have been added in 1981Q3. Table 2 provides a list of the survey variables including their start date and the abbreviations used in the remainder of this paper. [Insert Table 2 here] In terms of the dividend discount model, nominal GDP, corporate profits, industrial production and real GDP potentially affect current and future cash flows. Interest rates (like the T-bill rate) primarily relate to the discount rate used to value future cash flows. Additionally, Fama and French (1989) document that changes in short-term interest rates are associated with changes in economic conditions. Inflation may affect the relative attractiveness of different investment alternatives and change the value of real cash flows to stockholders. As Chen, Roll and Ross (1986) note, changes in the indirect marginal utility of wealth will influence pricing. A possible measure for this is real consumption. Other variables that may proxy for changes in marginal utility are the unemployment rate as information about future human capital and housing as one of the most important components of wealth. Apart from consumption, the SPF also contains details on other components of GNP. We do not separately consider these smaller components. Furthermore, we exclude the 10-year Treasury bond rate from the analysis because it is only available from 1992 onwards. Finally, we exclude the AAA-corporate bond yield, as the 9
  11. 11. definition was not uniform across forecasters prior to 1990Q4. This leaves us with the ten variables listed in Table 2. Laster, Bennett and Geoum (1999) claim that survey participants may have different incentives when submitting a forecast. For example, participants may be inclined to make extreme forecasts, because a bold forecast that proves to be correct has a higher payoff than an average forecast that turns out to be correct. This could influence the accurateness of survey data. We expect, however, that this is not a major concern for the SPF, as their participants are anonymous. Using the SPF, Giordani and Söderlind (2003) show that disagreement among forecasters on a point forecast is good proxy for uncertainty. We therefore calculate cross-sectional standard deviations for each variable in each quarter as our measure of uncertainty. For series that are not reported in percentage terms (all except unemployment, inflation and the T-bill rate), we first calculate predicted growth rates for each forecaster as follows: ΔYi ,tt+ k = (Yi ,tt+ k / Yi ,tt−1 ) − 1 , where ΔYi ,tt+ k is the predicted growth rate between the previous quarter and quarter t+k of variable Y at time t by forecaster i. Yi ,tt−1 is the level of variable Y in the quarter preceding the survey date as observed at time t by forecaster i. Theoretically, participants could disagree on this value but given that it is public information at the time the survey is taken, this rarely occurs. Yi ,tt+ k is the predicted value of variable Y in quarter t+k made at time t by forecaster i. Below we use the following notation for uncertainty (U), where U1 refers to k=1, U4 to k=4 and the current quarter to k=0. The cross-sectional standard deviations across all forecasters are calculated at each survey date for each of the ten variables that we consider. This is our measure of macroeconomic uncertainty in the remainder of this paper. When the Philadelphia Fed took over the survey in 1990, the survey was sent out too late for 1990Q2. To correct for this, the Philadelphia Fed mailed the survey out together with the 1990Q3 edition. Therefore, in filling in the 1990Q2 data, forecasters had the benefit of hindsight. We have re-run the analyses with a dummy included for 1990Q2, but this did not affect the results. 10
  12. 12. 3.2 Measuring stock market volatility We follow the approach of Schwert (1989) in calculating the standard deviation of quarterly stock returns: σ SP 500, t = ∑ (rSP 500, i − μ t ) 2 , Ni (3) i =1 where Ni is the number of daily returns in quarter t, rSP500,i is the return of the S&P 500 on day i and µt is the average daily return during quarter t. Figure 2 plots the quarterly standard deviation of the S&P 500. [Insert Figure 2 here] Overall, the stylized fact that stock market volatility is persistent is well reflected in Figure 2. Although predicting daily returns by past daily returns is difficult, predicting squared daily returns with past squared daily returns works remarkably well. This feature of financial data is captured by the ARCH- and GARCH-models pioneered by Engle (1982) and Bollerslev (1986), respectively. Figure 2 also shows the impact of the October 1987 crash on market volatility, which forms a clear outlier from a statistical point of view. Following Campbell, Lettau, Malkiel, and Xu (2001) we substitute the second highest quarterly stock market volatility from the sample for 1987 Q4 in the remainder of this paper. This is an ad hoc solution, but avoids a disproportionate influence of a single observation, while leaving in an important event (see Campbell et al., 2001). We experimented with different treatments of the 1987 stock market crash, but this did not affect our results materially. 1 Another remarkable observation is that volatility is trending upward since its low level in the mid-nineties, with the effects of the financial crises in Asia and Russia also visible in the figure. It is only since 2002 that the volatility of the S&P 500 has come down. Similar observations have been made by Schwert (2002) on the volatility of the Nasdaq during the 1 When taking the average volatility over the sample period and substituting this for 1987Q4, the link between stock market volatility and variability of the macroeconomy is more significant. The same holds when taking the average of the preceding and subsequent quarter. 11
  13. 13. nineties. The effects of the Internet bubble at the turn of the Millennium are also clear from Figure 2. 3.3 Measuring macroeconomic volatility We collect realizations for the macroeconomic variables in the SPF from two data sources. First, we use the February 2005 edition of the Real Time Dataset for Macroeconomists (RTDSM) from the Federal Reserve Bank in Philadelphia. We are able to match eight out of ten SPF series with the RTDSM database. Variable definitions are identical for these variables: when comparing median values across forecasters from the quarter preceding the survey date (that forecasters can know) with initial unrevised data from the RTDSM, we observe a perfect fit. We are not able to match the RTDSM with the SPF for industrial production and new private housing units started. For these two series, our data source is Thomson Financial Datastream (with mnemonics respectively USIPTOT.G and USHOUSE.O). These series are also closely related to the corresponding SPF data: correlations of levels (first differences) between SPF previous quarter values and these series are in excess of 0.99 (0.94). We follow Bansal, Khatchatrian and Yaron (2005) in applying a non-parametric measure for macroeconomic volatility. For each macroeconomic series Y, we estimate an AR(1)-model and collect the residuals ε tY . Volatility is then calculated as follows: ⎛ J ⎞ (4) σ tY−1, J = log⎜ ∑ ε tY− j ⎟ ⎜ ⎟ ⎝ j =1 ⎠ Below, we consider lag values for J = 1 and 4. Alternatively, different weights could be chosen in the summation of absolute residuals, but Andersen, Bollerslev and Diebold (2002) show that our current specification is more informative about ex-ante volatility. 12
  14. 14. 4. The relation between macroeconomic uncertainty and macro- economic volatility As discussed above, Schwert’s (1989) puzzle relates to the absence of a relationship between macroeconomic volatility and stock market volatility. In the same paper, however, Schwert presents evidence that stock market volatility is significantly higher during NBER indicated recessions than in non-recessionary periods. This suggests that the link between macroeconomic volatility and recessions is not very tight and sheds some doubts on the suitability of time-series based volatility measures. Possibly, dispersion-based macroeconomic uncertainty has a closer link to both recessions and stock market volatility. As a prelude to our main regressions, Table 3 therefore reports empirical results on the mutual relationships between macroeconomic uncertainty, macroeconomic volatility and NBER recessions. We estimate the following regression (see also Veronesi (1999)): (5) σ tY = α + β * NBER t + ε t , where σ tY measures either the cross-sectional standard deviation from the SPF (U1) or the corresponding macroeconomic volatility (V1). Our choice for a one-quarter horizon closely corresponds to the metric often used in empirical research, see e.g. Schwert (1989) and Errunza and Hogan (1998). NBER is a dummy variable equalling one during NBER indicated recession periods and zero otherwise. In order to use as many recession periods as possible, the analysis is confined to series that start in 1969. [Insert Table 3 here] Panel A shows that for all macroeconomic variables considered, macroeconomic uncertainty is significantly higher during recessions, confirming Veronesi’s (1999) theoretical model. In contrast to the uncertainty measures, volatility is significantly higher during recessions only for unemployment and industrial production. Further evidence in panels B-C shows correlations between uncertainty and volatility (panel B), among the uncertainty measures (upper triangle of panel C) and among the volatility measures (lower triangle of panel C). All coefficients significant at a 5% level are in bold. With the exception of two correlation 13
  15. 15. coefficients between volatility and uncertainty of the deflator and corporate profits, all correlations coefficients in panel B are significantly different from zero at a 5% level. Comparing panel B and panel C, the correlations among the uncertainty measures of different macroeconomic variables are in general higher than the correlations between uncertainty and volatility of the same macroeconomic variable and correlations among the volatility measures of different macroeconomic variables. This suggests that uncertainty measures are better able to capture moments of what we could call “general economic unease”, where forecasters disagree about the general direction in which the economy will go and dispersion-based uncertainty measures for different variables will reflect this at the same time. Summing up, the results so far indicate that dispersion-based uncertainty measures are more closely related to recessions than time-series based volatility measures. In the next section we will analyze whether this conclusion can be extended to stock market volatility. 5. Linking stock volatility to macroeconomic uncertainty and volatility We now turn to a more direct test of the explanatory power of macroeconomic uncertainty and volatility for stock market volatility. In the first subsection, we present results of contemporaneous regressions of stock market volatility on a constant and a single macroeconomic variable (either uncertainty or volatility). We move on to test the explanatory power of single macroeconomic variables beyond the information that is contained in lagged stock market volatility itself. Finally, in the third section we conduct a “horserace” between the uncertainty and volatility measures. 5.1 Direct effects Our first set of analyses examines regressions of the following form: (6) σ SP 500,t = α + βσ tY + ε t , where σ SP 500 ,t is the quarterly stock market volatility based on daily returns from equation (3) and σ tY is either macroeconomic uncertainty (U1/U4) or macroeconomic volatility (V1/V4) for variable Y. For the period before 1997, Table 4 contains parameter estimates for β as well as the Newey and West (1987) corrected t-values and R-squares. We use a 14
  16. 16. bootstrap experiment to determine the finite sample properties of the Newey and West (1987) t-statistics, R-squares and likelihood ratio tests. Based on fitted time-series models, we simulate stock market volatility, macroeconomic volatility and macroeconomic uncertainty 10,000 times. These processes are simulated independently from each other. In each run, we collect parameter estimates, t-values and R-squares, which form the bootstrap distributions under the null that macroeconomic risks are unrelated to stock market volatility. For macroeconomic volatility, we simulate the macroeconomic variable itself (rather than its volatility series) and construct the non-parametric volatility measure as described in section 3.3 in each run. Hence, t-values, R-squares and likelihood ratio test statistics from the simulation take into account the two-step procedure to generate macroeconomic volatility, just as in the original data. The appendix provides more details on the bootstrap procedure. [Insert Table 4 here] Table 4 shows that all U1 uncertainty variables are significantly different from zero at the 10% level at least, with the exception of T-bill uncertainty. The insignificance of the 1.99 t- value for T-bill uncertainty illustrates the effect of taking into account small sample properties. Using standard asymptotic tables, this entry would have been significant at the 5% level. Furthermore, these nine variables also individually account for a significant part of the variation in stock market volatility, as evidenced by the significant R-squares. Moving to the U4 measure, uncertainty regarding the GDP deflator and the inflation rate lose their significance. The results for the corresponding volatility measures are much weaker. Volatility of nominal GDP, the deflator, corporate profits and the T-bill rate are insignificantly related to stock market volatility. For the fourth quarter estimates the results deteriorate further, as the volatility of industrial production loses its significance. For the long sample period, the uncertainty variables are jointly significantly different from zero at at least 10%. For the shorter sample, joint insignificance cannot be rejected. Joint significance is weaker for the volatility measures in the long sample, but stronger in the short sample. The bootstrapped critical values for the likelihood ratio tests are substantially higher for macroeconomic uncertainty than for macroeconomic volatility for quarter one. This is caused by the degree of autocorrelation in both types of variables. For uncertainty, the 15
  17. 17. median first order autocorrelation of the long time-series is 0.66, compared to 0.07 for the volatility series. When we generate random series with first order autocorrelations corresponding to the median autocorrelation observed in the data, the bootstrapped critical values are substantially different from those using generated random series without autocorrelation. Critical values for the highly autocorrelated series are approximately twice as high as those for the marginally autocorrelated series in this experiment. This corresponds closely to what is observed in the data and stresses the importance of taking this issue into account. Overall, the message from Table 4 is that stock market volatility is more closely related to macroeconomic uncertainty than to macroeconomic volatility, especially for the variables that are available for the longer sample. In Table 5 we examine the same set of regressions for the period since 1997. [Insert Table 5 here] The results are now completely different. For the full set of estimates, only four entries are significantly different from zero while three of them have the wrong sign. These findings correspond to the pattern that we already observed in Figure 1: from the mid-nineties onwards, stock market volatility is trending upward without a clear link with either macroeconomic uncertainty or macroeconomic volatility. A similar observation has been made by Schwert (2002), who attributes the recent unusual behavior of stock market volatility to technology. Although the focus of Schwert’s (2002) analysis is on the Nasdaq where this pattern is even more pronounced, the conclusions may carry over to our case. The SPF does not contain technology-related information, so our variables are unlikely to capture the behavior of stock market volatility during the past decade. Nevertheless, previous attempts in the literature to associate macroeconomic factors with stock market volatility have met with little success even for pre-1997 samples. Our results for the 1969- 1996 period therefore imply that we can solve at least part of the volatility puzzle: using dispersion-based uncertainty measures instead of the times-series based volatility measures, a strong link can be established with stock market volatility for much of the post-1969 period. As the behavior of stock market volatility since 1997 cannot be explained using macro- variables, we proceed by further analyzing the pre-1997 sample. The documented contemporaneous association between stock market volatility and macroeconomic variables 16
  18. 18. has nothing to say about causality running either from the stock market to the macroeconomy or vice versa. In section 6 below, we will address this issue further. 5.2 Incremental Effects We next examine whether macroeconomic uncertainty and volatility provide information about stock market volatility beyond what is contained in lagged stock market volatility itself. To this end we run the following regressions: (7) σ SP 500,t = α + βσ tY + γσ SP 500,t −1 + ε t , where σ SP 500 ,t and σ SP 500 ,t −1 are respectively stock market volatility in quarters t and t–1 and σ tY is either macroeconomic uncertainty or macroeconomic volatility for variable Y. Table 6 contains the results. [Insert Table 6 here] Once lagged stock market volatility is included in the regression model, the contribution of the uncertainty variables weakens somewhat. Uncertainty about the deflator, industrial production, housing, the 3-month T-bill rate (for U1) and inflation (for U4) are no longer significantly different from zero at at least a 10% significance level. Still, for six out of ten variables uncertainty has incremental explanatory power for stock market volatility. In contrast, for the volatility measures all significance disappears, except for unemployment and inflation (at the 10%-level). These results are consistent with Schwert’s (1989) findings that macroeconomic volatility has a weak link with stock market volatility once lagged stock market volatility is included. 5.3 Incremental and Additional Effects Up to this point, we have separately considered the effects of macroeconomic uncertainty or volatility on stock market volatility. Table 7 contains the results of regressing stock market volatility on both uncertainty and volatility of macroeconomic variable Y: 17
  19. 19. (8) σ SP500,t = α + β uncert.σ tY ,uncert. + β vol.σ tY ,vol. + ε t (9) σ SP 500,t = α + β uncert.σ tY ,uncert. + β vol .σ tY ,vol . + γσ SP 500,t −1 + ε t , where σ SP 500 ,t and σ SP 500 ,t −1 are as defined above, σ tY ,uncert . is macroeconomic uncertainty of variable Y (U1/U4), and σ tY ,vol . is macroeconomic volatility of variable Y (V1/V4). Table 7 contains the regression results. [Insert Table 7 here] Panel A shows that the explanatory power of macroeconomic volatility largely disappears once macroeconomic uncertainty is taken into account. At the one-quarter horizon, eight uncertainty variables are significant, whereas only volatility of real consumption growth is significant. At the four-quarter horizon, six uncertainty variables remain significant, compared to one volatility measure. Panel B includes past stock market volatility as an additional regressor. At the one-quarter horizon, none of the volatility variables remains significant versus four uncertainty variables. Extending the horizon to four quarters, one volatility variable is significant versus five uncertainty variables. In sum, the effects of macroeconomic volatility further weaken once macroeconomic uncertainty is included in the regression model. We conclude that macroeconomic volatility contains little information beyond what is contained in macroeconomic uncertainty and lagged stock market volatility. 6. Forecasting stock market volatility using macroeconomic variables The previous section documents the contemporaneous association between stock market volatility and macroeconomic variables. In this section, we try to forecast stock market volatility using macroeconomic uncertainty and volatility. To this end, we need a different timing for stock market volatility. In previous sections we calculate stock market volatility from daily stock market returns during calendar quarters. We now recalculate stock market volatility over periods that match the deadlines for the survey. For example, the 1993Q1 and 1993Q2 survey deadlines were respectively February 19th 1993 and May 5th 1993. We now calculate 1993Q2 stock market volatility using the daily returns between these two dates. In 18
  20. 20. contrast, our calendar time measure would take returns between April 1st and June 30th. From 1990Q2 onwards, when the Philadelphia Fed took over the survey, deadline dates are exactly available. For the period prior to that we take the 20th as the deadline, which is the average date in the post-1990 period. This is an assumption, but varying this date does not have an impact on our conclusions. We employ the following framework to forecast stock market volatility: (10) σ SP 500,(t ,t +1) = α + β uncert.σ tY−,1uncert. + β vol .σ tY−,1vol . + γσ SP 500,(t −1,t ) + ε (t ,t +1) Equation (10) again takes the form of a “horse-race” between uncertainty and volatility measures. Lagged stock market volatility is also included. Table 8 summarizes the empirical results. [Insert Table 8 here] Uncertainty remains dominant over volatility in the forecasting context, as none of the volatility series is significantly different from zero. At the one-quarter horizon, four uncertainty variables are significant. Remarkably, just one variable (uncertainty about nominal GDP) has both explanatory and forecasting power. Uncertainty about the deflator, industrial production and inflation are significant in predicting stock market volatility, but not in explaining stock market volatility. For the four-quarter horizon, results are comparable, except for the significance of T-bill uncertainty instead of inflation uncertainty. 7. Conclusions In linking stock market volatility to macroeconomic factors, it is important to make a distinction between dispersion-based measures of macroeconomic uncertainty and time- series based measures of macroeconomic volatility. For much of the post-1969 sample period, stock market volatility is more closely related to contemporaneous uncertainty measures than to the more commonly used volatility measures. This result is robust to the inclusion of lagged stock market volatility. Uncertainty measures also outperform volatility measures in a prediction context. Additionally, macroeconomic uncertainty increases more strongly during recessions than macroeconomic volatility. This result is compatible with 19
  21. 21. earlier work showing that stock market volatility increases during recessions. Macroeconomic uncertainty measures also have more theoretical appeal than volatility measures, mainly because of the Peso-problem in using time-series data. We conclude that in periods in which macro-factors are important, dispersion-based macroeconomic uncertainty is more likely to capture economic reality than macroeconomic volatility. Schwert’s (1989) volatility puzzle can thus be reduced to the post-1996 period, in which developments in the technology sector instead of macro-factors seem to have driven stock market volatility. 20
  22. 22. Appendix: Bootstrapping critical values In order to provide evidence on the finite sample properties of the t-values and R-squares from our regressions, we bootstrap critical values. As Stambaugh (1999) points out, least squares estimates may be biased if regressors follow AR(1) processes. Furthermore, standard errors should take into account that macroeconomic volatility is calculated rather than observed. We build bootstrap distributions for the quantities of interest using the following steps, see also Mark (1995): Estimate σ SP 500 ,t = α + β 1σ SP 500 ,t −1 + ε t in the actual dataset. For each run i of the 10,000 replications, bootstrap a residuals sequence of length T + 50: {ε ti }T=+50 , either parametric (using a normal distribution with variance equal to that of the t 1 errors from the regression of the previous step) or non-parametric (resampling the original errors). T is the length of the original series. Generate {σ SP 500,t }T=+ 50 = α + βσ SP 500,t + {ε ti }T=+50 using the parameters from the first step, i t 1 ˆ ˆ i t 1 the last available observation on stock market volatility and the generated residuals from the second step. Delete the first 50 observations to prevent any dependence on starting values for the recursions. Do the same for the uncertainty series of macroeconomic variable Y. The bootstrapped stock market volatility is independent from the construction of macroeconomic uncertainty series and as a result we would expect no relation between the two. Estimate σ SP 500,t = α i + β iσ tY ,i + ε ti for each bootstrap run i. Collect estimates of β i , the i Newey and West (1987) t-value t ( β i ) and the R 2,i . For the specification in section 5.2, ˆ include lagged stock market volatility and for the specifications in section 5.3, include both macroeconomic uncertainty and macroeconomic volatility (see below) as well as lagged stock market volatility. 21
  23. 23. The 10,000 observations of t ( β i ) and R 2,i form the bootstrap distribution for the t-value and ˆ the R-squared under the null-hypothesis that macroeconomic risk factors have no relation with stock market volatility. The quantiles from these distributions are used as small sample corrected critical values. For macroeconomic volatility, the procedure is slightly different: Estimate Yt = α + βYt −1 + ε t in the actual data set. Note that Yt is the original macroeconomic series rather than the volatility of the series. Bootstrap a residuals sequence of length T + 50: {ε ti }T=+ 50 , again either parametric or non- t 1 parametric. Generate {Yt i }T=+50 = α + βYt i + {ε ti }T=+50 using the parameters from the first step, the last t 1 ˆ ˆ t 1 available observation on variable Y and the generated residuals from the second step. Estimate Yt i = γ 0 + γ 1i Yt i−1 + η tY ,i and generate the non-parametric volatility measure ˆ i ˆ ⎛ J ⎞ σ tY−,1i, J = log⎜ ∑ η tY−,ij ⎟ . Just as in the original data, we explicitly take into account the fact ⎜ ⎟ ⎝ j =1 ⎠ that macroeconomic volatility is generated, instead of measured, in the bootstrap. We do not provide the bias adjustments for the parameter estimates in the main tables, as these are very small compared to the parameter estimates. For the Likelihood Ratio (LR) tests, we bootstrap critical values by estimating n σ SP 500,t = γ 0 + ∑ β Yi σ tY ,i + ξ ti and calculating the LR-value on redundancy of all σ tY ,i (i.e. i Y =1 ∑β Y i Y = 0 ) for each bootstrap run. In the main text, critical values are taken from the parametric bootstrap experiment, but conclusions are insensitive to using the non-parametric procedure. 22
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  27. 27. Figure 1: Macroeconomic uncertainty versus macroeconomic volatility Unemployment uncertainty as measured by the cross-sectional dispersion from the Q4 SPF (lhs) and Q4 unemployment standard deviation plotted against stock market volatility (rhs, stock market crash of 1987 excluded). Shaded areas are NBER indicated recession periods. 1.0 20 0.8 15 0.6 10 0.4 5 0.2 0 0.0 -5 70 75 80 85 90 95 00 Unemp. uncert. S&P 500 vol. Unemp vol. Figure 2: Stock market volatility Quarterly standard deviation of S&P 500 stock returns based on daily returns for 1969:1 – 2004:4. 25 20 15 10 5 1970 1975 1980 1985 1990 1995 2000 2005 26
  28. 28. Table 1: The impact of SPF releases on the stock market The table provides Gaussian maximum likelihood estimates of the parameters of the GARCH(1,1) model from equations 1 and 2. The sample period is 1/1/1990 – 2/28/2005 with a total number of observations of 3955 in the estimation. ** and *** denote parameter estimates different from zero at the 5% and 1% level of significance, respectively, using Bollerslev and Wooldrige (1992) robust standard errors. The lower part of the table reports Wald tests on joint significance of the day-of-the-week effects. Mean equation Variance equation C 0.087 *** C -0.033 SPF release 0.287 *** ARCH 0.055 *** D January -0.007 GARCH 0.940 *** D Tuesday -0.047 SPF release -0.114 ** D Wednesday -0.015 D January 0.004 D Thursday -0.049 D Tuesday 0.062 D Friday -0.055 D Wednesday -0.069 D Thursday 0.108 D Friday 0.099 Hypothesis tests δ2 = δ3 = δ4 = δ5 = 0 γ2 =γ3 =γ4 =γ5 = 0 p-value: 0.57 p-value: 0.02 Table 2: List of variables Code Description Start date NGDP Nominal GDP (GNP prior to 1992) 1968-Q4 PGDP GDP price index (prior to '96 GDP implicit price deflator, 1968-Q4 prior to '92 GNP deflator) CPROF Corporate profits after taxes 1968-Q4 UNEMP Civilian unemployment rate 1968-Q4 INDPROD Industrial production index 1968-Q4 HOUSING New private housing units started 1968-Q4 CPI Consumer price index, %-change from prev. Quarter 1981-Q3 TBILL 3-month Treasury bill rate 1981-Q3 RGDP GDP in constant dollars (GNP prior to 1992) 1981-Q3 RCONSUM Real consumption expenditures 1981-Q3 27
  29. 29. Table 3: Relationships between uncertainty, volatility and recessions Panel A shows betas and Newey and West (1987) corrected t-values for β in the regression σ tY = α + β * NBER t + ε t , where σ tY is either macroeconomic uncertainty (U1) or macroeconomic volatility (V1) and NBER is a dummy variable with value one if the economy is in a recession and zero otherwise. Panel B provides correlations between macroeconomic uncertainty and macroeconomic volatility. The upper triangle of panel C holds the correlation matrix for the uncertainty series, the lower triangle holds the correlation matrix for the volatility series. Bold numbers indicate significantly different from zero at the 5%-level of significance at least. All findings are for the period 1969-2004. NGDP PGDP CPROF UNEMP INDPROD HOUSING PANEL A β(U1) 0.32 0.26 1.51 0.12 0.49 3.34 t-value 2.61 3.23 2.74 5.63 3.98 3.67 β(V1) 0.45 0.41 0.09 1.00 0.78 0.55 t-value 1.53 1.78 0.30 4.87 4.64 1.85 PANEL B ρ(U1,V1) 0.24 0.12 0.00 0.40 0.39 0.30 PANEL C NGDP -- 0.58 0.36 0.67 0.67 0.68 PGDP 0.01 -- 0.30 0.49 0.55 0.53 CPROF 0.15 0.05 -- 0.42 0.43 0.43 UNEMP 0.01 0.18 0.07 -- 0.75 0.70 INDPROD 0.30 0.06 0.10 0.28 -- 0.71 HOUSING 0.01 0.05 0.07 0.02 0.19 -- 28
  30. 30. Table 4: Stock market volatility and macroeconomic uncertainty and volatility: before 1997 The regression model σ SP 500,t = α + βσ tY + ε t contains a constant (not shown in the table) and various measures of macroeconomic uncertainty and volatility (U1, U4, V1 and V4). For each of the four sets of results, the table displays the beta-coefficient, its Newey and West (1987) t-value and the R-squared of the regression. *, ** and *** indicate parameter estimates significantly different from zero at the 10%-, 5% and 1%-level of significance, respectively. LR-long and LR-short are likelihood ratio values to test whether all macroeconomic variables (uncertainty or volatility) are redundant for the period 1969Q1–1996Q4 and 1981Q3-1996Q4, respectively. Critical values for the coefficients (parametric) as well as for the likelihood ratio redundancy tests (parametric) are based on the bootstrap experiment described in the main text with 10,000 replications. 1969Q1 – 1996Q4 1981Q3 – 1996Q4 NGDP PGDP CPROF UNEMP INDPROD HOUSING CPI TBILL RGDP RCONSUM U1 1.71 2.08 0.58 9.42 1.49 0.27 1.55 1.89 2.82 2.25 t-value 2.72 ** 1.96 * 4.37 *** 4.03 *** 4.07 *** 3.74 *** 2.56 * 1.99 3.13 ** 3.17 ** R-square 0.09 ** 0.08 ** 0.25 *** 0.16 *** 0.11 ** 0.12 ** 0.14 * 0.09 0.17 ** 0.16 ** LR-long 38.84 *** LR-short 18.66 V1 -0.02 0.23 0.02 0.52 0.41 0.31 0.33 0.42 0.44 0.56 t-value -0.09 1.36 0.14 3.17 *** 2.21 ** 2.14 * 2.38 ** 1.50 2.31 ** 2.36 * R-square 0.00 0.02 0.00 0.08 *** 0.05 ** 0.03 * 0.06 * 0.05 * 0.06 ** 0.08 ** LR-long 15.15 ** LR-short 14.47 *** U4 0.84 0.68 0.26 5.22 0.61 0.14 1.03 1.23 1.75 0.69 t-value 3.00 ** 1.45 3.49 *** 2.97 ** 2.25 * 3.51 ** 2.09 2.04 3.24 ** 2.32 ** R-square 0.09 ** 0.06 ** 0.11 *** 0.14 ** 0.07 ** 0.13 ** 0.06 0.06 0.16 ** 0.08 ** LR-long 23.90 * LR-short 11.84 V4 0.51 0.10 0.83 0.94 0.76 1.21 1.26 0.30 0.99 1.44 t-value 0.93 0.12 1.88 3.23 ** 2.01 2.63 ** 3.52 ** 0.51 2.73 * 2.78 * R-square 0.02 0.00 0.04 0.08 ** 0.04 0.06 * 0.19 ** 0.01 0.09 0.13 * LR-long 13.10 LR-short 21.34 *
  31. 31. Table 5: Stock market volatility and macroeconomic uncertainty and volatility: from 1997 The regression model σ SP 500,t = α + βσ tY + ε t contains a constant (not shown in the table) and various measures of macroeconomic uncertainty and volatility (U1, U4, V1 and V4). For each of the four sets of results, the table displays the beta-coefficient, its Newey and West (1987) t-value and the R-squared of the regression. * and ** indicate parameter estimates significantly different from zero at the 10%- and 5%-level of significance, respectively. LR are likelihood ratio values on the test that all macroeconomic variables (uncertainty or volatility) are redundant for the period 1997Q1–2004Q4. Critical values for the coefficients (parametric) as well as for the likelihood ratio redundancy tests (parametric) are based on the bootstrap experiment described in the main text with 10,000 replications. 1997Q1 – 2004Q4 NGDP PGDP CPROF UNEMP INDPROD HOUSING CPI TBILL RGDP RCONSUM U1 3.92 5.88 -0.19 8.49 1.00 -2.55 -4.44 -4.91 6.09 1.93 t-value 0.87 0.91 -0.59 0.82 0.62 -2.21 * -2.59 * -0.83 1.05 0.36 R-square 0.02 0.02 0.02 0.02 0.01 0.17 ** 0.10 0.02 0.04 0.00 LR-long 13.61 V1 0.53 -0.34 0.32 0.02 -0.07 -0.01 -0.74 0.34 0.45 -0.60 t-value 0.98 -0.72 1.03 0.03 -0.15 -0.03 -1.27 1.80 1.74 -1.97 R-square 0.02 0.02 0.02 0.00 0.00 0.00 0.04 0.02 0.05 0.06 LR-long 9.97 U4 1.29 -1.21 -0.11 16.27 0.82 -0.60 -7.46 -3.69 5.47 4.25 t-value 0.73 -0.26 -0.42 1.44 0.49 -0.82 -2.50 * -0.92 2.58 * 1.02 R-square 0.02 0.00 0.02 0.07 0.01 0.03 0.12 0.03 0.11 * 0.05 LR-long 14.36 V4 2.47 -2.21 -0.43 0.35 0.39 0.13 -2.21 0.68 0.14 0.79 t-value 2.37 -1.31 -0.37 0.38 0.41 0.11 -1.83 1.59 0.07 0.65 R-square 0.10 0.10 0.00 0.00 0.00 0.00 0.13 0.04 0.00 0.01 LR-long 19.93 30
  32. 32. Table 6: Incremental effects The regression model σ SP 500, t = α + βσ tY + γσ SP 500 ,t −1 + ε t contains a constant, lagged stock market volatility (both not shown in the table) and various measures of macroeconomic uncertainty and volatility (U1, U4, V1 and V4). For each of the four sets of results, the table displays the beta-coefficient, its Newey and West (1987) t- value and the R-square of the regression. *, ** and *** indicate significantly different from zero at the 10%-, 5%- and 1%-level of significance, respectively. Significance levels are based on bootstrapped critical values (parametric) with 10,000 replications. 1969Q1 – 1996Q4 1981Q3 – 1996Q4 NGDP PGDP CPROF UNEMP INDPROD HOUSING CPI TBILL RGDP RCONSUM U1 0.86 1.14 0.36 4.05 0.49 0.10 0.78 1.25 1.51 1.37 t-value 2.49 ** 1.48 3.06 *** 2.10 * 1.44 1.52 2.17 * 1.88 2.65 ** 3.69 *** R-square 0.37 0.37 0.43 0.37 0.36 0.36 0.42 0.43 0.44 0.45 V1 -0.15 0.13 0.06 0.28 0.16 0.14 0.23 0.18 0.20 0.26 t-value -1.04 1.45 0.81 2.87 ** 1.25 0.91 1.94 * 0.76 1.41 1.50 R-square 0.35 0.35 0.35 0.37 0.35 0.35 0.42 0.40 0.41 0.41 U4 0.45 0.40 0.16 2.72 0.14 0.05 0.37 0.88 1.13 0.44 t-value 2.28 ** 1.20 2.03 * 2.79 ** 0.75 1.41 1.28 2.23 * 3.83 *** 2.36 ** R-square 0.38 0.37 0.39 0.39 0.36 0.37 0.40 0.42 0.46 0.42 V4 0.20 -0.10 0.33 0.27 0.07 0.36 0.72 0.01 0.39 0.55 t-value 0.60 -0.28 1.06 1.20 0.30 1.30 2.80 ** 0.04 1.34 1.70 R-square 0.35 0.35 0.35 0.35 0.35 0.35 0.45 0.39 0.41 0.41 31
  33. 33. Table 7: Incremental and additional effects Panel A reports beta-coefficients and Newey and West (1987) t-values for the regression model σ SP 500,t = α + β uncert .σ tY ,uncert + β vol .σ tY ,vol + ε t with for each macroeconomic variable both uncertainty and volatility included (U1 & V1 and U4 & V4). Panel B gives beta coefficients, Newey and West (1987) corrected t-values of the regression σ SP 500,t = α + β uncert .σ tY ,uncert + β vol .σ tY ,vol + γσ SP 500,t −1 + ε t where lagged stock market volatility is included as additional regressor. *, ** and *** indicate significantly different from zero at the 10%-, 5%- and 1%-level of significance, respectively. Significance levels are based on bootstrapped critical values (parametric) with 10,000 replications. The constant and lagged stock market volatility are not shown in the table. 1969Q1 – 1996Q4 1981Q3 – 1996Q4 NGDP PGDP CPROF UNEMP INDPROD HOUSING CPI TBILL RGDP RCONSUM PANEL A U1 1.83 2.05 0.59 8.10 1.30 0.26 1.38 1.56 2.58 2.06 t-value 2.67 ** 2.00 * 4.35 *** 2.95 ** 3.59 *** 3.43 ** 2.02 1.60 2.97 ** 2.96 ** V1 -0.15 0.22 -0.04 0.24 0.20 0.18 0.12 0.18 0.31 0.46 t-value -0.78 1.38 -0.40 1.55 1.24 1.18 0.88 0.66 1.76 2.11 * U4 1.00 0.70 0.24 4.35 0.50 0.13 -0.03 1.62 1.47 0.57 t-value 2.86 ** 1.44 2.73 ** 2.52 * 1.59 3.06 ** -0.07 1.68 2.22 * 2.05 * V4 -0.35 -0.22 0.36 0.56 0.38 0.23 1.28 -0.33 0.36 1.29 t-value -0.58 -0.35 0.83 1.73 0.95 0.60 3.11 ** -0.39 0.75 2.56 PANEL B U1 1.02 1.14 0.36 3.05 0.40 0.09 0.57 1.28 1.42 1.31 t-value 2.49 ** 1.49 2.99 *** 1.30 0.98 1.30 1.33 1.73 2.57 ** 3.11 ** V1 -0.22 0.13 0.02 0.19 0.11 0.10 0.15 -0.02 0.16 0.23 t-value -1.43 1.42 0.24 1.56 0.72 0.63 1.10 -0.06 1.06 1.31 U4 0.57 0.43 0.15 2.55 0.15 0.05 -0.23 1.56 1.20 0.42 t-value 2.15 * 1.22 1.68 2.55 ** 0.67 1.20 -0.60 2.83 ** 3.35 *** 2.33 ** V4 -0.27 -0.38 0.16 0.14 -0.01 0.01 0.80 -0.59 -0.10 0.48 t-value -0.65 -1.22 0.53 0.60 -0.05 0.03 2.55 ** -1.46 -0.29 1.44 32
  34. 34. Table 8: Forecasting stock market volatility Panel A (B) reports beta-coefficients and Newey and West (1987) t-values for the regression model σ SP 500,(t ,t +1) = α + β uncert .σ tY−,1uncert + β vol .σ tY−,1vol + γσ SP 500,(t −1,t ) + ε (t ,t +1) with for each macroeconomic variable both U1 uncertainty (U4) and V1 volatility (V4) included. *, ** and *** indicate significantly different from zero at the 10%-, 5%- and 1%-level of significance, respectively. Significance levels are based on bootstrapped critical values (parametric) with 10,000 replications. The constant and lagged stock market volatility are not shown in the table. 1969Q2 – 1996Q4 1981Q3 – 1996Q4 NGDP PGDP CPROF UNEMP INDPROD HOUSING CPI TBILL RGDP RCONSUM PANEL A U1 0.85 1.85 0.22 2.60 0.77 0.04 1.46 1.36 -0.04 1.21 t-value 2.49 ** 2.35 ** 1.76 1.11 1.91 * 0.81 4.30 *** 1.83 -0.06 1.71 V1 -0.11 -0.11 -0.07 -0.09 -0.17 0.10 0.02 -0.12 -0.09 -0.15 t-value -0.71 -0.78 -0.72 -0.56 -1.22 0.72 0.13 -0.53 -0.35 -0.80 PANEL B U4 0.59 0.56 0.05 2.20 0.40 0.04 0.67 1.53 0.76 0.00 t-value 2.53 ** 2.09 * 0.67 1.83 1.87 * 1.04 1.68 2.68 ** 1.58 0.02 V4 -0.25 -0.62 0.12 -0.21 -0.31 -0.08 0.48 -0.58 -0.03 0.37 t-value -0.49 -1.44 0.30 -0.81 -0.91 -0.20 1.21 -1.35 -0.07 0.91 33
  35. 35. ����������������������� ����������������������� ����������������������� Nyenrode Business Universiteit Nyenrode Research Group ����������������������� Straatweg 25 Postbus 130, 3620 AC BREUKELEN t +31 346 291 696 f +31 346 291 250 e nrg@nyenrode.nl www.nyenrode.nl/nrg 8 YMP Your Leadership Development Program

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