Evaluating Stock Returns with Time-Varying Risk Aversion Driven By Trend Deviations From the Consumption-to-Wealth Ratio: An Analysis Conditional on Levels H. J. Smoluk, James Bennett School of Business University of Southern Maine, Portland, ME 04104 Abstract Based on the cointegrating relationship between consumption and wealth, we estimate the long run consumption-to-wealth ratio for each of five consumer income quintiles as well as national data for benchmarking purposes. Short run deviations from the consumption-to-wealth ratio for each quintile are examined for their ability to forecast changes in future consumption, income, housing values, and especially stock returns. We demonstrate that these trend deviations when combined with consumption growth in a multifactor model, significantly improve the ability of the dividend-to-price ratio to forecast future market returns over short and intermediate horizons for consumers in the highest-income quintile. This paper contributes to the financial economic literature by showing that the highest-income consumers are forecasting future stock returns with the help of the persistence in the dividend-to-price ratio and are modifying their consumption accordingly. JEL: D12, D91, E21, G12.
I. Introduction Many stochastically trending economic variables display a long-run relationship over time that may be characterized as an equilibrium condition. These variables share a common trend in the long run, but deviate from that trend in the short run. Recently, a line of research in financial economics that employs trend deviations derived from a system of cointegrated variables has made significant contributions to asset pricing. When economic variables are cointegrated and share a common trend, the deviations from the common trend represent a transitory disequilibrium with a capacity to forecast the path of variables within the system as it reverts back to this shared trend. As noted by Cochrane (2001), such deviations and the methods to measure them are transforming empirical work in both financial and macro-economics. Lettau and Ludvigson (2001) derive a methodology that estimates the long-run trend between log consumption and log wealth, where wealth includes labor income (human capital) and household assets. Deviations from the trend represent disequilibrium in the long-run consumption-to-wealth ratio as economic agents strive to intertemporally smooth consumption based on expected future stock returns. Time series regressions using these trend deviations as an explanatory variable show that they have a positive and statistically significant relation to expected future excess returns on the market portfolio. These regressions perform significantly better in predicting short- to intermediateterm horizon excess stock returns than the better-known forecasting variables such as dividend yield, price-to-earnings ratio, and other price-scaled variables. In addition to the trend deviation s predictive ability, Lettau and Ludvigson (2001) view the series as a proxy for time-varying risk aversion, as it exhibits countercyclical variation relative to the business cycle. When the trend deviation in the consumption-to-wealth ratio decreases late in an economic expansion, it does so because current wealth increases more than the increase in consumption. The relative decline in consumption signals that investors are more risk averse and cautious about the future. Lettau and Ludvigson also observe that transitory trend deviations in the 1
consumption-to-wealth ratio reflect changes in risk aversion in a way that is similar to the transitory deviations from habit. Declines in consumption relative to trend or habit reflect increases in risk aversion. More recently, Lustig and Van Nieuwerburgh (2005) have continued this line of research by arguing that trend deviations in the housing wealth-to-human wealth (labor income) ratio are an important factor in predicting future stock market returns. They suggest that swings in labor income represent a source of idiosyncratic consumption risk that is difficult for individuals to shed, and that the value of housing represents collateral that can be used to obtain liquidity to buffer these labor income shocks. Specifically, when labor income drops, individuals can more easily access liquidity when the value of their residential housing is high. When the market value of their housing is low, however, individuals experiencing labor income shocks are subject to liquidity constraints that, all else being equal, cause disruptions in their ability to smooth consumption growth. More volatile consumption growth causes volatility in the stochastic discount factor and leads to a higher conditional market price of risk. Lustig and Van Nieuwerburgh (2005) refer to this mechanism as the collateral channel. Thus, deviations from the common trend between labor income and the value of housing represents a conditioning factor for the market price of risk. A shortcoming of many of the empirical tests used to evaluate the predictive ability of trend deviations from a system of cointegrated variables is that they are performed on aggregate U.S. economic and financial data, which obscures the heterogeneity of consumers and limits of the conclusions that can drawn. We believe that one of the most illuminating dimensions of the data for evaluating the usefulness of trend deviations in the consumption-to-wealth ratio to forecast future housing values and stock returns is consumer income. An analysis conditional on income can be motivated on many levels and is supported by data from the Federal Reserve. First, according to the Survey of Consumer Finances (SCF), as shown in Panel A of Table 1 here, only about 40 percent of the lowest-income families own their own home, with the rate of ownership increasing steadily with 2
increased income. Second, only approximately 45 percent of American families hold common stock directly and indirectly. A disproportionate amount of financial assets is held by upper-income consumers so that the ability of trend deviations to predict future stock returns is more likely to be observed in the data of higher-income groups rather than lower-income groups. This relationship can also be seen in Table 1, Panel A. Only about 9.1 percent of the lowest-income quintile families hold common stock directly or indirectly, compared to 79 percent in the upper-income quintile. In the lowest-income quintile, only 15.5 percent of the families directly hold short-term interest bearing securities, while 51.0 percent of the families in the highest income quintile hold these assets. Thus, the inability to take advantage of changing housing values through the collateral channel in conjunction with lower stock market participation rates leads us to hypothesize that trend deviations from the consumption-to-wealth ratio for lower-income groups are not likely to forecast future housing values and are even less likely to forecast stock returns. 1 We conjecture that economically constrained lower-income groups may endure idiosyncratic labor and housing shocks as they are unable to trade them away, even under the assumption of complete markets. Thus, at any point in time, individuals from different income groups are likely to exhibit different degrees of risk aversion and that risk aversion is likely to vary over time. Similarly, the cyclical pattern in each income group s trend deviations from their consumption-to-wealth ratio may reflect varying degrees of optimism toward future income, future housing values, and future stock market returns. This paper examines the predictive ability of trend deviations from the consumption-to-wealth ratio conditioned on consumer income. We define wealth as total income plus the market value of housing, and estimate the consumption-to-wealth ratio for each income quintile. We hypothesize that trend deviations represent transitory shifts in consumption relative to wealth that reflect both time- 1 Data from the Survey of Consumer Finances support this thought. For example, 59.3 percent of the families without a checking account are in the lowest-income quintile. 3
varying degrees of optimism about future wealth and current levels of risk aversion. Thus, we hypothesize that trend deviations should forecast future housing values and stock market returns, but mainly for higher-income consumers. 2 To implement this study we use data from the Consumer Expenditures Survey (CEX) along with aggregate U.S. macroeconomic data for benchmarking purposes. The CEX provides a rich set of information for evaluating the collateral channel since it tracks household consumption, income, and the market value of residential housing sorted by income quintiles. The remaining sections of this paper are organized as follows: Section II describes the data used throughout the paper. Section III develops and estimates the cointegrating regressions between consumption and wealth. Section IV discusses and estimates cointegrating (vector autoregressions) VARs. Consistent with the collateral channel, we find that lagged trend deviations predict increases in housing values, but predominantly for middle-income consumers and the aggregate national data. In section V, we employ several multifactor models with the dividend-to-price ratio and consumption data to determine the ability of trend deviations from the consumption-to-wealth ratio to forecast future market returns. We find that combining trend deviations and consumption growth data with the dividend-to-price ratio significantly improves the ability of the dividend-to-price ratio to forecast future excess market returns, but only for the measures derived from the highest-income consumers. The paper concludes in Section VI. II. Data Description Consumption, income, and the market value of housing series, sorted by income, were obtained from the Consumer Expenditure Survey (CEX) for the sample period starting in the first quarter of 1984 through the fourth quarter 2003. The CEX is produced by the Bureau of Labor 2 Smoluk and Neveu (2002) employ a similar hypothesis concerning income groups and test the consumption- CAPM using generalized method of moments and instrumental variables techniques, to find a link between various types of consumption and returns. They are unable to find any pattern between income level, consumption, and stock returns. 4
Statistics (BLS), which periodically surveys 7,500 households throughout urban and rural areas of the United States. 3 The CEX reports quarterly household average income and expenditure details sorted by household income. 4 The CEX also publishes the average number of individuals in each household by income quintiles, thus all CEX data used in this paper is on a per capita basis. The housing data in the CEX, however, is only compiled on an annual basis. We adjusted this data to capture quarterly variability by multiplying the annual prices by gross quarterly returns computed from a national real estate price index of single family homes published by the Office of Federal Housing and Enterprise Oversight. We deseasoned the consumption, income, and housing data series using SAS s X12 program. 5 Seasonally adjusted national per capita data is also employed in this paper for comparative purposes to the CEX. Additional details on the data are discussed in the Data Appendix. A descriptive summary of the data is shown in Panel B of Table 1. Interestingly, the rankorder of the quintile groups in terms of consumption growth and the market value of housing growth rate is identical. In addition, the lowest-income group has the lowest consumption growth and housing value growth rates, but the highest-income growth within the quintile data for the sample period. In terms of growth rate variability, the lower-income groups tend to exhibit the most volatility for all three variables while the highest-income groups tend to have the lowest volatility. The national data in the last column is quite different from the CEX data. National consumption growth is higher than that of any individual income group, while the growth rate in the market value of 3 Prior to 1999, 5,000 households were sampled. 4 The BLS stopped publishing the CEX on a quarterly basis in 1999 to the general public; however, quarterly reports are prepared internally and are available through our sample period. The income data for our paper comes from the Consumer Expenditure Survey, which does not distinguish between the various types of income. Thus, our measure of income for each group does include capital gains from assets, interest, and dividend income. 5 SAS s X12 program is adapted from the U.S. Census Bureau s ARIMA model for deseasoning economic time series. 5
housing is relatively low. All three variables exhibit substantially lower volatility for their growth rates compared to the CEX data. Cointegration methods depend on nonstationary variables. Dickey and Fuller (1979) unit root test results, with a constant and a trend, on consumption, income, and the market value of housing separately are shown in Panel A of Table 2. The null hypothesis of a unit root is not rejected at the 5 percent level for each series. Asymptotic critical values, from Davidson and MacKinnon (1993, page 708), are employed. According to Davidson and MacKinnon, these asymptotic critical values are more robust than finite sample values in that they do not rely on normality or homoskedasticity assumptions. 6 Unit root tests applied to the first differenced series (not shown) of consumption, income, and the market value of housing reject the unit root null hypothesis. Kwiatkowski, Phillips, Schmidt, and Shin (1992) (KPSS) stationarity tests are shown in Panel B. The test statistics are modified according to Leybourne and McCabe (1994) to reflect moving average terms frequently found in economic data and lead us to reject the null hypothesis of stationarity for the variables at the 5 percent level. 7 In Panel C, Sim s Bayesian unit root test statistics and their Schwarz limits are presented. Test statistics smaller than the limit indicate a failure to reject the null hypothesis of a unit root. In only a few isolated cases (income for group one and the market 6 A close look at the t-test statistics reveals some positive values, which suggest explosive series. As discussed in Brooks (2002, page 370), positive coefficients, and hence positive t-test statistics, are generally not considered descriptive of data series in economics and finance. In these cases, it is typical to assume nonstationarity. To support this statement, we performed impulse response tests in the context of the cointegrating VARs, which showed rapidly declining responses (typically around 4 quarters) to unit shocks in each residual series. 7 Leybourne and McCabe (1994) find that the KPSS test statistics are dependent upon the lag truncation parameter selected and suggest removing the effects of moving average terms from the series in the estimate of p to rectify the problem. We simulated KPSS critical values and found they do decline dramatically as the truncation lag increases. Modifying the statistic according to the procedures outlined in Leybourne and McCabe, instead, results in critical values very close to the ones suggested in both articles (0.146, with a trend) and remained relatively stable over a wide range of truncation lags. See Panel B of Table 2. 6
value of housing for group four), do we reject a unit root. 8 Based on the preponderance of evidence supporting a unit root in Panels A through C, we conclude that each of the series is I(1). III. Estimating Trend Deviations in Consumption,, and the Market Value of Housing i. The Model Over the sample period, consumption, income, and the market value of housing series are all upward trending I (1) real per capita variables. If they share a common trend in the long run, then a linear combination of these nonstationary variables should be stationary. We estimate this linear combination using the dynamic ordinary least squares cointegrating regression, as developed in Stock and Watson (1993), based on the following equation: (1) The variables are in real, log per capita form, where denotes the first difference operator, c t denotes consumption, y t denotes income, and h t denotes the market value of housing. The right-hand-side variable is wealth, defined as income (human wealth) plus the market value of housing (nonhuman wealth). 9 Notice that equation (1) includes leads as well as lags for the differenced terms. The 8 It is not surprising that we arrived at different conclusions with classical methods of inference (the ADF unit root and KPSS stationarity tests) versus the Bayesian unit root test from Sims (1988) for at least a few variables. Classical and Bayesian methods employ very different assumptions about statistical inference. These differences, and the controversies involved, are extensive and are discussed in Sims (1988), Sims and Uhlig (1991), and Phillips (1991). 9 We combined income and housing value due to the estimation difficulties caused by multicolinearity between the levels of income and the levels of the market value of housing for many of the groups. The 7
leads/lags reduce the bias effects of regressor endogenity on the parameter estimates for the trend variable. The trend deviation is represented by: (2) The results for the cointegrating regressions are shown in Table 3. They indicate that the relationship between consumption and wealth is positive and statistically significant at the 5 percent level for all groups. The standard deviation for chy t for each income group is shown in the middle of Table 3. There is a tendency for the standard deviations to decrease as income increases, with the highest group slightly out of the pattern. Group one has the highest volatility, and the national group has the lowest volatility. At the bottom of the table are Phillips-Ouliaris (1990) Z statistics on chy t. 10 The null hypothesis of a unit root is rejected based on the critical values at the 5 percent significant level for the case of a time trend in the data. Therefore, from the results in Table 3 we conclude that consumption and wealth share a long-run common trend for each group and that trend deviations are transitory. ii. Perspective In our paper consumers use wealth to maintain their standard of living over the long-run as measured by (1) and in the short-run trend deviations measured by (2) are driven by expectations of future wealth. We hypothesize that consumption moves above trend, ahead of future housing values and expected stock returns, mainly for higher income individuals. In Bakshi and Chen (1996), on the other hand, investors acquire wealth not just for consumption purposes, as in standard models, but correlations between these two variables, in levels, are approximately 0.92 for income groups 3, 4, and 5. 10 The sample period is truncated on both ends of the sample to take into account the leads and lags in the estimation of the trend deviation in the cointegrating regressions. 8
also for absolute and relative (social) wealth status. Utility and risk aversion, therefore, are derived from consumption growth, wealth growth, and social wealth status. Indiviudals have different wealth endowments and they measure their social status by referencing their wealth levels to a social group with similar income. While Bakshi and Chen (1996) develop this model with three-sources of risk, they stop short of empirically estimating it based on concerns associated with identifying each consumer's reference group needed to measure social wealth status. Instead, they empirically estimate a reduced version by assuming that all investors have identical preferences and reference their wealth to an aggregate wealth measure derived from an initial condition and updated using the ratio of aggregate consumption growth to the return on the New York Stock Exchange. Thus, an aggregate consumption-to-wealth ratio is employed, in part, to measure the implied risk aversion associated with wealth. 11 Dybvig (1995) examines a model that incorporates the "ratcheting of consumption effect" discussed in Dusenberry (1949). The ratcheting of consumption occurs because consumers are intolerant of any decline in their standard of living. Consumption is constrained so that it never falls and only increases when wealth, (measured as stock holdings in Dybvig (1995)) reaches a new maximum. Consumers, therefore, have an extreme habit for the consumption of goods and services dependent upon wealth. Consumers optimize their utility by balancing the desire for smooth consumption (with small abrupt upward movements) and the expected profits from their stock market holdings. In our model, a long-run standard of living is assumed to be maintained relative to trends in wealth. Consumption can move above or below the trend reflecting changes in risk aversion and 11 Thus, Bakshi and Chen (1996) suggests that U.S. data should be dissaggregated based on income. An implication of moving away from aggregate U.S. data and conditioning on income is that the consumption streams of individuals within an income quintile are assumed to be perfectly correlated over time. While consumption levels may vary within a quintile, consumption growth for all individuals are the same as they endure the same economic shocks and share similar expectations for future wealth growth. Use of aggregate data, on the other hand, implies that the consumption of all individuals in the economy are perfectly correlated. 9
expected future wealth as consumers rationally smooth consumption. A cointegrating VAR system can estimate the relationships between trend deviations and expected future wealth. IV. Cointegrating VAR Using a VECM, we examine the short-run and long-run dynamics of the system. Specifically, we are interested in the ability of trend deviations to predict future income and, more importantly, future housing values. The results for the VECMs with three lags are presented in Table 4. The parameter estimates on consumption, income, and housing are combined for the lags, and the s correspond to block F-tests. In the consumption equation, the significant parameter estimates for the trend deviations, chy t, at lags one and two alternate in sign for each group. For groups one, three, five, and national, lagged trend deviations do not significantly impact changes in consumption. For groups two and four, both lags are statistically significant at the 5 percent level, with the sum of the two coefficients netting to a negative amount. Thus, consumption tends to revert back to its long-run trend with wealth after at least two quarters. In the income equations, lagged trend deviations also forecast higher income for groups two, four, and national. The signs on the lagged trend deviations that are significant at the 5 percent level also alternate. The first lag is positive for each income group that is statistically significant at the 5 percent level, with the exception of the national group. A positive coefficient indicates that consumers are increasing their consumption above trend in anticipation of higher future income. 12 In the housing equations, the first lag trend deviations are positive and statistically significant for each lag for the middle-income quintiles and the national group. This implies that consumers are increasing their consumption ahead of increases in housing values, as the collateral channel hypothesis suggests thus, 12 As shown, the trend deviations, chy t, extend back only two lags. To the extent that there are statistically significant second and third lags, etc., the coefficients would need to be netted to determine the full effect on current income. While the trend deviations in the income and also housing values equations lack statistical significance at the 5 percent level for groups one and five, we examined these VARs with three lags (not shown), and the last lag is statistically significant. 10
we fail to reject the collateral channel hypothesis for these groups. The lack of significance in the housing component, at least back two lags, for groups one and five causes us to reject the collateral channel mechanism for these groups, although as mentioned in footnote 11 additional lags are significant. 13 The overall results of Table 4 indicate that consumption, income, and the market value of housing tend to adjust to trend deviations to bring the system back into equilibrium, except for the lowest-income and highest-income groups. The results in Table 4 can be compared and contrasted to the cointegrating VAR shown in Table 1 of Lettau and Ludvigson (2001), where they include trend deviations with only one lag in a system that includes national consumption, asset wealth (which includes financial assets), and national income (human wealth). 14 In their asset wealth equation, they show that increases in trend deviations labeled cay predict increases in asset (stock) wealth. Lettau and Ludvigson interpret this finding to mean that investors smooth consumption derived from transitory changes in asset wealth. When higher future excess returns are expected next quarter, optimistic consumers increase consumption above the common trend relative to wealth this quarter. The results in our study, which at this point apply to housing wealth instead of stock returns, are similar for income quintiles two, three, four, and national. When consumption increases above trend (chy t is positive) this quarter, consumers are anticipating an increase in housing wealth next quarter. In other words, consumers are attempting to intertemporally smooth consumption driven by transitory changes in the market value of their homes, confirming the collateral channel hypothesis in Lustig and Van Nieuwerburgh (2005). Given that nearly 60 percent of the lowest-income families do not own their home, as seen in our Table 1, it is not surprising that there is an absence of a statistically significant relation between 13 As we will see later in the paper, this does not imply that group five consumers do not smooth consumption over time. For the highest-income consumers, trend deviations do not forecast increases in income or housing values. Instead, the highest income consumers are smoothing consumption via the stock market as seen in Table 5. 14 It is important to note that while consumption, income, and wealth are lagged two quarters in their model, the trend deviation is estimated with only one lag. 11
trend deviations in the lowest-income group's consumption-to-wealth ratio this quarter in anticipation of increases in housing values next quarter. The results for the highest-income group are puzzling. It seems that their consumption is deviating from trend for reasons other than the anticipation of higher levels of income and housing values. V. Short- to Intermediate-Horizon Regressions with Future Excess Market Returns The VECM discussed above examines the ability of lagged trend deviations to predict future increases in income and housing values. To the extent that consumers own stocks, trend deviations in the consumption-to-wealth ratio should also reflect consumers' expectations about future market excess returns. All else being equal, when trend deviations are negative and consumption is below trend, consumers anticipate lower stock returns. This idea can provide an interesting explanation for why the trend deviations of the highest income group did not exhibit any tendency to forecast future changes in income or housing values. Consequently, we estimate the following regression for each income group for horizons of one through seven quarters: (3) where the term r rp t+k denotes the market risk premium K quarters into the future and F t are factors defined according to the following four models: Model 1 - a benchmark model that employs the log dividend-to-price ratio as the only factor. A priori, it should be positively related to future returns. As discussed in Cochrane (2001) and Fama French (1988), the dividend yield is widely known to forecast future excess returns. 12
Model 2 - employs the trend deviation, chy t, as the only factor. 15 It should be positively related to future returns. Model 3 - scaled consumption-based variables: log consumption growth, trend deviations chy t, and their interaction, LCG t *chy t. These variables should all be positively related to future returns. Model 4 - combines models 1 and 3. The results of the four models are shown for the highest income group, five, and the national group for benchmarking purposes in Tables 5 and 6. 16 The top panel in both tables shows that the predictive ability of the dividend-to-price ratio increases with the horizon. The R 2 increases with the horizon because the small correlations between the variables at short horizons compounds as the horizon increases; see Cochrane (2001, chapter 20). As discussed in Lettau and Ludvigson (2001), the dividend-to-price ratio is a better predictor of future returns at the intermediate horizon, suggesting that it reflects risks related to the business cycle. Summarizing the other results in Tables 5 and 6, we find that the trend deviation alone (Model 2) is unable to forecast returns at short or intermediate horizons, through seven quarters. This is in contrast to Lettau and Ludvigson (2001), who show that cay t, their version of trend deviations from the consumption-to-wealth ratio, forecast returns at the national level for horizons up to 24 15 We use the non-normalized trend deviation here so that deviations below trend are negative and those above trend are positive. This allows us to use the signs on the estimated parameters to more easily interpret their effects on future expected returns. 16 We performed similar analysis for all income groups, but only show results for group five and the national group, due to space constraints. We briefly summarize the results here for the other income groups. For income groups one through four, the results for models 1 through 3 are similar to income group five in Table 5. Model 4 shows an increasing R 2 as in Table 5 and some significance for LDP t mainly for the longer lags, especially for group 4. Model 4 for the highest income group, five, stands out among the other income groups in terms of the number of statistically signifance variables. 13
quarters. 17 Similarly, the scaled consumption-based variables (Model 3) show no ability to forecast future market returns. Models 2 and 3 show no improvement with the highest income consumers. Model 4, when compared against Model 1, shows the most interesting results. The results indicate that when the consumption-based data is combined with the log dividend-to-price ratio, return predictability improves. However, the interactive terms in the short horizon have the wrong sign. group five in Table 5 shows, however, that when the dividend-to-price ratio is combined with consumption-based data, the predictive ability of the model significantly improves over the log dividend-to-price ratio alone, at all horizons shown. These results are consistent with Lettau and Ludvigson (2001), who find that trend deviations in the national consumption-to-wealth (human capital and financial assets) ratio are a better predictor over the short horizon. Interestingly, the log dividend-to-price ratio becomes statistically significant at short horizons and the consumption-based variables also become statistically significant with the correct sign at most horizons. This relationship is not found in the national income group in the bottom panel of Table 6, where the variables are not significant at the 5 percent level and are often the wrong sign. A concern that we may have with the results of Tables 5 and 6 is that since chy t is derived from full sample data we are contaminating our forecasting methods with "look-ahead bias." Lettau and Ludvigson (2001) investigate and dismiss this idea. They address this issue by estimating trend deviations that are computed at each time t from regressions using only lagged data and use the results for forecasting returns subsequent to time t. We perform a similar estimation process for the highest-income group for the model in Table 7. The adjusted R 2 s are lower for each horizon, but the conclusions reached from Table 5 remain unchanged. The signs, size, and statistical significance of the parameters are very similar. 17 Their sample period covers 1952:4 to 1998:3. 14
Overall, the results from Tables 5 through 7 indicate that there is an important interaction between the log dividend-to-price ratio and consumption-based data for the highest-income group. Only in the highest-income group do we see that consumption-based data improve the log dividendto-price ratio's ability to forecast returns at both the short and intermediate horizons. For graphing purposes, we normalize the trend deviation for each income group as follows: (4) The normalization recasts the trend deviation so that it is always positive, proxies for time-varying risk aversion, and equals 1.0 when the consumption-to-wealth ratio is on trend, chy t = 0. The denominator of the fraction in the brackets, chy max - chy min, represents the range of the trend deviation. A large positive TD t reflects a time when consumption is below its common long-run trend with wealth as consumers reduce consumption relative to wealth, implying higher risk aversion. Figure 1 shows each income group's normalized trend deviation without accounting for lookahead bias (solid line) plotted against the time detrended log dividend-to-price ratio (dashed line) that is scaled so that its mean is equal to 1.0. 18 Ignoring the short-run volatility in the trend deviation lines, there is a strong relationship between the two variables over the sample period, especially for the highest-income group, five. These results are remarkable given that our definition of wealth did not include financial asset balances. While we did not include stocks or other financial asset balances in our definition of wealth, 18 As discussed in Cochrane (2001, chapter 20) the dividend-to-price ratio is a very persistent, slow mean-reverting variable. Thus, we detrended the log dividend-to-price ratio by regressing the log dividend-to-price ratio on a constant and time and then subtracted the forecasted time component from the log dividend-to-price ratio. 15
we did use total income, which includes capital gains, interest income, and dividends as the Consumer Expenditures Survey does not separately disclose financial income information by income quintile. We doubt that financial income is driving our results, however. If it were, as mentioned at the top of this section, then we would expect statistical significance in the trend deviations in the income equations of the VECM (Table 4). All coefficients on chy t for the highest-income group are statistically insignificant by any reasonable measure. To better quantify the relation shown in Figure 1, we performed a series of regressions with group five trend deviations and the detrended log dividend-to-price ratio lagged as dependent variables. The results, in Table 8 indicate that group five trend deviations predict the future dividendto-price ratio as at least one of the lagged chy t coefficients is statistically significant at the 5 percent level, while the coefficients on the lagged dividend-to-price ratio and other plausible variables that may a role in forecasting the dependent variables do not. The estimated chy t coefficients, where the dividend-to-price ratio is the dependent variable, are negative (inversely related to the normalized trend deviations shown in Figure 1) and indicate that when consumption falls below trend, stock prices are expected to fall causing the dividend-to-price ratio to rise. The dividend-to-price ratio is sufficiently persistent that it in turn predicts future excess stock market returns. Our findings suggest that the highest-income consumers are forecasting future stock returns with the help of the dividendto-price ratio and smoothing their consumption growth based on these forecasts. VI. Conclusion This paper investigates whether trend deviations from the consumption-to-wealth ratio, measured across consumers with different income levels, provide additional insight about the ability of consumers to forecast future income, housing values, and stock market returns. Based on intuition and supported by the Survey of Consumer Finances, we hypothesize that lower-income consumers, who are economically constrained, will have a difficult time utilizing the collateral channel. We further 16
postulate that since a significant portion of stock wealth is held by upper-income consumers, we should see stronger evidence of consumption increasing ahead of increases in stock returns for these consumers. Using a cointergrating VAR system, we find that lagged trend deviations from the consumption-to- wealth ratio tend to positively predict changes in future housing values, but only for the middle-income quintiles and the national data. Our results suggest that consumers are increasing consumption above trend in anticipation of increases in housing wealth as suggested by the collateral channel for all consumers except those in the lowest and highest quintiles. If trend deviations for the highest-income groups do not forecast future changes in housing values, then what drives their consumption away from its long run trend with wealth? To answer this question, we examine whether trend deviations help to forecast expected future stock returns using several multifactor models with the dividend-to-price ratio and consumption-based variables. Here we find an important link between future excess market returns, consumption growth, trend deviations from the consumption-to-wealth ratio, and the dividend-to-price ratio through the intermediate horizon. When consumption growth and trend deviations are incorporated into regressions of future excess market returns onto the dividend-to-price ratio, there is a significant improvement in the ability of the model to explain future excess returns, but only for consumers in the highest-income group. Thus, it appears that only the highest-income consumers are using the dividend-to-price ratio as a signal for predicting expected future market returns and are modifying their consumption behavior accordingly. 17
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Newey, W. and Kenneth West. (1987) Hypothesis Testing with Efficient Method of Moments Estimation. International Economic Review, 28, 777-787. Phillips, Peter C. B. and S. Ouliaris. (1990) Asymptotic Properties of Residual Based Tests for Cointegration. Econometrica, Vol. 58, 165-193. Phillips, Peter C. B. (1991) To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends. Journal of Applied Econometrics, Vol. 6, 333-364. Sims, Christopher A. (1988) Bayesian Skepticism on Unit Root Econometrics. Journal of Dynamics and Control, Vol. 12, 436-474. Sims, Christopher A. and Harald Uhlig. (1991) Understanding Unit Rooters: A Helicopter Tour. Econometrica, Vol. 59, 1591-1599. Smoluk, H. J. and Raymond P. Neveu. (2002) Consumption and Asset Prices, An Analysis Across Groups. Review of Financial Economics, 11, 47-62. Stock, James H. and Mark W. Watson. (1993) A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems. Econometrica, Vol. 61, No. 4, 783-820. 19
Figure 1 Normalized quarterly trend deviations for 1985-2002 are estimated by equations (1) and (4), have a mean equal to 1.0, and are assumed to proxy for risk aversion. The detrended log dividend-to-price ratio is detrended by regressing the log dividend-to-price ratio on a constant and time and subtracting the forecasted time component from the regressor: 20
1 Table 1 Panel A Survey of Consumer Finances 1992/2001 2 3 4 5 National Percentage of families holding stocks directly, 1998-2001 average 3.75 10.45 17.15 23.85 45.98 20.25 Percentage of families holding stocks directly and indirectly, 1992-2001 average 9.05 27.30 44.35 62.60 79.04 44.48 Percentage of families holding certificates of deposit or savings bonds, 1998-2001 average 15.5 26.75 33.25 40.7 50.95 51.55 Percentage of families owning a primary residence, 1998-2001 average 39.70 56.30 66.65 80.45 91.45 66.95 Panel B Consumer Expenditure Survey and National and Product Accounts Annualized Descriptive Statistics in Percent 1984:1 to 2003:4 1 2 3 4 5 National Consumption Growth Rate Std Deviation Growth Rate Std Deviation Market Value of Housing Growth Rate Std Deviation 0.8338 7.3958 2.6516 12.7035 1.0291 7.7710 1.1335 6.2271 1.1255 6.4006 1.0406 4.9494 1.4150 6.7606 1.4383 4.5726 1.3134 5.2826 1.6374 4.4192 2.3481.9980 1.8392 1.4476 1.8851 11.6524 2.4956 7.5959 2.8308 6.3693 3.3749 5.3108 3.1830 5.5196 2.4397 1.5633 CEX denotes data source is the Consumer Expenditure Survey; NIPA denotes data source is the National and Product Accounts; SCF denotes data source is the Survey of Consumer Finances. Indirect holdings of common stock are those in mutual funds, retirement accounts, or other managed assets. 5 for the data in the SCF are an average of the 80-89.9 and 90-100 deciles. 21
1 Table 2 Unit Root and Stationarity Tests, Consumption, and Market Value of Housing 1984:1 to 2003:4 2 3 Panel A 4 5 National ADF Unit Root Tests: Consumption 3.0488-2.8829-3.1485-2.7423-3.3775-1.2303-2.8834-2.5131-2.3977-2.7423-2.3020-1.6238 Market Value of Housing -2.0091-1.6192 0.1326 2.4461 0.0096 1.6466 Critical Value -3.41-3.41-3.41-3.41-3.41-3.41 Lags 5 5 5 5 5 5 Panel B Modified KPSS Stationarity Tests: Consumption 0.3606 0.1234 0.2378 0.2296 0.1645 0.3078 0.8838 0.2557 0.2329 0.3000 0.2154 0.2433 Market Value of Housing 0.4295 0.4592 0.2990 0.3146 0.1964 0.2971 Critical Value 0.1356 0.1356 0.1356 0.1356 0.1356 0.1356 Truncation Lag 5 5 5 5 5 5 Panel C Sim's Bayesian Unit Root Tests: Consumption 0.6753 1.6302 1.3083 0.6106 1.3988 0.2779 Schwarz Limit 5.7694 5.7277 5.6565 5.8434 5.8200 10.7428 12.7501 2.9809 1.3560 0.0014 0.3954 0.0544 Schwarz Limit 6.0448 5.4877 5.5101 5.9696 6.4628 9.6703 Market Value of Housing 0.3722 1.0322 2.2233 12.1081 0.1047 4.1783 Schwarz Limit 6.1894 6.5162 6.7099 6.9686 7.0012 9.4664 Lags 5 5 5 5 5 5 In Panel A, Augmented Dickey-Fuller (ADF) unit root tests with asymptotic critical values at 5 percent significance level, assuming a constant and trend, from Davidson and MacKinnon (1993). Lag lengths were selected after a review of the Akaike and Schwarz s Bayesian criteria in conjunction with the periodicity of the data (quarterly). Tests statistics greater in absolute value than the critical value reject the null hypothesis of a unit root. In Panel B, Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) stationarity tests are modified according to Leybourne and McCabe (1994) using an ARIMA (p,1,1) to account for a moving average term. Critical values were simulated using a trend, a 5 percent significance level, T = 80 observations, and 10,000 repetitions. Our conclusions are robust to a variety of truncation lags and ARIMA p- specifications. Test statistics larger than the critical value reject the null hypothesis of stationarity. In Panel C, Sim's Bayesian unit root t-squared test and Schwarz Bayesian limit. Our conclusions are robust to a variety of lags. Test statistics larger than the limit reject the null hypothesis of a unit root. Rejection of the null hypothesis shown in bold for all three panels. 22
Table 3 Cointegrating Regressions 1984:1 to 2003:4 This table shows the results for the cointegrating regression equation (1). All variables are in log real per capita form. For the income quintile data, wealth is equal to log income plus the market value of housing with firstdifferenced lead/lag terms of log wealth. For national income, wealth parameters are estimated separately including their first difference lead/lag terms. Estimated coefficients for lead/lag terms are not shown. The variable chy t represents the trend deviation from the consumption-to-wealth ratio, equation (2). Regressor 1 2.4516 (3.2819) 0.5411 (13.4000) 2 5.2615 (5.3332) 0.7027 (8.9003) 3 3.1999 (3.4743) 0.5874 (10.3130) 4 2.7198 (2.8025) 0.6379 (8.2893) 5 2.2929 (2.4008) 0.5234 (8.5472) National Constant t-statistic 1.3119 (5.0615) Wealth t-statistic 0.4061 t-statistic (4.5525) Market Value 0.2347 housing (6.4252) t-statistic Time Trend 0.2427 t-statistic (7.9094) Leads/Lags 4 4 4 4 4 4 chy t std. deviation 4.0171 3.27 2.5167 2.4898 2.9407 0.4862 Philips-Ouliaris unit root test on the trend deviation: Z p -29.1216-29.6476-48.7716-28.5438-22.598-39.5061 Z t -4.2170-4.4411-6.2499-4.4073-3.5812-4.3358 t-statistics based on Newey-West (1987) standard errors are in parenthesis. Statistically significant estimates at the 5% level are in bold. Estimates for the cointegrating regression parameters and unit root Z statistics that are significant at the 5 percent level are in bold. Critical values for Z p and Z t are -20.5 and -3.37, respectively, for each quintile where the number of stochastic regressors on the right-hand side (n-1) of the cointegrating regression is equal to one, without a trend; critical values for Z p and Z t for national income, where the number of stochastic regressors on the right-hand side (n-1) plus a trend is three, are -32.2 and -4.16, respectively. See Hamilton (1994, page 598). Lead/lag lengths were selected based on the significance of the first-difference terms in the cointegrating regressions, sample size, and the sampling period, quarterly. Wealth is composed of income plus the market value of housing. All data, except the time trend, are in logs. The standard deviation of chy t is not annualized. Philips-Ouliaris unit root statistics, for the national group, are adjusted for moving average terms detected in the trend deviation due to seasonal adjusted data. 23
Log C t equation Constant Log C t-1,2,3 Log I t-1,2,3 Log H t-1,2,3 chy t-1, chy t-2, Log I t equation Constant Log C t-1,2,3 Log I t-1,2,3 Log H t-1,2,3 chy t-1, chy t-2, Log H t equation Table 4 Cointegrating Vector Autoregressions Real Per Capita Consumption,, and Market Value of Housing with trend deviations from the cointegrating regression, chy 1984:1 to 2003:4 1 0.7713 (0.1555) 0.2898 [0.5859] -0.2893 [0.3196] 0.1371 [0.4818] -0.7713 (0.1555) 0.3456 (0.5171) 1.1565 (0.1030) 0.7299 [0.3617] -0.4882 [0.3942] -0.6075 [0.2058] -0.6386 (0.4400) 0.2348 (0.7736) 2 0.6271 (0.1251) -2.0629 [0.0030] 0.3920 [0.0349] 0.6465 [0.0393] 1.5451 (0.0098) -1.8820 (0.0019) 0.5522 (0.1095) -1.6093 [0.0106] 0.1456 [0.1340] 0.4899 [0.0183] 1.6117 [0.0017] -1.7352 (0.0008) 3 0.2109 (0.5592) -0.2163 [0.4808] 0.4614 [0.5971] -0.1743 [0.8395] -0.2995 (0.5440) -0.5899 (0.2237) 0.3650 (0.2810) -0.3228 [0.4497] -0.0404 [0.2405] -0.2345 [0.2943] 0.1519 (0.7415) -0.4981 (0.2708) 4 0.0961 (0.7819) -1.5146 [0.0000] 0.1716 [0.0101] 1.0281 [0.0054] 1.0006 (0.0137) -1.2321 (0.0034) 0.1493 (0.5975) -1.0932 [0.0001] -0.1281 [0.0730] 0.7635 [0.0169] 1.2622 (0.0002) -1.2027 (0.0005) 5 0.1743 (0.5959) -0.3746 [0.1544] -0.0781 [0.4805] 0.2345 [0.0070] -0.5323 (0.2760) 0.4321 (0.3736) 0.2910 (0.3332) -0.1675 [0.7342] -0.1637 [0.1602] 0.1559 [0.3549] 0.0175 (0.9685) 0.0333 (0.9399) National 0.1127 (0.3140) 0.7069 [0.0132] -0.0782 [0.2931] 0.1340 [0.0411] -0.5013 (0.0544) 0.1629 (0.5390) -0.2893 (0.1250) 2.0634 [0.0040] -0.5469 [0.0096] -0.3195 [0.0572] -1.3446 (0.0026) 1.2954 (0.0048) Constant -0.5710 (0.4299) 0.8620 (0.0212) 1.0455 (0.0147) 0.4674 (0.1064) 0.6028 (0.1076) 0.0600 (0.6604) Log C t-1,2,3 2.1367 [0.0646] -3.7408 [0.0000] -1.5522 [0.1118] -2.3572 [0.0000] -0.5278 [0.7318] -1.0631 (0.0001) Log I t-1,2,3-0.5864 [0.2083] 0.5572 [0.0001] 0.0568 [0.2824] 0.4570 [0.0058] -0.2290 [0.5081] 0.4437 (0.0224) Log H t-1,2,3-0.6601 [0.1427] 1.3415 [0.0000] -0.0141 [0.1266] 1.2045 [0.0064] 0.3892 [0.2338] 1.0568 (0.0000) chy t-1, -1.2543 (0.1433) 3.6675 (0.0000) 1.5547 (0.0083) 1.6557 (0.0000) 0.1409 (0.7973) 1.2544 (0.0003) chy t-2, 0.8793 (0.2974) -3.5868 (0.0000) -1.3496 (0.0182) -1.5304 (0.0000) -0.0436 (0.9364) -1.3332 (0.0002) Lag 3 3 3 3 3 3 Coefficients are summed over the three lags, s for F-test statistics are in brackets for the combined lag coefficients, s for t-test statistics are in parentheses. Bold estimates are significant at the 5 percent level. Lag lengths were determined via the likelihood ratio test statistic using the general-to-specific method. 24