RDP 2011-06: Does Equity Mispricing Influence Household and Firm Decisions? 5. Results

5.1 Response Functions and Variance Decompositions

Figure 2 reports the impulse response functions associated with an exogenous 1 per cent increase in mispricing that is transitory, when using forecast dispersion, option volatility, and valuation confidence in turn as instruments.^[43] The results highlight that the mispricing shock has a persistent effect on equity prices, with more than one quarter of its initial effect still being observed after five years. In addition, prices do not appear to over-correct in response to a positive mispricing shock, suggesting that both positive and negative mispricing shocks are required to generate the boom and bust patterns often referred to in qualitative accounts of equity market bubbles.

In terms of the effects on other economic variables in the system, there is a persistent increase in consumption in response to a positive innovation in mispricing. Consumption exhibits a hump-shaped response with the maximum effect being in the order of 0.05 percentage points, which occurs around three years after the initial shock. This effect increases to around 0.5 percentage points in response to a one standard deviation mispricing shock.^[44]

An interesting pattern can be observed in the impulse response function for the quantity of equity held by households (equity quantities). Initially, households increase their equity holdings, when using either forecast dispersion or option volatility as instruments, and then subsequently reduce these holdings as the effects of the mispricing shock begin to dissipate. One interpretation consistent with this result is that households are able to perceive misvaluation in equity markets following a mispricing shock. This could help to explain why households reduce their equity holdings before prices have fully reverted to their fundamental value. The reduction in equity holdings is also consistent with households using the proceeds of equity sales to increase their level of consumption.

Nevertheless, it should be noted that the reduction in equity quantities is smaller than the increase in prices, and so the value of households' equity holdings increases in response to the mispricing shock. In this light, an alternative interpretation of the reduction in equity holdings is that it represents portfolio rebalancing given US households' increased exposure to domestic equities.

Turning to corporate dividend policies, the estimated results are less precise with the magnitude of the impulse response functions sensitive to the choice of instrument used. However, there is evidence to suggest that firms may bring forward the timing of their dividend payments in response to a positive mispricing shock. This could reflect firms using dividends as a signal of their more favourable expectations concerning their future profitability. Interestingly, only when using forecast dispersion as an instrument are dividends subsequently underpaid relative to their value without mispricing.

For the non-equity net wealth measure, the impulse response function is close to zero when using forecast dispersion as an instrument, but positive when using either option volatility of valuation confidence. Thus, whether positive mispricing in equity markets affects other components of household net worth remains an open questions based on these estimates. With regard to labour income, all three measures suggest that positive mispricing shocks have little effect on the after-tax income earned by households.

Table 4 reports a forecast error variance decomposition of equity prices and quantities, with the contributions of fundamental shocks and mispricing shocks separately identified at short- to medium-term forecast horizons.^[45] The results highlight that transitory mispricing shocks explain the majority of variation in equity prices growth at these forecast horizons. For example, when using forecast dispersion as an instrument, around two-thirds of the forecast error variance in prices growth can be explained by mispricing. In contrast, fundamental shocks are only able to explain between 16 and 40 per cent of the variation in equity prices growth at short to medium forecast horizons, depending on the instrument used. These results suggest that fundamental shocks to two of the most important variables emphasised by economic theory for equity pricing, consumption and dividends, explain some of the variation in equity prices. However, a larger part of this variation remains unexplained.

For equity quantities the proportion of the forecast error that can be explained by permanent and transitory fundamental shocks is much larger, in excess of 90 per cent according to these estimates. This suggests that changing fundamentals, as measured here, are much more able to explain variation in the quantity of domestic equity held by households, rather than the price of domestic equity.

Table 5 reports a similar forecast error variance decomposition for consumption and dividends. In this case fundamental shocks explain much of the short term variation in consumption. However, there is evidence to suggest that at medium horizons, from one to four years, a non-trivial fraction of the variation in consumption can be explained by mispricing shocks. These estimates suggest that although fundamental shocks are most important, non-fundamental transitory shocks do not necessarily have trivial effects on the consumption decisions of households.

For dividends, fundamental permanent and transitory shocks again explain the majority of the forecast error variation at all horizons. However, in line with the estimated impulse responses, there is mixed evidence on the importance of mispricing shocks for variation in dividends, with estimates ranging from close to zero to as much as 29 per cent of the variation in dividends at a medium-term horizon, depending on the instrument used.

5.2 Analysis of Historical Episodes

The previous forecast error variance decompositions compute the relative importance of alternative shocks over the full estimation sample. To provide additional insight into the importance of mispricing shocks in various historical episodes, Figure 3 compares each observed variable with a counterfactual estimate that assumes that all mispricing shocks are zero in the estimation sample from June 1986 to December 2006, and when using forecast dispersion as the relevant instrument. Estimates of the counterfactuals are conditioned taking the December 1985 and March 1986 observations as initial values.^[46] The equity prices panel in Figure 3 identifies two notable episodes of mispricing in the data. The first is under-valuation of US equity from 1987 to around 1995, which appears to be at least partly associated with the October 1987 stock market crash. After this time the equity market remains undervalued during the 1990–1991 recession. Prices then start to correct as the US economy recovers from this recession with prices being closer to their fundamental value from around 1992.

The second notable episode of mispricing is the familiar US dot-com bubble. From March 1995 to the height of the bubble in March 2000, the US equity market appears substantially overvalued. In March 2000, these estimates suggest that the US S&P 500 equity index was overvalued by around 45 per cent, before the subsequent collapse in equity prices was observed. Interestingly, equity was only slightly undervalued following the bursting of the dot-com bubble, and there was no clear evidence that equity markets were substantially mispriced in the lead-up to the financial crisis that began to emerge in September 2007.

Turning to consumption, it is clear that the level of consumption and the sign of mispricing shocks are positively correlated. In particular, observed per capita consumption appears lower than its counterfactual estimate during the late 1980s and early 1990s, and is above its counterfactual estimate during the dot-com boom. Between March 1997 and December 2000, consumption grew on average 0.6 per cent per annum faster than in the absence of mispricing associated with the dot-com bubble. This suggests that mispricing did have an effect on the consumption decisions made by households.

Again, an interesting pattern emerges with respect to household equity holdings. During the early stages of the dot-com boom, between 1995 and 1997, the counterfactual estimate of the quantity of equity held lies below its corresponding observed value. However, during the latter stages of the bubble, from 1997 onwards, households actually reduce their exposure to US equity. This finding is somewhat surprising given that many qualitative accounts of bubbles do not contend that households reduce their equity holdings when concerns surrounding a bubble are raised. Nonetheless, these results suggest that households may either be selling equity, in part to fund higher consumption, or are consciously reducing their equity exposure due to concerns about mispricing.

For dividends, labour income, and non-equity net worth, the observed and counterfactual estimates are much more closely aligned. This suggests that mispricing shocks had much less effect on the observed variation in these variables, when using forecast dispersion as an instrument.

Another approach for obtaining insight into the relative contributions of alternative shocks is to use a historical forecast error decomposition. Figures 4 and 5 report the relative contributions to the two-year-ahead forecast errors of transitory mispricing shocks, transitory fundamental shocks, and the reduced-form permanent shocks, again when using forecast dispersion as an instrument. Consistent with the counterfactual analysis discussed previously, it is clear that transitory mispricing shocks explain a non-trivial fraction of the forecast errors in equity prices and consumption. But they explain only a relatively small fraction of the errors for equity quantities, dividends, labour income and non-equity net worth. For these latter variables, reduced-form permanent shocks provide the largest contribution to the forecast errors observed.

5.3 Comparison with Existing Literature

The findings reported here are broadly similar to those obtained from related empirical literature. Focusing first on the effects of mispricing on consumption, Helbling and Terrones (2003) and Detken and Smets (2004) find a higher reduced-form correlation between consumption growth and equity prices growth during periods identified as equity market bubbles, and a weaker correlation during non-bubble periods, when using atheoretical procedures. The semi-structural approach to identification taken in this paper confirms these findings. A rule of thumb obtained from the estimates presented here would suggest that a one time over-valuation shock in equity markets, in the order of 10 per cent, results in the level of consumption being about 0.5 percentage points higher around three years after the initial shock, all else constant.

Turning to equity prices, the response of equity prices to a non-fundamental transitory shock estimated here is similar to estimates obtained from Lee (1998), who focuses solely on the identification of non-transitory shocks by assuming that such shocks have no real effects (on either dividends or corporate earnings). According to Lee's estimates, a one standard deviation mispricing shock increases equity prices in the order of 4–6 per cent at the end of the first year, with the full effect of the shock dissipating after about 12 years. The estimates presented in this paper are similar, with a one standard deviation mispricing shock increasing prices in the order of 5–7 per cent at the end of the first year, with the full effects dissipating in about 10 to 12 years. The estimated effects of mispricing on equity prices are very similar, notwithstanding different samples and data frequencies for estimation, and that Lee uses a different identification methodology for identifying non-fundamental transitory shocks.

One interesting difference with the previous literature on bubbles concerns the response of household equity holdings. Although this effect has received limited attention in previous empirical literature, it is interesting to note that the decline in household equity holdings in response to a positive mispricing shock is in contrast to qualitative accounts of bubbles. It is also in contrast to research by Gilchrist et al (2005) who find that firms tend to issue a small positive amount of stock in response to a mispricing shock. The results here suggest that households do not appear to be purchasing additional equity during the latter stages of a bubble episode. If correct, this would imply that either foreign residents or US corporates would need to be purchasing any additional equity issued.

A second remaining question is on the effects of mispricing on dividends. Previous literature has assumed a priori that bubbles do not affect corporate dividend policies.^[47] The results here suggest that bubbles can potentially influence corporate dividend policies, although the magnitude of this response is sensitive to the instrument used in identification.

Footnotes

Confidence intervals for these estimates are analysed in Section 6.1. [43]

A one standard deviation mispricing shock increases equity prices in the order of 9 to 10 per cent depending on the instrument used. [44]

Note that fundamental shocks include both the reduced-form permanent and transitory fundamental shocks identified. [45]

To ensure that these results are not sensitive to initial conditions, I also compute the observed and counterfactual paths for longer time series of historical data. Under the assumption that the structural model is stable over a period prior to the sample used in estimation, the results are qualitatively similar. [46]

See, for example, Lee (1998). [47]