Whose Disagreement Matters? Household Belief Dispersion and Stock Trading Volume*

Abstract

1. Introduction

Theoretical literature has long studied how disagreement among investors may help account for dynamics of trading activities and asset returns (see, e.g., Hong and Stein, 2007 for a recent treatment). However, empirical evidence on the effects of investors’ belief dispersion in the broad equity market remains quite limited. Notably, little is known regarding how belief dispersion among household investors may affect broad stock trading volume in spite of their substantial equity holdings.¹ Indeed, much of the existing literature treats household investors’ actions in the stock market as less sophisticated, uninformed, and often random (see, e.g., Barber, Odean, and Zhu, 2006; Campbell, 2007).

This article studies how belief dispersion about macroeconomic conditions among household investors may affect stock market trading volume. Our exercises contrast household belief dispersion against that among professional analysts, thereby shedding light on the merit of the broad information possessed by household investors. Relatedly, a nascent literature began exploring how household investors’ previous experience with macroeconomic shocks affect their economic beliefs and investment behaviors and market dynamics (see, e.g., Malmendier and Nagel, 2011; Malmendier, Pouzo, and Vanasco, 2020).

In a standard representative agent model, no trading occurs because all investors are assumed to be identical (Milgrom and Stokey, 1982). The theoretical significance of disagreement among investors on trading activities has been appreciated since at least Varian (1985) and Karpoff (1986), who show that trading arises if investors interpret signals differently or if they interpret signals in the same way but start with different prior beliefs. More recently, this relationship has been studied in Basak (2000), Adem and Suleyman (2018), and Osambela (2015).²

We first introduce a metric of belief dispersion among household investors using over three decades worth of data from the University of Michigan Surveys of Consumers (SCA) . We find a substantial and robust positive relationship between this measure of household belief dispersion and the broad stock market trading volume. Specifically, a one standard deviation increase in our metric implies an increase in monthly market-wide turnover of about one-quarter of its standard deviation. Notably, our results hold even after controlling for a wide range of indicators of belief dispersion among professional analysts, whereas, interestingly, the effects of professional belief dispersion on trading volume diminish in the presence of household belief dispersion. These results hold for both market-wide stock turnover rates and the gross equity mutual fund flows. The results are resilient to a wide range of robustness tests. In particular, noting our measure of household belief dispersion demonstrates appreciable cyclicality, we experiment with a number of alternative models to control for business cycle effects, and our baseline results hold against all these sensitivity tests.

We then present an array of analyses to explore the channels through which household belief dispersions affect stock market trading volume. We begin with documenting novel evidence of a strong, positive association between household expectations and stock ownership using data assembled through months when stock ownership information was collected in the SCA.³ We then exploit the extensive household socioeconomic and demographic information in the survey and show that trading volume is more sensitive to belief dispersion among richer and more educated households, who are more likely to own stocks. In a similar spirit, we find that household belief dispersion has a larger impact on the trading volume of stocks that are more visible to such investors. For example, an event study suggests that stocks of firms recently added to the S&P 500 index experience an increase in the trading volume sensitivity to household belief dispersion.

We then explore whether household belief dispersion can explain cross-sectional stock returns. Using the standard two-stage Fama–French regression framework to estimate the price of risk associated with our belief dispersion measure, we find that, for a wide range of test portfolios, stock portfolios whose returns are more sensitive to household belief dispersions have higher expected returns. In contrast, this relationship does not hold for dispersions among professional forecasters. Furthermore, similar to our findings on trading volume, stock returns are better explained by belief dispersions among households that are more likely to own stocks.

The result that belief dispersion among household investors outperforms that among professional analysts in explaining stock trading volume and returns is consistent with the notion that household investors may collectively possess richer and more diverse information than professional analysts, as the population of consumers is more heterogeneous than analysts in terms of income level, geographic location, profession, personal financial and economic experience, and industry affiliation. While the information each consumer possesses can be potentially biased or incomplete, the collective wisdom held by the population of such investors can still be a potent factor affecting the broad equity market.

The article proceeds as follows. Section 2 summarizes the literature on the theory and empirics regarding the relationship between investor belief heterogeneity and trading volume. Sections 3 and 4 describe the data and introduce our measures of belief dispersion, respectively. Section 5 presents the baseline results, and Section 6 explores the causality between belief dispersion and stock trading volume. Section 7 explores the cross-sectional asset pricing implications of household belief dispersion, and Section 8 concludes.

2. Related Literature

One surprising and elegant piece of economic theory is the No-Trade theorem (Milgrom and Stokey, 1982), which states that in a speculative market composed of fully rational agents with identical prior beliefs, no trade will occur in equilibrium, even in the presence of asymmetric information. The prediction is obviously not meant to hold in reality, but it provides a starting point for any attempt to answer the question—why do people trade in financial markets?

Tirole (1982) describes the conditions under which the No-Trade theorem does not hold: (i) there exist irrational traders, or noise traders who trade for liquidity reasons; (ii) some investors trade for hedging or diversification purposes; and (iii) agents have different prior beliefs. Our focus in this article is the third condition.⁴ This argument is, first and foremost, empirically sound. Considering “the glass is half full or half empty” argument, it speaks to the deep psychological roots of the dispersion of human optimism or pessimism. As Hong and Stein (2007) argue, “disagreement models uniquely hold the promise of being able to deliver a comprehensive joint account of stock prices and trading volume, which we consider to be one of the highest priorities for theoretical work in asset pricing.”

Various theoretical papers have demonstrated how differences in beliefs can be linked to trading volume. For example, Karpoff (1986) shows that both different interpretations of the same information and different prior beliefs can stimulate trading activities.⁵ By no means is our article the first attempt at providing empirical evidence for such a theory. Rather, we are motivated by the gaps in the existing, albeit vast, empirical literature. We highlight several major ways in which our article improves upon and extends the previous empirical work.

First, most existing empirical studies focus on belief dispersion among financial analysts. However, Dinh, and Gejewski (2007) point out that such proxies can be inaccurate since they represent only a distinct group of economic agents, who are often more informed and more sophisticated than the general public. In addition, analysts’ forecasts can be biased by their private incentives. Such bias may render their belief dispersion an inefficient proxy for traders’ disagreement. For example, analysts’ desire to win investment banking clients may lead them to adjust their forecasts to avoid earnings disappointments. Moreover, Hong, Kubik, and Solomon (2000) find that analysts, especially inexperienced ones, herd in their forecasts because of career concerns. These findings suggest caution is warranted when using and interpreting the forecasts made by professional analysts.⁶

In addition, previous studies have largely focused on earnings forecasts of individual firms, instead of beliefs about future macroeconomic conditions. However, expectations on future macroeconomic and business conditions play a pivotal role in shaping investors’ strategies and portfolio choices as these variables tend to influence the level and riskiness of future dividend flow of all firms and the interest rate at which future dividends are discounted.

Furthermore, most prior studies examine specific events, such as corporate earnings releases, and measure beliefs and trading volumes over a short period of time around such events (Comiskey, Walking, and Weeks, 1987; Lang and Litzenberger, 1989; Ziebart, 1990). Nevertheless, agents do not trade only on their opinions about earnings releases. Investors’ opinions about the economy and their perspectives on interest rates and employment should all be critical in forming their opinions about financial investment and trading strategies. In reality, agents receive new information on a continuous basis, especially information concerning the economy. As new information comes, investors update both their short- and long-term outlooks for the economy and financial markets. It is therefore an empirical question as to what extent each piece of information matters in generating trades. We address these concerns by constructing metrics of belief dispersion using data of self-reported expectations directly collected in a nationwide representative survey of consumers.

Finally, our article is also related to a growing literature that studies the financial decisions and trading behaviors of household investors and, in particular, the role of their experiences and expectations. For example, Malmendier and Nagel (2011) show that individuals who have previously experienced low stock market returns are less likely to participate in the stock market; Amromin and Sharpe (2014) examine stock market beliefs and portfolio choices of household investors, and Kelley and Tetlock (2013) study the role of retail investors in stock pricing. Using 1-year worth of data from a large discount broker from the Netherlands, Hoffmann, Post, and Pennings (2013) present evidence that retail investors’ beliefs affect their trading activities. More recently, Malmendier, Pouzo, and Vanasco (2020) introduce an overlapping-generation model to characterize how experience-based learning affects investors’ beliefs, portfolio choices, and learning. Such a model is able to generate a positive correlation between investor belief dispersion and trading volume. Our analysis corroborates Malmendier, Pouzo, and Vanasco (2020) by constructing survey-based household belief dispersion metrics and presenting rich and robust empirical evidence on this prediction.

3. Data Description

3.1 SCA

We use self-reported beliefs of households from the Thomson Reuters/University of Michigan SCA, which is used to build the Consumer Sentiment Index. Introduced in the late 1940s, the Index has established itself as one of the most widely followed indicators of households’ sentiments about current and future economic and business conditions.

The information content of the survey has long been recognized by the research community. Validation studies by the SCA staff show that the information collected in the SCA predicts the dynamics of the nationwide economy quite well. For example, the time series correlation between the index of consumer assessment of economic conditions and real Gross Domestic Product  (GDP) growth was 0.9. The correlation between the index of unemployment expectation and subsequent realized unemployment rate was 0.8. In addition, Carroll, Fuhrer, and Wilcox (1994) find the Index of Consumer Sentiment (ICE) derived from the SCA predicts future changes in household spending. In addition, Ang, Bakaert, and Wei (2007) find that the mean inflation projection of the same survey outperforms statistical time series and term structure forecast models. More recently, Barsky and Sims (2012) document that the “Michigan Survey of Consumers have powerful predictive implications for the future paths of macroeconomic variables.” These studies consistently demonstrate that, despite the substantial dispersion among household beliefs, their expectations on future macroeconomic conditions appear to be quite accurate on average.

Since 1978, the SCA has been conducting monthly surveys of a minimum of 500 consumers, the majority of whom were contacted within about 2 weeks.⁷ Our sample covers the period from 1978 to 2011, containing nearly 35 years’ worth of monthly consumer-level data. The SCA survey data have a few notable advantages over various surveys of professional forecasters. The size of the SCA cross-section is more than 500, significantly larger than the sizes of professional forecasts, which typically have fewer than 50 respondents. Therefore, belief dispersion can be calculated more reliably from the household surveys. In addition, collecting all answers within a short window of 2 weeks ensures that forecasts are made based on roughly similar information set across respondents. Another critical and unique feature of the SCA is that it collects key information about the demographic characteristics and the economic status of sampled consumers, which helps us predict the respondents’ likelihood of owning stocks in the years when stock ownership data were not collected.

Each month, the SCA asks about 50 core questions broadly related to consumers’ assessments of current economic conditions and their expectations about the future economic conditions of both their households and the country.⁸ We focus on the dispersion of beliefs (and its changes) about future business conditions, personal financial conditions, unemployment, and interest rates. The upper panel of Table I lists the survey variables that our study focuses on. Four of the five questions are about consumers’ expectations in the near term, typically within the next 12 months. The only question regarding long-term expectations is about consumers’ expectations of business conditions during the next 5 years.

Most SCA questions have categorical, instead of numerical, answers.⁹ For example, when asked about unemployment expectations, consumers choose from three answers—“more unemployment,” “about the same,” and “less unemployment.” Similarly, when asked about future business conditions, consumers choose from “better off,” “same,” and “worse off.” Categorical answers are likely easier for a typical household to answer. They are also less affected by “wild answers.” However, constructing dispersion measures from categorical answers is less straightforward. We address this challenge by introducing a new measure of belief dispersion that is explained in detail in Section 4.

Finally, questions regarding individual stock ownership and trading activities were added to the SCA from 1990 in various “riders” to the survey.¹⁰ Not being part of the core questionnaire, these questions changed substantially over time. Roughly speaking, the SCA has information on direct stock and stock mutual fund ownership through early 2003; and information on expected stock transactions through early 1998. After March 2003, only an indicator of broad stock ownership is available in the SCA.¹¹ We will take advantage of this stock investment-related information to inform our analysis on the relationship between household belief and stock trading.

3.2 Forecasts of Professionals

Earlier research has documented that dispersion of beliefs regarding corporate earnings among business analysts can influence trading activities of individual stocks (Comiskey, Walking, and Weeks, 1987; Lang and Litzenberger, 1989; Ziebart, 1990). Conceivably, wider belief dispersion among professional forecasters regarding future macroeconomic conditions can also induce higher trading volume—a hypothesis we test in this article. Should professional-based disagreement matter for stock trading volume, we are particularly interested in whether household-based belief dispersion has any net effects on trading volume beyond the extent to which their belief dispersion is correlated with those among professional forecasters. To study this, we collect professional forecasters’ beliefs from the following three sources:

• Survey of Professional Forecasters

  The Survey of Professional Forecasters (SPFs) is a survey of professional investors and analysts on their views about macroeconomic conditions.¹² The SPF began in the late 1960s, and we use the later portion of the SPF data that overlaps with the SCA data, from 1978 to 2011. The number of respondents for the SPF in recent years varies between thirty and fifty. In addition to survey participants, the SPF differs from the SCA in two other aspects. First, the SPF is conducted quarterly whereas the SCA is done monthly. We interpolate the SPF data to a monthly frequency to facilitate comparison. Moreover, the SPF answers are numerical, unlike the categorical answers in the household survey. The middle panel of Table I describes the SPF variables our study focuses on—growth of GDP, industrial production and corporate profit, and unemployment.¹³

• Blue Chip Economic Indicator Survey

  Blue Chip Economic Indicator Survey is survey data collected by a monthly newsletter published by Wolters Kluwer. Similar to the SPF, participants in the Blue Chip surveys are a mix of economists at large banks, consulting firms, or academic institutions. On average, the survey has around fifty participants each month. Our study focuses on the forecasts of the following variables—summarized in the lower panel of Table I—GDP growth, industrial production growth, nonresidential investment growth, unemployment rate, short-term interest rate, and longer-term interest rate.¹⁴ Our sample of the Blue Chip survey data covers the period from 1984 to 2011.

• I/B/E/S Analyst Forecasts of Corporate Earnings

  The I/B/E/S database contains monthly updates of financial analyst forecasts of near-term levels of earnings-per-share (EPS) for the firms they cover. Pinto (2010) constructs a series of analysts’ earning forecasts dispersion as the coefficient of variation of analysts’ EPS estimates averaged across companies, which we use in this study. The series begin in 1976, and we use the period from 1978 to 2011 that overlaps with our main SCA data. While the earnings forecasts are not exactly about macroeconomic conditions, the aggregate measure of forecasts’ dispersion on earnings likely contains relevant information about the belief dispersion of macroeconomic variables that are particularly relevant for the stock market.

3.3 Trading Volume and Control Variables

Our measure of trading volume is the monthly turnover rate of the aggregate US stock market (the total number of shares traded in a period divided by the average total number of shares outstanding during that period). Normalizing trading volume with shares outstanding allows us to abstract from increases in volume that are due mainly to the growth of the economy and the stock market. The turnover measure has been used in various studies, such as Campbell, Grossman, and Wang (1993). Data on both the number of shares traded and shares outstanding are from the Center for Research in Security Prices (CRSP). In our baseline analysis, we aggregate the monthly trading volume and shares outstanding of all securities traded on the New York Stock Exchange, American Stock Exchange, and NASDAQ.

As shown in the upper panel of Figure 1, turnover rates in the US stock market steadily increased during the SCA data sample period. Many explanations have been offered to explain this trend. For example, Smidt (1990) suggests that the long-run trend in equity turnover can be attributed to transaction cost changes. Some researchers also attribute this trend to the increasing importance of high-frequency trading. The Dickey–Fuller test we conduct suggests that the series is trend stationary. We then remove the trend using various detrending methods. The middle panel of Figure 1 shows the cubic detrended series of turnover, which is used in our baseline analysis. The cubic detrending method leaves smaller residual autocorrelation than linear, quadratic, or fourth-order polynomial detrending methods.¹⁵ The series has a zero mean and a standard deviation equal to 0.024.

Figure 1.

Stock market turnover and aggregate flows to stock market mutual funds. This figure plots monthly time series of our proxies for household trading activities in the US stock market. The top panel shows the turnover rates, the middle panel shows the turnover rates after cubic detrending and the bottom panel shows the aggregate flows to stock market mutual funds. All three variables are in fractions. Turnover rate is defined as the combined number of shares traded in New York Stock Exchange, American Stock Exchange, and NASDAQ in a given month divided by the average total number of shares outstanding during the same month. Mutual fund flow is defined as the sum of outflow and inflow as a fraction of total asset under management by equity mutual funds in the same month. The date range is from 1978 to 2011 for turnover rates and from 1984 to 2011 for total fund flow variable. Shaded areas correspond to NBER recessions.

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As an alternative measure of market trading volume, we also use the gross flow of equity mutual funds. The data are from the Investment Company Institute. Monthly gross flows to the equity market are calculated as the sum of sales and redemption, normalized by total assets under management by equity mutual funds. The fund flow data start from January 1984 and are presented in the lower panel of Figure 1. Unlike the turnover rates, gross flows of equity mutual funds do not show any pronounced upward trend. One plausible explanation is that mutual fund flows reflect low-frequency trading that is not affected by the increasing importance of high-frequency trading, which likely contributed to the increase in stock turnover.

We include the S&P 500 index return and the S&P 500 index volatility as control variables. Both variables are calculated from the CRSP data. In addition, we control for stock market liquidity, which is the Pastor–Stambaugh series (Lubos and Stambaugh, 2003) from WRDS. A higher value of the measure indicates more liquid market conditions.

4. Measures of Belief Dispersion

4.1 Dispersion Measures—Weighted Herfindahl Index

The weighting scheme of the measure not only allows us to preserve the rankings among categorical answers, but also provides flexibility in giving different importance to answers that are different in informational values. Answers of “about the same” are potentially “lazy answers” and reveal less information about the beliefs of the respondents.¹⁶ We can adjust for this by giving a high ω_i to these answers. That said, our results do not rely on any particular choice of weights; we alter the weights in the robustness analysis, and show that the results are qualitatively preserved.¹⁷

4.2 Composite Dispersion Measure—a Principal Component Approach

Figure 2 presents the time series of belief dispersion, measured using WNHI, for each SCA question we study. Recall that higher values of the WNHI (closer to zero) suggest more dispersed distribution of beliefs. Belief dispersions on different questions seem to follow a common pattern. In particular, consistent with Patton and Timmermann (2010), three of the five series of belief dispersion exhibit strong counter-cyclicality. The peaks in dispersion of expectations about near-term economic conditions (BEXP), interest rate, and unemployment largely coincide with recessions as defined by the National Bureau of Economic Research. However, the cyclical patterns in the belief dispersion for expectations about personal financial (PEXP) and longer-term business conditions (BUS5) are more muted. Moreover, it appears that beliefs about longer-term business conditions in the next 5 years (BUS5) are more dispersed than beliefs about shorter-term economic conditions in 1 year (BEXP).

Figure 2.

Monthly belief dispersion from household surveys. This figure plots time series of dispersion of beliefs on five expectation variables in the SCA. The five expectation variables are unemployment, interest rates, short-term business conditions (BEXP), personal financial conditions (PEXP), and long-term business conditions (BUS5). The last panel plots the first principle component of the five dispersion series. Belief dispersion is measured using WNHI described in Equation (2). Larger values indicate higher dispersion. Shaded areas are NBER recession periods.

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Expectations on various macroeconomic indicators held by the same investor are likely correlated (people expecting lower unemployment also tend to expect better business conditions), potentially making dispersion of beliefs on these macroeconomic indicators also correlated. To summarize in a parsimonious manner the information contained in the five series of belief dispersion, following Buraschi and Whelan (2010), we compute the principal components of these series. Our subsequent analyses focus on the first principal component, which accounts for 50% of total variance. Each of the successive principal components explains no >20% of the total variance. As shown in the lower-right panel of Figure 2, the first principal component exhibits pronounced countercyclicality. Heuristically, people may disagree more when greater uncertainty prevails. The cyclicality in our belief dispersion measures is broadly consistent with the cyclicality of economic uncertainty as documented in Bloom (2009).

The SPF and Blue Chip surveys provide numerical forecasts by professionals, which allow us to calculate belief dispersion as the cross-sectional standard deviation of the forecasts. As with the SCA, we compute the first principal components of the SPF and Blue Chip data, respectively. Finally, belief dispersion in the I/B/E/S data is summarized into a single series by taking a weighted average of firm-specific analysts’ dispersion in their earnings forecasts Pinto (2010).

4.3 Visual Comparison of Various Dispersion Measures

Figure 3 contrasts the belief dispersion series derived from the four data sources. First, we notice that all four series demonstrate countercyclicality to some extent, with the cyclical pattern being more pronounced in the household belief dispersion series (SCA). A closer examination of the chart also reveals that household belief dispersion tends to rise sharply just before recessions (over the past 20 years in particular), whereas dispersion of professional forecasters tends to peak toward the end of recessions. This suggests that some household investors may have information predicting business cycles that is not possessed by professional analysts.¹⁸

Figure 3.

Comparison of household belief dispersion measure to professional belief dispersion measures. This figure compares belief dispersion among households in the SCA survey to the belief dispersions among professional forecasters in the SPF, IBES, and Blue Chip surveys. Detailed description of the construction of these dispersion series is given in Section 4. Data frequency is monthly. The date range is from January 1978 to December 2011 for all the time series except the Blue Chip time series, which is only available from July 1984. Shaded areas correspond to NBER recessions.

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It is too early to declare household investors a winner of the race, as each series shows some idiosyncratic dynamics that could be crucial for stock market trading volume. Indeed, as shown in the upper panel of Table II, correlations among these series can be quite low, albeit positive. The SCA and SPF series have the highest correlation coefficient—0.63, while the SCA and the Blue Chip series have the lowest correlation coefficient—0.20, suggesting that the household belief dispersion series contain information orthogonal to what is reflected in the disagreement among professional analysts.

5. Belief Dispersion and Trading Volume

5.1 Baseline Analysis

Our baseline model is motivated by previous studies of the time series properties of trading volume (e.g., Tauchen, Gallant, and Rossi, 1992) and studies of the relationships between trading volume and stock returns and volatility (see e.g., Campbell, Grossman, and Wang, 1993; Llorente et al., 2002).

In the above specification, the parameter of interest is β. Recall that we construct the WNHI in such a way that higher (closer to zero) WNHI indicates greater belief dispersion. Should greater belief dispersion induce larger trading volume, we will observe $β>0$ in Equation (3). Column Model 1.a of Table III reports that the estimated β coefficient is 0.241 without including any controls, and the estimate is statistically significant.²⁰ Column Model 1.b reports the results of Equation (3), including the full set of control variables. All standard errors are adjusted for auto-correlations and heteroskedasticity using the Newey–West method.²¹ Our estimates continue to show that greater belief dispersion among household investors is indeed associated with higher stock turnover rates, and the estimated β coefficient is positive, larger than in the model without controls, and highly statistically significant. Putting the point-estimate in perspective, if the dispersion among household investors increases one standard deviation, our baseline estimate implies that the detrended monthly turnover rate will increase 0.65 percentage point, slightly above one-quarter of the standard deviation of the detrended turnover rate.

Regarding the effects of the control variables on stock turnover rate, we find that contemporaneous stock market returns are positively related to turnover rates, with a 1% higher return inducing an approximately 0.4% higher detrended turnover rate. In addition, we find that the mean level of the household expectation index, Mean(ICE), has a positive effect on turnover rates. Consistent with the literature, we find S&P 500 index volatility (annualized) to be significantly positively related to stock market trading volume. Somewhat surprisingly, stock market liquidity, as in Lubos and Stambaugh (2003), is negatively related to stock market trading volume, potentially due to the fact that episodes of high trading volume caused by fire sales tend to coincide with time of low market liquidity. Finally, unemployment rate appears to have an insignificant negative drag on stock trading.

5.2 Introducing Professional Analysts’ Belief Dispersion Indicators

Columns with heading Model 1.b through Model 1.d of Table III explore the relationships between stock market turnover and various belief dispersion measures for professional analysts. The models are almost identical to the one in Equation (3), except that the households’ belief dispersion, WNHI, is replaced with that of professional analysts. Perhaps not surprisingly, estimated coefficients for belief dispersion in all three models are positive and statistically significant. An increase of one standard deviation in the belief dispersion among IBES, Blue-Chip, and SPF analysts correspond to increases in detrended turnover rate of 10.5%, 16.2%, and 13.1%, respectively. These numbers, though somewhat smaller than what is found for household belief dispersion, remain economically significant. To the best of our knowledge, this is the first exercise that documents a significant positive relationship between aggregate stock market trading volume and belief dispersion among professionals regarding macroeconomic conditions.

Since professional investors are typically deemed more sophisticated and informed than household investors, we are then interested in any incremental explanatory power of household belief dispersion over that among professional analysts. We do this by adding professional belief dispersions into our baseline model cumulatively. The results of the horse race are presented in columns Model 2 through Model 4 in Table III. As shown in column Model 2, where the I/B/E/S dispersion series is added to Equation (3), the coefficient on household belief dispersion is little changed and remains statistically significant, whereas the estimated coefficient for the I/B/E/S dispersion shrinks in magnitude compared to the result in Model 1.b and becomes statistically insignificant. In Model 3, we add Blue Chip dispersion to Model 2, and find that the size of the estimated coefficient for household belief dispersion somewhat increases and remains statistically significant. By contrast, the coefficient on Blue Chip dispersion series becomes smaller than in Model 1.c and less significant. Finally, when all four belief dispersion series are included, the coefficient on household belief dispersion (shown in the column Model 4) becomes the only one among four dispersion measures that is sizeable and significant at the 99% level. In contrast, statistical significance disappeared for the estimated coefficients on I/B/E/S and the SPF dispersion.²²

The horse race results highlight the additional information in household belief dispersion that has a material bearing on the dynamics in stock market trading volume. Our results thus challenge the traditional view of households as uninformed and insignificant participants in the stock market. Since disagreement among household investors is significantly related to stock market trading volume, they may collectively possess market-relevant information beyond what professional analysts have, a hypothesis we explore further in Section 7.²³

Our results are robustness to an array of alternative specifications. We use several techniques to control for potential business cycle effects, experiment with alternative measures of household belief dispersion, employ different turnover rate detrending methods, and re-estimate our model using various stock exchanges and sample periods. In addition, we estimate our model using a 10% random sample of the SCA data to ensure that household belief dispersion outperforms those of professional analysts not because the former has a larger sample size. The detailed robust analysis is reported in  Appendix A.

5.3 Belief Dispersion and Mutual Fund Flows

A substantial portion of stocks is held by households through equity mutual funds. We therefore hypothesize that greater disagreements among household investors may also leave footprints on equity mutual fund flows as they alter their exposures to market risks by changing their allocations to equity mutual funds. To test this hypothesis, we estimate Equation (3) with Turnover being replaced by the gross equity fund flow rate. The flow rate is calculated as the ratio between gross volume of equity mutual fund flows—the sum of new sales and redemption—and the total assets under management by stock mutual funds.²⁴ The results, shown in Table IV, present several notable findings.

First, household belief dispersion is strongly positively related with gross equity fund flows. Model 1.a of Table IV includes only the household belief dispersion variable. Professional dispersion series are added cumulatively in Model 2 through Model 4. Similar to the results for stock market turnover, we find equity fund flows to be positively related to household belief dispersion with a high level of statistical significance. Second, the magnitude of household belief dispersion’s effect on equity fund flows is significant across all models—a one standard deviation increase in household dispersion is associated with an increase in gross flow of 10% of its standard deviation. However, disagreement among professional forecasters is either unrelated or negatively related to equity mutual fund flows. Finally, coefficients of most control variables have the same signs as in Table III, with a notable exception that unemployment rate is estimated to be positively correlated with equity mutual fund flows.

We estimate that gross equity mutual fund flows account for as much as 10% of total stock trading volume, and the time series variations in mutual fund flows account for 20–25% of those in the detrended stock market turnover series. Thus, trading of equity mutual funds may also lead to stock turnover. Therefore, the belief dispersion among households who own stocks only indirectly through equity mutual funds may also affect broad stock market trading volume.

5.4 Why Do Household Beliefs Matter?

We argue that the households in the SCA sample are more heterogeneous and represent more diverse beliefs and information than professional analysts as it consists households that straddle different geographic locations, professions, personal financial and economic experience, and industry affiliations. Many studies document how economic shocks can vary among people across these dimensions. For example, Souleles (2004) finds household forecast errors in the SCA to be correlated to their demographic characteristics, as aggregate shocks do not hit all people equally. Favara and Song (2014) argue that dispersion of income shocks is a good proxy for information dispersion among city residents. The dispersion of income shocks also varies across cities, which helps explain cross-sectional differences in house price volatilities across US cities. In addition, two recent episodes of recessions affected specific industries—technology, and financial services—disproportionately. Households who have directly linked to those industries likely form systematically different expectations from people linked to other industries.

Compared to the SCA household data, the cross-section of professional forecasters in Blue-Chip, SPF, and I/B/E/S likely comes from a more homogeneous pool. They typically work for the same industry (financial industry), live in a smaller set of metropolitan areas (likely financial center cities), and likely share similar personal financial experience. Thus, belief dispersion among professional forecasters may not capture all aspects in which investors disagree with each other.

6. Examine the Statistical Relationships

Lack of exogenous shocks to and proper instruments for the belief dispersion measure, it is difficult to establish that the correlations presented above are causal. In this section, we examine this statistical relationship in various perspectives and present a rich set of evidence that is broadly consistent with a causal interpretation. It is important, however, to underscore that such an approach has limitations and cannot rule out certain alternative stories, particularly those regarding the origins of the belief dispersion.²⁵

First, we demonstrate a pronounced connection between households’ economic expectations and their financial investment behavior, leveraging the rich, under-explored stock and mutual fund ownership and expected trading data collected in the SCA. We show that more optimistic investors (higher ICE) being more likely to own stocks/mutual funds, to increase holdings, or to enter these markets, and the results hold controlling for rich individual characteristics and year × month fixed effects (FEs). Taking advantage of the panel structure of the survey, our analysis also indicates that a larger increase in ICE over 6 months is correlated with higher odds of entering the stock and stock mutual fund market during this period. The detailed data description and results are presented in  Appendix B.

We then study whether the correlations between household belief dispersion and trading volume differ across subpopulations. The premise of this test is that if household belief dispersion affects trading volume, such an effect should be most pronounced for the belief dispersion among stock-investing households. We further examine the cross-sectional variations in stock trading volume sensitivity to household belief dispersion. First, we conduct an event study and show that the sensitivity of a stock trading volume to household belief dispersion increases after this stock is included in the S&P index, which increases its visibility to household investors. Second, we show that that household belief dispersion has a greater impact on the trading volume of stocks that have larger capitalization and higher book-to-market ratios. These stocks tend to be more visible to retail investors (Zhi, Engelberg, and Gao, 2011) and more sensitive to macroeconomic conditions (Lettau and Ludvigson, 2001).

6.1 Analysis by Stock Ownership and Demographic Characteristics

Because the stock ownership indicator is only available in the SCA data after 1990, we split the sample by age, educational attainments, and household income, as existing studies, such as Hong, Kubik, and Stein (2004), document that prime-age, more educated, and higher-income investors are more likely to hold stocks. The results, presented in lower panels of Table V, consistently show the β coefficients for the subsamples more likely to own stocks to be both economically and statistically significant, whereas those for the subsamples less likely to own stocks are small and insignificant. As shown in the table and in Figure 4, the belief dispersion series estimated for the subsamples by age, education, and income have similar standard deviations and cyclical patterns.

Figure 4.

Comparison of belief dispersion series among subpopulations by propensity to own stock. This figure compares belief dispersion among subpopulation of households with different propensity of investing in stocks in the SCA survey. The stock ownership information is collected after 1990. The upper-left panel contrasts belief dispersion among the households younger than 35 years old versus that among older households; the upper-right panel contrasts belief dispersion among the households with high school education or below versus that among household with some college education or above; the lower-left contrast belief dispersion among households below versus above the median income; the lower right panel contrast belief dispersion among households investing in stocks versus that among households not investing in stocks. Shaded areas correspond to NBER recessions.

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6.2 Evidence from S&P 500 Index Inclusion and Exclusion

One way for individual stocks to gain visibility among household investors is to be included in widely used indices, such as the S&P 500 index. We use events of index inclusion and exclusion to examine the changes in sensitivities of trading volume to household belief dispersion after changes in visibility. If household investors gravitate more toward highly visible stocks, such as those included in the S&P 500 index, we expect the sensitivity of trading volume to the belief dispersion among household investors to increase after index inclusion.

We use the S&P 500 index composition history file in CRSP to come up with a list of 728 index inclusion events, and 252 index exclusion events during the period of 1978–2011. The monthly turnover of these stocks around the index change events is calculated. The event window is chosen to be [−6, +6] months, and the event month, Month 0, is removed. Since we are interested in time series variations, firm FEs are included in the model. The panel setting in this exercise distinguishes itself from our baseline model where only aggregate stock market trading volume is studied.

We find that after being included in the S&P index, a stock’s trading volume becomes more sensitive to household belief dispersion (Columns (1)–(4) of Table VI), as suggested by the significantly positive coefficient for the term “$PostEvent×HouseholdDisp$⁠,” which is an interaction term between the post-event indicator and household belief dispersion. Trading volume’s sensitivity to belief dispersion is not lowered immediately after index deletion (Columns (5)–(8)), where the interaction term becomes insignificant. The asymmetric results are consistent with similar asymmetric patterns of abnormal stock returns around index inclusion and exclusion events (Chen, Noronha, and Singal, 2004), which is explained by changes in investor awareness around index change events. Our results support the idea that stocks gain visibility to retail investors after being included in the index, but do not lose that visibility after being removed from the index.

6.3 Trading Volume of Large-Cap and Value Stocks

We now focus on the trading volume of stocks that have large capitalization and high book-to-market ratios (value stocks). Zhi, Engelberg, and Gao (2011) find that a direct measure of retail investors’ attention to stocks—the Google search volume on the stock ticker—is significantly higher for stocks of larger capitalization. Such stocks, therefore, are more visible to and followed more closely by household investors. In addition, empirical asset pricing literature suggests that large stocks and value stocks tend to be more sensitive to macroeconomic conditions (see, e.g., Lettau and Ludvigson, 2001). The household expectations we consider here are primarily about macroeconomic factors and therefore are more pertinent for these stocks.

We estimate Equation (3) with the stock market turnover rates being replaced with turnover rates of companies in the top-, medium-, and bottom-terciles of market cap and book-to-market ratio distribution, respectively. The results, controlling for all three belief dispersion series of professional analysts, are reported in Table VII. The β coefficient estimated for large-cap companies is similar to our baseline result (the left column), whereas household belief dispersion does not appear to materially affect trading volume of stocks of small- or medium-cap companies. Regarding the book-to-market ratio, household belief dispersion is the only one among the four belief dispersion measures we consider that appears to have a consistent, statistically significant effect on stock trading volume, and the effect is the strongest for stocks with the highest book-to-market ratios.