Do private firms (mis)learn from the stock market?

Abstract

1. Introduction

How financial markets affect real economic activity has been a central question for financial economists. Over the last decade, increasing attention has been paid to the stock market’s role in producing information and its possible feedback effects on corporate decisions. As information does not flow freely among investors and firms, diverse pieces of information produced by different market participants can be aggregated into stock prices through trading (Grossman and Stiglitz 1980 and Kyle 1985). As a result, stock prices could reflect information that may not be known to corporate managers. If managers learn from this information and use it when making real decisions, the stock market can have a real effect via the transmission of information, even without any capital flowing to firms.¹

The learning mechanism predicts a positive relationship between a firm’s investment and the price signal. However, identifying learning through the investment-to-price sensitivity is challenging because corporate managers’ information sets are not perfectly observable to econometricians, and a positive investment-to-price sensitivity could be confounded by other channels. For example, the stock price may passively reflect what the manager has already known. Unobserved investment opportunities may also simultaneously affect the firm’s stock price and investment. Furthermore, public firms, which are predominantly used in the literature, have long been known to suffer from agency problems (Jensen and Meckling 1976). They may adjust their investments in response to fundamental and non-fundamental movements in stock prices due to managers’ catering incentives (Polk and Sapienza 2009).

In this article, I adopt a novel empirical strategy, which combines the unique features of privately held firms and a price noise measure based on public firms’ conglomerate structure, to more plausibly establish the learning channel. My empirical setting builds on the fact that private firms do not have shares listed on the stock exchanges and hence do not have their own stock prices. This feature mitigates the concern for the passive reflection problem since it is less likely that firm-specific information known by a private firm manager is only passively reflected in public peers’ stock prices. Moreover, as mostly owned by their managers, private firms’ investments are less distorted by short-termism (Asker, Farre-Mensa, and Ljungqvist 2014) and other agency concerns. Thus, alternative channels that have confounded public firms’ learning behavior have a much narrower scope when inferring learning from private firms.

Building on these advantages, I first draw predictions on private firms’ investment sensitivity to price. To the extent firms are exposed to common shocks, peer firms’ stock prices could inform about industry-wide investment opportunities (Foucault and Frésard 2014). Hence, private firms should learn from their public peers’ stock prices, and when they do so, their investment is expected to be positively associated with the industry valuation. Using a large panel data set for the UK, I test this baseline prediction and find strong evidence that the investment of private firms reacts positively to the industry valuation, proxied by the average beginning-of-period market-to-book ratio of assets of all public firms in the industry.

Still, there is room for endogeneity: If some industry-wide information reflected in stock prices were already known by private firms, an association between private firms’ investment and industry stock valuation could still be generated even without learning. I rely on noise in stock prices to sharpen the identification. As suggested by Morck et al. (1990), the prices are noisy signals (or “faulty informants”). If corporate managers learn from stock prices and cannot completely filter out the noise in the price signal, their investment will be sensitive to the noise component ex post. On the contrary, if they do not learn from prices, the noise should not play a role since it is unrelated to the firm’s investment opportunities. Therefore, the investment-to-noise sensitivity provides a unique prediction for the learning mechanism.

I develop a noise measure for private firms using their public peers’ conglomerate structure. The idea is based on the fact that, while private firms are mostly pure players, many public firms have multiple business segments, sometimes in industries unrelated to the major line of business (and hence unrelated to private firms in the major industry). When learning from industry valuation, private firms react to the price signal, which incorporates a noisy component reflecting their public peers’ unrelated minor-segment industries. Consequently, their investment will be sensitive to noise. For each private firm, I construct the noise as the average valuation of industries in which its public industry leaders have unrelated minor segments.² To satisfy the exclusion restriction, I exclude minor industries that potentially share economic links with private firms, such as industries proximate to the major industry, industries in which private firms also have minor segments, and industries likely to have supply-chain relationships. In the end, the price noise constructed using the remaining minor-segment industries is, to a large extent, unrelated to the investment opportunities of private firms.

The identification strategy requires that the decision-maker cannot completely filter out the noise. Otherwise, investments will not follow the noise even if learning takes place. This condition is likely to hold here for two reasons. First, as public pure players are more scarce, private firms often have to consider multi-segment firms as their peers. Second, since pure players are usually much smaller in size, their valuation is contaminated by that of larger firms, often conglomerates, in the industry (Hou 2007 and Cen et al. 2013). Thus, even when private firms only select peers from pure players, the noise is likely to be embedded in the price signal.

Consistent with learning, I find that the investment of private firms reacts positively and significantly to the noise in the price signal, and the economic magnitude is considerable: A one standard deviation increase in the valuation of industry leaders’ unrelated minor-segment industries is associated with a 0.8 percent increase in capital expenditure of private firms, which is about 4 percent of the average investment-to-capital ratio in my sample. This effect is estimated after controlling for the component of industry valuation that relates to the major industry, lagged characteristics of the firm and industry known to affect investment, contemporaneous investment of public and private peers, characteristics of minor-segment industries, unobserved time-varying shocks common to all firms (by using year fixed effects), and unobserved heterogeneity at the firm level (by using firm fixed effects). Again, as catering and market timing are less likely to drive private firms’ investment, especially those that never attempted Initial Public Offerings (IPOs) and remain private throughout their lives, the inferences drawn from the investment-to-noise sensitivity can largely be attributed to managerial learning.

I also perform several additional tests to validate the learning framework. First, I find that private firms with financial institutions as their investors react to a lesser extent to the price noise, consistent with the notion that they are better able to filter out the noise. Second, using various proxies, I show that the sensitivity of private firms’ investment to industry valuation and price noise is stronger when the stock prices are more informative and when firms in the same industry are more likely to face common shocks. Third, I perform a dynamic analysis and find that private firms operate a correction in the subsequent year to their mistake. But due to their limited capacity to understand stock prices and the more persistent nature of the noise, the correction is only partial.

Finally, I show that the results are not driven by alternative channels such as competition, internal resource allocation, and market timing. I first examine segment-level investments of public leaders and find that their major-segment investment is not affected by the minor industry valuation.³ Therefore, private firms’ reactions are not due to strategic responses to public firms’ internal resource allocation. Furthermore, I adopt a similar strategy as in Baker, Stein, and Wurgler (2003) to address the concern that the external financier’s sentiment may affect the cost of capital of private firms. I find that the reaction of financially unconstrained firms is as strong as that of constrained firms, which suggests that market timing cannot explain the findings.

My article contributes to a few strands of literature. The idea that stock prices aggregate information and improve the efficiency of the real economy dates back to Hayek (1945), and has been enriched by theoretical works including Dow and Gorton (1997), Subrahmanyam and Titman (1999), Goldstein and Guembel (2008), Peress (2014), among others. Based on reduced-form sensitivities of public firms, several studies show empirically that stock prices are associated with decision-making for capital investment (Chen, Goldstein, and Jiang 2007 and Foucault and Frésard 2014), mergers and acquisitions (Luo 2005), and cash savings (Frésard 2012). My article is the first to utilize the identification advantages of private firms to more plausibly establish the learning channel.⁴ My results suggest that stock prices provide informative signals to private firms and, through the learning channel, can have real effects on their investment even when private firms do not list their shares.

Also, I extend the existing identification based on the “faulty informant” hypothesis (Morck et al. 1990) by implementing the noise test on private firms and using a new measure exploring public firms’ conglomerate structure. My article complements recent studies using price pressure caused by mutual fund outflows to instrument non-fundamental shocks for public firms (cf Dessaint et al. 2019). Moreover, by showing a source of noise that does not result from public firms’ mis-valuation can have real impacts on private firms’ investment, my article provides a new case in which price efficiency and (ex post) real efficiency may diverge. Lastly, I document that whether the noise has any real effects through learning depends on agents’ ability to filter it out. This notion reconciles the findings that mispricing does not affect investments (Morck et al. 1990 and Bakke and Whited 2010) with the literature that finds the opposite.

The article is organized as follows. Sections 2 describes the data. Section 3 develops the hypotheses and the empirical strategy under a “learning” framework. Section 4 discusses the empirical findings. Section 5 shows additional evidence. Section 6 concludes the article.

2. Data

2.1 Panel data for public and private firms

My sample starts with all private and public firms in the UK for the period 1993 to 2010. The primary data source is the Financial Analysis Made Easy (FAME) database provided by Bureau Van Dijk (BvD), which contains accounting variables in the balance sheet, the profit & loss account, and the statement of cash flow for all private and public companies. I also rely on the Worldscope database to cross-check the financial data of public firms and to obtain their stock prices. All pound values are converted to 2005 constant million pounds using the UK consumer price index from the World Development Indicators (WDI).

The primary advantage of FAME is that the 1967 Companies Act in the UK requires that all limited liability companies, private and public, file their financial statements annually with the UK Companies House. The 1981 Companies Act further requires that all companies submit full financial statements, except for the “small”- and “medium”-sized firms which meet two of the three criteria: (1) sales less than £1.4 million, (2) book assets less than £1.4 million; and (3) number of employees less than 50. Thus, compared to other databases, FAME has a much broader coverage of private firms and their financial items.⁵ Moreover, private and public firms in the UK face equivalent tax laws and accounting standards. All their statements must be audited if the annual sales exceed £0.35 million before June 2000 and £1 million after.

FAME does not remove historical information if a firm stops reporting financial data. But it only keeps information for up to 10 years in the web version, and hence may bias toward firms that survived or incorporated in recent years. To avoid this “survivorship” bias, I obtained the archived disks from BvD from their earliest possible release (release 90, 1996) to the more recent ones (release 270, 2011). Each disk contains a snapshot of the web version in December of each year. Therefore, by appending the archived disks, I collect financial data backward in time and expand the time series to 18 years.⁶ Also, static (“header”) information such as listing status and ownership structures in the web version only reports the most recent value. The archived disks allow me to obtain this type of information at an annual frequency.

Following Brav (2009) and Michaely and Roberts (2012), I classify firms as public if they are quoted on the London Stock Exchange, OFEX or AIM, and as private if their company type in FAME is “Private,” or “Public Unquoted.” I only keep firms that do not change their status from private to public (or public to private) over the sample period. This is to address the concern that the transition firms may not represent the general population of private firms, and the stock prices may affect these IPO firms for reasons other than learning.

I collect firms’ ownership information (at an annual frequency) from the archived disks of FAME, which contains the number and identity of shareholders at the end of each filing date. I classify shareholders as institutional shareholders if their type in FAME is “Bank,” “Financial company,” “Insurance company,” “Mutual & Pension fund,” “Trust,” or “Private equity firms.”

2.2 Segment information

I obtain segment industry codes and financials of public firms from Worldscope and aggregate product segments within each firm at the two-digit Standard Industrial Classification (SIC) level each year. My results are robust if I use three-digit SIC segments. But using two-digit SIC helps ensure that minor-segment industries are unrelated to the major industry. Private firms in the UK are required to report the SIC codes for all the industries they operate, providing another advantage to the setting. I retrieve their secondary SIC codes from FAME to identify their minor-segment industries.

I use the 2012 US Input-Output Tables from the Bureau of Economic Analysis to identify potential supply-chain relationships between two industries. For a given industry, I define its supplier or customer industries as those industries that account for over 25 percent of the total flows of the goods and services that comprise the product process of that industry.

2.3 Sample selections

My sample selections follow Michaely and Roberts (2012). First, I keep consolidated financial statements and restrict the sample to limited liability companies to which the Companies Act applies. Second, I exclude small firms as defined by the Companies House to prevent a large number of missing data, observations that do not satisfy the auditing requirements, and firm-year observation that has missing values on the book value of assets, sales, or shareholders’ equity. Third, I require that each firm should have five consecutive years of data. Following standard practice, I exclude financial, insurance, and real estate firms (SIC code 6000–6900), utilities (SIC code 4900–4999), and public sector firms (SIC code above 8999). My final sample consists of 14,033 private firms and 1,761 public firms.

Variable constructions are presented in the Appendix. Ratios are winsorized separately for public and private firms at the 1 percent level at both tails of the distribution to alleviate the impact of outliers. Table 1 presents summary statistics for the sample.

Consistent with previous studies, private firms are much smaller in size than public firms. They depend more on debt and have fewer institutional shareholders. While private firms do not have lower capital expenditures than public firms, their investments in fixed assets are significantly lower. This is likely due to less intensive mergers and acquisitions by private firms. Finally, the distribution of public firms’ q is consistent with those using the US sample.

3. Hypothesis development and empirical strategies

In this section, I develop hypotheses for empirically examining the stock market’s impact on private firms’ investment through learning. In doing so, I also outline the endogeneity issues and my identification strategy to tackle the problem.

3.1 The informational role of stock prices

The rationale for managers to learn from stock prices stems from the role of the stock market in producing and aggregating information. The financial market is a place where investors with different beliefs and information meet to trade (Hayek 1945). Through their trading activities, diverse pieces of information can be aggregated into stock prices (Grossman and Stiglitz 1980 and Kyle 1985). As a result, stock prices could reflect information incremental to managers. In turn, managers should use this information to guide their real decisions because doing so allows them to form more precise predictions about the future state of the economy.⁷

Note that for the stock market to have a real effect through the learning channel, it does not require that investors have superior knowledge to managers, but only that they possess new information that could complement managers’ information set. For example, investors may come across valuable information about the demand for a product in their day-to-day activities. When they trade, such “serendipitous information” could be aggregated in stock prices (Subrahmanyam and Titman 1999). Moreover, stock prices may reveal investors’ information and assessment of other aspects of uncertainty facing a firm, such as its potential investment opportunities, the prospects of the industry, the state of the economy, the position of competitors, and the likely synergies in an acquisition (cf Morck et al. 1990; Luo 2005; Bond, Edmans, and Goldstein 2012), and hence provide useful signals for corporate managers when they make real decisions.

As stock prices are observable to all, managers can also learn from peer firms’ stock prices (see Foucault and Frésard 2014 and Dessaint et al. 2019). This is particularly relevant to private firms, which do not have their own stock prices but are exposed to common shocks as their public peers. Intuitively, when the industry has a sufficiently large number of public firms, as firm-specific shocks are canceled out, the industry valuation can inform about industry-wide (demand and cost) shocks. This signal still contains some noise.⁸ But as long as private firm managers do not possess perfect information about the common component, relying on the industry valuation signal improves their ex ante investment efficiency.

3.2 The response of private firms to the industry valuation

To guide the empirical specification, I compare the investment responses of private firms when they learn from the industry valuation with a counterfactual scenario when they do not.⁹

Under the “No Learning” scenario, the manager of a private firm will update her prior belief based on the private signal she receives. Thus, her posterior belief about future productivity (and the firm’s optimal investment) will reflect her prior knowledge and private signal but not the industry valuation. Under the “Learning” scenario, however, her posterior expectation will reflect the industry valuation signal, as long as the firm faces uncertainty about the common environment and that her private information is not perfect. It follows that, in this case, the private firm’s investment will respond positively to the industry valuation. 

Hypothesis 1 predicts $β>0$ under the “Learning” mechanism, assuming we can perfectly control for managers’ information set. However, neither her prior belief nor private signal is observable to us as econometricians. As the private signal may also contain information about common shocks, omitting it will result in a positive coefficient on the industry valuation even in the absence of learning. In Section 3.3, I discuss a sharper test strategy using the price noise.

3.3 The response of private firms to the price noise

3.3.1 The “faulty informant” hypothesis

As suggested by Morck et al. (1990), stock prices are “faulty informants” for managers, and the noise in the price signal could influence corporate investment through the learning channel. This prediction also extends to the setting I analyze. Since it is unlikely that a private firm manager can completely filter out the noise when learning from their industry valuation, the noise in the industry valuation will affect private firms’ investment.

Hypothesis 1b: The investment of private firms responds positively to the noise in the industry price signal, if and only if private firm managers learn from the stock market.

Hypothesis 1b is a unique prediction from the learning mechanism. This is because the noise component is (by construction) orthogonal to the firm’s investment opportunities. Under the “No Learning” scenario, it does not affect the manager’s posterior belief and the firm’s investment. Thus, the investment-to-noise sensitivity can identify the learning channel even when the manager’s private signal cannot be perfectly controlled for.

3.3.2 The noise measure: industry leaders’ minor-segment industry valuation

An ideal noise measure to test learning must satisfy two conditions. First, the decision-maker cannot completely filter it out from the signal. Otherwise, she will only react to the relevant component, and we should not observe any relationship between investment and the noise even when learning takes place. Second, the noise should be unrelated to the fundamental investment opportunities of private firms (the exclusion restriction). If violated, a spurious relationship between investment and noise could still be observed in the absence of learning.

In light of these conditions, I develop a measure of noise for private firms in the context of learning based on the valuation of public peers’ unrelated minor-segment industries. The rationale for this measure is the following. While private firms are mostly pure players, many public firms have fairly complicated business segments, which often involve industries unrelated to their major line of business. To the extent that the stock valuation of conglomerate firms reflects the information in both their major and minor segments, private firms’ price signals contain a noise component reflecting minor segments of public firms.

There are two reasons why the noise reflecting minor-segment industries could have a feedback effect on private firms’ real decision-making. First, as public firms are more scarce, even when it is in the interest of private firms to find pure players that are more comparable to them, it is not always feasible. As a result, they often have to consider firms with multiple business segments as their peers in trading off the quality of the match and estimate consistency. Second, due to market imperfections, new information is usually incorporated into the stock prices of large firms before it spreads to other firms within the industry, and less sophisticated investors often price smaller firms based on the valuation of industry leaders (Hou 2007; Cen et al. 2013). As pure public players are usually much smaller in size, their valuation is contaminated by that of larger firms, often conglomerates, which ensures the identifying condition is met even when private firms only select peers from pure players.

To construct the noise measure, I define “industry leaders” as firms whose major-segment sales rank in the top five among all firms in that industry, where the “major-segment industry” of a firm is defined as the two-digit SIC industry in which the firm generates more than 50 percent of its total sales. In turn, “Industry pure players” are defined as firms that are not industry leaders and generate all their sales from the major-segment industry. When industry leaders have product segments in industries other than the “major-segment industry,” these industries are defined as “minor-segment industries,” and the leaders in minor-segment industries are called “minor-segment industry leaders.”¹¹ For each private firm, I first obtain a list of minor-segment industries of its public industry leaders. To satisfy the exclusion restriction, I exclude minor-segment industries that potentially share economic links with the major-segment industry, such as industries within the same one-digit SIC industry as the major-segment industry, industries whose leaders have a minor segment in the major industry, industries likely to have supplier or customer relationships with the major industry, and industries in which private firms also have minor segments. So, the remaining minor-segment industries (referred to as “unrelated minor-segment industries”) are, to a large extent, unrelated to private firms in the major-segment industry. I then construct my main noise measure, “unrelated minor-segment industry valuation” (⁠$Minor_Industry_q$⁠), as the average industry valuation across all unrelated minor-segment industries.¹² As a robustness test, I construct an alternative noise measure, denoted by $Minor_PurePlay_q$⁠, which includes only pure-play firms to compute the industry valuation of each unrelated minor-segment industry.

As a sanity check for the exclusion restriction, I find that cash flows generated by industry leaders’ major segment are not correlated with cash flows by their unrelated minor segments, suggesting that the unrelated minor-segment industries do not co-move with the major industry in fundamentals.¹³ I also show in a later section that industry leaders’ major-segment investment is not affected by the valuation of their unrelated minor-segment industry, which again confirms that my noise measure does not likely capture underlying fundamentals related to the major industry.

3.3.3 The proxy for the fundamental component

Table 2 presents summary statistics for the industry-level variables. The distribution of the industry valuation is largely consistent with those of previous studies using the US sample.

3.3.4 Testing the “faulty informant” hypothesis

3.4 The role of key parameters

The learning mechanism also generates predictions regarding several key parameters, such as the role of the manager’s ability to filter out the noise, price informativeness, and the relative importance of common shocks. Testing firms’ heterogeneous responses with respect to these parameters offers validation for the learning mechanism.

I first examine the heterogeneity across firms in managers’ ability to filter out noise from the overall industry valuation. If some managers are better informed or less attention constrained than others, their reaction to the noise component will be more muted. Therefore,

Hypothesis 2: The sensitivity of private firms’ investment to the noise in the price signal is less pronounced when it is easier for the manager to filter out the noise.

Next, the precision of the price signal affects how much weight the manager puts on the average stock price when updating her belief: The more precise is the industry price signal, the more pronounced is the investment-to-price sensitivity. This is consistent with Chen, Goldstein, and Jiang (2007) and Foucault and Frésard (2014) for the case of public firms.

Hypothesis 3: The sensitivity of private firms’ investment to the industry valuation is stronger when the price informativeness is higher.

Finally, the rationale behind learning from the industry valuation is that the average stock price provides useful information about common shocks (cf Foucault and Frésard 2014 and Dessaint et al. 2019). When uncertainty is more likely to come from industry-wide shocks, this additional piece of information is more valuable and accounts for a higher weight when managers decide on the optimal investment. Therefore,

Hypothesis 4: The sensitivity of private firms’ investment to industry valuation is stronger when the common shock is more important relative to the firm-specific shock.

While Hypotheses 3 and 4 directly apply to the overall industry valuation, as noise is a component of the overall industry valuation, when it is challenging for managers to filter it out, both hypotheses apply to the noise. Therefore, in Section 5, I perform the cross-sectional tests on the investment sensitivity to both the industry valuation and noise.

3.5 Empirical inferences on the response of public firms

When public firms learn from the stock prices of their own and their peers, their investment also responds to the industry valuation and the noise component (see Foucault and Frésard 2014; Dessaint et al. 2019 and the Supplementary Appendix of this article). However, additional insights into their empirical inferences are worth discussing.

First, the optimal response of public firms’ investment to the industry valuation can be negative under the learning framework. When the price noise terms are highly correlated or when the common shock accounts for a small proportion of the uncertainty, managers could subtract the industry valuation from their own price to obtain the firm-specific shock. When the industry average valuation is higher, they will infer a lower firm-specific shock and adjust investment downward.¹⁶ For private firms, the sign is not sensitive to model specifications.

Second, since public firms’ noise terms are correlated, when their own and industry valuations are included in the same regression, the estimates are likely biased. This bias can further be magnified by agency problems. As public firm managers may cater to investors’ opinions and protect their own livelihood (Polk and Sapienza 2009), they have additional incentives than learning to respond to the price and noise (of their own and peers). In contrast, testing the investment-to-noise sensitivity of private firms is less subject to such concerns.

Finally, since public firms are less dependent on the industry valuation when their own price is informative, the learning framework predicts a larger weight on the industry valuation by private firms than “twin” public firms. However, testing this prediction requires that (1) private and public firms have the same underlying fundamentals, (2) managers’ private signals are equally precise, and (3) public firms do not have any agency cost. Given that these conditions do not hold in the data, the observed difference is likely an outcome of all these forces.

3.6 Remarks

The conceptual framework in my article also broadly relates to firms’ decision to go public. In a preceding article, Subrahmanyam and Titman (1999) examine the incentive to learn from prices and private firms’ decisions to go public. Their model does not feature a common shock across firms. Hence, unless going public, firms cannot learn about the incremental “serendipitous” information in stock prices. In my framework, private firms can interpolate the common component through learning, and the extent to which they can exploit the positive externality depends on price informativeness. If peer firms’ stock prices become too noisy about common shocks (a potential result of massive delistings), private firms cannot free-ride as much from prices. In that case, private firms will have a higher incentive to go public, converging to the setting in Subrahmanyam and Titman (1999).

Furthermore, while my article focuses on firms that remain private throughout their lives to achieve sharper identification, my empirical predictions are likely to hold for firms that attempt IPOs and other players in the private domain, such as venture capital firms and private equity funds. For example, Liu and Tian (2021) examine whether venture capital funds (VCs) learn from the stock market. However, VCs may have their own information production.¹⁷ Also, VCs’ information is more likely to correlate with that of the stock market, and their exit decision depends more on market sentiment. My setting is less likely to incur these empirical challenges.

4. Empirical results

4.1 Baseline: private firms’ investment and industry valuation

I test Hypothesis 1 with the classic linear investment regression, as in equation (1). In the baseline specification, I control for firm characteristics such as lagged cash flow scaled by beginning-of-period assets and the logarithm of its lagged total assets, and the average characteristics of all public firms and private peers in the industry. In an extended specification, more firm and industry characteristics (such as sales growth and leverage), as well as lagged industry valuation and peer firms’ average contemporaneous investments, are controlled for. The results are reported in Table 3.

Consistent with Hypothesis 1, the sensitivity of private firms’ investment to the industry valuation is significantly positive (columns 1 and 2 of Table 3). The economic magnitude is considerable: A one standard deviation increase in the industry valuation is associated with a 1.5 percent increase in the investment of private firms (⁠$β×SD(Industry_q)=0.023×0.635=1.5%$⁠), which is about 7 percent of the average investment-to-capital ratio in my sample.

My results are robust to how industry valuation is measured. In columns 3 and 4 of Table 3, I measure $Industry_q$ by the median market-to-book ratio of assets at the beginning of period t of all public firms in the same three-digit SIC industry. The results are consistent with the baseline results.¹⁸ Moreover, Raff and Verwijmeren (2013) and Bustamante and Frésard (2020) find that the investment of public firms responds to peer firms’ investment. Since the control variables in columns 2 and 4 include the investment of all public firms and private peers in the same industry, the findings I show here suggest that the effect of stock prices on private firms’ investment goes beyond their influence through peer firms’ investment.

4.2 Identification: private firms’ response to the noise

I dig deeper into identification by examining whether the investment of private firms reacts to the noise in the price signal (Hypothesis 1b). As demonstrated in Section 3.3, the noise, by construction, is orthogonal to the investment opportunities of private firms. Therefore, regardless of whether the unobserved investment opportunities are omitted, a positive investment-to-noise sensitivity can only be obtained under the “Learning” scenario. To implement, I estimate equation (3) using my noise measure based on the industry leaders’ unrelated minor-segment industry valuation. The results are reported in Table 4.

As shown in column 1 of Table 4, the evidence supports the learning mechanism. Specifically, I find that the investment of private firms in the industry leaders’ major-segment industry reacts positively and significantly to the price noise originating from the valuation of industry leaders’ unrelated minor-segment industries: A one standard deviation increase in unrelated minor-segment industry valuation is associated with a 0.82 percent increase in capital expenditure (scaled by the beginning-of-year capital) of private firms in the major segments (⁠$β×SD(Minor_Industry_q)=0.022×0.373=0.82%$⁠), about 4 percent of the average investment-to-capital ratio. The results are obtained after controlling for the unobserved time-varying shocks common to all firms (by using year fixed effects), the unobserved heterogeneity at the firm level (by using firm fixed effects), and an extended set of firm and industry controls that may affect investment. In addition, I control for the component of the industry valuation that relates to the major-segment industry, $Major_q¯i,t−1$⁠. As expected, this fundamental component is positively associated with the investment of private firms. Its economic magnitude is larger than that of the response to noise and comparable to that of the overall industry valuation.¹⁹

To further alleviate the possibility that minor-segment industries affect the investment of private firms in the major-segment industry through channels other than stock prices, I also control for the characteristics of the minor-segment industries and major-segment industries separately, where major-industry characteristics are obtained by operating the same decomposition as for the valuation variable.²⁰ As shown in column 2 of Table 4, the investment-to-noise sensitivity is not affected.

4.3 Robustness tests

I conduct a number of robustness checks in this section. First, I use an alternative measure for the price noise. My main noise measure includes all public firms in the unrelated minor-segment industries to construct the industry valuation, as long as they do not have any minor segment related to the major-segment industry (in case they do, the entire minor-segment industry is removed from the measure). This follows the notion that industry average valuation provides a consistent estimate of the common shock for the industry and the work by Hou (2007) and Cen et al. (2013) that the stock prices of industry leaders incorporate fundamental information relatively quickly as they are closely watched by analysts and other sophisticated market participants. As a robustness test, I construct an alternative noise measure, namely “unrelated minor-segment industry pure-play valuation” (⁠$Minor_PurePlay_q$⁠), using only pure-play public firms in each unrelated minor-segment industry to construct industry valuation. As in columns 3 and 4 of Table 4, I find consistent results with this alternative noise measure: A one standard deviation increase in this alternative noise measure is associated with a 0.92 percent increase in capital expenditure of private firms in the major segments (⁠$β×SD(Minor_PurePlay_q)=0.020×0.458=0.92%$⁠), which is comparable to the economic magnitude estimated with the main noise measure.

Second, I perform additional screenings to ensure that the results I obtained are, to a large extent, from unrelated minor-segment industries. One may argue that some minor-segment industries could still relate to the major industry. This concern is likely far-fetched because minor-segment industries proximate to or potentially share vertical relationships with the major industry have already been excluded. Also, if the remaining minor-segment industries were to capture fundamental information of the major industry, we would observe it to be associated with the cash flows or investments in the major segments. Nonetheless, I remove economic ties that may not be observable by excluding minor-segment industries in which private firms also have operations. I retrieve the secondary SIC codes of private firms from FAME, exclude all common industries shared by private firms and public industry leaders, and repeat the tests in Section 4.2. The results are presented in Table 5.

I find consistent results using both noise measures, $Minor_Industry_q$ (columns 1 and 2 of Table 5) and $Minor_PurePlay_q$ (columns 3 and 4 of Table 5). The findings again support the prediction that private firms learn from the stock prices and cannot filter out the noise from the industry valuation.

4.4 Firm heterogeneity in the ability to filter noise

In this section, I examine the heterogeneity across firms in their ability to filter out the noise (Hypothesis 2). While private firms, on average, cannot perfectly distinguish the noise component from the overall valuation signal, the fact that their reaction to the noise is to a lesser extent than that to the overall industry valuation implies that (some) private firms are capable of doing so.²¹ I hypothesize that institutional investors, such as private equity firms, insurance companies, and banks, are better informed and less attention constrained than individuals. They often have their in-house information production and are better able to scrutinize the information in the stock market. In turn, private firms held by financial institutions should respond less to the noise relative to firms without institutional holdings.

I define a dummy variable, Inst. Shareholder, which equals 1 if the private firm has one or more institutional shareholders at any point in time and 0 otherwise. I estimate equation (3) with this variable and its interaction with the noise, controlling for the proxy for major-segment industry valuation, its interaction with the institutional shareholder dummy, as well as the full set of firm and industry controls. The results are reported in Table 6.

Private firms with one or more institutional investors account for 20 percent of the full sample. As shown in Table 6, they react significantly less to the noise.²² The median private firm, however, does not have any institutional shareholders (see Panel A of Table 1). They are more difficult to precisely estimate the noise component ex ante and, therefore, present a more pronounced investment-to-noise sensitivity.

My findings suggest that when agents learn from the stock prices, whether a positive association between investment and noise could be observed depends on the agents’ ability to filter the noise out. This notion can reconcile the findings that mispricing does not affect investments (Morck et al. 1990 and Bakke and Whited 2010) with the literature that finds mispricing to have real effects. Essentially, the same prediction and test strategy can be applied to mispricing measures used in various contexts.²³ Whether they have any real effect through learning depends on the agent’s ability to filter them out.

4.5 Persistence of the real effect

I further examine whether firms realize ex post that they conditioned on noise and whether they learn from their mistakes. In a related context, Dessaint et al. (2019) show that public firms operate a correction in subsequent periods after transient, non-fundamental shocks to stock prices. Following this line of investigation, I perform a dynamic analysis to study the persistence of the effect of noise on private firms’ investment.

I look at firms without institutional shareholders, as these firms incur the mistake in the first place. I estimate equation (3) with lagged values of $Minor_qt−1$ (namely, $Minor_qt−2, Minor_qt−3$⁠, and $Minor_qt−4$⁠), as well as the contemporaneous value (⁠$Minor_q$⁠). To better assess the dynamics of private firms’ investment, I also include lagged and contemporaneous values of $Major_q¯t−1$ and standardize all the coefficients by multiplying the corresponding standard deviation. Point estimates and 95% confidence intervals are displayed in Figure 1.

Figure 1.

Sensitivity of private firms’ investment to the noise and the fundamental components. This figure presents the standardized regression coefficients from estimating equation (3) with leads and lags. The upper panel displays the estimates for the noise, $Minor_qt−1$⁠, and its lead and lags. The lower panel does so for the fundamental component $Major_q¯t−1$ and its lead and lags. 95% confidence interval for each estimate is presented.

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Consistent with the findings so far, private firms’ investment in year t responds positively and significantly to the noise measured by the valuation of unrelated minor-segment industries in year t − 1. Similar to the pattern documented in Dessaint et al. (2019), firms respond negatively to the noise in year t − 2, which implies that some firms realize that their responses were partly due to movements unrelated to their investment opportunities (maybe after observing realizations of cash flows to the major segment) and attempt to correct the mistake. However, compared to public firms’ corrections to non-fundamental shocks in Dessaint et al. (2019), the corrections made by private firms are both smaller in magnitude and weaker in statistical significance (only half of the impact of noise is corrected and is insignificant at 10 percent).

There are two possible explanations for why the real effect of noise on private firms is more persistent. First, unlike their public peers whose managers care about stock prices for their shareholders’ interest or their own compensation, private firm managers’ day-to-day operations do not involve stock prices (that is, except for the need to learn from prices). Therefore, they naturally lack the attention and expertise to fully understand the information contained in stock prices, especially if they do not have any institutional shareholders. Second, the noise I adopt depends less on the mis-valuation of public firms and hence is not normally accompanied by a notable price reversal (which is often the case for mispricing). This feature makes it more challenging for managers to completely correct the investment in subsequent periods.

Taken together, the evidence I show suggests that private firms rely on stock prices as an important source of information for real decisions. Upon observing the price movements of public firms in the same industry, private firms adjust their investment in the same direction. Doing so is ex ante more efficient than ignoring it because stock prices can inform about common shocks. Since the price signals are noisy, the first-best scenario for private firms would be to filter out the noise and only react to the fundamental component. However, I show that the vast majority of private firms are not able to do so. For them, an inevitable consequence when managers (rationally) learn from noisy price signals is that they make investment decisions in response to noise, which compromises real efficiency from an ex post perspective. I present further evidence suggesting that these mistakes can be reduced if decision-makers possess more sophisticated knowledge about the stock market and are partially corrected in the subsequent year after observing realizations of fundamentals.

5. Additional evidence

To further validate that the evidence is consistent with learning, this section examines the cross-sectional predictions with respect to price informativeness (Hypothesis 3) and the industry competition structure (Hypothesis 4). Alternative mechanisms are also addressed.

5.1 Cross-sectional tests on price informativeness

I use three measures for the industry price informativeness. The first is the industry price non-synchronicity. Under the learning framework, stock prices are more informative if they synchronize less with the market. As is standard in the literature (cf Durnev, Morck, and Yeung 2004; Chen, Goldstein, and Jiang 2007), I first construct price non-synchronicity for individual prices as $1−Ri,t2$ in each year, where $Ri,t2$ is obtained by regressing public firm i’s weekly stock returns on the market portfolio returns and the industry portfolio returns. Following Foucault and Frésard (2014), I then construct the industry non-synchronicity by taking the average of the price non-synchronicity of all public firms in a three-digit SIC industry in a given year. I define a dummy $H_Nonsynchronisity$⁠, which equals 1 if the industry non-synchronicity is above the 70th percentile in that year, and equals 0 if it is below the 30th percentile.²⁴

The second measure is based on the number of public firms in the industry. Under the learning framework, each individual stock price can be considered as a noisy signal about the common and idiosyncratic shocks. With a higher number of public firms in the industry, the industry valuation will be more informative about common shocks because idiosyncratic shocks will be more likely to be canceled out, and also, the noise of the industry valuation will be less volatile.²⁵ Also, as in Chemmanur, He, and Nandy (2010), the more firms that are already listed in an industry, the easier it is for outsiders, such as unsophisticated investors, sophisticated investors, financial analysts and market makers, to evaluate firms in that industry. Therefore, I use a dummy $H_#Public$⁠, which equals 1 if the logarithm of 1 plus the number of public firms in the industry is above the 70th percentile and equals 0 if it is below the 30th percentile.

Finally, I use $H_%Public$⁠, a dummy based on the fraction of public firms in a three-digit SIC industry, as the third measure for price informativeness. Badertscher, Shroff, and White (2013) argue that a high fraction of public firms indicates a more transparent information environment of the industry. While they use the measure to show that financial statements of public firms reduce information uncertainty for all firms in the industry, the cross-sectional prediction also applies here when examining the effect of stock prices beyond what public information provides.

As shown in columns 1, 3, and 5 of Table 7, the interaction terms of industry valuation and informativeness measures are positive and significant across all specifications. The results are consistent with Hypothesis 2 that in industries where the stock prices are more informative about future fundamentals, private firms’ investment responds more to the industry. Moreover, I show that when firms are not likely to filter out the noise, these industries also present a higher investment-to-noise sensitivity (see columns 2, 4, and 6 of Table 7).