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## Which firms follow the market? An analysis of corporate investment decisions. Review of Financial Studies 23:1941–1980 (2010)

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@MISC{Bakke10whichfirms,

author = {Tor-Erik Bakke and Toni M Whited and Toni M Whited},

title = {Which firms follow the market? An analysis of corporate investment decisions. Review of Financial Studies 23:1941–1980},

year = {2010}

}

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### Abstract

Abstract We test whether stock-market mispricing or private investor information in stock prices affects corporate investment. We develop an econometric methodology that disentangles stock-price movements that are relevant for investment from those that are not. We combine this decomposition with proxies for private information and mispricing to devise unbiased tests for the effects of mispricing and information on investment. We depart from much of the literature by finding that stock-market mispricing does not affect investment, especially that of large firms and firms subject to mispricing. In contrast, we confirm previous evidence that managers incorporate private investor information when making investment decisions. Keywords: Investment; Stock market; Signal extraction; Errors-in-variables; GMM How does a firm's stock price affect its investment decisions? In a perfect world of symmetric information, efficient capital markets, and no regulatory distortions, this question is uninteresting because movements in asset prices reflect changes in underlying economic fundamentals, and the fundamental value of investment is the market value. However, the question has been of interest at least since Keynes ' (1936) idea that "animal spirits" influence the real economy, precisely because many accept the notion that capital markets are not entirely efficient; that is, that information does not flow freely among investors and firms. The question is also relevant for monetary policy because a link between stock prices and real economic activity opens the door for policy makers to target the stock market. The question is challenging because even an inefficient stock market passively reflects at least some of a firm manager's knowledge about genuine investment opportunities. Therefore, to answer the question one needs to disentangle such managerial knowledge from other sources of stock-price variation, such as private investor information or mispricing. Complicating any such disentanglement is the possibility of feedback from mispricing or from private information embedded in the stock price to the manager's perception of investment opportunities. No single answer to the question has emerged. The numerous papers that tackle this question find conflicting results, and the historical evidence has been similarly mixed. Similarly, the often cited increase in investment during the stock-market bubble of the late 1990s is small in comparison to the movement in the market. Given this background of scattered anecdotal and formal evidence, this paper takes a step back, identifies the difficulties to overcome in ascertaining whether a firm's stock price affects its investment, and then develops and applies a new econometric methodology that can tackle these difficulties. We examine two related questions: whether investment responds to mispricing or to private information embedded in the stock price. Our innovations take into account important conceptual issues previously ignored by much of the literature. Accordingly, our new approach disputes many previous empirical findings concerning the importance of mispricing for firm investment. However, we confirm previous evidence that private investor information does affect investment. 1 Explaining our empirical approach requires an elaboration of the basic question. On one hand, managers may be better informed about the investment opportunities of their firms than are outside investors. In this case market signals provide no new knowledge to managers, who can, therefore, safely ignore stock market movements. In addition, managers may be reluctant to issue equity to exploit overvaluation of their company's shares because equity issuance can be a negative signal that, in the spirit of We consider two related alternatives to this point of view. First, in This discussion of the mechanisms whereby stock prices affect investment is couched in terms of unobservable quantities such as mispricing and information. Any empirical examination of these issues, therefore, must deal convincingly with biases that inevitably arise in empirical studies that contain unobservables. Our methodology does. It uses a model in which investment is determined primarily, though not solely, by Tobin's q: the market value of the capital stock divided by its replacement value. Because most of the variation in Tobin's q stems from variation in equity, this model is ideal for investigating the effect of the stock market on investment. To isolate the effects of private information and mispricing on investment, we turn to the errors-in-variables remedy in Our technique allows decomposition of the variance of Tobin's q into a component the manager considers relevant for investment and a component the manager considers irrelevant. We use this decomposition to conduct two types of tests. First, if private investor information is reflected in the stock price and if the manager pays attention to this information, the relevant component should be larger. We therefore test whether groups of firms sorted by measures of private information have higher relevant components. Second, to ascertain whether these components depend on mispricing, we regress Tobin's q on proxies for mispricing and collect the residual, thereby removing variation from Tobin's q. We then test whether this variation has been removed from the part of Tobin's q that is relevant for investment or the part that is irrelevant for investment. To distinguish these two alternatives, our tests compare the sizes of the relevant and irrelevant components before and after we regress Tobin's q on the mispricing proxies. We structure our tests so that noise in our proxies does not affect test consistency. Finally, we use our technique to identify characteristics of firms that exploit stock-market mispricing, focusing on access to external finance and the level of mispricing. Because our technique is new, and because a skeptic may also find our econometric model and some of our assumptions questionable, we demonstrate the accuracy of our tests in finite samples in Monte Carlo experiments, and we go to great lengths to check the robustness of our results. To put this method in perspective, we examine the rest of the literature, which can be divided into two strands, the first of which examines the effects of mispricing on investment. In support of this idea, The second strand examines whether external information in the stock price affects investment. Chen, Our paper brings many of these results together by isolating specific mechanisms through which the stock market influences investment. We do find limited evidence that firms invest after issuing overpriced equity in order to relieve a binding finance constraint. However, we find much stronger evidence that many other groups of firms ignore mispricing. Finally, we find that the portion of the variation in Tobin's q that is relevant for investment rises with the amount of private investor information in the stock price. Why do our results depart from those in the literature? The difference stems in part from more accurate identification of firms that face financial constraints. A more important difference, however, arises from the improved ability of our technique to produce unbiased tests. Many of the papers surveyed above include proxies for mispricing, information, and fundamentals in regressions of investment on Tobin's q. Because Tobin's q is itself only a proxy for investment opportunities, such regressions contain more than one proxy. As such, the coefficients on any other proxies are therefore also biased, but, as explained in However, everything else held constant, investment-q sensitivity can also be high in the absence of mispricing or private information if the price fully reflects investment opportunities. Finally, both physical and financial frictions affect investment-q sensitivity. Given these difficulties, one goal in this paper is to determine in which instances previous approaches have been misleading. The paper is organized as follows. Section 1 presents our econometric model and testing strategy. Section 2 summarizes the data, Section 3 presents the results, and Section 4 concludes. The Appendix describes the estimators a Monte Carlo experiment that evaluates their performance. Methodology This section describes our methodology. First, we outline our econometric model and describe our tests. Because our methods are somewhat unusual, we demonstrate in several ways that the results produced by these methods are credible. In this section we address this issue on an intuitive level by discussing the applicability of the underlying empirical model. In later sections we take a more quantitative approach by performing specification tests, conducting robustness checks, and running Monte Carlo experiments designed to assess possible finite-sample bias in our tests. Econometric Model Our testing strategy starts with the estimators in in which y i is the ratio of investment to assets for firm i, χ i is the true incentive to invest (true q), x i is an estimate of its true q, and z i is a row vector of perfectly measured regressors, whose first entry is one. The regression error, u i , and the measurement error, ε i , are assumed to be independent of each other and of (z i , χ i ), and the observations within a cross section are assumed i.i.d. The intercept in (2) allows for bias in the measurement of true q . Using the third and higher order moments of (x i , y i ), the Erickson and Whited estimators provide consistent estimates of the slope coefficients, α and β, as well as of the variances of the unobservable variables (χ i , u i , ε i ). These estimators are identified only if β 6 = 0 and χ i is nonnormally distributed. Erickson and Whited To explain the intuition behind these estimators, we consider a simple example based only on third-order moments, in which γ and α have been set to zero. This estimator has a familiar instrumental variables representation, which we demonstrate as follows. First, substitute (2) into (1), and set γ = α = 0 to obtain This regression clearly suffers from a correlated error and regressor. However, the product of x i and y i can serve as a valid instrument for x i because the independence of u i , ε i , and χ i implies that this instrument is orthogonal to the composite error Premultiplying both sides of (3) by y i x i , taking expectations, and rearranging produces The moments This technique produces an estimate of our parameter of interest, which is the population R 2 of 6 equation From a purely econometric point of view, a value of τ 2 close to one implies that the proxy is quite informative about variation in χ i . Conversely, a value close to zero implies that the proxy is nearly worthless. We discuss the economic interpretation of τ 2 below. Because these estimators can be applied only to samples that are arguably i.i.d., we obtain our estimates in two steps. First, we estimate τ 2 for each cross section of our unbalanced panel. Second, we pool these estimates via the procedure in Test Description Before describing our tests we need to interpret τ 2 in economic rather than econometric terms. To begin we note that equations Our tests combine the two most common methods for dealing with unobservables in empirical work: the use of proxies and the imposition of structure on the econometric model. We have already described our structure. An estimate of τ 2 measures the ratio of the distance between points a and b to the distance between points a and c. However, although estimating τ 2 can separate these components, this estimation cannot by itself provide information on whether either component contains any mispricing. To complete our identification strategy, we combine estimation of τ 2 with a more common method for econometrically estimating the effects of unobservables: the use of proxies, in particular, proxies for market mispricing. Use of proxies typically results in biased regression coefficients and misleading tests. However, we structure our tests in such a way that the use of possibly noisy proxies 8 does not produce bias and only lowers the power of our tests. Specifically, we perform a first-stage regression of Tobin's q on each of these proxies and then make the observation that the variation thus removed has to be either relevant for investment (i.e., lie in the interval a to b) or irrelevant for investment (i.e., lie in the interval b to c). Consider first the former case, in which market mispricing is relevant for managerial investment decisions, and which is depicted in Panel B of Tobin's q in To describe the testing strategy more formally, let ω i be a proxy for mispricing, and letδω i be the fitted value from regressing x i on ω i . Next, rewrite (2) as in which χ * i and v i are defined in terms of the null and alternative hypotheses below. In this framework, the null hypothesis that ω i has no effect on Tobin's q, x i , can be written as H 0 :δ = 0. With reference to the original measurement equation, (2), ifδ = 0, then χ * i = χ i and v i = ε i ; and, therefore, τ 2 m = τ 2 . The first alternative joint hypothesis is that ω i affects x i and that the manager pays attention to ω i . This hypothesis can be written as H 1 :δ 6 = 0, χ i = χ * i +δω i , and ε i = v i . Under this first alternative τ 2 m < τ 2 . The second alternative joint hypothesis that ω i affects x i and that the manager ignores ω i can be written as H 2 :δ 6 = 0, χ i = χ * i , and ε i = v i +δω i . Under this second alternative τ 2 m > τ 2 . To examine the significance of τ 2 m , we first estimate (1) and (2) using x i . We then reestimate (1) 9 and (2) using x i −δω i in place of x i , thus producing estimates of τ 2 m . We then form the difference τ 2 m − τ 2 and test whether this difference is significantly greater or less than zero. In this framework, our null hypothesis is τ 2 m − τ 2 = 0. Our first alternative hypothesis that firms react to mispricing can be expressed as τ 2 m − τ 2 < 0. Our second alternative hypothesis that firms ignore mispricing can be expressed as τ 2 m − τ 2 > 0. We next discuss intermediate cases in which we cannot reject our null hypothesis. An obvious scenario that leads to a failure to reject is the absence of mispricing. However, our data analysis reveals thatδ = 0 for only one of the subsamples of firms we investigate. Because ω i is a proxy, its slope coefficient is biased toward zero. Therefore, our findings of nonzero slopes make this scenario unlikely. A second reason for a failure to reject is managerial attention to a portion of mispricing combined with managerial inattention to the rest. We deal with this possibility in the robustness section below. A final scenario that can lead to a failure to reject the null is noise in our imperfect proxies for mispricing. As shown in a Monte Carlo simulation in the Appendix, however, the presence of measurement error in these proxies only lowers the power of our tests relative to a situation in which we use (hypothetical) perfect measures. It does not bias the tests. These Monte Carlo experiments also show that even the diminished power of our tests is still quite effective in detecting the alternative hypotheses that τ 2 m − τ 2 is either greater than or less than zero. Three features of our testing strategy are important. First, we can quantify the extent to which the market influences investment, which is a calculation that cannot be made using previously formulated approaches. In particular, we can calculate an upper bound on the percent of the variation in χ i that is due to ω i if τ 2 m − τ 2 < 0. To obtain this bound, we substitute (5) into the expression for the R 2 from regressing x i on ω i , which we denote as R 2 xω ≡ var If ω i explains none of the variance of ε i , then Second, because our test is formulated as a difference between coefficients of determination, it is 10 robust to misspecification of the basic investment-q regression (1). For example, in Abel and Eberly (1994) the investment-q relationship can be nonlinear because a wedge between the purchase and sale prices of capital causes the level of q to affect the response of investment to q. For this problem to affect our tests, however, the source of nonlinearity needs to be correlated with our mispricing proxies because nonlinearity affects both the regression (1) and the version of (1) in which x i −δω i has been substituted in for x i . We view this possibility as unlikely. Third, the structure of our tests differs dramatically from those in previous studies, all of which are based on the null hypothesis that firms ignore the market. In contrast, this null is one of our two alternative hypotheses. Therefore, although previous findings that firms do not follow the market can be critiqued as resulting from low test power, any such findings on our part cannot. Applicability of the Model Is a linear errors-in-variables model appropriate for studying the effect of stock prices on investment? No econometric model ever represents reality perfectly, so the real question is whether this model captures the relevant features of the data. Our answer focuses the interpretation of the measurement error, ε i , because if factors other than mispricing influence ε i , and if our proxies for mispricing are correlated with these factors, our tests may simply pick up variation in these other factors. To organize our discussion, we start with a candidate definition of fundamental investment opportunities as marginal q-the manager's expectation of the future marginal product of capital. As discussed in 11 We view this correlation as unlikely because this source of error primarily arises from technological considerations, whereas the proxies for mispricing and information depend on investor behavior. The next link between fundamental investment opportunities and an observable proxy is the equality of average q and Tobin's q, which is the financial markets' valuation of average q. A discrepancy between these two quantities arises if stock market inefficiencies create variation in the stock price that is irrelevant for investment. This component of ε i is the one on which we focus. The third link arises because researchers estimate Tobin's q from accounting data that do not adequately represent market and replacement values. These well-known mundane measurement issues admit a further interpretation of ε i as literal data recording error. Nonetheless, we view this interpretation as unimportant, given the evidence in Erickson and Whited A further complication is the existence of two different ways to calculate Tobin's q. The first is the market-to-book ratio, which is the market value of assets divided by their book value. The second is what we call macro q, which is the sum of the market values of debt and equity less the value of current assets, all divided by the capital stock. The use of macro q dates back to In sum, although a series of links joins Tobin's q (x i ) to true investment opportunities (χ i ), the link most likely to be broken is the one due to stock market inefficiencies. Further, other possible sources of variation in ε i are unlikely to be correlated with our proxies for mispricing or information. Therefore, our testing strategy based on a signal extraction exercise is indeed appropriate. 12 Data and Summary Statistics This section describes our data sources. It then explains how we construct measures of financial constraints, mispricing, and information. It concludes by presenting summary statistics. Data and Variable Construction The data come from several sources. The first is the combined annual, research, and full coverage 2005 Standard and Poor's Compustat industrial files. We select the sample by first deleting any firm-year observations with missing data. Next, we delete any observations for which total assets, the gross capital stock, or sales are either zero or negative. Then for each firm we select the longest consecutive times series of data in which it did not undertake a merger greater than 25% of the book value of assets. We exclude firms with only one observation. Finally, we omit all firms whose primary SIC classification is between 4900 and 4999, between 6000 and 6999, or greater than 9000, because our model is inappropriate for regulated, financial, or quasi-public firms. Data variables from Compustat are defined as follows: book assets is Item 6; the gross capital stock is Item 7; capital expenditures is Item 128; R&D is item 46; cash flow is the sum of Items 18 and 14; net equity issuance is Item 108 minus Item 115; total long-term debt is Item 9 plus Item 34; total dividends is Item 19 plus Item 21; cash is Item 1; research and development costs are Item 46; inventories is Item 3; and sales is Item 12. The debt overhang correction represents the current value of lenders' rights to recoveries in default and is computed following Our monthly and daily return data are from the 2005 CRSP tapes, and our data on analysts' earnings forecasts are from I/B/E/S. After merging the CRSP and I/B/E/S data with the Compustat data and after deleting the top and bottom 1% of our regression variables, we are left with a sample that contains between 2,684 and 3,891 observations per year, with a sample period that runs from 1991 to 2004. We obtain data on one of our measures of information from Duarte and Young Measures of Mispricing We use three measures of mispricing. Our use of multiple proxies is important, given that mispricing is difficult to measure. Our first proxy is a measure of belief heterogeneity. Denoted SDEV , this proxy is defined as the standard deviation of analysts' earnings-per-share forecasts. As argued in We obtain the analysts' forecast data from the Summary History file from I/B/E/S. The Summary History file is potentially less accurate than the Detail History file because of the presence of stale forecasts and coding errors. However, 14 Because mispricing is transitory, a necessary (but not sufficient) condition for SDEV to be a good proxy is the existence of low returns for high SDEV firms. We find this pattern in our sample. The firms in the highest SDEV quartile have on average negative returns in months 5 through 12 after the measurement of SDEV . This result has the further implication that mispricing, although transitory, persists long enough to open the avenue for firm investment to respond. In contrast, firms in other SDEV quartiles exhibit no pronounced pattern of returns in either direction. Our second measure of mispricing is the analysts' consensus estimate of earnings per share minus the realized level of earnings per share, which we denote ES. issue that arises in measuring ES is timing. The earnings announcement cannot occur before the time at which Tobin's q is measured because the earnings announcement releases information. The ensuing market reaction then ameliorates any mispricing. We therefore consider the first earnings announcement that occurs from 1 to 5 months after the beginning of the fiscal year, which is when we measure Tobin's q. In results not reported we also examine longer time windows. For lengths of up to one year our results are robust. For lengths longer than one year our results are insignificant. Our final measure of mispricing is the cumulative abnormal stock return from the beginning of the fiscal year to the end. This proxy in part follows We reject several candidate measures of mispricing. For example, Measures of Information We examine two measures of private investor information, one measure of managerial private information, and one measure of public information. Our first proxy for private investor information is from from the regression of firm-specific weekly returns on value-weighted market and value-weighted industry indices. The industry is defined at the three-digit SIC-code level. We hereafter refer to Ψ as price nonsynchronicity. Chen, Goldstein, and Jiang (2007) provide a detailed survey of the literature that supports the idea that high idiosyncratic volatility is related to the existence of private investor information. They also survey several papers that argue and show that stock-price co-movement is related to a lack of private information in the stock price. Our second measure of private information is a variant of the probability of informed trading, or Our measure of managerial private information is from Chen, Goldstein, and Jiang and is based on insider trading activities. This measure is constructed as the total number of insider stock transactions for the year divided by the total year's transactions. The intuition is that managers are more likely to trade the more private information they possess. We measure this activity using both buys and sells. Isolating buys produces almost identical results in the tests that follow, whereas isolating sells produces insignificant results, possibly because managers can also be motivated to sell for liquidity or diversification reasons. 5 These data have only enough observations for us to run Finally, our measure of public information is the number of analysts covering a firm measured in the year preceding the measurement of Tobin's q. To the extent that analysts transfer information from managers to investors, high analyst coverage should indicate a small discrepancy between managerial and market expectations about investment opportunities. Measures of Financial Constraints Because financial constraints are endogenously determined with investment, we need an instrument. We use firm size, because small firms tend to be young, and young firms tend to face frictions in obtaining external capital. Indeed, Several authors have used these logit coefficients on data from a broad sample of firms to construct a "synthetic KZ index" to measure financial constraints. It is constructed as −1.001909CF + 3.139193T LT D − 39.36780T DIV − 1.314759CASH + 0.2826389Q, in which CF is the ratio of cash flow to book assets, T LT D is the ratio of total long-term debt to book assets, T DIV is the ratio of total dividends to book assets, CASH is the ratio of the stock of cash to book assets, and Q is the market-to-book ratio. As argued in Baker, Stein, and Wurgler Summary Statistics Summary statistics for the sample stratified into quartiles by size and the KZ index are in The first panel contains the sort on size. Small firms clearly do not finance with debt, and they issue