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...measurement-error estimators Erickson and Whited (2002) to estimate the extent to which variation in true unobservable q explains variation in different proxies for q. We find most proxies for q are poor: careful algorithms for calculating q do little to improve measurement quality. Using elaborate algorithms, however, depletes the number of usable observations and possibly introduces sample selection bias.
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Since Brainard and Tobin (1968) and Tobin (1969) introduced the concept of Tobin's q over thirty years ago, it has become the most widely used measure of a firm's incentive to invest. To understand Tobin's q, it is useful to turn back to these original papers. They begin with the intuition of Keynes (1936) and Grunfeld (1960) that a firm should invest in additional assets if this activity increases the stock market's valuation of the firm. In other words, a firm should not acquire new assets unless they are used by the firm to create at least as much market value as the cost of reproducing them; otherwise, the assets would be better employed elsewhere. They then build upon this idea by arguing that the firm should acquire more assets if the ratio of the market valuation of these assets to their replacement value, Tobin's q, exceeds one. Tobin's q is quite likely the most commonly used regressor in empirical corporate finance.
As has been widely discussed in the corporate finance and macroeconomics literature, however, all observable measures or estimates of the true incentive to invest, hereafter termed q proxies, are likely to contain measurement error. In principle, Tobin's q is observable: the market value of the firm's assets can be measured by examining the market value of the firm's debt and equity, and the replacement cost of assets can be computed via accounting information and the price at which the assets can be purchased or sold. In practice, measuring Tobin's q presents numerous difficulties because accountants do not directly keep track of the market value of a firm's debt or the replacement cost of a firm's assets, especially intangible assets. These difficulties force a data analyst to use some sort of algorithm to estimate the replacement costs and market values from accounting figures. Further complicating the measurement problem is that Tobin's q only equals the true incentive to invest under stringent assumptions.
In response to the measurement-error problem, numerous authors have developed different algorithms for estimating Tobin's q. Among the most widely used are those in Lindenberg and Ross (1981), Salinger and Summers (1983), Hall, Cummins, Laderman, and Mundy (1988), Perfect and Wiles (1994), and Lewellen and Badrinath (1997). We build upon this previous research by quantitatively assessing the measurement quality of a number of the q proxies obtained by using these algorithms. Specifically, we estimate the proportion of the variation in each proxy that is due to variation in the true underlying incentive to invest (true q). Estimating this quality index for a proxy, and then comparing the estimate to those obtained for alternative proxies, will aid the empirical researcher in choosing the best proxy. It will also reveal whether the best proxies are largely error-free or still disturbingly noisy.
Previous approaches to evaluating q proxies include Perfect and Wiles (1994), Perfect, Peterson, and Peterson (1995), and Lee and Tompkins (1999), who compare different proxies by examining their means, variances, correlation coefficients, and the coefficient estimates they produce in a variety of regressions. A different approach is in Lewellen and Badrinath (1997), who tackle the problem by constructing an example in which they know the true value of Tobin's q. A third approach is in Adam and Goyal (2003), who construct a presumably superior proxy from a real-options model and then compare other proxies to theirs.
In contrast, our approach is based on estimating investment regressions under the assumptions of an explicit errors-in-variables model. A component of this model is an equation expressing the proxy as a linear function of true q plus an error. The population [R.sup.2] of this equation is our index of measurement quality. A value of one for this index denotes a perfect proxy, while a value of zero denotes a worthless proxy. This is a more comprehensible scale of proxy performance than that given by comparing slope-coefficient estimates to prior beliefs about their likely values because, as explained in Erickson and Whited (2000), economic theory tells us little about what these likely values ought to be.
Our method is also superior to observing the correlation coefficients between different proxies for true q, because two proxies can be highly correlated with each other merely because their (possibly very large) measurement errors are highly correlated. Because many proxies are derived from other proxies by modifying one or two members of the set of algorithms needed for their construction, measurement-error correlations are to be expected. Conversely, two proxies can have similar values of our measurement quality index and yet have a low correlation. Finally, our method does not require assuming the superiority of a certain proxy. Rather, it requires assuming the structure of an econometric model, which, unlike the assumption of a superior proxy, is an assumption we can and do test for.
Assessing the measurement quality of q proxies is important because measurement error can seriously bias inference. Error in even one regressor can bias all of the regression coefficients. For example, it is well known that in the classical errors-in-variables model, the OLS estimate of the coefficient on the mismeasured regressor is biased towards zero. Less well known is that coefficient estimates for any accompanying perfectly measured regressors are also biased, even if the measurement and equation errors are uncorrelated with each other and with all regressors. Furthermore, the bias for perfectly measured regressors is not necessarily towards zero. For example, Erickson and Whited (2000) show that mismeasuring q has distorted our understanding of the sensitivity of investment in tangible fixed capital to movements in cash flow by biasing estimates of the coefficient on cash flow away from its true value of zero.
Assessing the measurement quality of q proxies is also important because they are widely used. Naturally enough, the question addressed by the first empirical studies using q proxies was the sensitivity of investment outlays to changes in the incentive to invest (Summers, 1981; Hayashi, 1982). These proxies have also been used to study the impact of taxes on investment decisions (Salinger and Summers, 1983) and the impact of financing constraints on investment (Fazzari, Hubbard, and Petersen, 1988).
Although only a small segment of the corporate finance literature has used q proxies to study investment expenditures explicitly, such proxies have often been used to represent the incentive to invest. The reason for this widespread use is simple: many theoretical models of corporate financial decisions rest on the assumption that the incentive to invest is given. See, for example, Myers (1977, 2000), Diamond (1993), and Park (2000). Therefore, testing these theories requires a control for investment incentives. For example, q proxies have been used to study the relation between industry structure and firm profitability (Lindenberg and Ross, 1981), the nature of the incentive for takeovers (Lang, Stulz, and Walkling, 1989, 1991; Servaes, 1991), the relation between managerial stock ownership and firm market value (Morck, Shleifer, and Vishny, 1988), the effect of deposit constraints on bank lending (Jayaratne and Morgan, 2000), the impact of the announcement of dividend changes on market value (Denis, Denis, and Sarin, 1997), the costs of corporate diversification (Lang and Stulz, 1994; Shin and Stulz, 1998; and Rajan, Servaes, and Zingales, 2000), the motivations for leveraged buyouts (Lehn, Netter, and Poulsen, 1990), the determinants of capital structure (Titman and Wessels, 1988; Rajan and Zingales, 1995; Leary and Roberts, 2005) and the motive for corporate cash holdings (Opler, Pinkowitz, Stulz, and Williamson, 1999).
Our resulting estimates show that true q explains very little of the variation in its best proxies. The average of our [R.sup.2]-type measures is close to 0.5. With a few minor exceptions, elaborate algorithms for calculating the replacement values of assets or the market value of liabilities appear to add little in the way of measurement quality beyond the use of simple balance sheet figures.
This result is new in the sense that it cannot necessarily be inferred from the poor measurement quality of the q proxy in Erickson and Whited (2000) and the observed high correlations between all of the proxies. For example, two q proxies can be highly correlated because of the high correlation between their measurement errors, but if one measurement error has a larger variance than the other, its [R.sup.2]-type measure of proxy quality will be lower. Finally, because some proxies have more stringent data requirements than others, the size of the sub-samples varies substantially. Our result on the approximate equality of the measurement quality of all of the proxies clearly implies that a researcher choose the proxy with the largest number of usable observations to avoid sample selection bias.
Using a variant of the Erickson and Whited (2002) technique, we also estimate a model in which the numerator and denominator of Tobin's q are measured with error. Although we find that the numerator contains appreciably more measurement error than the denominator, we also find that this model does not fit the data as well as the simple linear model in Erickson and Whited (2002).
We organize the article as follows. Section I describes various measures of true q. Section II presents the model and estimators. Section III describes the data; Section IV presents the empirical results. Section V outlines our alternative estimator and the results from applying it, and Section VI interprets our results for the case in which the researcher is interested in alternative interpretations of a q proxy. The final section concludes by explaining the economic significance of measurement error in q, and the Appendix presents the derivation of our alternative estimator, along with Monte Carlo experiments to study its finite sample properties.
I. Measuring q
This section starts by discussing general conceptual issues involved in measuring q. It then moves on to describe the various algorithms proposed for constructing q proxies.
A. Some Conceptual Issues
The previous section documents some of the various measures of Tobin's q that have been used to control for investment incentives in a wide variety of regressions. The most rigorous justification for this use is the case of investment regressions derived from formal structural models. These models generate relations between investment and its determinants that can be characterized in some detail. This detail lets us both determine a theoretically appropriate true q and provide a series of conditions under which this theoretical ideal deviates from its common proxies.
Characterizing the true incentive to invest is complex. It is often represented by a quantity called marginal q--the firm manager's valuation of the future stream of marginal profits attributable to an additional unit of capital, divided by that unit's price. Assuming convex costs of adjusting the capital stock, Lucas and Prescott (1971) and Hayashi (1982) show that the incentive to invest is completely described by marginal q. Hayashi (1982) also shows that under perfect competition and linearly homogeneous technology, marginal q can equal average q, which is the manager's valuation of the existing capital stock divided by its replacement value. The manager's valuation of the capital stock equals his expectation of the stream of discounted total future profits.
More recent papers have questioned the plausibility of convex capital-adjustment costs--the assumption that yields marginal q as a sufficient statistic for investment incentives. Caballero and Leahy (1996) and Caballero (1999) show that if changing the capital stock incurs a fixed cost, then relatively strong additional assumptions are needed to obtain a scalar measure of investment incentives: interestingly, the scalar measure so produced is average q. Also, Gomes (2001) develops a general equilibrium model with financial frictions in which average q is the more appropriate explanatory variable. Given this more recent research, in what follows we use average q as the appropriate true q; (1) and we turn, therefore, to the sources of deviations between average q and its most common proxies.
Because most of these proxies are estimates of Tobin's q, the first potential deviation is a discrepancy between average q and true Tobin's q, (2) which is the market's valuation of the capital stock divided by its replacement value. The difference between the two arises because the numerator of average q (the manager's valuation of capital) need not equal the numerator of Tobin's q (the market's valuation of capital.) The two quantities are otherwise identical. Two main factors cause average q and true Tobin's q to differ. First, market inefficiencies or information asymmetry may cause the manager's valuation of capital to diverge from the market valuation. Second, managers' incentives can differ from those of shareholders, and these problems are likely to remain unresolved in many reasonable situations. (See the survey in Becht, Bolton, and Roell, 2005.) For example, managers can undertake unprofitable investments in order to build large firms, as in Jensen (1986). Similarly, they can use investment to hide bad news about the firm from the stock market, thus achieving a higher than warranted stock-market valuation as in Brandenburger and Polak (1996). Both of these sorts...
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