Marginal q, Tobin's q, cash flow, and investment.

1. Introduction

Cash flow has always been somewhat of a puzzle in the literature on the determinants of investment. In a strictly neoclassical world, cash flow does not belong in an investment equation, and yet empirical studies dating back over 40 years almost invariably find that cash flow and investment are positively related. (1) A variety of hypotheses have been put forward to account for this empirical regularity including the existence of transaction costs, agency problems, and asymmetric information. (2) This paper provides tests of the latter two hypotheses using a sample of 560 U.S. companies over the period 1977 to 1996.

Under the asymmetric information (AI) hypothesis firms with attractive investment opportunities may be unable to finance them because of inadequate internal cash flows and because the cost of external funds is too high due to the capital market's ignorance of the firm's investment opportunities. (3) Thus, only firms with large cash flows can finance their attractive investment opportunities, and the puzzle of the relationship between cash flow and investment is resolved. To test this hypothesis, we need to identify those firms that may be subject to AI problems. The very nature of AI makes it difficult if not impossible to cleanly identify firms in this situation. If a researcher can identify a firm with attractive investment opportunities and cash constraints, why can the market not do so? Previous studies have used size, level of dividends, age, concentration of share ownership, and extent of cross-shareholdings to identify firms that are possibly subject to AI problems. (4) Although the capital market may have difficulty judging the investment opportunities of small firms, this in itself need not imply that the firm has attractive investment opportunities or that its cash flows are inadequate to finance them, if it does. Similar criticisms can be lodged against the other characteristics used to identify firms subject to AI problems. (5) One of this article's contributions is to use a characteristic of firms that better identifies whether they suffer from AI problems.

The AI hypothesis assumes that the firm's managers seek to maximize their shareholders' wealth but are prevented by a shortage of cash from undertaking investments with expected returns above the firm's cost of capital. Any firm caught in this predicament should, therefore, have a return on its investment, r, that is greater than its cost of capital, i. Our procedure for identifying firms subject to such cash constraints is thus to estimate the ratio r/i for each firm over our sample period and to categorize any firm for which this r/i > 1 as possibly cash constrained. (6)

The agency hypothesis links investment to cash flows by assuming that managers obtain financial and psychological gains from managing a large and growing firm and thus invest beyond the point that maximizes shareholder wealth. (7) When this occurs, a company's returns on investment will be less than its cost of capital. Accordingly we identify firms for which r/i < 1 as possibly subject to agency or managerial discretion (MD) problems.

Both the AI and MD hypotheses treat cash flow as a measure of financial constraints. It is possible, however, that current cash flows merely proxy for the profitability of future sales. Thus, in testing for the importance of cash flows as a source of capital it is necessary to control for the investment opportunities of firms (Chirinko and Schaller 1995, p. 528). Many studies have used Tobin's q as such a control. Tobin's q reflects the average return on a company's capital, but what is relevant for investment is the marginal return on capital. What is needed, therefore, is an estimate of marginal q. The existing literature has continued to use measures of average q, even though the conditions under which it equals marginal q are quite stringent (e.g., constant returns to scale, perfect competition in all product markets). (8) When firms operate in imperfectly competitive markets, some earn rents, and these rents are capitalized in their market values. Differences in average qs may be dominated by differences in inframarginal returns on capital and, thus, may be poor predictors of investment. An important contribution of this paper is to replace Tobin's average q as a control for the investment opportunities of firms with the theoretically appropriate marginal q. (9) Throughout the paper we use qa to represent average q and qm to represent marginal q.

Although qa is likely to be a poor proxy for the investment opportunities of a company, it can be a good indicator of the presence of asymmetric information for firms with r greater than i. The higher qa is, the cheaper it should be for firms to raise funds by, say, issuing equity, and the less important cash flow should be as a constraint on investment. We thus predict for firms that are likely to suffer from AI problems that the less responsive their investment is to cash flow differences, the higher their qas are.

Tobin's q also figures in our tests of the MD hypothesis. The chief constraint on managers' exercising their discretion over the allocation of a firm's cash flows is the threat of a takeover and dismissal should the firm's share price fall too low. The higher the firm's share price is, therefore, the greater the freedom managers have to overinvest. We thus predict for the sample of firms that is likely to suffer from agency problems that the more responsive their investment is to cash flow differences, the higher their Tobin's qs are.

We see the three main contributions of this paper as follows: First, to estimate a marginal q and use it to separate the population of firms into those that are likely to fit the AI and MD hypotheses. Second, to use marginal q to control for investment opportunities so that cash flows' effect is limited to its role as a source of liquidity. Third, to use qa not as a control for investment opportunities as in other studies but as a measure of the cost of external finance for firms potentially subject to cash flow constraints and as a measure of the tightness of the takeover constraint for firms potentially suffering from agency problems. As already stressed, our use of both marginal and average q is new to the literature. Only Kathuria and Mueller (1995) have estimated a marginal q and used it to separate firms into different subsamples as we do. They did not employ marginal q to control for the investment opportunities of the firm, however, nor did they use Tobin's q in the way we do to discriminate between the two hypotheses.

A fourth contribution of the paper will be to see whether the merger wave of the late 1980s, which included many hostile takeovers, tightened the takeover constraint on managers and led to a reduction in their discretion to invest internal cash flows for the purpose of pursuing growth. The wave of spin-offs in the early 1990s, the emphasis on "downsizing" and "returning to core competences," and the renewed interest in "shareholder value" as evidenced by share buy backs are all consistent with the hypothesis that the existence and/or exercise of managerial discretion declined during the late 1980s and 1990s. (10) We find no evidence in support of this hypothesis, however.

We proceed as follows. Section 1 reviews various theoretical arguments for including qa and cash flow in an investment equation. In it we also explain the methodology for calculating marginal q. In section 2 we briefly describe the data set and the procedures used to make the estimates. The results are presented in section 3, and conclusions are drawn in the final section.

2. Theoretical Issues

The Calculation of Marginal q

The arguments for putting Tobin's q in an investment equation rest on the assumptions of perfect competition, constant returns to scale, and that firms are price takers, which imply that the marginal and average returns on capital ale equal to each other and to a firm's cost of capital. (11) When firms are not price takers and markets are imperfectly competitive, however, marginal and average returns on capital do not coincide and equilibria may exist in which a firm's average return on capital differs from its marginal return. The same level of investment may be optimal for a monopolist as for a competitive firm even though the monopolist's profits on existing assets, and hence qa, are much larger than for the competitive firm. To predict the investments of these two companies more accurately, we need a measure of their marginal returns on capital relative to their costs of capital, which we now derive. (12)

Let It be a firm's investment in period t, [C.sub.t + j] the cash flow this investment generates in t + j, and [i.sub.t] the firm's cost of capital in t. Then the present value of this investment is

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

We shall assume capital market efficiency and, thus. that the capital market makes an unbiased estimate of the present value, P[V.sub.t], of any investment [I.sub.t] in t. We can then take the market's estimate of P[V.sub.t] and the investment [I.sub.t], that created it and calculate the ratio of a pseudo-permanent return [r.sub.t] on [I.sub.t] to [i.sub.t]

(2) P[V.sub.t] = [I.sub.t][r.sub.t]/i[sub.t] = [qm.sub.t][I.sub.t]

If the firm had invested the same amount It in a project that produced a permanent return [r.sub.t], this project would have yielded the exact same present value as the one actually undertaken. The ratio of [r.sub.t] to [i.sub.t] is the key statistic in our analysis, If a firm maximizes shareholder wealth, then it undertakes no investments for which [qm.sub.t], < 1. That qm is a marginal q can easily be seen from Equation 2 by contrasting it with qa. Average q is the market value of a firm divided by its capital stock. Marginal q is the change in the market value of the firm, PV, divided by the change in its capital stock ([I.sub.t]) that caused it.

The market value of the firm at the end of period t can be defined as

(3) [M.sub.t] = [M.sub.t-1] + P[V.sub.t] - [[delta].sub.t][M.sub.t-1] + [[mu].sub.t],

where [[delta].sub.t] is the depreciation rate for the firm's total capital and [[mu].sub.t], the market's error in evaluating [M.sub.t]. Substituting from Equation 2 into Equation 3 and rearranging yields

(4) [M.sub.t] - [M.sub.t-1] + [qm.sub.t][I.sub.t] - [[delta].sub.t][M.sub.t-1] + [[mu].sub.t].

The assumption of capital market efficiency implies that the expected value of [[mu].sub.t] is zero. Setting [[mu].sub.t] = 0 and rearranging Equation 4 yields

(5) [qm.sub.t] = [M.sub.t] - (1 - [delta])[M.sub.t-1]/[I.sub.t]

Equations 4 and 5 illustrate the logic underlying our calculation of qm. Assume, for example, that a firm's cost of capital, [i.sub.t], is 0.10; [[delta].sub.t] = 0; and it invests 100 at a return [r.sub.t], = 0.12. The predicted increase in its market value using Equation 4 is then 120, and [qm.sub.t] = [r.sub.t]/[i.sub.t] = 1.2. More generally, a firm's market value rises by more than the amount invested whenever [r.sub.t] > [i.sub.t] and falls short of the value of [I.sub.t] when [r.sub.t] < [i.sub.t], abstracting from depreciation. Imagine now that [M.sub.t-1] = 1000 and [[delta].sub.t] = 0.10. Then the firm must invest 100 at an [r.sub.t] = [i.sub.t] for its market value to remain unchanged.

It should be noted that because we calculate the ratio of [r.sub.t] to [i.sub.t] and not r, alone, there is no need to calculate a firm's cost of capital to determine whether it is overinvesting or underinvesting. Moreover, the methodology automatically allows for differences in risk across firms. If firm A's investments involve greater risk than B's, it has a higher cost of capital [i.sub.t] than B. Any investment [I.sub.t] by A must then produce a greater expected stream of profits (possess a higher [r.sub.t]) than the equivalent investment by B to produce the same change in market value.

Equations 3-5 incorporate the assumption that the market value of a firm at the end of year t - 1 is the present discounted value of the expected profit stream from the assets in place at t - 1. Changes in market value are due to changes in assets in place as a result of investment and depreciation. To calculate [qm.sub.t], one needs an estimate of the depreciation rate of a firm's total capital, [[delta].sub.t], where the value of this capital is measured by the market value of the firm. The depreciation rate depends on the composition of tangible and intangible assets in total market value, and these will differ across industries. If we assume that industry depreciation rates are constant over time, a variant of Equation 4 can be used to estimate a separate [[delta].sub.D] for each industry D.

In Equation 4 it is assumed that the market makes an unbiased estimate of the value of a firm's assets at the end of year t - 1, [M.sub.t-1], and that the change in market value during year t is due solely to the depreciation of its existing assets, the investment made in t, and the random error. However, some random shock, such as the Gulf War, might systematically raise or lower the market's valuation of the existing assets of all firms in an industry or sector of the economy. To allow for this possibility, we shall also estimate an industry-specific time shock, [[sigma].sub.Dt], for each industry and year. Adding this to Equation 4, rearranging, and dividing by [M.sub.t-1] to correct for heteroscedasticity, we obtain

(6) [M.sub.t] - [M.sub.t-1]/[M.sut.t-1] = -[[delta].sub.D] + [[sigma].sub.Dt] + [qm.sub.t] [I.sub.t]/[M.sub.t-1] + [[mu].sub.t]/[M.sub.t-1]

Under the condition that the qmt are the same over time and across firms, Equation 6 can be used to estimate [[delta]sub.D] and [[sigma].sub.Dt] with our panel data set. Using these estimates, we can modify Equation 5 to calculate a marginal q for each firm and each year allowing for both industry differences in depreciation rates and industry-specific time shocks.

(7) [qm.sub.t] = [M.sub.t] - (1 - [[delta].sub.D] + [[sigma].sub.Dt])[M.sub.T-1]/[I.sub.t]

TWO additional points are worth noting with respect to our calculations of marginal qs. Although it is conceptually useful to separate industry depreciation rates from industry shocks, some shocks may change the rate of depreciation for all firms in an industry. Thus, Equations 6 and 7 effectively allow industry depreciation rates to vary over time. Second, a given shock may have the same impact on several industries, implying that the [[sigma].sub.Dt], for these industries are the same.

Equation 5 defines qm in year t. For the purpose of classifying firms into subsamples that fit each hypothesis, we shall calculate a weighted average qm. Using Equation 3 to replace the first right-hand term in successive periods and assuming again industry-specific depreciation rates and industry-specific time shocks yields a generalized, multiperiod version of Equation 3,

(8) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Using Equation 2, we can calculate a weighted average qm with each year's investment as weights

(9) [bar]qm = [[summation of].sup.n.sub.j=0][qm.sub.t+j]/[[summation of].sup.n.sub.j=0][I.sub.t+j] = [[summation of].sup.n.sub.j=0] P[V.sub.t+j]/[[summation of].sup.n.sub.j=0][I.sub.t+j].

Dividing Equation 8 by [[summation of].sup.n.sub.j=0][I.sub.t+j], substituting from Equation 9, and rearranging yields

(10) [bar]qm = [M.sub.t+n] - [M.sub.t-1]/[[summation of].sup.n.sub.j=0][I.sub.t+j] + [[summmation of].sup.n.sub.j=0][[delta].sub.Dt+j[M.sub.t+j-1]/[[summation of].sup.n.sub.j=0][I.sub.t+j] - [[summation of].sup.n.sub.j=0] [[sigma].sub.Dt+j[M.sub.t+j-1]/[[summation of].sup.n.sub.j=0][I.sub.t+j] - [[summation of].sup.sub.j=0][[mu].sub.t+j]/[[summation of].sup.n.sub.j=0][I.sub.t+j]

Stock market efficiency implies E([[mu].sub.t+j]) = 0 for all j, and thus that the last term on the right in Equation 10 becomes small relative to the other two terms as n grows large. The market values and investments of the firm are observable. Therefore, [bar]qm can be calculated to a close approximation using Equation 10 for any assumed set of [[delta].sub.D]s and [[sigma].sub.Dt]s when n is large. We make these calculations using our estimates of [[delta].sub.D] and [[sigma].sub.Dt] from Equation 6. This [bar]qm, the weighted average of the ratio of returns on investment to the cost of capital, is used to discriminate between the different hypotheses regarding investment behavior.

Before describing how we use estimates of [bar]qm to test the different hypotheses about investment determinants, we must point out a possible bias in these estimates. We assume that the capital market at time t correctly values a firm's existing assets at that time and that the change in its market value between t and t + 1 reflects the combined effects of the depreciation of its existing assets and the investments made in that period. It is also possible, however, that the market can anticipate future investments. If, for example, the market correctly anticipates at t - 1 the stream of investments [I.sub.t+j], j = 1, ..., n and the return r on these investments, then [M.sub.t-1] will be higher (lower) than we assume in Equation 10, if r > i (r < i). Our calculated [bar]qms are thus biased toward 1.0 to the extent that the market can predict returns on future investments. Nevertheless, as we shall see, we estimate substantial differences in [bar]qms across firms, and they seem to perform as our hypotheses predict. (13)

The Determinants of Investment with Asymmetric Information

Under the neoclassical theory of investment, a firm invests to the point where its marginal returns on investment equal its cost of capital. A firm with marginal returns, mr, in Figure 1a would invest [I.sub.0]. Since this exceeds its internal cash flows, CF, it would raise the difference between [I.sub.0] and CF on the external capital market. A firm with marginal returns, [mr.sub.1], in Figure 1b would again invest [I.sub.0]. Since this falls short of its internal cash flows, CF, this firm would either pay the difference between [I.sub.0] and CF out as dividends or use these funds to purchase its own shares. Under the neoclassical theory a firm's marginal returns on investment would always equal its cost of capital.

[FIGURE 1 OMITTED]

These predictions do not necessarily hold when the kind of AI posited by Myers and Majluf (1984) or Stiglitz and Weiss (1981) is present, even when managers seek to maximize shareholder wealth. When the external capital market cannot accurately evaluate the returns on a company's capital and investment, the firm may find it difficult to raise as much capital as it needs to finance all investment projects promising returns greater than i, and mr > i, and thus [bar]qm >. In the extreme case, the firm is unable to raise any capital externally, and its investment is limited to its internal cash flows. Our first prediction for companies for which [bar]qm [greater than or equal to] 1 is, therefore, that their investment should be positively associated with their cash flows. (14)

The greater the difference between mr and i, the greater the firm's incentive to raise capital externally, even when its cost of external finance exceeds i. Thus, our second prediction for firms with [bar]qm [greater than or equal to] 1 is that their investment in year t should be positively associated with [qm.sub.t].

Under the AI hypothesis companies pass up investments for which mr > i because their common shares are currently undervalued given the firm's returns on both capital and investment. Such an undervaluation seems more likely, the lower the value that the market places on the firm's existing units of capital. Thus, if some firms with [bar]qm [greater than or equal to] 1 are subject to AI problems, we also expect a positive correlation between qa and investment. The reason for this expected positive association is not because qa accurately measures investment opportunities as assumed in the q theory; however, in our model qm plays that role. Instead, a positive relationship between qa and investment for firms with [bar]qm [greater than or equal to] 1 is expected because the ease with which they can raise capital externally should vary directly with qa. By the same logic, firms with high qas should be less dependent on internal fund flows to finance their investments. We test this implication of the asymmetric information hypothesis by including an interaction term between qa and cash flow in the investment equation. The predicted sign on this interaction term is negative. The higher qa is, the weaker is the predicted relationship between cash flow and investment for firms with [bar]qm [greater than or equal to] 1. (15)

The reader might be concerned that we have assumed capital market efficiency in estimating individual [qm.sub.t] and their weighted average, [bar]qm, and yet seek to test a hypothesis that presumes asymmetric information between managers and the capital market. Here it should be noted that we categorize companies as being potentially subject to AI problems based on their weighted average return on investment over the 18 years in our panel data. Our procedure for calculating this average qm uses the change in the firm's market value over the full 18-year period. The market could incorrectly evaluate a firm's returns on investments in some years and our [bar]qm would still be an accurate measure of its average [qm.sub.t], if the market corrected its mistake in a later period.

The Determinants of Investment with Managerial Discretion

When [bar]qm < 1, managers have overinvested from the point of view of the shareholders. Such overinvestment is predicted by the hypothesis that managers have discretion to pursue their own goals and use this discretion to expand their firms.

MD has two sources: (1) slackness in monitoring by shareholders and the market for corporate control and (2) nonbinding resource constraints. In a perfectly competitive world, managers would not be able to finance investments with mr < i for very long. The product market would play an effective monitoring role, even if the stock market could not. When the discipline of the product market is weak, however, and managers have greater cash flows than needed to finance what would be the optimal investment level from the point of view of their shareholders, they use some of the extra cash they have to finance additional investment. This is the situation depicted in Figure 1b. Our first prediction for firms with [bar]qm < 1 is thus that their investments are positively related to their cash flows. (16)

If all firms had the same cost of capital and marginal returns on investment schedule, say i and [mr.sub.2] in Figure 1b, mr would vary inversely with investment, and we would predict a negative relationship between qm and investment for the subsample of companies with [bar]qm < 1. But the assumption that all firms face the same mr schedule and have the same i is untenable. With different mr schedules and is, there may be no relationship between qm and investment. For example, if firms 1 and 2 in Figure 1b had the same i and invested amounts [I.sub.1] and [I.sub.2], respectively, their qms would be identical (qm = j/i), although their investments would differ. We predict, therefore, that [qm.sub.t] and [I.sub.t] are unrelated in the subsample of firms for which [bar]qm < 1.

Both the threat of a hostile takeover and the resource constraints on managers should be lower for firms with relatively high share prices. We thus predict that managerial discretion increases with Tobin's q and expect a positive relationship between investment and qa for companies with [bar]qm < 1. Since MD manifests itself as overinvestment out of cash flows, the relationship between cash flow and investment should grow stronger as MD increases. We thus again include an interaction term between qa and cash flow in the investment equation, as we did for firms with [bar]qm [greater than or equal to] 1. For firms with [bar]qm < 1, however, the predicted coefficient on this interaction term is positive, the opposite sign from that predicted under the AI hypothesis. Although the MD hypothesis claims that managers favor internal cash flows as a source of funds, it does not preclude their resorting to the external capital market. Their willingness to do so is likely to be positively related to qa, and thus we also include it as a separate term in this investment equation.

Summary of Hypotheses

The basic logic of the two hypotheses applies equally well to investments in capital equipment and in research and development (R&D), and so we estimate separate equations for each

(11) [I.sub.t]/[K.sub.t-1] = a + b* [qm.sub.t-1] + c * C[F.sub.t]/[K.sub.t-1] + d * [qa.sub.t-1] + e * C[F.sub.t] * [qa.sub.t-1]/[K.sub.t-1] + [[mu].sup.I.sub.t,

(12) [R.sub.t]/[K.sub.t-1] = f + g * C[F.sub.t]/[K.sub.t-1] + h * [qa.sub.t-1] + 1 * C[F.sub.t] * [qa.sub.t-1]/[K.sub.t-1] + [[mu].sup.R.sub.t],

where [I.sub.t] and [R.sub.t] are capital investment and R&D in year t. These equations resemble the reduced-form equations that have been used to test either the AI or the MD hypotheses in other studies. They differ from them, however, in that the investment equation includes the theoretically preferred marginal q to control for differences in investment opportunities across firms, and average q enters not as a measure of investment opportunities as in other studies but as an index of either capital market constraints on managers or market for corporate control constraints. Equations 11 and 12 also differ from those usually estimated in the inclusion of an interaction term between cash flow and qa to take account of the varying intensities of the constraints on managers with respect to the use of cash flows to finance investment. All of the independent variables except for cash flow are lagged one period to avoid their being partly endogenous. (17)

We have classified firms for the purpose of testing the different hypotheses using qm calculated over 18 years. A company's investment opportunities can be expected to vary from year to year, however, and thus to predict a firm's investment in a given year, we need a short-run estimate of returns. We thus use a one-period qm, namely, the change in a company's market value from the previous year adjusted for depreciation and industry-specific time shocks divided by its total investment in that year (see Eqn. 7). Since both share prices--and thus market values--and investment are highly volatile, these one-period [qm.sub.t]s vary considerably over the sample period. For example, the variance in [qm.sub.t] is 10.4 times the variance in qat. (18) Choosing a variable with such a large variance to explain investment puts the theory to a severe test.

While we predict that this measure of the short-run attractiveness of investment is significantly related to investments in plant and equipment for the subsample of companies for which the AI hypothesis applies, we do not make this prediction for R&D. There are significant transaction costs in expanding and contracting R&D activities, and we do not expect R&D to be responsive to shortrun changes in returns on investment. We thus exclude [qm.sub.t-1] from the R&D equation. Table 1 summarizes the predictions of the different theories. For completeness, we include the predictions from neoclassical/q theory. A zero appears wherever the theory makes a clear prediction of no relationship, as, for example, for cash flow under the neoclassical theory, and a question mark appears where there is no obvious relationship from the underlying hypothesis.

3. Data

To calculate qm using Equations 7 and 10 we need data on the market values and investments of each firm. The market value of a firm at the end of year t, [M.sub.t], is defined as the market value of its outstanding shares at the end of t plus the value of its outstanding debt. Since this number reflects the market's evaluation of the firm's total assets, we wish to use an equally comprehensive measure of investment when calculating qm. Accordingly we define investment as

(13) I = after-tax profits + depreciation - dividends + debt + equity + R&D + ADV,

where [DELTA]debt and [DELTA]equity are funds raised using new debt and equity issues. Since R&D (Compustat item 46) and advertising (ADV, item 45) can produce intangible capital, which contributes to a company's market value, we add them to investment to obtain a measure of a firm's additions to its total capital.

Tobin's q is defined as the ratio of the market value of a firm to its total assets (Compustat item 6) where the market value of the firm equals the market value of common equity (item 199 [share price at the end of the fiscal year] times item 25 [common shares outstanding]) plus the book value of preferred stock (items 56, 10, 130) plus the book value of total debt (the sum of total short-term debt [item 9] and total long-term debt [item 34]). (19) Cash flow is the sum of after-tax profits (item 18) and depreciation (item 14) minus total dividends (item 21 plus item 19 if available). (20) We adjust cash flow by adding the portion of R&D that is expensed for tax purposes. (21) Capital stock is measured as net fixed assets (item 8). Capital expenditures are reported in the statement of cash flows (item 128). All variables are expressed in real 1987 U.S. dollars.

The data are taken from the 1996 version of the Compustat data set. This data set contains accounting and financial data on 9862 active companies with listed stocks in North America starting in 1977. We exclude all firms with Standard Industrial Classification (SIC) codes 5000 and above because the nature of capital and investment in these industries is so different from that in other industries. (22) Other companies were dropped because investment and market values were not reported for all of the 1977 to 1996 period. To minimize the weight of outliers, we cap our variables at both the 1st and 99th percentiles, which further reduces the sample to 560 companies. Tables 2 and 3 report summary statistics and correlations of the variables used.

Before turning to our main findings, a few comments on Tables 2 and 3 are warranted. As noted above, studies that have tried to test the AI hypothesis have assumed that they are small, young firms with attractive investment opportunities and such limited cash flows that they pay little or no dividends. The MD literature, on the other hand, leads one to expect that the firms that fit this hypothesis are large, mature companies with limited investment opportunities and large cash flows. These characterizations of the two types of companies are largely consistent with the figures in Tables 2 and 3. Companies with [bar]qm < 1 are on average roughly twice as large as those with [bar]qm [greater than or equal to] 1, although their median size is about the same. Thus the distribution of firm sizes for [bar]qm < 1 companies is positively skewed with a fat right tail. An examination of the distribution of firms by industry also revealed that there were four times as many petroleum companies with [bar]qm < 1 than with [bar]qm [greater than or equal to] 1. Companies with [bar]qm [greater than or equal to] 1 grow 3.3 times faster than [bar]qm < 1 companies and have somewhat higher ratios of investment to total capital (means 0.29 vs. 0.25). These statistics fit the small, young, fast-growing image for [bar]qm [greater than or equal to] 1 companies and large, mature, slow growth for the others. On the other hand, the mean dividend payout ratios are only slightly smaller for [bar]qm [greater than or equal to] 1 firms than for the [bar]qm < 1 firms, with the medians for the two groups being the same (0.20). Thus, clearly all of the [bar]qm [greater than or equal to] 1 companies were not cash constrained in all years, or they would not have paid out such high fractions of their cash flows as dividends.

From Table 3 it can be seen that the simple correlation between the ratio of cash flow to capital stock and Tobin's q is fairly high, 0.27. This is not surprising, since both are measures of average returns on capital. The correlations between cash flow and our two measures of marginal q, on the other hand, are much lower, both being around 0.12. These low correlations suggest that any relationship that we find between cash flow and investment in our sample is unlikely to come about because cash flow is proxying for a firm's investment opportunities, since marginal q is a measure of these. (23)

4. The Findings

Main Results

The top half of Table 4 presents the results for investment in plant and equipment with observations pooled over the 18-year time period. For the grand sample, the coefficients on cash flow, [qm.sub.t-1] and [qa.sub.t-1], are highly significant. The positive and significant coefficient on cash flow is, of course, inconsistent with the neoclassical/q theory hypothesis. Our measure of marginal q, [qm.t-1], takes on a positive sign as predicted, with a t value over five. The coefficient on the interaction term between cash flow and qa is insignificant. This is not surprising, since we predict opposite signs for this coefficient for the two subsamples that make up the full sample.

Equation 2 presents the results for companies with [bar]qm [greater than or equal to] 1. The coefficients on both [qm.sub.t-1] and [qa.sub.t-1] are positive and significant. Given that [qm.t-1] is included to capture the attractiveness of a company's investment opportunities, we interpret the positive coefficient on [qa.sub.t-1] as an inverse measure of the importance of AI for a company. When cash flow is constant, companies with high qas invest more because they have less difficulty raising cash externally. This interpretation of the role played by qa in the investment equation is reinforced by the performance of the qa/cash flow interaction term. Its negative and significant coefficient implies that the sensitivity of a company's investment to the level of its cash flow declines as the value that the market places on its existing capital rises, and thus as its access to external capital improves. Similarly, the link between qa and investment grows weaker, the greater the firm's cash flows, and thus the less important access to the external capital market becomes.

Cash flow also has a positive coefficient in the equation for firms with [bar]qm < 1. In contrast with the subsample where [bar]qm [greater than or equal to] 1, the interaction term between qa and cash flow is positive and significant for firms with [bar]qm < 1 (5% level, one-tailed test). We hypothesized that Tobin's q would proxy for MD in this subsample. Equation 3 is consistent with this hypothesis. For firms with [bar]qm < 1, the marginal impact of cash flow on investment increases as qa increases. Tobin's q also has an independent positive and significant impact on investment. Taken together these results offer considerable support for the MD hypothesis. Many managers of firms with relatively high share prices and cash flows appear to take advantage of the discretion they have to expand their companies beyond the point that is optimal from the point of view of their shareholders.

The estimates for Equations 2 and 3 imply a somewhat greater marginal impact of cash flow on investment for the subsamples of firms with [bar]qm [greater than or equal to] 1 ([differential][I.sub.t][differential]C[F.sub.t]/[K.sub.t-1] = 0.22), than for the [bar]qm < 1 subsample ([differential][I.sub.t]/[differential]C[F.sub.t]/[K.sub.t-1] = 0.18), when qa is evaluated at the respective sample means (see the last two rows). In contrast, the marginal impact of [qa.sub.t-1] on investment is much larger for [bar]qm < 1 firms ([differential][I.sub.t]/[differential][qa.sub.t-1] = 0.052) than for [bar]qm [greater than or equal to] 1 companies ([differential][I.sub.t][differential][qa.sub.t-1] = 0.022), with C[F.sub.t]/[K.sub.t-1] evaluated at its subsample mean (difference significant at 1% level). (24) Increases in qa appear to have a greater impact on MD and managers' use of their discretion than on easing external capital market constraints for firms that may be cash constrained.

We have stressed the logical superiority of marginal q over average q as an index of investment opportunities. Marginal q, [qm.sub.t-1], has a positive and significant coefficient in all three investment equations. The coefficient on [qm.sub.t-1] for the firms with [bar]qm < 1 is, however, less than half of the value for the subsample with [bar]qm [greater than or equal to] 1. The capital investment of companies that appear to be overinvesting is much less sensitive to the returns on investment than is the case for firms that are possibly cash constrained. (25) For the [bar]qm [greater than or equal to] 1 subsample, an increase in marginal q, which we interpret as an improvement in investment opportunities, has about one fourth the impact of a comparable increase in average q, which we interpret as an improvement in a firm's access to external capital (see the predicted partial derivatives for qaH in the top half of the table). In contrast, for companies with [bar]qm < 1, an increase in average q, which we interpret as a relaxation of the threat of takeover, has over 25 times as large an impact on investment as a comparable increase in marginal q. What predominantly drives the investment of companies with [bar]qm < 1 is not the height of their investment opportunities but their resources and discretion to pursue additional investment.

We gave reasons above for expecting a weakening of the extent of MD over time. Such a development should manifest itself as a decline in the coefficients on either cash flow or qa over time. To test for this, we interacted each term in Equation 3 with 1/t. This method of allowing for time-related changes in coefficients imposes the reasonable restriction that the magnitude of the changes itself declines over time, and the coefficients on each variable asymptotically approach given values.

The coefficients on the interaction terms with 1/t were all insignificant, however. Our data reveal no tendency for the effects of managerial discretion on investment to attenuate over time. We also interacted 1/t with the variables in Equation 2 and again found no tendency for the effects of asymmetric information to disappear over time. This finding suggests that the appearance of asymmetric information problems for firms in the [bar]qm [greater than or equal to] 1 subsample is not confined to the beginning of the sample period. Rather, AI problems would appear to arise at different points in time for different firms throughout the 18-year sample period.

The bottom half of Table 4 presents the results when R&D is the dependent variable. The equations are identical to those for investment except that [qm.sub.t-1] has been omitted, since R&D is not expected to respond to short-run estimates of returns on investment. The results are quite similar to those reported for capital investment. We see that for [bar]qm [greater than or equal to] 1 firms, the coefficients on both cash flow and qa are positive and significant, and the coefficient on the interaction term is negative and significant. Support for the AI hypothesis can be claimed from both the capital investment and R&D equations.

In the [bar]qm < 1 subsample, coefficients on both the cash flow and the cash flow/qa interaction terms are positive and significant as predicted. The coefficient on qa by itself is negative, however. Increases in qa, which we interpret as implying increases in managerial discretion in the [bar]qm < 1 subsample, lead to increases in R&D spending only in the presence of sufficient cash flows. As can be seen in the bottom row of Table 4, the marginal impact of qa on R&D is positive for a firm with the mean level of cash flows. For such a firm either an increase in cash flow or an increase in qa produces an increase in R&D spending.

The difference between the marginal effects of qa on R&D spending in the two subsamples is quite revealing. An increase in qa for a firm with the mean level of cash flows has nine times the marginal impact on R&D spending for firms with [bar]qm < 1 than for firms with [bar]qm [greater than or equal to] 1. For companies with sufficient cash an increase in managerial discretion over the use of that cash leads to a substantial increase in R&D spending. On the other hand, an increase in qa in the [bar]qm [greater than or equal to] 1 subsample implies a greater potential for raising funds in the external capital market. Our results in Table 4 imply, however, that firms in this subsample cannot or choose not to raise external capital to finance R&D. This may be due to the intangible nature of the assets created by R&D and the greater risks surrounding this form of investment. Whatever the interpretation, the results in the bottom half of Table 4 reveal a significant difference in the impact of qa on R&D spending for the two groups of companies.

In contrast, the marginal impacts of cash flows on investment are quite large and similar for the two groups. Note also the large t values on the two cash flow coefficients and the [R.sub.2]s of around 0.50 for the two equations. These are quite high for large, pooled cross-section samples like ours. Thus, the results for R&D in the bottom half of Table 4 underscore both the importance of cash flows as a source of finance for R&D, and the different reasons for this importance depending on whether a firm suffers from AI or MD problems.

Additional Splits and Robustness Checks

Tables 5-7 present various robustness checks. Columns 1-3 in Table 5 present investment equations including an accelerator term. This term is highly significant; nevertheless, the basic results concerning our hypotheses are not altered.

In Table 4 separate coefficients on the deflated intercept term (1/[K.sub.t-1]) were estimated for each two-digit SIC industry. In the investment equation this amounts to assuming different depreciation rates for each industry, while in the R&D equation the procedure amounts to controlling for differences in R&D intensity across industries. We also estimated the basic equations using deviations from firm means for each variable, thereby removing firm fixed effects and effectively allowing for firm-specific rates of depreciation in the investment equation and fixed differences in R&D intensity across firms. The results are qualitatively similar to those reported, and are presented in columns 4-9 in Table 5 for the basic model. Once we allow for differences in depreciation rates across firms, the coefficient for [qm.sub.t-1] in the [bar]qm 1 subsample becomes insignificant (t = 1.63). This result accords with our prediction that the investment of firms that are overinvesting is unrelated to the returns on these investments. The coefficients on all other variables in both the investment and R&D equations are of the predicted signs except for qa in the R&D equation for the [bar]qm < 1 subsample. It again picks up a negative coefficient. The coefficient on the interaction term in this R&D equation is again quite large, however, and so the partial derivatives of R&D with respect to both cash flow and qa remain positive. Although the coefficients on the cash flow/qa interaction terms are all of the predicted signs, only the coefficient on this term in the R&D equation for firms with [bar]qm < 1 is statistically significant. The role of this interaction term in each equation is to capture the effects of differences across firms in the degrees of asymmetric information or managerial discretion on the cash flow/investment and qa/ investment relationships. The effects of some of these differences across firms now appear to be accounted for by the firm effects.

Several studies have hypothesized that firm size is an important determinant of either AI or MD or both. (26) Smaller firms may face higher asymmetry of information and transaction costs implying a greater reliance on internal funds. Larger firms may have lower threats of takeover and thus be more susceptible to discretionary managerial spending. Table 6 splits the sample into small and large firms based on their median sales. In columns 3 and 4, the sample is further divided into small firms with [bar]qm [greater than or equal to] 1 and large firms with [bar]qm < 1. (27) These two subsamples might be expected to exhibit the greatest degrees of AI and MD. The results reinforce the earlier findings. In the full sample (Eqns. 1 and 3), marginal q's impact on investment is much larger and significantly different for small firms than for large firms. Cash flow has a larger (and significantly different) impact on investment for large firms than for small firms (see second to last row). Both coefficients on the cash flow/qa interaction terms in columns 1 and 2 are of the predicted signs, but both are statistically insignificant. In contrast, both coefficients on these interaction terms in columns 3 and 4 are of the predicted signs and are statistically significant, despite the fact that the sample sizes in columns 3 and 4 are much smaller than in 1 and 2. This difference in results highlights the superiority of using mean marginal qs to discriminate between firms that are potentially subject to AI problems and those potentially subject to MD problems. Although small firms may be more likely to suffer from AI problems than large ones, not all small firms have these problems. In contrast, every firm with an AI problem should have a marginal q > 1, just as every firm with MD problems should have a [bar]qm < 1. These criteria for identifying companies that are likely to have AI or MD problems are superior to other proxies like size.

The reader might be somewhat concerned about the weight that we place on our measures of in forming the two subsamples, which we use to test the two hypotheses. As a third robustness check, therefore, we have used cutoffs of [bar]qm [greater than or equal to] 1.1 to form the subsample for which the AI hypothesis should hold and [bar]qm [less than or equal to] 0.9 to form the MD subsample. Equations 1-4 in Table 7 present the results when the two subsamples are selected in this way. They closely resemble those in Table 4 and continue to support the two hypotheses tested. The investment and R&D of companies with returns on investment considerably above their costs of capital fit the AI hypothesis; the investment and R&D of companies with returns considerably below their costs of capital fit the MD hypothesis.

Two additional criteria for splitting the sample, given the logic underlying the two hypotheses, are by dividend payments and Tobin's q. (28) Firms subject to A1 problems should be cash constrained and thus pay no (little) dividends and earn high returns on investment. The investment of firms with [bar]qm [greater than or equal to] 1 and qa < 1 should be most susceptible to cash constraint problems, while managers of companies with [bar]qm < 1 and qa > 1 are most likely to have the discretion to overinvest and to be using it. Such splits using dual criteria greatly reduce the number of observations in each subsample. Nevertheless, the predictions of the two hypotheses continue to be confirmed. (29)

We have stressed the importance for investment models of the distinction between marginal and average q. We have employed our own measure of marginal q, but for Tobin's q we have chosen one of the many measures others have used, namely, firm market value divided by total assets. Although more complicated measures of qa may have conceptual advantages for other purposes, we think that this simple measure is well-suited for the role qa plays in our model-particularly with respect to the AI hypothesis. The capital market can readily ascertain the book value of a company's total assets from its balance sheet. If the market value of the firm is much above this balance sheet figure, it is reasonable to assume that the company will not have difficulty in raising capital externally. Nevertheless, we have checked the robustness of our results with respect to other definitions of Tobin's q. Our conclusions do not change if we define qa as in Lindenberg and Ross (1981), or in Kaplan and Zingales (1997), (30) or when we adjust its denominator for the intangible capital stock due to R&D. (31)

5. Conclusions

Our goal has been to shed light on the question of why investment outlays are so strongly correlated with cash flows. To do so we have tested the two leading hypotheses about this question--the AI and MD hypotheses. To conduct these tests it was necessary to identify the firms that may fit each hypothesis. Since the AI hypothesis predicts that firms underinvest and have returns on investment greater than their costs of capital, while the MD hypothesis predicts overinvestment and returns on investment less than the costs of capital, using the ratio of returns on investment to costs of capital for each firm is a natural way to make this identification. We have constructed such a ratio and divided our sample of 560 companies by it. The data support both hypotheses for their respective subsamples of firms.

Unlike most recent studies we did not use Tobin's q to control for differences in investment opportunities because it measures the ratio of a firm's average return on capital to its cost of capital, while for investment what is relevant is a ratio that includes the marginal return on capital. Our marginal q, [qm.sub.t], is such a ratio. It was found to be a significant determinant of investment for the AI subsample. With investment opportunities controlled for by the inclusion of [qm.sub.t-1] in the equation, we could conclude with some confidence that cash flow's positive relationship to investment was due to its role as a source of finance.

Although we did not use Tobin's q (qa) to control for differences in investment opportunities, it did play an important role in the tests of the two hypotheses. In the AI subsample, the sensitivity of investment and R&D to internal cash flows declined as qa increased because, we hypothesized, the cost of external funds for these firms declines as qa rises.

As predicted, increases in qa increased the sensitivity of investment and R&D to internal cash flows for companies with returns on investment less than their costs of capital. As qa rises managers feel less threatened by hostile takeovers, and thus have more freedom to use their companies' cash flows to pursue their own goals. Investment and [qm.sub.t-1] were more weakly related in the MD subsample than for the AI subsample, and the coefficient on [qm.sub.t-1] became insignificant with firm effects removed. The investment decisions of firms earning returns on investment below their costs of capital are likely to be driven by other objectives than maximizing shareholder wealth and consequently are more closely related to the measures of MD--cash flow and qa--than to the heights of their investment opportunities.

The findings of this article have potentially important policy implications. At any point, while some firms are underinvesting because of a shortage of cash, others are overinvesting because of an excess of managerial discretion. Any governmental policies that increase the investment levels of all firms, mitigate the first problem while aggravating the second. Optimal investment policies would target funds to companies suffering from asymmetric information problems and extract funds from companies with agency problems. Space precludes our taking up these issues here, but we hope to have at least demonstrated their relevance.

Table 6. Robustness II: Split according to firm size, I/K

                                        All

                       Small (a)                    Large (a)
Variables                 (1)                          (2)

C[F.sub.t-1]/            0.169           <            0.266
 [K.sub.t-1]
 t value                10.05                        12.92

[qm.sub.t-1]             0.004           >            0.001
 t value                 4.53                         2.01

[qa.sub.t-1]             0.047           >            0.021
 t value                 6.26                         3.10

[qa.sub.t-1] *          -0.005     [approximately     0.0004
 C[F.sub.t-1]/                        equal to]
 [K.sub.t-1]
 t value                -0.46                         0.03

Firms                    280                           280

No. obs.                 3680                         3680

[[bar]R.sup.2]           0.19                         0.32

Predicted partial derivatives (evaluated at respective means)

C[F.sub.t-1]/            0.164 *          <           0.266 *
 [K.sub.t-1]

[qa.sub.t-1]             0.045 *          >           0.022 *

                       [bar]qm
                       [greater
                       than or
                        equal                       [bar]qm
                         to] 1                         < 1

                       Small (a)                    Large (a)
Variables                 (3)                          (4)

C[F.sub.t-1]/            0.289           >            0.191
 [K.sub.t-1]
 t value                 8.01                         6.98

[qm.sub.t-1]             0.006           >            0.001
 t value                 3.62                         1.38

[qa.sub.t-1]             0.044           >            0.003
 t value                 3.59                         0.31

[qa.sub.t-1] *          -0.048           <            0.092
 C[F.sub.t-1]/
 [K.sub.t-1]
 t value                -2.76                         4.21

Firms                     112                          207

No. obs.                 1067                         2644

[[bar]R.sup.2]           0.19                         0.34

Predicted partial derivatives (evaluated at respective means)

C[F.sub.t-1]/            0.218 *          <           0.281 *
 [K.sub.t-1]

[qa.sub.t-1]             0.022 *    [approximately    0.029 *
                                     equal to]

(a) Small, Annual sales < median sales; Large, Annual sales >
median sales.

* Significant at the 1% level.

Table 7. Robustness III: Split by [bar]qm
[greater than or equal to] 1.1 and [bar]qm [less than or equal to] 0.9

                                  I/K

                                [bar]qm
                              [greater than
                              or equal to]
                                   1.1
                                   (1)

Variable                     Coef     t val

C[F.sub.t]/[K.sub.t-1]       0.280     9.48    >
[qm.sub.t-1]                 0.005     3.65    >
[qa.sub.t-1]                 0.041     4.62
[qa.sub.t-1] * C[F.sub.t]/
 [K.sub.t-1]                -0.040    -2.91    <
Firms                         134
No. obs.                     1662              >
[[bar]R.sup.2]               0.21              <

Predicted partial derivates (evaluated
at respective means)

C[F.sub.t]/[K.sub.t-1]       0.216 *           >
[qa.sub.t-1]                 0.023 *           <

                                 I/K

                            [bar]qm < 0.9
                                 (2)

Variable                    Coef      t val

C[F.sub.t]/[K.sub.t-1]      0.157     9.87
[qm.sub.t-1]                0.002     2.07
[qa.sub.t-1]                0.045     5.76
[qa.sub.t-1] * C[F.sub.t]/
 [K.sub.t-1]                0.025     3.58
Firms                        366
No. obs.                    4938
[[bar]R.sup.2]              0.24

Predicted partial derivates (evaluated
at respective means)

C[F.sub.t]/[K.sub.t-1]      0.182
[qa.sub.t-1]                0.053

                                 R/K

                               [bar]qm
                             [greater than
                              or equal to]
                                  1.1
                                  (3)

Variable                    Coef      t val

C[F.sub.t]/[K.sub.t-1]       0.323    15.32     >
[qm.sub.t-1]
[qa.sub.t-1]                 0.022     3.52     >
[qa.sub.t-1] * C[F.sub.t]/
 [K.sub.t-1]                -0.040    -4.02     <
Firms                         134
No. obs.                     1662               <
[[bar]R.sup.2]               0.51               <

Predicted partial derivates (evaluated
at respective means)

C[F.sub.t]/[K.sub.t-1]                 0.260 *  <
[qa.sub.t-1]                           0.005    <

                                  R/K

                             [bar]qm < 0.9
                                   (2)

Variable                     Coef      t val

C[F.sub.t]/[K.sub.t-1]       0.238     18.39
[qm.sub.t-1]
[qa.sub.t-1]                -0.009     -1.50
[qa.sub.t-1] * C[F.sub.t]/
 [K.sub.t-1]                 0.059      5.98
Firms                         366
No. obs.                     4938
[[bar]R.sup.2]               0.50

Predicted partial derivates (evaluated
at respective means)

C[F.sub.t]/[K.sub.t-1]       0.296 *
[qa.sub.t-1]                 0.010 **

Table 1. Predicted Signs of Coefficients from the Different Theories

                                                Neoclassical q
                                              Theory, Sample of
                                                  All Firms
Independent                                [I.sub.t]/   [R.sub.t]/
Variables                                  [K.sub.t-1]  [K.sub.t-1]

Intercept                                    +            +
C[F.sub.t]/[K.sub.t-1] (b)                   0            0
[qm.sub.t-1] (c)                             NA (d)       NA (d)
[qa.sub.t-1] (e)                             +            +
[qa.sub.t-1] * C[F.sub.t]/[K.sub.t-1] (f)    0            0

                                           Asymmetric Information
                                           Theory, Sample of Firms
                                           with [bar]qm [greater
                                           than or equal to] 1 (a)

Independent                                [I.sub.t]/   [R.sub.t]/
Variables                                  [K.sub.t-1]  [K.sub.t-1]

Intercept                                       +            +
C[F.sub.t]/[K.sub.t-1] (b)                      +            +
[qm.sub.t-1] (c)                                +            ?
[qa.sub.t-1] (e)                                +            +
[qa.sub.t-1] * C[F.sub.t]/[K.sub.t-1] (f)       -            -

                                             Managerial Discretion
                                           Theory, Sample of Firms
                                             with [bar]qm < 1 (a)

Independent                                [I.sub.t]/   [R.sub.t]/
Variables                                  [K.sub.t-1]  [K.sub.t-1]

Intercept                                       +            +
C[F.sub.t]/[K.sub.t-1] (b)                      +            +
[qm.sub.t-1] (c)                                ?            ?
[qa.sub.t-1] (e)                                +            +
[qa.sub.t-1] * C[F.sub.t]/[K.sub.t-1] (f)       +            +

(a) [bar]qm is the calculated sample period marginal q.

(b) C[F.sub.t]/[K.sub.t-1] is cash flow divided by the book value of
capital stock lagged one period.

(c) [qm.sub.t-1] is our yearly measure of marginal q lagged on period.

(d) NA = not applicable. Under the neoclassical theory qa should equal
qm and only one variable enters the equation.

(e) [qa.sub.t-1] is Tobin's q lagged one period.

(f) [qa.sub.t-1] x C[F.sub.t]/[K.sub.t-1] is an interaction term of
Tobin's q and cash flow.

Table 2. Summary Statistics

                                  All Firms

Variables                    Mean    Med     SD

Sales (Mn. $) (b)           2835.9  383.1  8774.6
DSAL (c)                    0.039   0.026  0.277
Div. payout ratio (d)       0.241   0.202  0.645
[I.sub.t]/[K.sub.t-1] (e)   0.263   0.221  0.169
[R.sub.t]/[K.sub.t-1] (f)   1.139   0.082  0.164
[qa.sub.t-1] (g)            1.136   0.966  0.597
[qm.sub.t-1] (h)            0.769   0.794  1.900
C[F.sub.t]/[K.sup.i.sub.t]  0.370   0.311  0.312

Number of                           560
  firms
Number of                           7361
  obs.

                            [bar]qm [greater than
                              or equal to] 1 (a)

Variables                    Mean    Med     SD

Sales (Mn. $) (b)           1698.3  374.3  4441.4
DSAL (c)                    0.078   0.054  0.289
Div. payout ratio (d)       0.210   0.202  0.207
[I.sub.t]/[K.sub.t-1] (e)   0.291   0.253  0.75
[R.sub.t]/[K.sub.t-1] (f)   0.149   0.089  0.158
[qa.sub.t-1] (g)            1.504   1.334  0.736
[qm.sub.t-1] (h)            1.131   1.120  2.035
C[F.sub.t]/[K.sup.i.sub.t]  0.432   0.378  0.312

Number of                           167
  firms
Number of                           2103
  obs.

                               [bar]qm  1 (a)

Variables                    Mean    Med     SD

Sales (Mn. $) (b)           3290.9  391.3  9959.1
DSAL (c)                    0.024   0.014  0.271
Div. payout ratio (d)       0.258   0.207  0.754
[I.sub.t]/[K.sub.t-1] (e)   0.252   0.211  0.165
[R.sub.t]/[K.sub.t-1] (f)   0.136   0.079  0.166
[qa.sub.t-1] (g)            0.989   0.874  0.454
[qm.sub.t-1] (h)            0.582   0.663  1.797
C[F.sub.t]/[K.sup.i.sub.t]  0.345   0.281  0.308

Number of                           393
  firms
Number of                           5258
  obs.

(a) [bar]qm is the calculated sample period marginal q.

(b) Sales is average total annual sales.

(c) DSAL is average annual growth rate of total sales.

(d) Div. payout ratio is the average of total dividends paid over the
sample period divided by total cash flows over the sample period.

(e) [I.sub.t]/[K.sub.t-1] is capital expenditures divided by the
beginning of period book value of capital stock.

(f) [R.sub.t]/[K.sub.t-1] is expenditures of research and development
divided by the beginning of period book value of capital stock.

(g) [qa.sub.t-1] is Tobin's q calculated as the market value of equity
plus the value of debt divided by total assets.

(h) [qm.sub.t-1] is the yearly measure of marginal q.

(i) C[F.sub.t]/[K.sup.i.sub.t] is cash flow (income before
extraordinary items plus depreciation minus dividends plus (1 - tax
rate) times R&D expenditures) divided by the beginning of period book
value of capital stock.

Table 3. Matrix of Correlation Coefficients: All Firms

                       [bar]qm  [qa.sub.t-1]  [I.sub.t]/[K.sub.t-1]

[bar]qm                 1
[qa.sub.t-1]            0.398       1
[I.sub.t]/[K.sub.t-1]   0.081       0.199             1
[R.sub.t]/[K.sub.t-1]   0.020       0.204             0.318
C[F.sub.t]/[K.sub.t]    0.121       0.272             0.436
DSAL                    0.090       0.139             0.281
Sales                  -0.083      -0.095            -0.022
[qm.sub.t-1]            0.037       0.186             0.115

                       [R.sub.t]/[K.sub.t-1]  C[F.sub.t]/[K.sub.t]

[bar]qm
[qa.sub.t-1]
[I.sub.t]/[K.sub.t-1]
[R.sub.t]/[K.sub.t-1]          1
C[F.sub.t]/[K.sub.t]           0.618                  1
DSAL                           0.183                  0.385
Sales                         -0.077                 -0.083
[qm.sub.t-1]                   0.026                  0.119

                        DSAL   Sales   [qm.sub.t-1]

[bar]qm
[qa.sub.t-1]
[I.sub.t]/[K.sub.t-1]
[R.sub.t]/[K.sub.t-1]
C[F.sub.t]/[K.sub.t]
DSAL                    1
Sales                  -0.012    1
[qm.sub.t-1]            0.149   -0.015       1

Abbreviation as in Table 2.

Table 4. Ordinary Least Squares (OLS) Regression Results

                                Equation 1 All  Equation 2 [bar]qm
                                                 [greater than or
                                                   equal to] 1

Variable                         Coef    t val    Coef    t val

Dependent variable I/K
    C[F.sub.t-1]/[K.sub.t-1]     0.199   15.93   0.298   11.350
    [qm.sub.t-1]                 0.003    5.42   0.005    4.210
    [qa.sub.t-1]                 0.039    8.11   0.044    5.350
    [qa.sub.t-1] *
      C[F.sub.t-1]/[K.sub.t-1]  -0.007   -0.87  -0.049   -3.79
    Firms                             560             167
    No. obs.                         7361            2103
    [[bar]R.sup.2]                   0.23            0.22

  Predicted partial derivatives (evaluated at respective means)
    C[F.sub.t-1]/[K.sub.t-1]        0.191 *         0.224 *
    [qa.sub.t-1]                    0.037 *         0.022 *

  Dependent variable R/K
    C[F.sub.t]/[K.sub.t-1]       0.273   27.98  0.294    15.77
    [qa.sub.t-1]                -0.002   -0.58  0.012     2.19
    [qa.sub.t-1] *
      C[F.sub.t-1]/[K.sub.t-1]   0.007    1.17  -0.026   -2.84
    Firms                             560             167
    No. obs.                         7361            2103
    [[bar]R.sup.2]                   0.49            0.49

  Predicted partial derivatives (evaluated at respective means)
    C[F.sub.t-1]/[K.sub.t-1]        0.281 *         0.254 *
    [qa.sub.t-1]                    0.001           0.001

                                                           Equation 3
                                                          [bar]qm < 1

Variable                                                  Coef    t val

Dependent variable I/K
    C[F.sub.t-1]/[K.sub.t-1]                >             0.153    9.93
    [qm.sub.t-1]                            >             0.002    3.29
    [qa.sub.t-1]                [approximately equal to]  0.045    6.17

    [qa.sub.t-1] *
      C[F.sub.t-1]/[K.sub.t-1]              <             0.021    1.86
    Firms                                                      363
    No. obs.                                                  5258
    [[bar]R.sup.2]                                            0.23

  Predicted partial derivatives (evaluated at respective means)
    C[F.sub.t-1]/[K.sub.t-1]                >                0.175 *
    [qa.sub.t-1]                            <                0.052 *

  Dependent variable R/K
    C[F.sub.t]/[K.sub.t-1]                  >             0.229   18.49
    [qa.sub.t-1]                            >            -0.011   -1.91
    [qa.sub.t-1] *
      C[F.sub.t-1]/[K.sub.t-1]  <                         0.059    6.32
    Firms                                                      363
    No. obs.                                                  5258
    [[bar]R.sup.2]                                            0.50

  Predicted partial derivatives (evaluated at respective means)
    C[F.sub.t-1]/[K.sub.t-1]    <                            0.288 *
    [qa.sub.t-1]                <                            0.009 **

Less than (<), greater than (>), and approximately equal
([approximately equal to]) symbols mean significant smaller, larger, or
not significantly different, respectively. The qa/cash flow interaction
term is evaluated at the subsample means, when we test for the impacts
of cash flow and Tobin's q. All regressions include two-digit industry
and year dummies. For the other variable definitions see Tables 1
and 2.

* Significant at the 1% level.

** Significant at the 5% level.

Table 5. Robustness I: Different Specifications and Firm Fixed Effects

                                         OLS I/K

                                   [bar]qm
                                  [greater
                                    than or                    [bar]qm
                           All    equal to] 1                    < 1
Variables                  (1)        (2)                        (3)

Accelerator                0.032   0.032       [approximately   0.031
                                               equal to]
  t value                 13.88    6.52                        12.03
C[F.sub.t-1]/[K.sub.t-1]   0.159   0.249       >                0.119
  t value                 12.59    9.22                         7.66
[qm.sub.t-1]               0.003   0.004       >                0.002

  t value                  4.4     3.36                         2.63
[qa.sub.t-1]               0.039   0.043       [approximately   0.045
                                               equal to]
  t value                  8.03    5.37                         6.31
[qa.sub.t-1] *            -0.005  -0.043       <               -0.020
  C[F.sub.t-1]/
  [K.sub.t-1]
  t value                 -0.63   -3.35                         1.80
Firms                      560     167                          393
No. obs.                  7361    2103                         5258
[[bar]R.sup.2]            0.25    0.23                         0.25

                                      Fixed Effects I/K

                                    [bar]qm
                                  [greater
                                    than or                    [bar]qm
                           All    equal to] 1                    < 1
Variables                  (4)        (2)                        (6)

Accelerator

  t value
C[F.sub.t-1]/[K.sub.t-1]   0.211   0.280                        0.183
  t value                 15.22    9.74                        10.97
[qm.sub.t-1]               0.002   0.002       [approximately   0.001
                                               equal to]
  t value                  2.69    2.11                         1.63
[qa.sub.t-1]               0.052   0.036                        0.071

  t value                  8.04    3.52                         7.99
[qa.sub.t-1] *             0.004  -0.014       [approximately   0.012
  C[F.sub.t-1]/                                equal to]
  [K.sub.t-1]
  t value                  0.51   -0.99                         1.02
Firms                      560     167                          393
No. obs.                  7361    2103                         5258
[[bar]R.sup.2]            0.34    0.30                         0.35

                                      Fixed Effects R/K

                                    [bar]qm
                                  [greater
                                    than or        [bar]qm
                           All    equal to] 1        < 1
Variables                  (7)        (2)            (9)

Accelerator

  t value
C[F.sub.t-1]/[K.sub.t-1]   0.130   0.170       >     0.103
  t value                 18.86   12.34             12.29
[qm.sub.t-1]

  t value
[qa.sub.t-1]              -0.001   0.011       >    -0.012

  t value                 -0.41    2.39             -2.89
[qa.sub.t-1] *             0.021   0.005       <     0.046
  C[F.sub.t-1]/
  [K.sub.t-1]
  t value                  4.97   -0.72              7.62
Firms                      560     167               393
No. obs.                  7361    2103              5258
[[bar]R.sup.2]            0.82    0.80              0.83

Less than (<), greater than (>) and approximately equal ([approximately
equal to]) symbols mean significantly smaller, larger, or not
significantly different, respectively, where the qa/cash flow
interaction term is evaluated at the subsample means when we test for
the impacts of cash flow and Tobin's q. Accelerator is lagged
difference in sales divided by the capital stock. All other variables
are defined in Tables 1 and 2.

The research in this article was supported in pan by the Austrian National Bank's Jubilaumsfonds, Project 8090. The article has benefited from the comments of the two referees on an earlier draft.

(1) Meyer and Kuh (1957) is the pioneering study. Chirinko (1993) presents a comprehensive survey of the investment determinants literature.

(2) The transaction costs hypothesis was first developed by Duesenberry (1958). Grabowski and Mueller (1972) were the first to hypothesize that the cash flow/investment relationship was caused by agency problems. The first empirical test of the asymmetric information hypothesis was by Fazzari, Hubbard, and Petersen (1988).

(3) See Stiglitz and Weiss (1981) and Myers and Majluf (1984).

(4) See Fazzari, Hubbard, and Petersen (1988); Hoshi, Kashyap, and Scharfstein (1991); Carpenter (1995); Carpenter. Fazzari, and Petersen (1994, 1998); and Chirinko and Schaller (1995).

(5) See Kaplan and Zingales (1997) for further discussion and evidence.

(6) It is always possible, of course, that a firm earned higher returns on investment than its cost of capital because its managers underestimated these returns or were merely overly cautious (Kaplan and Zingales 2000, p. 711), and not because the firm was cash constrained. Hence, the modifier "possibly."

(7) Marris (1964, 1998) first motivated and developed the growth maximization hypothesis.

(8) Hayashi (1982) demonstrates that marginal q is the theoretically correct measure of investment opportunities and establishes the conditions under which it equals average q. Osterberg (1989) proves that marginal q is a "sufficient statistic" for investment.

(9) Other attempts to come up with a measure of marginal q, which differ from ours, include Abel and Blanchard (1986), Gilchrist and Himmelberg (1995), and Cummins, Hassett, and Oliner (1998).

(10) See Economist (1994) and Mikkelson and Partch (1997), who report a more active market for corporate control in the period 1984 to 1988 than the 1989-1993 period, which could imply a reduction in agency problems after 1988.

(11) See, again, Hayashi (1982) for a formal development of the theory.

(12) This derivation was first presented by Mueller and Reardon (1993). For other applications and additional discussion, see Mueller and Yurtoglu (2000) and Gugler and Yurtoglu (2003).

(13) For further discussion of this possible bias see Mueller and Yurtoglu (2000, pp. 194-95).

(14) Indeed, if all companies with [bar]qm [greater than or equal to] 1 had investment opportunities as depicted in Figure 1a, and none could raise any external capital, their investments should exactly equal their cash flows, and the coefficient on cash flow in an investment equation for this subsample would equal 1.0.

(15) Kaplan and Zingales (1997, 2000) are concerned about previous studies' failure to control for differences in the costs of external finance across cash-constrained companies. Our use of qa should capture an important component of these differences.

(16) See Jensen (1986) and references in footnote 4. Kathuria and Mueller (1995) assume that managerial utilities are a function of the growth of the firm and security from takeover and derive the prediction that both investment and dividends increase with increases in cash flows and thus that the coefficient on cash flow in an investment equation is positive and less than one.

(17) Some studies have lagged cash flow also on the grounds that managers need some time to react to changes in cash flows. We also estimated the model substituting cash flow lagged one period for the current level and obtained very similar results to those reported here. These are available from the authors upon request.

(18) The standard deviations of each variable appear in Tables 2 and 3. [(1.9).sup.2]/[(0,597).sup.2] = 10.4.

(19) We tried a number of other definitions of Tobin's q, see the discussion in section 3.

(20) By defining cash flow to be net of dividends, we effectively assume that dividends have higher priority than investment and are determined before it. This assumption appears particularly appropriate for the MD subsample, since dividends for these firms should be positively related to share prices and are a means of "buying" security from takeover. Substituting a predividend definition of cash flow produces very similar results to those reported here. These are again available from the authors on request.

(21) We add (1 - tax rate) times the R&D expenditures to cash flow. The tax rate that we use is 50% for the 1979-1987 period and 34% for the 1988-1996 period.

(22) When the model was estimated for firms in these industries, the results were largely consistent with our predictions for capital investment. Companies in these industries do little R&D (median firm zero), and so not surprisingly the fit for the R&D equation was poor.

(23) Kaplan and Zingales (1997) conclude from 10-K reports and balance sheet data for Fazzari, Hubbard, and Petersen's (1988) sample that fewer than a sixth of the companies were cash constrained. Kaplan and Zingales speculate that cash flow may be proxying for investment opportunities for the unconstrained companies. Since this does not appear to be a likely explanation for a positive relationship between cash flow and investment in our sample, we are left with the MD and AI hypotheses to explain such a relationship.

(24) Throughout the paper all partial derivatives with respect to either C(F.sub.t] or [qa.sub.t-1] are evaluated at the mean of the other variable in the interaction term. To perform simple t tests on the difference between coefficients from different samples we have to assume that the regression error terms are independent across subsamples. Statistical insignificance between regression coefficients is indicated by an equality sign between columns 2 and 3.

(25) We argued above that there might actually be no relationship between [qm.sub.t-1] and [I.sub.t] for firms with [bar]qm < 1, but this prediction was obviously too strong.

(26) See, for example, Vogt (1994), Bond and Meghir (1994), and Kadapakkam, Kumar, and Riddick (1998).

(27) The results for small and [bar]qm < 1 firms and for large and [bar]qm [greater than or equal to] 1 firms lie in between the two "extreme" subsamples and are available from the authors upon request.

(28) A split by dividends underlay the test of the AI hypothesis in the seminal contribution of Fazzari, Hubbard, and Petersen (1988).

(29) Results available from the authors upon request.

(30) The most controversial part of Tobin's q is the replacement cost of the firm's fixed assets (see, e.g., Lewellen and Badrinath 1997). We experimented with a number of different definitions for qa and obtained the following results (detailed results are available upon request). (1) When we define qa in the spirit of Kaplan and Zingales (1997) (qa = [market value of the firm plus total assets minus book value of common equity minus balance sheet deferred taxes]/total assets), all of our results carry over, some are even more pronounced. (2) When we define it in the spirit of Lindenberg and Ross (1981) (qa = [market value of the firm]/[total assets plus replacement cost of fixed assets minus book value of fixed assets plus Last In First Out (LIFO) reserve plus total debt minus total liabilities]), all results carry over qualitatively although there is some reduction in significance.

(31) We thank Bruce Petersen for suggesting this test. We estimated R&D capital as R&D spending times 5 or 10 assuming that the firm is in a steady state and the R&D stock depreciates at a constant 20% or 10% rate. These rates are consistent with the range of depreciation rates presented in the literature (Nadiri and Prucha 1996). With qa defined as the ratio of the market value to total assets plus this R&D stock, [qm.sub.t-1] remains much more important for the [bar]qm [greater than or equal to] firms compared to [bar]qm < 1 firms, and the reverse is true for qa. The cash flow/qa interaction term is negative for the [bar]qm [greater than or equal to] 1 subsample and positive for the [bar]qm < 1 subsample; however, the difference is now not significant at conventional level.

References

Abel, Andrew B., and Olivier J. Blanchard. 1986. The present value of profits and cyclical movements in investment. Econometrica 54:249-73.

Bond, Stephen, and Costas Meghir. 1994. Dynamic investment models and the firm's financial policy. Review of Economic Studies 61:197-222.

Carpenter, Robert E. 1995. Finance constraints or free cash flow? A new look at the life cycle theory of the firm. Empirica 22:185-209.

Carpenter, Robert E., Steven M. Fazzari, and Bruce C. Petersen. 1994. Inventory investment, internal-finance fluctuations, and the business cycle. Brookings Papers on Economic Activity 2:75-122.

Carpenter, Robert E., Steven M. Fazzari. and Bruce C. Petersen. 1998. Financing constraints and inventory investment: A comparative study with high-frequency panel data. Review of Economics and Statistics 80:513-9.

Chirinko, Robert. 1993. Business fixed investment spending: Modeling strategies, empirical results, and policy implications.

Journal of Economic Literature 31 : 1875-911.

Chirinko, Robert S., and Huntley Schaller. 1995. Why does liquidity matter in investment equations? Journal of Money, Credit, and Banking 27:527-48.

Cummins, Jason G., Kevin A. Hassett, and Stephen R. Oliner. 1998. Investment behavior, observable expectations, internal funds. Unpublished paper, New York University.

Duesenberry, James S. 1958. Business cycles and economic growth. New York: MacGraw Hill.

Economist. 1994. Ready to take on the world. 15 January, pp. 65-6.

Fazzari, S. M., R. G. Hubbard, and B. Petersen, 1988. Financing constraints and corporate investment. Brookings Papers on Economic Activity 1:141-95.

Gilchrist, Simon, and Charles P. Himmelberg. 1995. Evidence on the role of cash flow for investment. Journal of Monetary Economics 36:541-72.

Grabowski, H., and Dennis C. Mueller. 1972. Managerial and stockholder welfare models of firm expenditures. Review of Economics and Statistics 54:9-24.

Gugler, Klaus. and B. Burcin Yurtoglu. 2003. Average q, marginal q, and the relation between ownership and performance. Economics Letters 78:379-84.

Hayashi, Fumio. 1982. Tobin's marginal q and average q: A neoclassical interpretation. Econometrica 50:213-24.

Hoshi, Takeo, A. Kashyap, and D. Scharfstein. 1991. Corporate structure, liquidity, and investment: Evidence from Japanese industrial groups. Quarterly Journal of Economies 106:33-60.

Jensen, Michael C. 1986. Agency costs of free cash flow, corporate finance, and takeovers. American Economic Review 76: 323-9.

Kadapakkam, P. R., P. C. Kumar, and L. A. Riddick. 1998. The impact of cash flows and firm size on investment: The international evidence, Journal of Banking and Finance 22:293-320.

Kaplan, Steven N., and Luigi Zingales. 1997. Do investment-cash flow sensitivities provide useful measures of financing constraints? Quarterly Journal of Economics 112:169-215.

Kaplan, Steven N., and Luigi Zingales. 2000. Investment-cash flow sensitivities are not valid measures of financing constraints. Quarterly Journal of Economics 155:707-12.

Kathuria, R., and Dennis C. Mueller. 1995. Investment and cash flow: Asymmetric information or managerial discretion. Empirica 22:211-34.

Lewellen, G. Wilbur, and S.-G. Badrinath. 1997. On the measurement of Tobin's q. Journal of Financial Economics 44:77-122.

Lindenberg, E., and S. Ross. 1981. Tobin's q ratio and industrial organization. Journal of Business 54:1-33.

Marris, Robin. 1964, The economic theory of managerial capitalism. London: Macmillan.

Marris, Robin. 1998, Managerial capitalism in retrospect. London: Macmillan.

Meyer, John R., and Edwin Kuh. 1957. The investment decision. Cambridge, MA: Harvard University Press.

Mikkelson, Wayne H., and M. Megan Partch. 1997. The decline of takeovers and disciplinary managerial turnover. Journal of Financial Economics 44:205-28.

Mueller, Dennis C., and Elizabeth Reardon. 1993. Rates of return on corporate investment. Southern Economic Journal 60: 430-53.

Mueller, Dennis C., and B. Burcin Yurtoglu, 2000. Country legal environments and corporate investment performance. German Economic Review 1:187-220.

Myers, Stewart C., and Nicholas S. Majluf. 1984. Corporate financing and investment decisions when firms have information that investors do not have. Journal of Financial Economics 12:187-221.

Nadiri, M. Ishaq, and Ingmar R. Prucha. 1996. Estimation of the depreciation rate of physical and R&D capital in the U.S. total manufacturing sector. Economic Inquiry 1:43-56.

Osterberg, William P. 1989. Tobin's q, investment, and the endogenous adjustment of financial structure. Journal of Public Economics 40:293-318.

Stiglitz, Joseph E., and Andrew Weiss. 1981. Credit rationing in markets with imperfect information. American Economic Review 71:393-410.

Vogt, Stephen C. 1994. The cash flow/investment relationship: Evidence from U.S. manufacturing firms. Financial Management 23:3-20.

Received October 2000; accepted March 2003.

Klaus Gugler, * Dennis C. Mueller, ([dagger]) and B. Burcin Yurtoglu ([double dagger])

* University of Vienna, Department of Economics, BWZ, Bruennerstr. 72, A-1210, Vienna, Austria; E-mail klaus. [e-mail].

([dagger]) University of Vienna, Department of Economics, BWZ, Bruennerstr. 72, A-1210, Vienna, Austria; E-mail dennis. [e-mail]; corresponding author.

([double dagger]) University of Vienna, Department of Economics, BWZ, Bruennerstr. 72, A-1210, Vienna, Austria; E-mail [e-mail].