Corporate Precautionary Cash Savings: Prudence versus Liquidity Constraints

Transcription

1 Corporate Precautionary Cash Savings: Prudence versus Liquidity Constraints Martin Boileau and Nathalie Moyen April 2009 Abstract Cash holdings as a proportion of total assets of U.S. corporations have roughly doubled between 1971 and We investigate which motive for precautionary cash holdings is responsible for the large increase. Precautionary savings can arise because various taxes, adjustment and issuing costs induce the firm to be prudent and save more in the face of increased risk. Precautionary savings can also arise because liquidity constraints require the firm to save more in the face of increased risk to satisfy the constraint. We find that the prudence motive is no longer empirically relevant in explaining cash holdings, because firms capital intensities have significantly decreased over time. When a firm does not rely as much on capital to produce revenues, the firm no longer uses return-dominated cash holdings as a way to shift resources through time and instead uses capital investments and asset sales. In contrast, we find that the liquidity constraint motive can by itself explain the observed increase in cash holdings. Boileau: Department of Economics and CIRPÉE, University of Colorado, 256 UCB, Boulder Colorado 80309, United States. Tel.: Fax: boileau@colorado.edu. Moyen: Leeds School of Business, University of Colorado, 419 UCB, Boulder Colorado 80309, United States. Tel.: Fax: moyen@colorado.edu.

2 1 Introduction Cash holdings as a proportion of total assets of North American COMPUSTAT firms have roughly doubled since the 1970 s. Bates et al. (2008) show that, by the mid-2000 s, U.S. corporations have more cash than debt outstanding, so that the average U.S. firm s net leverage ratio is negative. Figure 1 documents this large cash-to-total assets increase for our sample of North American COMPUSTAT firms. Corporate cash holdings have risen steadily over the last few decades. Figure 1 also documents that this increase is accompanied by a steady decline in the capital share of total assets. Our findings indicate that the increase in cash is related to the decrease in the capital share. Leverage is volatile in Figure 1, but does not display an obvious trend. Bates et al. attribute this astounding increase in cash holdings to firms precautionary savings. The rise in precautionary savings is consistent with the observed post-wwii increase in firms idiosyncratic risk documented by Campbell et al. (2001). We investigate the precise mechanisms by which increased idiosyncratic risk leads to more precautionary savings. Carroll and Kimball (2001) study the motives of consumer precautionary savings. Precautionary savings arise when the marginal utility is convex, inducing the consumer to be prudent and save more in the face of increased risk as a precaution against future shocks. Precautionary savings also arise with a liquidity constraint, requiring the consumer to save more in the face of increased risk to satisfy the constraint. Evidently, an increase in risk can increase precautionary savings through both motives. In our context, firms precautionary savings behavior can similarly arise through the two motives. A firm faces various tax rates, adjustment and issuing costs, which may lead to convex marginal payouts. With convex marginal payouts, the firm saves more in the face of increased risk as a precaution against future shocks. A firm also faces liquidity constraints, requiring the firm save more in the face of increased risk to satisfy the constraint. Given the documented increase in idiosyncratic risk, both the prudence and liquidity constraint motives may independently account for the increase in corporate precautionary savings. In this paper, we investigate the relative strengths of the two motives, and evaluate which motive offers a better explanation for the large 2

3 increase in cash holdings. We find that the liquidity constraint motive can by itself explain the increase in cash holdings in our sample period. As for the prudence motive, its importance has decreased to the point of no longer generating any precautionary savings. In other words, the firm no longer accumulates more cash in the face of increased risk as a precaution against future shocks. It only accumulates cash to satisfy its immediate liquidity constraint. The empirical disappearance of the prudence motive is due to the sharp decrease in firms capital intensities over time. Firms physical capital intensities in producing revenues decreased from during the period to in the period. The decrease in the capital share reduces the importance of capital in producing revenues. When faced with the choice between using return-dominated cash holdings and using capital investments and asset sales to shift resources through time, the less capital intensive firm opts for the latter. Using capital assets to smooth payouts through time decreases the volatility of the returns to capital, so that the returns to capital never fluctuate below the return to cash. The less capital intensive firm therefore never accumulates more cash than strictly necessary to cover its immediate liquidity constraint. The firms changing capital intensities has been noted empirically by Bates et al. Accompanying the large increase in cash holdings, Bates et al. highlight that firms also face riskier cash flows, hold fewer substitute liquid assets such as inventories and accounts receivable, conduct more research and development, and are less capital intensive. Our neoclassical framework suggests that the increased risk of cash flow contributed to the accumulation of cash holdings, but that cash holdings would have been even larger if firms had remained as capital intensive as before. In our neoclassical framework, we do not include any feature of agency problems. Our modeling simplification can be motivated by the fact that Opler et al. (1999) find little evidence that cash holdings lead to larger capital investments or mergers and acquisitions as predicted by the free cash flow hypothesis of Jensen (1986). Bates et al. also obtain results that fail to support the agency problem explanation for the overall rise in cash holdings of U.S. firms. We recognize that, in other contexts, the relationship between higher cash holdings (or lower cash value) and higher agency 3

4 costs is well documented. 1 In addition, our model does not include any feature relating to the tax optimization of multinational firms. Foley et al. (2007) show that U.S. multinationals accumulated cash rather than repatriated foreign profits that would have become taxable once in the United States. Bates et al. note that the large increase in cash holdings is also observed for domestic firms. There are already a number of papers using liquidity constraints in their analysis of the cash hoarding behavior of U.S. firms. Nikolov (2008) shows that increased market competition can in part explain the rise in cash holdings, especially for financially constrained firms in riskier industries. Almeida et al. (2004) and Han and Qiu (2007) document that financially constrained firms accumulate cash out of cash flow, while unconstrained firms do not. Acharya et al. (2007) show that this behavior is strongest for constrained firms that suffer from a low correlation between operating income flow and their investment opportunities. When controlling for measurement errors, Riddick and Whited (2008) find that cash holdings are negatively associated with cash flows. Because cash flow shocks as persistent through time, a high cash flow shock today means that the firm can also rely on high cash flows in the future, which lessens the need to accumulate cash for future investments. The model of Gamba and Triantis (2007) is closely related to our model in that a firm can finance its investment through debt issues, equity issues, and internal funds, where only internal funds do not trigger transaction costs. Their focus is on valuing financial flexibility, while we explore which precaution motive explains the increased cash holdings. In addition, our paper recognizes the fact that cash is a dominated security in terms of return. The rate of return associated with cash holdings is lower than the risk-less rate, because much of the cash is held in the actual currency rather than invested in short-term instruments. Another closely related model that recognizes the fact that cash is dominated in return is Bolton et al. (2009). Bolton et al. propose a general dynamic model of investment decisions for financially constrained firms with constant returns to scale in production. Among other contributions, they 1 For example, see Dittmar and Mahrt-Smith (2007), Dittmar et al. (2003), Faulkender and Wang (2006), Harford (1999), Harford et al. (2008), and Pinkowitz et al. (2006). 4

5 find that Tobin s marginal q may be inversely related to investment when a firm uses more credit, and that financially constrained firms may have lower equity betas because of precautionary cash holdings. Our paper departs from the assumption of constant returns to scale in production and examines the effect of a lower capital share on firms precautionary cash holdings. The paper is organized as follows. Section 2 of the paper presents the model, and provides some analytical results characterizing the behavior of cash holdings. The model however does not possess an analytical solution. Section 3 discusses the calibration of the model. Section 4 presents our simulation results. We first ensure that the model broadly reproduces observed facts. We then use the model to study the rise in cash holdings. Section 5 offers some concluding remarks. 2 The Model In an otherwise standard dynamic model of a firm s financing and investment decisions, we concentrate our attention on how the firm manages its cash holdings. Cash is not negative debt. Cash holdings serve as a precaution against future shocks so that the firm can deal with rainy days. We assume that the firm faces shocks to its revenues and expenses. The firm is well aware of its current revenues when making financial and investment decisions. The firm, however, may incur unknown expenses during the year. These two types of shocks in principle yield different responses in cash holdings. As we explain in details below, the firm holds cash as a precaution against the unknown expenses during the year. In addition, the firm may also hold cash as a precaution against future shocks to revenues. 2.1 The Firm The firm, acting in the interest of shareholders, maximizes the discounted expected stream of payouts D t taking into account taxes and issuing costs. When payouts are positive, shareholders pay taxes on the distributions according to a tax schedule T D. The schedule recognizes that firms can minimize taxes for smaller payouts by distributing them in the form of share repurchases. Firms, however, have no choice but to trigger the dividend tax for larger payouts. Following Hennessy and Whited (2007), the tax treatment of payouts is captured by a schedule that is increasing and 5

6 convex: T D t τ D D t + τ D φ exp φdt τ D φ, (1) where φ > 0 denotes the convexity parameter and 0 < τ D < 1 is the tax rate. When payouts are negative, shareholders send cash infusions into the firm as in the case of an equity issue. The convex schedule T D also captures the spirit of Altinkilic and Hansen (2000), where equity issuing costs are documented to be increasing and convex. 2 We represent net payouts as U(D t ) D t T D t. (2) For finite values of D t, this function is increasing U (D t ) = 1 τ D + τ D exp( φd t ) > 0, concave U (D t ) = φτ D exp( φd t ) < 0, and its third derivative is positive U (D t ) = φ 2 τ D exp( φd t ) > 0. As a result, the net payout function ensures that the firm is risk averse and has a precautionary motive. In this context, the parameter φ is the coefficient of absolute prudence: φ = U (D t )/U (D t ). The firm faces two sources of risk. The first source of risk comes from stochastic revenues. As is standard, revenues Y t are generated by a decreasing returns to scale function of the capital stock K t : Y t exp(z t )ΓKt α, (3) where z t is the current realization of the shock to revenues, the parameter 0 < α < 1 denotes the capital share, and Γ > 0 is a scale parameter. The revenue shock follows the autoregressive process z t = ρ z z t 1 + σ ɛ ɛ t, (4) where ɛ t is the innovation to the revenue shock, and the parameters 0 < ρ z < 1 and σ ɛ > 0 denote persistence and volatility. The innovations are independent and identically distributed random variables drawn from a standard normal distribution. The second source of risk comes from stochastic expenses F t. The firm s expenses are given by F t F + f t, (5) 2 Alternatively, and without any qualitative impact on the results, we can add to the model complexity by separately modeling equity costs as Ω D t = (ω D/2) Dt 2 1(D t 0), where ω D is the equity issuing cost parameter. 6

7 where F 0 is the predictable level of expenses and f t is the current realization of the expense shocks. For simplicity, we restrict the expense shock to two equally probable realizations f t = σ F [ 1, 1], where σ F > 0. The firm makes its investment and financial decisions with knowledge of the current realization of the revenue shock but not the realization of the expense shock. When making the investment and financing decisions, the firm may take great precaution in anticipation of the yet-unknown expenses. The firm accumulates precautionary cash savings to respond to the expense shock when it occurs during the year. The firm chooses how much to pay out D t, how much to invest I t, how much debt to raise B t+1, and how much cash to hold M t+1. The sources and uses of funds equation defines M t+1 = Y t F t I t + B t+1 (1 + r)b t D t + (1 + ι)m t T C t Ω K t Ω B t, (6) where B t and M t are the beginning-of-the-year stocks of debt and cash, T C t represents corporate taxes, and Ω K t and Ω B t are adjustment costs to capital and debt. The constant r and ι are the real interest rates applied to debt and cash. Investment is described by the capital accumulation equation I t = K t+1 (1 δ)k t, (7) where the depreciation rate is denoted by 0 < δ < 1. For simplicity, capital adjustment costs are assumed quadratic: Ω K t ω K 2 ( ) 2 It δ K t, (8) K t where ω K 0 is the capital adjustment cost parameter. Debt issuance is given by B t+1 B t+1 B t. Similar to investment, we assume a quadratic cost to varying the debt level away from B 0: Ω B t ω B 2 ( Bt+1 B ) 2, (9) where ω B 0 is the debt adjustment cost parameter. 7

8 Cash accumulation is given by M t+1 M t+1 M t. Importantly, there is no adjustment cost on cash holdings. Finally, corporate taxes are imposed on revenues after depreciation, interest payment, and interest income: Tt C τ C [Y t F t δk t rb t + ιm t ], (10) where 0 < τ C < 1 is the corporate tax rate. The firm faces a constant discount rate r. The after-tax discount factor is β 1/(1 + (1 τ r )r), where τ r is the personal tax rate on interest income. Because individuals pay taxes on their interest income at a lower rate than the rate at which corporations deduct their interest payment τ r < τ C, debt financing is tax-advantaged. To counter this benefit of debt financing, the convex cost in equation (9) bounds the debt level. In this sense, the adjustment costs plays a role similar to a collateral constraint. 3 Similar to the constant discount rate r, the interest rate received on cash holdings ι is also assumed to be constant over time. Moreover, the model recognizes that cash is a dominated security in terms of return: ι < r. In practice, a firm holding cash incurs a real return loss equal to the inflation. 2.2 The Intertemporal Problem As discussed above, the firm makes financial decisions knowing the current realizations of the revenue shock. During the year, however, the firm may face expenses that are either lower or higher than expected back at the beginning of the year. When expenses turn out to be higher than expected, we assume that the firm cannot take back its distributed dividend, scale back its investment commitments, or go back to external markets with more favorable issuing conditions. This assumption is similar to that in Telyukova (2008) and Telyukova and Wright (2008). Of course, foreseeing all this, the firm may have already been cautious and paid out less in dividends, invested less, or raised more funds externally so that its accumulated cash could cover a large expense realization. As a result, the stock of cash next year, M t+1, is equal to the firm s choice of 3 Adding a collateral constraint does not alter our results. 8

9 cash savings S t at the beginning of the year less the after-tax expenses: M t+1 = S t (1 τ C )f t, (11) where the beginning-of-the-year cash saving is S t = (1 τ C ) [ Y t F δk t rb t + ιm t ] (Kt+1 K t ) + B t+1 + M t Ω K t Ω B t D t. (12) In this economic environment, the firm s intertemporal problem can be described by the following two Bellman equations. At the beginning of the year, the firm s problem is V (K t, B t, M t ; z t, f t 1 ) = max U(D t) + E1t[W (K t+1, B t+1, M t+1 ; z t, f t )] (13) {D t,k t+1,b t+1,s t} subject to equations (1) to (4), (8), (9), and (12), as well as the non-negativity constraints K t+1 0, B t+1 0, and S t 0. Note that the conditional expectation is taken on an information set Φ 1t that includes all lagged variables as well as the current values of the capital stock K t, debt level B t, cash holding M t, and revenue shock z t, but not the year-end realization of the expense shock f t. We denote this conditional expectation by E1t. During the year when the expense realization becomes known, the firm s problem is W (K t+1, B t+1, M t+1 ; z t, f t ) = max {M t+1 } β E2t[V (K t+1, B t+1, M t+1 ; z t+1, f t )] (14) subject to equation (11) and the non-negativity constraint M t+1 0. At this point, the firm makes its decision using the information set Φ 2t that includes all the variables in Φ 1t plus the year-end realization of the expense shock f t. Solving backwards, equation (11) and the non-negativity constraint M t+1 0 imply that the firm always chooses to set aside enough cash to cover the highest expense realization σ F : S t (1 τ C )σ F. (15) It is not clear that (15) holds with equality. In addition to saving as a precaution against the higher expense realization, the firm may save even more cash when it wants to shift resources from better states as a precaution against future worse states. Solving the model will indicate the relative importance of these two sources of precautionary savings. 9

10 Equation (15) becomes a constraint at the beginning of the year when the firm makes its investment and financing decisions. The investment, debt, and cash saving decisions are described by the three Euler equations below. Investment is characterized by β E1t [ U (D t+1 ) Debt financing is characterized by ( ( { }) U Kt+1 (D t ) 1 + ω K 1 K t 1 + (1 τ C )(α exp(z t+1 )ΓK (α 1) t+1 δ) + ω K 2 = { (Kt+2 ) 2 1})] K t+1. (16) U (D t ) ( 1 ω B {B t+1 B} ) [ = β E1t U (D t+1 ) (1 + (1 τ C )r) ]. (17) Finally, the beginning-of-the-period cash saving decision is characterized by U [ (D t ) λ t = β E1t U (D t+1 ) (1 + (1 τ C )ι) ], (18) where λ t is the multiplier on the liquidity constraint (15) satisfying the complementary slackness conditions. 2.3 Precautionary Cash Holding The model contains two motives to hold cash. One motive is related to the liquidity constraint (15). The complementary slackness conditions attached to the liquidity constraint ensure that λ t 0, S t (1 τ C )σ F, and λ t [S t (1 τ C )σ F ] = 0. When λ t > 0, the firm holds enough cash only to satisfy the liquidity constraint with equality. That is, all cash holdings are driven by the liquidity constraint motive. When λ t = 0, the firm may hold more cash. Proposition 1 When λ t > 0, S t = (1 τ C )σ F so that the firm holds cash only as a safeguard against the year-end expense shock realization. When λ t = 0, S t (1 τ C )σ F so that the firm may hold more cash. Cash holdings are characterized by equation (18), rewritten as U (D t ) λ t = βr M [ E1t U (D t+1 ) ], (19) 10

11 where R M = 1 + (1 τ C )ι. Note that βr M < 1 reflects the impatience embedded in cash holdings. In equilibrium where the distribution of dividends {D t, D t+1, } is stationary over time, the expression (19) is naturally satisfied when λ t > 0. In this case, as Proposition 1 describes, only the liquidity constraint motive is operative in determining cash holdings. The other motive to hold cash is the prudence motive. It can be operative when λ t = 0. When λ t = 0, expression (19) implies that U (D t ) < E1t [U (D t+1 )]. For this expression to hold in a stationary equilibrium, the marginal net payout function U (D) must be convex. As is well known, Jensen s inequality states that U (E[D]) < E[U (D)] for a convex function U ( ). In the model, the marginal net payout function is convex because of our assumptions about taxes and issuing costs T D t. The convexity generates the prudence motive, where beginning-of-the-year cash savings can be greater than the after-tax year-end expenses S t (1 τ C )σ F. Proposition 2 When λ t = 0 and U (D t ) is convex, S t (1 τ C )σ F and the firm may hold cash as a safeguard against both the year-end expense shock realization and future revenue shocks. The relative strengths of the prudence and liquidity constraint motives depend on the firm s decisions with respect debt and investment. To see the effect of the debt decision on cash holdings, we rewrite equation (17) and (18) as 1 ω B {B t+1 B} = E1t [m t+1 ] (1 + (1 τ C )r) (20) and 1 λ t U (D t ) = E1t [m t+1 ] (1 + (1 τ C )ι), (21) where m t+1 = βu (D t+1 )/U (D t ) > 0. Subtracting equation (21) from equation (20) reveals that λ t U (D t ) E1t [m t+1 ] = (1 τ C) (r ι) + ω B{B t+1 B} E1t [m t+1 ]. (22) Equation (22) shows two effects of debt decisions on cash holdings. First, the term (1 τ C )(r ι) > 0 denotes the extent to which cash is dominated in return by debt. All else equal, cash is more desirable when the return on debt is lower. Second, the term ω B {B t+1 B} represents the adjustment cost to debt. Equation (22) states that λ t > 0 whenever ω B (B t+1 B) 0. That is, 11

12 the firm holds cash only as a safeguard against the expense shock, S t = (1 τ C )σ F, either when there is no cost to adjusting its debt, ω B = 0, or when the firm takes an aggressive debt policy, B t+1 > B. In these times, the firm is not concerned about future shocks, as it levers up and does not accumulate more cash than required to satisfy the liquidity constraint. Conversely, the firm may hold cash to safeguard against both expense and future revenue shocks, λ t = 0 and S t (1 τ C )σ F, when the firm incurs debt adjustment costs, ω B > 0, and chooses a conservative debt policy, B t+1 < B. In those times, the firm becomes concerned about future shocks and acts prudently. Because the convex debt adjustment costs limit the extent to which debt financing can be adjusted downward, there comes a point at which the firm decides to accumulate cash at the dominated interest rate ι rather than face onerous debt adjustment costs. Proposition 3 When (1 τ C )(r ι) + ω B (B t+1 B)/ E1t [m t+1 ] > 0, λ t > 0 so that the firm holds cash only as a safeguard against the year-end expense shock realization. When (1 τ C )(r ι) + ω B (B t+1 B)/ E1t [m t+1 ] = 0, λ t = 0 so that the firm may hold cash as a safeguard against both the year-end expense shock realization and future revenue shocks. The relative strengths of the liquidity constraint and prudence motives also depend on the capital investment decision. To see the effect of the capital decision on cash holdings, we rewrite equation (16) as 1 = E1t [ ] m t+1 Rt+1 k, (23) where R k t+1 = We further decompose equation (23) as 1 + (1 τ C )(α exp(z t+1 )ΓK (α 1) t+1 δ) + ω K 2 { ( Kt+2 K t+1 ) 2 1 } 1 = E1t [m t+1 ] E1t 1 + ω K { Kt+1 K t 1 }. (24) [ ] Rt+1 k + Cov 1t (m t+1, Rt+1). k (25) Comparing equations (19) and (25) reveals that ( ) λ ( [ ] ) t U (D t ) E1t [m t+1 ] = E1t Rt+1 k R M + Cov 1t m t+1, Rt+1 k. (26) E1t [m t+1 ] 12

13 Equation (26) shows two effects of capital investment on cash holdings. The first term, E1t [ ] Rt+1 k R M, represents the extent to which cash is dominated in return by capital. All else equal, cash is more desirable when the expected return to capital is lower. The second term with ) Cov 1t (m t+1, Rt+1 k represents covariance risk. All else equal, cash is more desirable when the covariance term is lower. For example, a negative covariance indicates that future returns to capital are high when future dividends are also high (and future marginal net payouts are low). All else equal, the firm would prefer a positive covariance providing insurance in terms of higher returns when future dividends are low. Proposition 4 When E1t [ ] ( ) Rt+1 k R M + Cov 1t m t+1, Rt+1 k / E1t [m t+1 ] > 0, λ t > 0 so that the firm holds cash only as a safeguard against the year-end expense shock realization. When [ ] ( ) E1t Rt+1 k R M + Cov 1t m t+1, Rt+1 k / E1t [m t+1 ] = 0, λ t = 0 so that the firm may hold cash as a safeguard against both the year-end expense shock realization and future revenue shocks. 3 Data and Calibration Because the model does not possess an analytical solution, we solve it numerically. The numerical method, described in the appendix, requires values for all parameters. We employ two methods to parameterize the model. We fix a number of parameter values by directly estimating them in the data. We then fix the remaining parameter values so that the simulated series from the model replicate important features of the data. The data comes from the North American COMPUSTAT file and covers the period from 1971 to Because we aim to explain the large change in cash holdings, we focus the analysis on two extreme time periods: the first third of the sample period from 1971 to 1982 and the last third from 1995 to The COMPUSTAT sample includes firm-year observations with positive values for total assets (COMPUSTAT Mnemonic AT), property, plant, and equipment (PPENT), and sales (SALE). The sample includes firms from all industries except for utilities and financials. We also winsorized the data to limit the influence of outliers at the 1% and 99% tails. The final sample contains 60,033 firm-year observations for the 1971 to 1982 period and 93,122 firm-year observations for the

14 to 2006 period. 3.1 Parameters Estimated from the Data Table 1 presents the first set of parameter estimates for both periods. We estimate the capital share of revenues α, the scale of revenues Γ, the persistence of the revenue shock ρ z and its volatility σ ɛ using the firm s revenue equation (3) and the autoregressive shock process of equation (4). To estimate the four parameters, we require at least five years of consecutive data for revenues and beginning-of-the-period capital stock. Revenues Y t are measured as sales, and the beginning-ofthe-period capital stock K t is measured as lagged property, plant, and equipment. For each of the two time periods, we estimate four parameters per firm, and then we average the estimates over all firms. For the subperiod, these averages are α = , Γ = , ρ z = , and σ ɛ = For the subperiod, the averages are α = , Γ = , ρ z = and σ ɛ = The share α of physical capital that explains revenues has decreased over time but the scale Γ has increased. Note that the values for the capital share α are in line with the values used in Moyen (2004), Hennessy and Whited (2005, 2007), and Gamba and Triantis (2008). Over time, the economic environment became less predictable and more volatile. The persistence ρ z of the revenue shock has decreased and the volatility σ ɛ has increased. The parameters of the stochastic process indicate a significant increase in the unconditional variance of the revenue shock σɛ 2 /(1 ρ 2 z) from 4.71 percent during the period to 9.99 percent during the period. We calibrate the corporate tax rate τ C to the top marginal rate. The top marginal tax rate was 48% from 1971 to 1978 and 46% from 1979 to Averaged over the twelve years from 1971 to 1982, we set the corporate tax rate to τ C = Since 1993, the top corporate marginal tax rate has been constant at 35%, so we set τ C = 0.35 for the time period from 1995 to We calibrate the personal tax rates to the average marginal tax rates reported in NBER s TAXSIM. Over the period, the marginal interest income tax rate averaged τ r = while the marginal dividend tax rate averaged τ D = Since the Reagan era, the U.S. tax rates are lower. Thus, over the period, the marginal interest income tax rate averaged 14

15 τ r = while the marginal dividend tax rate averaged τ D = We calibrate the real interest rate r to the average of the monthly annualized t-bill rate deflated by the consumer price index. High inflation characterized much of the period from 1971 to As a result, the real interest rate was quite low, at r = %. As for the later period of 1995 to 2006, the real interest rate was higher, at r = %. For the interest rate earned on cash holdings ι, we disentangle how much cash and short-term investments (CHE) firms held in short-term investments (IVST) rather than in cash (CH). In , firms held only percent of their cash in short-term investments. Given an average inflation rate of 7.93%, we calibrate ι = r +( )( ) = 5.32%. In , firms held even less of their cash savings in short-term investments but the inflation rate was much lower at 2.60%, so that ι = r + ( )( ) = 1.94%. The calibrated value of ι is an important aspect of the model, explicitly recognizing that cash is dominated in return. 3.2 Parameters Estimated by Matching Moments The last set of parameters cannot be estimated in isolation directly from the data. Instead, we match moments to ensure that the simulated series from the model replicate important features of the data. These parameters include the depreciation rate δ, the capital adjustment cost ω K, the constant debt level B, the debt adjustment cost ω B, the average expense level F, the standard deviation of expenses σ F, and the coefficient of absolute prudence φ. The important features of the data relate to selected moments of capital, debt, and cash policies. To match moments, we use the simulated method of moments. The estimate of the vector of parameters θ is the solution to min θ [ H (x) 1 [ S H s (θ)] W H (x) 1 ] S H s (θ) S S s=1 s=1 (27) where H (x) is an m-vector of moments computed on the actual data matrix x, H s (θ) is an m-vector of moments computed on the simulated data for panel s, and W is a positive definite weighting matrix. In practice, we simulate S = 5 panels with about the same number of firm-year observations as in the data. The appendix describes in more details the method we use. 15

16 In spirit, our strategy targets a particular moment for each parameter. In practice, a change to one parameter affects all simulated moments. For the depreciation rate δ and the adjustment cost parameter ω K, we target two moments of the capital policy. Our estimate of δ ensures that the average investment simulated from the model matches the average investment found in the data. Investment is measured in the data as capital expenditures (CAPX) over total assets. In terms of the data simulated from the model, standardizing investment I t by total assets corresponds to standardizing by the sum of equity and debt values A t = V t + (1 + (1 τ i )r)b t B t+1. For both COMPUSTAT and simulated data, we compute the mean investment for each firm and report the average of the firm means. Our estimate of the capital adjustment cost ω K ensures that the simulated standard deviation of investment I t /A t normalized by the standard deviation of revenues Y t /A t matches that of the data. We normalize by the standard deviation of revenues so that the capital adjustment cost ω K can target the volatility of investment in reference to the volatility of the revenue shock σ z. For the constant debt level B and the adjustment cost parameter ω B, we target two moments of the debt policy. Our estimate of B ensures that the simulated average leverage B t /A t matches that of COMPUSTAT firms. Leverage is measured by the sum of long-term debt (DLTT) and debt in current liabilities (DLC), divided by total assets. Similarly to ω K, our estimate of ω B ensures that the simulated standard deviation of debt relative to the standard deviation of revenues matches that of the actual data. Because adjustment costs are more relevant to long-term debt than to shortterm debt, and because changes in debt are often related to changes in collateral, we focus on the standard deviation of long-term debt-to-capital stock. This standard deviation is then normalized by the standard deviation of revenues-to-capital stock. For the average expense level F, the standard deviation of expenses σf, and the convexity parameter φ, we target the following moments. Our estimate of F ensures that the average operating income-to-total assets ratio OI t /A t matches the data, where operating income OI t Y t F t is measured before depreciation (OIBDP). Our estimate of σ F ensures that the standard deviation of net income-to-total assets NI t /A t matches the data, where net income is measured as NI t = 16

17 (1 τ C )(Y t F t δk t rb t + ιm t ). We target net income because we want to allow for expenses similar to extraordinary items: expenses that may not be part of the regular operations of the firm but that can affect the firm s financial health. Finally, the convexity parameter φ is the coefficient of absolute prudence and, as such, it dictates the strength of the firm s prudence motive. In the first time period from 1971 to 1982, we estimate φ to ensure that the average cash holdings-to-total assets M t /A t matches the data. Cash holdings are measured by cash and short-term investments (CHE). As measuring the relative strengths of the precautionary motives is the central question of the paper, we are interested in predicting average cash holdings during the period without changing the coefficient of prudence from its parameter value. The model is solved numerically under the two sets of parameters using a finite element method. The appendix provides details on the numerical method. The resulting policy functions for capital K t+1, debt B t+1, cash M t+1, and the equity value V t of equation (13) are simulated from random outcomes of the revenue shock innovation ɛ t and the expense shock f t. These simulated series serve to build other series including dividends D t, operating income OI t, net income NI t, and the total firm value A t. Using these policies for each of the subperiod calibrations, we construct 5 panels that have roughly the same number of firm-year observations as observed in the COMPUSTAT panel. 4 Results 4.1 Moment Matching Results Tables 2 and 3 present the results of the moment matching exercise. Table 2 shows the parameter values and the target moments for the period covering 1971 to 1982, while Table 3 does so for the period covering 1995 to In the data, the average investment-to-total assets is 8.60 percent in the first time period and 6.23 percent in the second time period. To hit these moments, we estimate a depreciation rate of δ = in the first time period and δ = in the second time period. The lower capital investment I t /A t of in recent years results mostly from the lower share of capital α. As an 17

18 illustration, the deterministic steady state of the capital stock in the model is ( K = Γ(1 τ C )βα 1 β(1 (1 τ C )δ) ) 1 1 α. (28) Using our calibrations, K shrinks from for the period to for the period. The lower steady state level of capital K corresponds to lower capital investments I. In COMPUSTAT data, investment has an average standard deviation of percent of the average standard deviation of revenues during the years and a relative average standard deviation of percent during the years. To replicate these moments, we estimate the capital adjustment cost to ω K = in the first time period and to ω K = in the second time period. The capital adjustment cost estimates are of magnitudes similar to those estimated by Cooper and Haltiwanger (2006). All else equal, the lower capital adjustment cost in recent years stimulates the volatility of investments I t /A t. This higher volatility, however, is overwhelmed by the higher volatility of revenues Y t /A t. This denominator effect explains why the lower capital adjustment cost parameter ( < ) replicates the lower ratio of standard deviation of investment to the standard deviation of revenues (12.47% < 18.13%) in recent years. The average leverage B t /A t of COMPUSTAT firms has been fairly constant over time: during the period and during the period. To replicate this fairly constant leverage through time, we estimate B = in the first time period and B = in the last time period. The large difference in B arises because of the dramatic reduction in the capital share α. As discussed above, a smaller capital share α generates a smaller capital stock K t. In the model, the lower capital stock translates into a smaller firm A t and a corresponding lower debt level B t. To maintain a similar leverage ratio over time, B must be significantly lower in the last time period. In COMPUSTAT data, long-term debt-to-capital stock has an average standard deviation of percent of the average standard deviation of revenues-to-capital stock during the years and a relative average standard deviation of percent during the years. To replicate these moments, we estimate the debt adjustment cost to ω B = in the first time period and to ω B = in the last time period. 18

19 During the period, operating income was percent of total assets in COMPU- STAT data. An average expense level of F = delivers this moment in the model. During the period, operating income was on average slightly negative, at 3.02 percent of total assets, and a higher average expense of F = delivers that negative moment in the model. In the data, the standard deviation of net income-to-total assets has greatly increased over time: from during the years to during the years. Parameter values for σ F of and are required to replicate these moments in and respectively. Note that, for these values, the liquidity constraint threshold (1 τ C )σ F falls over time from to However, given the important reduction in the capital share α and therefore in firm size, the constraint threshold of represents a significantly higher proportional hurdle than before. Finally, the average of COMPUSTAT firms cash holdings-to-total assets M t /A t was 9.69 percent during the years. This requires a small convexity parameter value of φ = Note that this value is smaller than the values ranging from 0.73 to 0.83 estimated in Hennessy and Whited (2007). In that sense, our explanation for cash holdings does not rely on a large coefficient of prudence. Figure 2 plots the marginal net payout function U (D t ) = 1 τ D + τ D exp( φd t ) for the calibrations of both periods. The figure suggests that the marginal net payout function is near linear at the equilibrium payouts, but that the function exhibits overall convexity. 4.2 Do the Simulated Dividend, Investment, and Debt Policies Behave as in the Data? Before studying cash holdings in detail, we wish to verify that the model provides a reasonable description of firms overall behavior. It has long been recognized that firms smooth dividends (e.g., Lintner 1956). We verify whether firms simulated from our model smooth payouts. Among the moments presented at the bottom of Tables 2 and 3, we show the standard deviation of equity payouts-to-total assets. In COMPUSTAT data, dividend policies are smooth. The standard deviation of payouts is only 4.67 percent during the 1971 to 1982 period and rises to percent during the 1995 to 2006 period. In the model, 19

20 the standard deviation is only 4.55 percent for the first period calibration and rises to percent for the second period calibration. As in the data, the model suggests that payout policies have become more volatile. In the model, firms smooth payouts because the firm s objective function is concave. Specifically, the net payout function U(D t ) describes firms as risk averse. To avoid large convex equity issuing costs or large convex taxes on payouts, firms employ many instruments to smooth payouts. Table 4 describes the particular smoothing behavior at play in the model. For the first period calibration, firms smooth payouts by using the higher revenues to invest more, retire debt, and accumulate cash. For the second period calibration, firms smooth payouts by using the higher revenues to invest more and retire debt. Interestingly, cash holdings do not do much to smooth payouts in the second period. Unsurprisingly, investment is procyclical in both COMPUSTAT data and in the model. Debt levels and debt issues, however, are countercyclical in both COMPUSTAT data and the model. The countercyclicality of debt in the model is surprising because standard dynamic capital structure models with a tax benefit of debt but no risk aversion generate procyclical debt. In persistent good times, firms take on more debt to benefit from the tax advantage because their abilities to repay the debt is solid. In our model with risk aversion generated by convex equity issuing costs and taxes, firms choose to smooth the effect of revenue shocks on payouts using (countercyclical) debt policies. The last two moments of Tables 2 and 3 document this countercyclicality. In COMPUSTAT data, the correlation between the debt level and revenues is for the 1971 to 1982 period and for the 1995 to 2006 period. In the model, the corresponding correlations are and Both in the data and in the model, the debt level is countercyclical, although the negative correlation attenuates in the recent time period. A similar pattern is observed for the correlation between changes in debt levels and revenues. The COMPUSTAT data correlation between debt issues and revenues is for the 1971 to 1982 period and for the 1995 to 2006 period. In the model, the correlations are and 20

21 Do the Simulated Cash Policies Behave as in the Data? We begin the analysis of cash holdings by investigating whether the model provides a reasonable overall description of cash holdings. The results appear in Table 5. In COMPUSTAT data, cash holdings as a fraction of total assets is 9.69 percent in the period, and that fraction dramatically rises to percent in the period. In the model, the mean ratio of cash holdings-to-total assets is specifically targeted by our calibration using the convexity parameter φ. With the same calibrated value of the convexity parameter, the model predicts cash holdings of percent of total assets in the second period. It is remarkable that the model generates cash holdings (17.24 percent) in the second period that are so close to those observed in the data (17.36 percent). Cash policies are relatively smooth in COMPUSTAT data. The standard deviation of cash-tototal assets is only 5.20 percent during the 1971 to 1982 period and rises to 7.91 percent during the 1995 to 2006 period. In the model, the standard deviation is 7.31 percent in the first period calibration and rises to percent in the second period calibration. As in the data, the model predicts that cash policies have become more volatile, although we note that the model overstates the increase in volatility. Table 5 also reports that, in COMPUSTAT data as in the model, cash holdings and cash flows (measured as net income minus dividends) are positively correlated. Also in COMPUSTAT data as in the model, cash holdings are procyclical. 4.4 Which Motive Explains the Increase in Cash Holdings? We investigate the relative strengths of the two precautionary cash motives: the liquidity constraint motive related to (15) and the prudence motive related to the curvature of the marginal net payout function (2). Figure 3 displays the cash policy M t+1 /A t of a firm facing typical realizations of the shocks. As expected, the figure suggests that cash holdings are on average higher and much more volatile 21

22 in the second period. This is consistent with the means and standard deviations of the simulated data presented in Table 5. Figure 4 displays the frequency distribution of firm-year cash-to-total assets observations in the data for both periods. The figure shows that the fraction of firm-year observations with very small cash holdings has increased in the second period, and that the fraction of firm-year observations with very large cash holdings has also increased. This is consistent with the COMPUSTAT means and standard deviations presented in Table 5. Figure 5 graphs the cash saving decision S t /Āt of a firm facing the same realizations of shocks as in Figure 3. We scale the cash saving decision S t by the average total assets Āt, so as to focus on the variations in cash savings S t while maintaining a scale similar to M t+1 /A t in Figure 3. In the first period, firms do not save as much as in the second period. Cash savings in the first period have a clear lower bound, but firms often choose to hold cash above the threshold. This lower threshold corresponds to the lowest cash savings required to meet the liquidity constraint. That is, when cash saving is at the lower threshold, firms hold cash only as a precaution against year-end expense shocks. When cash saving is above the threshold, firms hold cash also as a precaution against future revenue shocks. In the second period, firms save more than in the first period. Firms, however, always decide to save an amount equal to the second period liquidity constraint threshold. That is, firms hold cash only as a precaution against expense shocks. Explicitly, the term S t /Āt becomes equal to (1 τ C )σ F /Āt in the second period. In the period, our model suggests that firms no longer act prudently. Only the liquidity constraint motive explains the cash saving behavior. Despite the fact that one precautionary cash motive is turned off in the recent past, the liquidity constraint can effectively explain the observed cash holdings which represent percent of total assets. Figure 6 plots the multiplier λ t that results from the same realizations of shocks. Figure 6 provides another view into the mechanism that generates the cash saving decision graphed in Figure 5. Recall that λ t = 0 is necessary for the prudence motive to become active. The figure 22

23 shows that the multiplier is more volatile in the first period than in the second period. The figure also shows that λ t sometimes touches zero in the first period, but never does in the second period. In what follows, we investigate the mechanism by which the prudence motive vanishes in the second period. To do so, we perform a sensitivity analysis starting from the first period calibration of the model. In turn, we reset each parameter to its second period calibrated value leaving all other parameters to their first period values. The sensitivity analysis, presented in Table 6, focuses on three different groups of parameters influencing the prudence motive. We discuss the likely suspects explaining why firms no longer hold cash for prudence Cash Parameters Proposition 2 suggests that the coefficient of absolute prudence φ and the impatience regarding cash holdings βr M are important factors in understanding the prudence motive. The coefficient of absolute prudence φ controls the convexity of the marginal net payout function. Because the coefficient remains constant over the two periods, it cannot explain the change in the relative strength of the prudence motive. The impatience factor βr M grows from in the first period to during the second period. Because firms become less impatient, it should be easier for the cash Euler equation (18) to hold with λ t = 0. The prudence motive should become more active Debt Parameters Proposition 3 suggests that debt decisions affect cash holdings via two terms. The first term, (1 τ C )(r ι), describes the extent to which cash is dominated in return by debt. In the data, the extent to which cash is dominated in return declines between the two period: (1 τ C )(r ι) decreases from 3.11 percent in the first period to 2.31 percent in the second period. All else equal, this should make the prudence motive more active. Proposition 3 also suggests that debt adjustment costs play an important role in understanding the prudence motive. The sensitivity analysis reveals that these factors play only minor roles. For example, Table 6 shows that the very small changes in ω B has no noticeable effect on cash holdings. 23

24 As for the debt level B, it is set to keep leverage constant over time. With a near constant leverage, there is little effect on cash holdings Capital Parameters Proposition 4 suggests that capital decisions affect cash holdings via two terms. The first term, [ ] E1t Rt+1 k R M, describes the extent to which cash is dominated in return by capital. The ) second term, Cov 1t (m t+1, Rt+1 k / E1t [m t+1 ], represents covariance risk. We numerically compute these conditional moments. The fluctuations in λ t reported in Figure 6 are almost entirely [ ] matched by fluctuations in the first term, E1t Rt+1 k R M, as fluctuations in the second term, ) Cov 1t (m t+1, Rt+1 k / E1t [m t+1 ], are small. The covariance varies between and In the first period, the extent by which cash is dominated in return fluctuates wildly. For some realizations, cash is dominated only slightly by expected returns on capital such that λ t = 0 and the firm saves as a precaution against future shocks. In the second period, the extent by which cash is dominated in return fluctuates much less, and cash is always dominated by a large margin. The return to capital Rt+1 k depends on several parameters. Some of these parameters have little impact on cash holdings, while other parameters would justify more prudence. The depreciation rate δ, the capital adjustment costs ω K, and the persistence ρ z barely affect cash holdings. The rise in the variance σ 2 z increases risk and therefore amplifies the need for precautionary cash holdings via the prudence motive. As for the increase in the scale parameter Γ, it raises the level of the capital stock. The larger scale magnifies the effects of the multiplicative revenue shocks, and therefore raises the need for precautionary cash holdings via the prudence motive. Interestingly, the reduction in the capital share α has a large impact on cash holdings. In fact, the reduction in the capital share from to is entirely responsible for the disappearance of the prudence motive. It is the only parameter change that generates no prudent cash savings in the second period. Figure 7 supplements the cash saving decision S t /Āt of Figure 5 with two additional parameterizations. One additional parameterization uses the first period calibration but sets the capital share to its second period value of α = The other uses the second period calibration but sets the 24