Online Appendix: Corporate Cash Holdings and Credit Line Usage

Transcription

1 Online Appendix: Corporate Cash Holdings and Credit Line Usage 1 Introduction This is an online appendix to accompany the paper titled Corporate Cash Holdings and Credit Line Usage. 2 The Benchmark Model 2.1 The Model At the beginning of the year, the firm chooses D t, K t+1, B t+1, and S t knowing an information set Φ t that includes all state variables (K t, B t, L t, and M t ) and the current realization of z t, but not f t. During the year, the firm chooses the allocation of S t between M t+1 and L t+1 knowing an information set Φ t + that includes all the information included in Φ t, plus all the new relevant states (K t+1, B t+1, and S t ) as well as the realization of f t. Given the firm s choice of cash savings S t, the firm s mid-year problem consists of choosing the allocation between cash holdings and credit line. Of course, if z t < z, the firm looses access to the credit line. In this circumstance, the solution is L t+1 = 0 and M t+1 = S t + (1 τ C )f t. If z t z, the firm solves subject to W (K t+1, B t+1, S t ; z t, f t ) = max β E t + [V (K t+1, B t+1, L t+1, M t+1 ; z t+1, f t )] (1) {M t+1,l t+1 } M t+1 L t+1 = S t (1 τ C )f t (2) M t+1 0 (3) L t+1 0 (4) L t+1 L, (5) where the E t + denotes that the expectation is taking conditional on the information set Φ t +. The solution must satisfy the following first-order conditions: ζ t + γ M t + = β E t + [V M (K t+1, B t+1, L t+1, M t+1 ; z t+1, f t )] (6) 1

2 ζ t + + γt L γ U + t = β + E t + [V L (K t+1, B t+1, L t+1, M t+1 ; z t+1, f t )] (7) γt M 0, + M t+1 0, γt M M + t+1 = 0 (8) γt L 0, + L t+1 0, γt L L + t+1 = 0 (9) γt U 0, + L Lt+1 0, γt U ( L L + t+1 ) = 0, (10) where ζ t + is the multiplier associated with constraint (2), γt M is associated with (3), γ L + t with (4), + and γt U with (5). + At the optimum, we have W K (K t+1, B t+1, S t ; z t, f t ) = β E t + [V K (K t+1, B t+1, L t+1, M t+1 ; z t+1, f t )] (11) W B (K t+1, B t+1, S t ; z t, f t ) = β E t + [V B (K t+1, B t+1, L t+1, M t+1 ; z t+1, f t )] (12) At the beginning of the year, the firm s problem is subject to V (K t, B t, M t ; z t, f t 1 ) = W S (K t+1, B t+1, S t ; z t, f t ) = ζ t +. (13) max U(D t) + Et [W (K t+1, B t+1, S t ; z t, f t )] (14) {D t,k t+1,b t+1,s t} S t = (1 τ C ) ( Y t + F δk t rb t ξl t + ιm t ) Kt+1 + B t+1 L t +M t Ω K t Ω B t D t (15) Y t = exp(z t )K α t (16) S t + L1(z t z) (1 τ C )σ f 0 (17) Ω K t = ω ( ) 2 K It δ K t 2 K t (18) Ω B t = ω B ( Bt (19) where Et denotes that the expectation is taking conditional on the information set Φ t, and is the first difference operator. The first-order conditions of this problem are η t = U (D t ) (20) η t λ t = Et [W S (K t+1, B t+1, S t ; z t, f t )] (21) [ ( )] Kt+1 η t 1 + ω K 1 = Et [W K (K t+1, B t+1, S t ; z t, f t )] (22) K t η t [ 1 ωb (B t+1 B) ] = Et [W B (K t+1, B t+1, S t ; z t, f t )] (23) 2

3 λ t 0, S t + L1(z t z) (1 τ C )σ f 0, λ t [ St + L1(z t z) (1 τ C )σ f ] = 0, (24) where η t is the multiplier associated with constraint (15), λ t is associated with (17), and { [ V K (K t, B t, L t, M t ; z t, f t 1 ) = η t 1 + (1 τ C )(α exp(z t )K (α 1) t δ) + ω (Kt+1 ) 2 K 1]} 2 K t (25) V B (K t, B t, L t, M t ; z t, f t 1 ) = η t (1 + (1 τ C )r) (26) V L (K t, B t, L t, M t ; z t, f t 1 ) = η t (1 + (1 τ C )ξ) (27) V M (K t, B t, L t, M t ; z t, f t 1 ) = η t (1 + (1 τ C )ι). (28) We can write the Euler equations that describe the different decisions as U (D t ) λ t = βr M [ Et U (D t+1 ) ] [ ] + Et γ M t + U (D t ) λ t = βr L [ Et U (D t+1 ) ] [ Et γ L t + γt U ] + (29) (30) U (D t ) = βr B t [ Et U (D t+1 ) ] (31) where R M = 1 + (1 τ C )ι, R L = 1 + (1 τ C )ξ, Rt B [ ] Rt+1 (1 K = + (1 τ C ) α exp(z t+1 )K (α 1) t+1 δ Equations (29), (31), and (32) can be rewritten as U [ (D t ) = β Et R K t+1 U (D t+1 ) ], (32) = [1 + (1 τ C )r] / [ ( 1 ω B Bt+1 B )], and [ ( )] 1 + ω Kt+1 K K t 1. + ω K 2 [ ( Kt+2 K t+1 ) 2 1 ]) / Et [m t+1 ] R M = 1 { [ ] } Et γ M t + + λt /U (D t ) (33) Rt B Et [m t+1 ] Rt B = 1 (34) [ Et mt+1 Rt+1 K ] = 1, (35) where m t+1 = βu (D t+1 )/U [ (D t ) and Et mt+1 Rt+1 K ] [ ] [ ] = Et [m t+1 ] Et R K t+1 + Covt R K t+1, m t Data The data comes from the North American COMPUSTAT file and covers the period from 1971 to 2006 excluding the crisis period. To explain the large change in cash holdings, the data is split in 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). Our measure of cash holdings is COMPUSTAT Mnemonic CHE, and it is composed 3

4 of cash (CH) and short-term investments (IVST). 1 The sample includes firms from all industries with at least five years of consecutive data, excluding utilities and financials. The data is winsorized to limit the influence of outliers at the 1 percent and 99 percent tails. The final sample contains 2,093 firms for the period and 4,526 firms for the period. For the numerical analysis, several parameters are set to values chosen to ensure that simulated series from the model replicate important features of the data. The target moments are presented in Tables 3 and 4 of the paper. Table A.1 Targeted Moments Moments Mean(I/A) SD(I/A)/SD(Y/A) Mean(B /A) SD(B /K )/SD(Y/K ) Mean(OI/A) SD(N I/A) Mean(M /A) We have examined the effects of filtering out certain firms. First, we have examined the effects of excluding firms with zero (or very low) tax rates. Following the work of John Graham, we have supplemented our database with the marginal tax rate estimates provided in COMPUSTAT. We identify firm-year observations with very low tax rates as those with a marginal tax rate less than 5%. This represents 8.51% of firm-year observations. In the data as in the simulated model, we expect firms experiencing losses in a certain year to have an effective zero marginal tax rate that year, and these firm-year observations should not be excluded from the data as they are at the center of the motivation for holding cash liquidities. Indeed, firms that anticipate losses in the 1 The cash (CH) item includes: bank and finance company receivables; bank drafts; bankers acceptances; cash on hand; certificates of deposit included in cash by the company; checks; demand certificates of deposit; demand deposits; letters of credit; and money orders. The short-term investments (IVST) item includes accrued interest included with short-term investments by the company; cash in escrow; cash segregated under federal and other regulations; certificates of deposit included in short-term investments by the company; certificates of deposit reported as separate item in current assets; commercial paper; gas transmission companies special deposits; good faith and clearing house deposits for brokerage firms; government and other marketable securities (including stocks and bonds) listed as short term; margin deposits on commodity futures contracts; marketable securities; money market fund; real estate investment trusts shares of beneficial interest; repurchase agreements (when shown as a current asset); restricted cash (when shown as a current asset); time deposits and time certificates of deposit, savings accounts when shows as a current asset; treasury bills listed as short term. 4

5 model save more at the beginning of the year. Therefore, we consider excluding only firms with permanently low tax rates, i.e., firms with very low (< 5%) tax rates for every year within a given sub-sample. As it turns out, the exclusion of those permanently low tax rate firms does not lead to significantly different moments calculated from the data. This can be seen in the first two columns of moments in the table below, where we present the results for the last sub-period ( ). 2 The first column shows all firms for which there is tax information and exclude the permanently low tax rate firms. The second column shows all firms for which there is tax information. Evidently, the moments from the first two columns are very similar. Requiring data on marginal tax rates, however, reduces the sample considerably: we are able to obtain marginal tax rates for only 70.7% of firms in our sample. This data restriction leads to different moments, as can be seen by comparing either of the first two columns to the last one. Therefore, we chose not to filter out firms with very low tax rates or those with no information on their marginal tax rates. Table A.2 Low Tax Rate Firms: Excluding All Firms with Moments Low Tax Firms Tax Info. All Firms Mean(I/A) SD(I/A)/SD(Y/A) Mean(B /A) SD(B /K )/SD(Y/K ) Mean(OI/A) SD(N I/A) Mean(M /A) We also examine the effects of excluding low tangibility firms. We identify firm-year observations with very low tangibility as those with a ratio of Net Property, Plant and Equipment to Total Assets less than 5%. The overall median for firm-year observations is 24.8%. Firms with very low tangibility represent 12.05% of firm-year observations. Similarly as above for the marginal tax rates, for a firm to be entirely excluded from the sample in any given sub-period, the firm needs to have a tangibility ratio below 5% for all years within a sub-period. In the data as in the 2 The marginal tax rates are available in COMPUSTAT starting in 1980, and therefore the period cannot be examined. 5

6 simulated model, we expect firms experiencing low revenue shocks in a certain year to invest less, endogenously leading to lower tangibility. These firm-year observations should not be excluded from the data as the model predicts that such firms would have accumulated more cash holdings at the beginning of the year. Therefore, we consider excluding only firms with permanently low tangibility (< 5%) within a given sub-sample. As shown in the table below, the exclusion of those permanently low tangibility firms does not make a difference for the early period ( ): similar moments are calculated from the data, when excluding permanently low tangibility firms compared to including all firms. For the later period ( ), however, a difference in the standard deviation of the long-term debt arises. Firms with more tangible assets experience less volatility in their debt choices. The average leverage remains very similar, so does investment, average operating income, net income volatility and cash holdings. Only the volatility of their debt policy changes significantly. Table A.3 Low Tangibility Firms Moments No Low Tang. All Firms No Low Tang. All Firms Mean(I/A) SD(I/A)/SD(Y/A) Mean(B /A) SD(B /K )/SD(Y/K ) Mean(OI/A) SD(N I/A) Mean(M /A) Although the data above shows that a change in tangibility (from the whole sample to the restricted sample excluding very low tangibility firms) is linked to a change in our measure of debt volatility (23% versus 20.4%), it is not linked to a significant change in cash holdings: 20.6% versus 20.3% of total assets. The measure of debt volatility does not seem central to explaining why cash holdings have increased so much over time. 2.3 What Does Liquidity Look Like? To gain some intuition about the model, Figures A.1 and A.2 show different aspects of the liquidity decisions. The figures are constructed by drawing one series of TFP shock innovations (ɛ zt ) and 6

7 one series of mid-year shock innovations (ɛ ft ). The same series of innovations are used to describe firm behavior in both periods. The figures illustrate how a firm may allocate liquidity optimally over time in response to a particular string of shocks in an economic environment describing the and periods. Figure A.1 illustrates how beginning-of-the-year cash savings S t generate cash holdings. The figure graphs the cash saving decision scaled by mean total assets S t /Ā. Standardizing each observation by the overall mean of total assets Ā rather than standardizing each observation by its corresponding total assets A t focuses attention on the variations in cash savings S t while maintaining the appropriate scale. With the calibration of L and z discussed in the paper, the liquidity constraint (17) reduces to S t 0 when the firm can count on the credit line (z t z) and S t (1 τ C )σ f when the firm looses access to the credit line (i.e., when z t < z). The threshold, standardized by mean total assets, is 4.3 percent of total assets for the calibration and 17.8 percent for The figure shows that the firm saves strictly positive amount even when TFP shocks are high and often saves more than the threshold when TFP shocks are low. Figure A.2 shows that the model-simulated cash holdings are on average higher and more volatile for the calibration. 0.3 Figure A.1: Cash Savings S/Mean(A) Calibration Calibration

8 0.5 Figure A.2: Cash Holdings M'/A of Simulated Firms Calibration Calibration What Drives Liquidity: A Detailed Sensitivity Analysis Table A.4 presents the results of a sensitivity analysis, which proceeds on the basis of the first period parametrization. In turn each parameter is reset from its value to its value, leaving all other parameters to their values. Table A.4 Sensitivity Analysis The simulated moments are computed using 5 simulated panels of 4,526 firms over 10 years. For each parameter, we report the cash holdings and credit line usage obtained from changing the first period parameter value to its second period value, holding all other parameters constant. 8

9 Predicted Moments Mean(M /A) Mean(L + /A) Benchmark Calibration Liquidity Policy Parameters interest rate on cash (%) ι interest rate on debt (%) r interest rate on credit line (%) ξ corporate tax rate τ C interest income tax rate τ r dividend tax rate τ D mid-year shock average F / Ā mid-year shock volatility σ f /Ā Debt Policy Parameters debt adjustment cost ω B debt target B/ Ā Capital Policy Parameters depreciation rate δ capital adjustment cost ω K capital intensity α TFP persistence ρ z TFP volatility σ z The sensitivity analysis focuses on three groups of parameters: liquidity, debt, and capital parameters Liquidity Parameters It seems natural to investigate first the liquidity policy parameters embedded in the constraint, S t (1 τ C )σ f L1 (zt z). The firm s cash saving decision depends directly on the volatility of the mid-year shock σ f and the corporate tax rate τ C. Over the two periods, the shock volatility (standardized by mean total assets) grows from to 0.273, while the corporate tax rate decreases from to The associated increase in the cash-saving constraint forces the firm to save more cash to meet its current liquidity needs. Accordingly, Table A.4 shows that, by changing only the mid-year shock volatility σ f /Ā to its last period value, the calibration otherwise based on the first period increases its predicted cash holdings from 7.9 percent of total assets to 17.7 percent. Changing only the mid-year shock volatility also increases the credit line usage from 0.9 percent to 6.9 percent, in part because its upper limit L = (1 τ C )σ f also increases. Table A.4 shows that 9

10 the reduction in the corporate tax rate increases cash holdings and credit line usage, but to a far lesser extent. The large change in average mid-year shock F /Ā barely affects cash and credit. This is noteworthy as the change of average operating income calculated from COMPUSTAT data is very large, from 15.5 percent of total assets during the period to essentially zero (0.6 percent) during the period. When changing the mean of the mid-year shock to match the nearly zero operating income in the data for the period, cash holdings increase only slightly from 7.9 percent to 8.1 percent of total assets. Euler Equation (29) suggests that the coefficient of absolute prudence φ and the impatience regarding cash holdings βr M are important factors in determining the cash saving decision. The coefficient of absolute prudence φ controls the convexity of the marginal net payout function U (D). Because the coefficient remains constant over the two periods, it obviously cannot explain the increase in cash holdings and credit line usage. As for the impatience factor βr M, it grows from in the first period to during the last period. Because firms become more patient, the firm should be more willing to accumulate precautionary savings. Table A.4 shows that the large increase in volatility σ f /Ā is not the only driver of the dramatic increase in cash holdings. Another important driver is the interest rate on cash holdings ι. The return to holding cash increases dramatically from a real rate of during the high inflation years of to in the period. All else equal, the increase in ι alone would spur an otherwise similar firm to hold 25.1 percent of its assets in cash in the period, overshooting the observed average cash holdings of 21.8 percent. With such large cash liquidities, the firm would substitute entirely away from the credit line. Armenter and Hnatkovska (2011) attribute an important role to the dividend tax τ D. In their paper, a reduction of the dividend tax rate makes it easier for firms to raise funds by issuing equity. Firms trade off the current cost of issuing equity against the future benefit of building net worth and insuring against future low cash flow realizations. A reduction in the cost of issuing equity allows the firm to issue more equity and build up its net worth. In our model, a reduction of the dividend tax rate has an additional effect. A reduction of τ D reduces the cost of issuing equity (when payouts are negative), but it also reduces risk aversion. The tax reduction in our model reduces the incentive for firms to smooth dividends, as the tax rate cost of large payouts (dividends) over small payouts (repurchases) is reduced. Because volatile distributions become less costly to the firm, the firm is less inclined to hold cash to smooth payouts. 10

11 When the interest rate on the credit line ξ increases from percent to percent, the credit line usage naturally decreases and the firm substitute their liquidities to more cash holdings. Disentangling the effect of the discount factor β = 1/(1 + (1 τ r )r), Table A.4 shows that the increase in the interest rate r and the decrease in the interest income tax rate τ r should reduce cash holdings and the credit line usage, but interestingly they do not. A more detailed analysis reveals that the increase in the interest rate r reduces cash holdings and credit line usage, but it also reduces total assets, such that the cash holdings-to-total asset ratio increases. Total assets decrease because they are valued at a higher discount rate r Debt Parameters The firm s liquidity decisions may be affected by its debt decisions through the interdependence of the Euler Equations (29) and (31). In Equation (31), the term ω B (B t+1 B) is related to debt costs. Table A.4 shows that cash holdings are not significantly affected by changes in the debt cost parameter ω B and target leverage B/Ā. Because debt is relatively stable over time, frictions on debt financing does not seem to propagate significantly to the firm s liquidity decisions Capital Parameters In Equation (35), we see that capital decisions are affected by two terms: the expected return, [ ] [ ] R K t+1, and the covariance risk, Covt R K t+1, m t+1. An analysis of the conditional moments Et reveals that the second term is negligible: the covariance varies between and In the first period, the conditional expected return fluctuates wildly. For some realizations, the expected return on capital is so low that it is close to the return on cash. In this case, λ t = 0 and the firm may save in a precautionary manner. In the last period, the conditional expected return to capital fluctuates much less, and it often dominates cash by a large margin so that the firm often saves only the minimum required by the constraint. [ ] The effects of parameter changes on the conditional average net return to capital Et R K t+1 are difficult to study analytically because they cause an endogenous investment reaction. To gain some insight, we examine the deterministic steady state value of the net return to capital. Equation (35) reduces to βr K = 1 so that R K = 1/β = 1+(1 τ r )r. The deterministic net return to capital has increased from in the first period calibration to in the last period calibration, and all else equal this is consistent with a smaller firm size. However, the extent to which capital dominates cash in steady state return R K R M has fallen from in the first period to in the last period. 11

12 [ ] Turning to the stochastic behavior of Et R K t+1, we see that the increase in the standard deviation of the TFP shock innovation σ z, from in the first period calibration to in the last period calibration, stimulates cash holdings above the minimum threshold and substitutes the credit line away. Interestingly, the reduction in the capital intensity α reduces cash holding and, as a complement, raises credit line usage to 4.3 percent. Finally, the reductions in the depreciation rate δ slightly raises cash holdings, but the adjustment costs to capital ω K does not significantly affect liquidities. 3 Robustness and Extensions 3.1 The Middle Period The first robustness exercise estimates our model on data from the middle period of Table A.5 documents that the middle period characterizes the progressive change in firm policies very well, as the average moments calculated from the data in lie within the moments for the period and the moments from the period. Based on the moments from the period, we have estimated the model parameters as we did in Tables 2 to 4 for the other two time periods. Importantly, we held constant the absolute prudence parameter to the level estimated in the first period φ = Holding constant this parameter allows us to predict what the cash holdings would have been in assuming firms kept the same preference for prudence as in The model predicts average simulated cash holdings of 13.8% of total assets for the middle period, while the observed cash holdings in the data during the same period are 13.9%. Cash holdings are virtually the same, which suggests that firms in had similar prudence behavior as in the period. For the period, we conclude that (1) the parameter estimates provide a good match between the simulated and observed moments, (2) the middle period is a good representation of the progressive change in firm policies, and (3) the simulated cash holdings match the observed cash holdings, holding prudence constant. The values of the parameters that are calibrated outside of the structural model are as follows. The revenue parameters are calibrated to α = 0.584, ρ z = 0.459, and σ z = The tax rates are τ C = 0.387, τ r = 0.234, and τ D = Finally, the interest rates are r = 0.029, ι = 0.014, and ξ =

13 Table A.5 Matching Moments for the Period The observed moments are computed using a sample of North American data from COMPUSTAT for the sample period 1983 to The simulated moments are computed using 5 simulated panels of 3,161 firms over 10 years. I denotes investment, A total assets, Y revenues, B debt level, K capital stock, OI operating income, NI net income, M cash holdings, L + credit line used, D dividends, B debt issues, and primed variables refer to time t + 1 values rather than time t values. The model is solved using a finite-element method. The parameters are estimated using a just identified system of moment matching. Panel A: Targeted Moments across all Periods Targeted Moments Mean(I/A) SD(I/A)/SD(Y/A) Mean(B /A) SD(B /K )/SD(Y/K ) Mean(OI/A) SD(N I/A) Mean(M /A) Panel B: Matching Moments for the Period Parameters Values Targeted Moments Calibrated δ Mean(I/A) ω K SD(I/A)/SD(Y/A) B/Ā Mean(B /A) ω B SD(B /K )/SD(Y/K ) F /Ā Mean(OI/A) σ f /Ā SD(NI/A) Other Moments Simulated Observed Mean(M /A) Mean(L + /A) n.a. 3.2 Book Market Value As is current practice, we standardize moments by Total Assets. Bates, Kahle, and Stulz (2009) standardize cash holdings by Total Assets, precisely to show that the increase in cash outweighs possible confounding factors in other asset categories. In considering the closest measure of Total Assets in the model, we do not abstract from all other influences than capital and cash. Our 13

14 approach instead compares moments standardized by accounting values for Total Liabilities and Owner s Equity (i.e., Total Assets) in COMPUSTAT to moments standardized by the sum of debt and equity values generated from the model. For robustness, we verify that our results obtain with a standardization that more closely relates empirical and simulated data. For this, we standardize by year-end values for Property, Plant, and Equipment (PPENT) and Cash and Marketable Securities (CHE) in the data, and standardize by end-of-year capital (K t+1 ) and cash holdings (M t+1 ) in the model. The resulting moments matched to the data are different but our qualitative results remain the same. Table A.6 Robustness: Matching Moments Standardized by Book Values In the model, we standardize all firm variables by end-of-year capital (K ) and cash holdings (M ), where A B = K + M. In COMPUSTAT data, we standardize by year-end values for Property, Plant, and Equipment (PPENT) and Cash and Equivalents (CHE). For this exercise, the prudence parameter φ is calibrated to match cash holdings in the period. All other parameters are estimated using a just identified system of moment matching. Parameters Observed Moments δ Mean(I/A B ) ω K SD(I/A B ) B/ĀB Mean(B /A B ) ω B SD(B /A B ) F /ĀB Mean(OI/A B ) σ f /ĀB SD(NI/A B ) φ Mean(M /A B ) Simulated Moments Observed Moments Mean(M /A B ) Mean(L + /A B ) n.a. n.a. 3.3 The Prudence Parameter φ We perform two experiments to verify the robustness of our results to different parametrizations of the prudence parameter φ. In the first experiment, we set the prudence parameter to match cash holdings in the period and use this value to predict cash holdings in the earlier

15 period. In both cases, all other parameter are re-estimated. The results of this experiment appear in Table A.7 below. As can be seen, the different calibration does not affect our results. Table A.7 Matching the Cash Holdings The observed moments are the same as those reported in Tables 3 and 4. For this exercise, we calibrate the prudence parameter φ to match cash holdings in the period. All other parameters are estimated using a just identified system of moment matching. Parameters Observed Moments δ Mean(I/A) ω K SD(I/A)/SD(Y/A) B/Ā Mean(B /A) ω B SD(B /K )/SD(Y/K ) F /Ā Mean(OI/A) σ f /Ā SD(NI/A) φ Mean(M /A) Simulated Moments Observed Moments Mean(M /A) Mean(L + /A) n.a In the second experiment, we set the prudence parameter φ to match the volatility of payouts in both periods. As before, all other parameters are re-estimated. The results of this experiment appear in Table A.8 below. The model calibrated for the period underpredicts the extent of cash holdings. 15

16 Table A.8 Matching Payout Volatility The observed moments are the same as those reported in Tables 3 and 4, and the simulated moments are computed as in these Tables. All other parameters are estimated using a just identified system of moment matching. Parameters Observed Moments δ Mean(I/A) ω K SD(I/A)/SD(Y/A) B/Ā Mean(B /A) ω B SD(B /K )/SD(Y/K ) F /Ā Mean(OI/A) σ f /Ā SD(NI/A) φ SD(D/A) Simulated Moments Observed Moments Mean(M /A) Mean(L + /A) n.a The Model with a Flexible Payout Policy In this version, the firm chooses K t+1, B t+1, S t knowing an information set Φ t that includes all state variables (K t, B t, L t, and M t ) and the current realization of z t, but not f t. Then, the firm chooses the allocation of S t between D t, M t+1 and L t+1 knowing an information set Φ t + that includes all the information included in Φ t, plus all the new relevant states (K t+1, B t+1, and S t ) as well as the realization of f t. Given the firm s choice of cash savings S t, the firm s problem during the year consists of choosing the allocation between cash holdings and credit line. W (K t+1, B t+1, S t ; z t, f t ) = subject to max U(D t) + β E t + [V (K t+1, B t+1, L t+1, M t+1 ; z t+1, f t )] (36) {D t,m t+1,l t+1 } M t+1 L t+1 = S t D t (1 τ C )f t (37) as well as the non-negativity constraints (3) and (4), as well as the credit line limit (5). 16

17 The solution must satisfy the following first-order conditions: ζ t + = U (D t ) (38) ζ t + γt M = βe + t + [V M (K t+1, B t+1, L t+1, M t+1 ; z t+1, f t )] (39) ζ t + + γt L γ U + t = βe + t + [V L (K t+1, B t+1, L t+1, M t+1 ; z t+1, f t )] (40) γt M 0, + M t+1 0, γt M M + t+1 = 0 (41) γt L 0, + L t+1 0, γt L L + t+1 = 0 (42) γt U 0, + L Lt+1 0, γt U ( L L + t+1 ) = 0, (43) where ζ t + is the multiplier associated with constraint (37), γt M is associated with (3), γ L + t with (4), + and γt U with (5). + At the optimum, we also have that W K (K t+1, B t+1, S t ; z t, f t ) = βe t + [V K (K t+1, B t+1, L t+1, M t+1 ; z t+1, f t )] (44) W B (K t+1, B t+1, S t ; z t, f t ) = βe t + [V B (K t+1, B t+1, L t+1, M t+1 ; z t+1, f t )] (45) At the beginning of the year, the firm s problem is W S (K t+1, B t+1, S t ; z t, f t ) = ζ t +. (46) subject to V (K t, B t, M t ; z t, f t 1 ) = max {K t+1,b t+1,s Et [W (K t+1, B t+1, S t ; z t, f t )] (47) t} S t = (1 τ C ) ( Y t + F δk t rb t ξl t + ιm t ) Kt+1 + B t+1 L t + M t Ω K t Ω B t (48) as well as the revenue (16), and the adjustment costs (18) and (19). The first-order conditions of this problem are S t 0 (49) η t λ t = E t [W S (K t+1, B t+1, S t ; z t, f t )] (50) [ ( )] Kt+1 η t 1 + ω K 1 = E t [W K (K t+1, B t+1, S t ; z t, f t )] K t (51) η t [ 1 ωb (B t+1 B) ] = E t [W B (K t+1, B t+1, S t ; z t, f t )] (52) λ t 0, S t 0, λ t S t = 0, (53) 17

18 where η t is the multiplier associated with constraint (48) and λ t with (49). We also have that V K (K t, B t, L t, M t ; z t, f t 1 ) = η t { 1 + (1 τ C )(α exp(z t )K (α 1) t δ) + ω K 2 [ (Kt+1 K t ) 2 1]} (54) V B (K t, B t, L t, M t ; z t, f t 1 ) = η t (1 + (1 τ C )r) (55) V L (K t, B t, L t, M t ; z t, f t 1 ) = η t (1 + (1 τ C )ξ) (56) V M (K t, B t, L t, M t ; z t, f t 1 ) = η t (1 + (1 τ C )ι). (57) Table A.9 Matching Moments for Flexible Payout Policy The observed moments are the same as those reported in Tables 3 and 4. For this exercise, we use the variant of the model where payouts are chosen after realization of the mid-year shock. The prudence parameter φ is calibrated to match cash holdings in the period. All other parameters are estimated using a just identified system of moment matching. Parameters Observed Moments δ Mean(I/A) ω K SD(I/A)/SD(Y/A) B/Ā Mean(B /A) ω B SD(B /K )/SD(Y/K ) F /Ā Mean(OI/A) σ f /Ā SD(NI/A) φ Mean(M /A) Simulated Moments Observed Moments Mean(M /A) Mean(L + /A) n.a