A Business Cycle Model of Aggregate Debt and Equity Flows

A Business Cycle Model of Aggregate Debt and Equity Flows∗ David Amdur Muhlenberg College† This Version: October 2010 Abstract Why do U.S. firms issu...
Author: Josephine Wells
2 downloads 3 Views 377KB Size
A Business Cycle Model of Aggregate Debt and Equity Flows∗ David Amdur Muhlenberg College† This Version: October 2010

Abstract Why do U.S. firms issue more debt and pay more to shareholders when aggregate output is high? I develop a business cycle model that explains these cyclical patterns. A tax advantage on debt makes borrowing attractive, but lenders must pay a credit insurance premium that increases with the firm’s leverage ratio. The calibrated model with total factor productivity shocks alone matches key business cycle moments in the data quite well. I compare my model with Jermann and Quadrini (2009), who emphasize the role of credit shocks in explaining the dynamics of debt and equity. JEL Classification: E3, G1, G3 Keywords: Debt-equity finance, business cycles, capital structure, tradeoff theory, DSGE models ∗

An earlier draft of this paper circulated under the title “Capital Structure over the Business Cycle.” I would like to thank Martin Evans, Behzad Diba, Dale Henderson, Jinhui Bai, Camilo Mondrag´ on, Olena Mykhaylova, George Waters, and Sami Alpanda – as well as seminar participants at the MEA Annual Meetings, the Workshop in Macroeconomic Research at Liberal Arts Colleges, Georgetown University, Penn State Harrisburg, and Muhlenberg College – for helpful comments. Any remaining mistakes are my own. † Department of Accounting, Business and Economics, 2400 Chew Street, Allentown, PA 18104, USA. Tel: 484-664-3257. E-Mail: [email protected].

1

1

Introduction

When aggregate output is high, U.S. firms as a whole issue more debt and increase their equity payouts (Jermann and Quadrini, 2009b). In this paper, I propose a business cycle model that captures this behavior. The key elements of the model are a tax advantage on debt and a credit insurance premium that depends on the firm’s leverage ratio. The calibrated model with total factor productivity (TFP) shocks alone captures the cyclical behavior of debt and equity as well as the dynamics of standard macro aggregates. I compare my model with Jermann and Quadrini (2009b) (henceforth, “JQ”), who emphasize credit shocks as drivers of debt and equity dynamics. The framework I develop is a dynamic stochastic general equilibrium (DSGE) model with flexible prices. Following a “tradeoff theory” of capital structure, firms decide how much to borrow by weighing the costs and benefits of debt relative to equity financing. I assume that interest payments are tax deductible. All else equal, this makes debt financing preferred to equity. However, lenders must pay a credit insurance premium to guarantee firms’ debt against default. I assume that the insurance premium increases with the firm’s leverage ratio. The tradeoff between the tax advantage and the insurance premium determines the optimal level of debt. After a positive shock to TFP, the real interest rate rises. In the presence of the tax advantage, if the volume of borrowing were held constant, the return on bonds to households would exceed the cost of borrowing for firms. This prompts firms to borrow more from households, driving up the insurance premium and equalizing the households’ return with the firms’ cost of borrowing. Firms use the additional proceeds raised in debt markets to finance higher payouts to shareholders, replicating the pattern observed in the data. The credit insurance premium is a simple way of modeling the fact that highly leveraged firms are particularly risky. It is widely recognized that credit rating agencies look at a firm’s leverage ratio when rating its bonds. Firms with higher leverage ratios tend to have lower ratings, as shown in Figure 1. It is also well

2

Figure 1: Median leverage (debt-to-capital) ratios for publicly listed firms in the U.S. in 2006, grouped by S&P credit rating on long-term debt. Here “capital” refers to a firm’s outstanding debt plus equity. Each bar in the graph shows the median debtto-capital ratio of all active Compustat firms with the given credit rating. Source: Compustat, author’s calculations. known that lower-rated firms must offer a substantial risk premium when issuing debt. Another way of thinking about it is that a bond investor wishing to insure against default would have to pay a higher premium to insure bonds issued by a lower-rated (riskier) firm. In the model, the more highly leveraged the firm, the greater the cost of insuring its debt. Evidence from the field suggests that such a “ratings effect” may be an important determinant of corporate debt levels in practice. For example, a wide-ranging survey of CFOs by Graham and Harvey (2001) revealed that businesses often consider the impact on credit ratings when deciding how much debt to issue. I calibrate the model with U.S. quarterly data for the nonfinancial business sector for the period 1984.1 – 2009.4. The calibrated model with TFP shocks alone matches key business cycle moments in the data quite well. I also consider an alternative calibration with shocks to the insurance premium (“credit shocks”) instead

3

of TFP shocks. In the credit shock calibration, the model gets the cyclicality of debt and equity flows right, but it predicts countercyclical consumption, which is counterfactual. Overall, the model appears to fit the data better with TFP shocks than with credit shocks. I compare my model (henceforth, the “benchmark model”) with JQ, which is the closest to mine in the literature. Instead of a credit insurance premium, JQ impose a binding enforcement constraint on firms that limits the amount of debt that they can take on. The JQ model with TFP shocks alone predicts that firms borrow less and reduce equity payouts in booms, exactly the opposite of the pattern in the U.S. However, as JQ show (and I replicate), the JQ model with shocks to the enforcement constraint (“credit shocks”) correctly predicts procyclical debt issuance and equity payouts. Both the benchmark and JQ models offer plausible explanations for the cyclical behavior of debt and equity. However, in both models, consumption declines in response to an expansionary credit shock. The benchmark model, when driven by TFP shocks, captures the cyclical behavior of debt and equity while preserving procyclical consumption. The question of how much debt firms should issue has been vigorously debated since at least 1958. Under the assumptions of frictionless capital markets, no taxes, and no bankruptcy costs, Modigliani and Miller (1958) showed that the value of a firm does not depend on its capital structure. However, the authors acknowledged in their original article and in a subsequent comment (Modigliani and Miller, 1963) that the tax deductibility of interest payments does make debt valuable to the firm in practice. A subsequent literature developed “tradeoff theories” of firm financing, in which firms pursue an optimal capital structure that balances the costs and benefits of different forms of finance (Leary and Roberts (2005)). For example, Scott (1976) constructed a model in which a firm’s optimal debt level emerges from the interplay between an interest tax deduction (the benefit of debt) and liquidation costs in the event of bankruptcy (the cost of debt). The debt-issuance decision in my model follows Scott (1976) in spirit, although I model the “bankruptcy” side of the tradeoff indirectly through an insurance premium rather than explicitly with a 4

probability of default. Moreover, I embed the capital structure decision in a general equilibrium business cycle model that has testable predictions for both macro and financial variables. This paper contributes to a growing literature on the business cycle behavior of debt and equity. Bernanke et al. (1999) (henceforth, “BGG”) introduced the pathbreaking concept of a “financial accelerator” into business cycle research. Given asymmetric information between entrepreneurs (borrowers) and lenders, as well as liquidation costs in the event of bankruptcy, the optimal financial contract pins down entrepreneurial debt as a function of net worth. The impact of TFP shocks on output is then magnified via the effect on entrepreneurs’ net worth and borrowing capacity. Relative to Bernanke et al. (1999), my model allows for equity issuance and studies the joint dynamics of firms’ debt and equity flows.1 Levy and Hennessy (2007) study a general equilibrium model in which managers can finance investment with debt or equity but may divert resources from bondholders and shareholders. I differ by assuming that the firm’s objective function is aligned with that of its shareholders. Covas and den Haan (2010) analyze a heterogeneous-agent model of debt and equity finance with a constant (exogenous) required rate of return for investors. In contrast, as in JQ, I take a representative agent approach, and all rates of return are determined endogenously in general equilibrium. Recent contributions include Christiano et al. (2010) and Gilchrist et al. (2009). Christiano et al. (2010) estimate a sophisticated monetary DSGE model with a BGG-style financial accelerator and sixteen different shocks. Gilchrist et al. (2009) estimate a similar model, using a new empirical measure of credit spreads to identify the structural parameters of the financial accelerator mechanism. Both papers find that financial frictions and financial shocks have played major roles in driving the U.S. business cycle. In contrast, I use a much simpler model to address a much narrower question: why aggregate debt issuance and equity payouts are strongly procyclical in U.S. data. 1

Kiyotaki and Moore (1997), Carlstrom and Fuerst (1997), and Cooley et al. (2004) also develop models in which financial frictions amplify the effects of macroeconomic shocks.

5

The rest of the paper is structured as follows. Section 2 reports some business cycle facts about aggregate debt and equity flows in the U.S. nonfinancial business sector. Section 3 presents the benchmark model. Section 4 presents results from the benchmark model for two calibrations: one with TFP shocks and one with credit shocks. Section 5 performs a similar analysis for the JQ model and compares the results with the benchmark model. Section 6 concludes.

2

Debt and equity flows in the U.S. business sector

This section briefly reviews some stylized business cycle facts about aggregate debt and equity flows in the U.S. These facts were first reported by JQ.2 For the U.S. nonfinancial business sector (corporate and noncorporate), net debt repurchases and net equity payouts are negatively correlated over the business cycle. Figure 2 plots net debt repurchases and net equity payouts in this sector, expressed as shares of sector output. Data are quarterly flows from the Federal Reserve’s Flow of Funds for the period 1984.1 – 2009.4. “Net Debt Repurchases” is the net decrease in credit market liabilities over the quarter.3 “Net Equity Payouts” equals dividends plus net repurchases of equity shares in the corporate sector (net of new stock issuance), less proprietors’ net investment in the noncorporate sector. This variable captures net flows to shareholders as a group, including small business owners.4 Both variables are divided by output in the nonfinancial business sector. The strong negative comovement between debt repurchases and equity payouts is apparent from the graph. Table 1 computes business cycle moments for net equity payouts and net debt repurchases, along with the typical macro variables. I detrend all variables using 2

I followed JQ’s methodology to generate the statistics in this section. See the Appendix of Jermann and Quadrini (2009b) for more details about the data. My empirical analysis differs from JQ in two minor ways: (1) I use data from 1984.1 – 2009.4, rather than 1984.1 – 2009.1; and (2) I use a Hodrick-Prescott filter rather than a band-pass filter. 3 Net debt repurchases is simply the negative of net debt issuance. I analyze repurchases rather than issuance for consistency with JQ. 4 In the model to be presented, dividends and equity repurchases are formally equivalent: a firm that wishes to “pay shareholders” may do so by increasing its dividend, by repurchasing shares, or both. Similarly, a firm that wishes to “raise capital” through equity may do so by lowering its dividend, by offering new shares, or both.

6

Figure 2: Aggregate debt and equity flows in the U.S. nonfinancial business sector (corporate and noncorporate), as shares of sector output, 1984.1 – 2009.4. “Net Debt Repurchases” is the net decrease in credit market liabilities over the quarter. “Net Equity Payouts” equals dividends plus net repurchases of equity shares in the corporate sector (net of new stock issuance), less proprietors’ net investment in the noncorporate sector. Both variables are divided by output in the nonfinancial business sector. Sources: Federal Reserve Flow of Funds, author’s calculations.

7

Variables Net Equity Payouts Net Debt Repuchases GDP Consumption Investment Hours Worked

Standard Deviation (x100) 1.77 2.17 1.05 0.90 6.77 1.71

Correlation with GDP 0.56 -0.71 – 0.86 0.88 0.86

Table 1: Business cycle moments for selected real and financial variables from 1984.1 – 2009.4. “Net Equity Payouts” and “Net Debt Repurchases” are computed using data from the Fed Flow of Funds for the nonfinancial business sector. GDP, Consumption, and Investment are from the BEA NIPA accounts. Hours Worked are from the Bureau of Labor Statistics. All variables are logged except for Net Equity Payouts and Net Debt Repurchases, which are expressed as shares of output in the nonfinancial business sector. I detrend all variables using a Hodrick-Prescott filter with a smoothing parameter of 1600.

a Hodrick-Prescott filter with a smoothing parameter of 1600. However, the key findings are unchanged if I use a Baxter-King band-pass filter instead (results available on request). Net equity payouts are positively correlated with output (“procyclical”), and net debt repurchases are strongly negatively correlated with output (“countercyclical”). The nonfinancial business sector as a whole takes on more debt and pays more to shareholders in booms. Conversely, in recessions and downturns, the business sector reduces its borrowing (sometimes even repaying debt) and lowers its payments to shareholders. The business cycle correlation between net debt repurchases and net equity payouts (not given in the table) is -0.61. The moments in Table 1 also reflect some well-known facts from the real business cycle literature. Consumption, investment and hours worked are all strongly procyclical. Consumption is less volatile than GDP, while hours worked are more volatile than GDP, and investment is much more volatile than GDP. Note that net debt repurchases and net equity payouts are more volatile than GDP, but not as volatile as investment. Finally, debt repurchases are more volatile than equity payouts.

8

3

The Benchmark Model

The benchmark model economy consists of a continuum of identical households and a continuum of identical, perfectly competitive firms. Since firms are the main actors of interest, I discuss the firm’s problem first.

3.1

Firm’s problem

A representative firm uses capital, kt−1 , and labor, lt , to produce output, yt , according to a standard Cobb-Douglas production function:

θ yt = zt kt−1 lt1−θ

(1)

where zt is total factor productivity (TFP) and θ ∈ (0, 1) is the share of capital in income.5 The firm owns its own capital stock but hires labor period-by-period at the competitive real wage, wt . Each period, after producing output and paying wages, the firm decides how much to invest (or disinvest) in its capital stock, how much to borrow in debt markets, and how much to pay (or take from) shareholders. Interest payments on the firm’s debt are tax-deductible. Following JQ, I capture the interest tax deduction by assuming that firms can issue discount bonds at a price that reflects the after-tax real interest rate. JQ also argue that equity payouts are “sticky”, because firms tend to smooth dividends over time. Following JQ, I assume that it costs the firm ϕ(dt ) to make a net equity payout of dt :

ϕ(dt ) = dt + κ (dt − d)2

(2)

where d is the long-run (steady-state) value of the equity payout. Investment is just the net change in the firm’s capital stock, which depreciates at the rate δ ∈ (0, 1): 5

All variables subscripted t are chosen or realized in period t.

9

it = kt − (1 − δ)kt−1

(3)

The firm issues bt one-period discount bonds in period t that each pay the holder 1 unit of the output good in period t + 1. The firm’s budget constraint can be written as follows:

yt − wt lt +

bt = bt−1 + it + ϕ(dt ) 1 + rt (1 − τ )

(4)

where rt is the real interest rate and τ ∈ (0, 1) is the marginal tax rate on firms’ earnings. The firm maximizes the expected present discounted value of equity payouts, discounted using the stochastic discount factor mt (to be discussed in the next section). That is, the firm maximizes:

" E0

∞ X

# mt dt

t=0

subject to (1), (2), (3), and (4). The Appendix lists the first-order conditions for the firm’s problem.

3.2

Household’s problem

A representative household supplies labor to firms and consumes the firm’s output good. The household’s period utility function is as follows:

    U ct , lth = ln (ct ) + α ln 1 − lth where ct is consumption and lth ∈ (0, 1) is the amount of labor supplied by the household. α > 0 indexes the household’s disutility of working.

10

The household receives wage income wt lth and can hold the firm’s equity shares as well as its bonds. Each bond purchased in period t promises to pay one unit of the output good in period t + 1. If the bond were truly risk-free, the purchase price would be 1/(1 + rt ). However, I assume that the household must also pay a credit insurance premium, µt , to guarantee the bond against default. The household could, in principle, choose not to pay the insurance premium; however, the bond would then default with certainty. Therefore, in equilibrium, the household always pays the insurance premium.6 The household’s problem is as follows:

max E0

"∞ X

t

βU



ct , lth



#

t=0

s.t.

wt lth

+

bht−1

 + st−1 (dt + pt ) =

 1 + µt bht + st pt + ct + Tt 1 + rt

(5)

Here bht denotes the number of bonds purchased by the household in period t, st denotes the number of equity shares purchased in period t, dt is the per-share equity payout, pt is the market price of a share, and Tt is a lump-sum tax used to finance the interest tax deduction enjoyed by firms. Because I normalize the supply of shares to 1, dt also equals the firm’s total equity payout. The Appendix lists the household’s first-order conditions. Households take the insurance premium µt as given. However, I further assume that in equilibrium, µt is given by:

 µ t = at

bt kt−1

 (6)

6 I do not explicitly model the firm’s decision to default, but one can interpret the insurance premium as the resolution of an agency problem. Absent some monitoring by an outside agency (e.g., a bank or a regulator), a firm’s manager could steal borrowed funds. Monitoring prevents the firm from defaulting, but it is costly. Under this interpretation, the assumptions outlined above imply that (i) without monitoring, the manager will steal all borrowed funds; (ii) with monitoring, the manager cannot steal any borrowed funds; and (iii) monitoring is the only mechanism available to households to prevent the manager from stealing.

11

where at is an exogenous variable. I refer to bt /kt−1 as the firm’s leverage ratio. As outlined in the introduction, the motivation for (6) is that more highly leveraged firms are more likely to default, making their debt more costly to insure. A rise in at increases the insurance premium for reasons unrelated to leverage. Such a change could arise, for example, from off-balance-sheet activity that makes it harder for outsiders to monitor the firm’s financial condition. In equilibrium, the stochastic discount factor used by firms, mt , must be consistent with household optimization. The required condition is as follows:

 mt = β

3.3

ct

−1

ct−1

(7)

Market clearing

In equilibrium, the following market-clearing conditions must hold:

lth = lt

(8)

bht = bt

(9)

st = 1

(10)

yt − µt bt − κ (dt − d)2 = ct + it

(11)

The first two equations are the market-clearing conditions for labor and bonds. (10) says that households’ demand for equity shares must equal the supply of shares, which is normalized to 1. (11) is the goods market-clearing condition. It says that output, net of deadweight losses due to financial frictions, must equal the sum of consumption and investment spending.

3.4

Shock processes

There are two possible sources of uncertainty in the model: TFP, zt , and the exogenous component of the insurance premium, at (“credit shocks”). However, in this 12

paper, I only consider one stochastic shock at a time. When analyzing TFP shocks, I fix at at its steady-state value, a, and I assume that zˆt ≡ ln(zt /z) follows an AR(1) process:

zˆt = ρz zˆt−1 + z,t (12)

When analyzing credit shocks, I fix zt at its steady-state value, z, and I assume that a ˆt ≡ ln(at /a) follows an AR(1) process:

a ˆt = ρa a ˆt−1 + a,t

z,t and a,t are normally distributed, zero-mean, independent and identically distributed (iid) shocks with variances σz2 and σa2 , respectively.

3.5

Equilibrium

An equilibrium is a sequence of state-contingent values for kt , bt , dt , lt , wt , rt , ct , mt , µt , and pt such that all markets clear when consumers and firms behave optimally, taking equilibrium prices as given. I solve the model using a standard, first-order perturbation technique around the unique non-stochastic steady-state. For convenience, the Appendix summarizes all the equations of the model.

4

Results for the Benchmark Model

I consider two separate calibrations of the benchmark model: one with technology (TFP) shocks only, and one with credit shocks only.

13

Parameter β α θ δ τ z ρz σz a κ

Description Discount factor Disutility of labor Share of capital Depreciation rate Tax rate Steady-state TFP Persistence of TFP Std of TFP shock Steady-state insurance parameter Equity cost parameter

Value 0.9825 1.8991 0.3600 0.0250 0.3500 1.0000 0.9500 0.0054 0.0260 0.0043

Table 2: Calibration: Benchmark model with technology (TFP) shocks only.

4.1

Technology (TFP) shocks

In this section, I fix the exogenous component of the insurance premium, at , to its steady-state value (a). First, I describe calibration. Second, I discuss impulse response functions for the key variables of the model. Finally, I present business cycle moments from the model and compare them with the data. Table 2 summarizes the model calibration. β, the quarterly discount factor, is 0.9825, which corresponds to an annual steady-state real interest rate of about 7%. The utility function parameter α is calibrated to make the steady-state fraction of time spent working equal to 0.3. I set θ, the share of capital in income, to 0.36, and δ, the depreciation rate, to 0.025. The marginal tax rate on firms’ earnings is 0.35, and the steady-state level of TFP is normalized to 1. All of the parameters above are calibrated following JQ. I set ρz , the persistence of (log) TFP, to 0.95. Recall that a is the exogenous component of the insurance premium in the steady-state. I calibrate a to match the average debt-to-capital-stock ratio in the nonfinancial business sector, which is about 0.35 from 1984.1 – 2009.4. I then jointly calibrate σz , the standard deviation of (log) TFP, and κ, the equity cost parameter, to match the standard deviation of output and the standard deviation of net equity payouts (as a share of output). Figure 3 presents selected impulse response functions to a positive, one standard

14

Figure 3: Impulse responses to a positive, one standard deviation shock to log TFP (“TFP shock”) in the benchmark model.

15

deviation shock to (log) TFP. On impact, net equity payouts rise sharply, and net debt repurchases fall sharply. Since borrowing is positive in the steady-state, the fall in debt repurchases indicates increased debt issuance. To understand the economic mechanism behind this result, it’s helpful to look at the first-order conditions for firms’ borrowing and households’ lending for the case of no equity deviation costs (κ = 0):

1 = Et [mt+1 ] · Rtf

(13)

1 = Et [mt+1 ] · Rth

(14)

Rtf = 1 + rt (1 − τ ) Rth =

1 1+rt

1 + µt

Here Rtf is the cost of borrowing for firms, and Rth is the return on bonds to households, net of the insurance premium.7 From the first-order conditions, we must have Rtf = Rth in equilibrium. The positive TFP shock increases the lifetime wealth of households, inducing a hump-shaped response for consumption. Since consumption is expected to increase, the expected stochastic discount factor, Et [mt+1 ], falls (see (7)), and Rtf must rise. However, because firms enjoy a tax advantage on borrowing, the real interest rate, rt , must rise proportionally more than Rtf . Absent any change in the insurance premium, µt , the return on bonds to households, Rth , would exceed Rtf , and households would want to make unbounded loans to firms. However, as the amount lent to firms, bt , increases, the firm’s leverage ratio rises, driving up µt (see (6)). The higher insurance premium ratchets Rth back down. In equilibrium, on impact, borrowing and the insurance premium both rise, such that Rtf = Rth .8 What does the firm do with the extra funds raised in debt markets? From the 7 Note that in a frictionless model, with τ = 0 and µt = 0, the two returns would both equal one plus the real interest rate. 8 Equation (14) assumes that κ = 0 for ease of exposition. See the Appendix for the complete first-order condition. When κ > 0, Rtf need not exactly equal Rth outside of the steady-state. This does not change the basic economic logic. In particular, a falling expected stochastic discount factor still triggers a larger rise in rt than in Rtf , forcing µt to rise in order to make Rth nearly equal to Rtf .

16

Variables – Standard Deviations (x100) Net Equity Payouts Net Debt Repurchases GDP Consumption Investment Hours Worked Variables – Correlations with GDP Net Equity Payouts Net Debt Repurchases Consumption Investment Hours Worked

Data 1.77 2.17 1.05 0.90 6.77 1.71 Data 0.56 -0.71 0.86 0.88 0.86

Model 1.77 2.17 1.05 0.35 3.61 0.54 Model 0.32 -0.56 0.86 0.98 0.97

Table 3: Business cycle moments: Data versus benchmark model with technology (TFP) shocks only. All variables are logged except for Net Equity Payouts and Net Debt Repurchases, which are expressed as shares of output in the nonfinancial business sector. I detrend all variables using a Hodrick-Prescott filter with a smoothing parameter of 1600.

firm’s budget constraint (4), the firm can spend its extra income on capital investment, equity payouts, or both. In the calibrated model it does both. Intuitively, higher investment is optimal, but only up to a point, due to diminishing returns to capital. As long as the cost of paying equity (κ) is not too large, the firm uses some of the borrowed funds to increase the equity payout on impact, which directly increases the firm’s objective function. Table 3 compares moments from the TFP-calibrated benchmark model with moments from the data. All variables are Hodrick-Prescott filtered with a smoothing parameter of 1600. Overall, the calibrated model matches the data quite well. Net equity payouts are positively correlated with output, and net debt repurchases are negatively correlated with output, consistent with the data. Consumption, investment, and hours worked are all strongly procyclical in both model and data. In terms of volatilities, the model produces a very close match for the standard deviation of net debt repurchases.9 One shortcoming of the model is that the macro variables (except GDP) are less volatile than in the data. 9

Note that the standard deviation of net debt repurchases was not used as a calibration moment.

17

Parameter ρa σz σa κ

Description Persistence of exog. insurance premium Std of TFP shock Std of credit shock Equity cost parameter

Value 0.9500 0.0000 0.2380 0.5300

Table 4: Calibration: Benchmark model with credit shocks only. All parameters not listed here take the same values as in Table 2.

4.2

Credit shocks

Since the financial crisis of 2007 – 2009, there has been renewed interest in shocks to credit availability as a driving force behind macroeconomic fluctuations.10 These shocks also play an important role in the JQ model. In this section, I analyze the benchmark model with credit shocks only. I fix the level of TFP, zt , at its steadystate value (z), and I allow the exogenous component of the insurance premium, at , to follow an AR(1) process in logs as described in Section 3. Table 4 lists the parameters that have changed. I set the persistence parameter, ρa , to 0.95 to facilitate comparison with TFP shocks. I then jointly calibrate the volatility of the shocks, σa , and the equity cost parameter, κ, to match the standard deviation of output and the standard deviation of net equity payouts (as a share of output). Figure 4 plots impulse response functions to a negative, one standard deviation shock to the (log) insurance premium. The negative shock is expansionary, in the sense that it increases output. The responses of net equity payouts and net debt repurchases are similar to the case of TFP shocks, but the economic mechanism is different. The sudden drop in the credit insurance premium directly increases the return to households from holding bonds. In order to equate the households’ return on bonds with the firms’ cost of borrowing, households must lend more to firms, which partially offsets the effect of the shock on the insurance premium, µt (see (6)). As before, the firm uses some of the additional debt financing for capital investment and some to increase equity payouts. A problematic implication of this 10

See, for example, Christiano et al. (2010), Gilchrist et al. (2009), and Kiyotaki and Moore (2008).

18

Figure 4: Impulse responses to a negative (expansionary), one standard deviation shock to the log insurance premium (“credit shock”) in the benchmark model.

19

Variables – Standard Deviations (x100) Net Equity Payouts Net Debt Repurchases GDP Consumption Investment Hours Worked Variables – Correlations with GDP Net Equity Payouts Net Debt Repurchases Consumption Investment Hours Worked

Data 1.77 2.17 1.05 0.90 6.77 1.71 Data 0.56 -0.71 0.86 0.88 0.86

Model 1.77 4.39 1.05 1.38 13.11 1.60 Model 0.93 -0.95 -0.79 0.95 0.93

Table 5: Business cycle moments: Data versus benchmark model with credit shocks only. All variables are logged except for Net Equity Payouts and Net Debt Repurchases, which are expressed as shares of output in the nonfinancial business sector. I detrend all variables using a Hodrick-Prescott filter with a smoothing parameter of 1600.

calibration is that consumption falls in response to an expansionary credit shock. On impact, new capital investment exceeds the increase in output, so consumption must fall. Table 5 compares moments from the credit-shock-calibrated benchmark model with moments from the data. The credit shock calibration does not fit the data as well as the TFP shock calibration did. Of particular concern is the strong negative correlation between consumption and output, which is counterfactual. The model also predicts excessively volatile net debt repurchases, consumption, and investment. Note that the credit shock needs to be very volatile in order to replicate the standard deviation of GDP.11 This induces higher volatility in the non-calibrated variables, compared to the TFP shock calibration.

5

Comparison with Jermann and Quadrini (2009b)

This section compares the benchmark model with Jermann and Quadrini (2009b) (“JQ”), who provide an alternative explanation for the cyclical behavior of aggregate 11

Compare the standard deviation of at in the credit shock calibration, 0.2380, with the standard deviation of zt in the TFP shock calibration, 0.0054.

20

debt and equity flows. First, I briefly review the JQ model. I then separately analyze the JQ model with TFP shocks and with credit shocks, in each case comparing the results to the benchmark model.

5.1

Overview of model

In JQ, households do not pay an insurance premium to protect the firm’s bonds against default. Instead, the firm is limited in its borrowing by an enforcement constraint that is always binding in equilibrium. The enforcement constraint states that the ex-dividend equity value of the firm must exceed a certain multiple of the firm’s current output. The form of this constraint derives from an agency problem. The authors assume that the firm takes on an intratemporal loan of yt to pay for working capital, in addition to standard intertemporal debt. The firm’s owners (equity holders) have the option of defaulting on the intratemporal loan at the end of the period. If the firm’s owners default, they forfeit the residual equity value P V¯t = Et [ ∞ j=1 mt+j dt+j ], which is the expected present discounted value of equity payouts starting next period. However, the lenders can recover only a fraction of this value (e.g., due to bankruptcy costs). Because the firm loses value whenever the owners default, both parties have an interest in renegotiating the intratemporal loan. If they fail to reach an agreement, the firm’s owners walk away with yt and the lenders recover the amount ξt V¯t , where ξt < 1 is the exogenous recovery fraction. Incentive-compatibility imposes the following enforcement constraint:

ξt V¯t ≥ yt

JQ write the firm’s problem recursively, noting that the individual states for the firm are capital, k, and intertemporal debt from last period, b:

21

   V (k, b) = max d + E m0 V k 0 , b0 0 0 l,d,k ,b

b0 = b + ϕ (d) + k 0 1 + r (1 − τ )   ξE m0 V k 0 , b0 ≥ y

s.t. y + (1 − δ)k − wl +

(15) (16)

y = zk θ l1−θ 2 ϕ(d) = d + κ d − d¯

where expectations are understood to be conditioned on all available information at the start of the period. d¯ is the steady-state value of the firm’s equity payout. The authors treat ξt as a stochastic variable, and they refer to innovations in ξt as “credit shocks”. In particular, an increase in ξt relaxes the enforcement constraint by reducing the required residual equity value of the firm. This relaxation lets the firm take on more debt, b0 , which lowers the residual equity value but also lets the firm increase its current equity payout. I model ξˆt ≡ ln(ξt /ξ) as an AR(1) process:

ξˆt = ρξ ξˆt−1 + ξ,t

The rest of the model is essentially the same as in Section 3. I refer the interested reader to Jermann and Quadrini (2009b) for more details.

5.2

Technology (TFP) shocks

I follow the same approach as in Section 4 and analyze the JQ model separately with TFP shocks and credit shocks. In this section, I fix the recovery fraction ξt at its steady-state value, ξ. Most of the calibration follows the TFP shock calibration from the benchmark model; Table 6 lists only the new parameters and those that have changed. I calibrate the steady-state recovery fraction, ξ, to match the average debt-to-capital ratio in the nonfinancial business sector from 1984.1 – 2009.4, which

22

Parameter σz ξ κ

Description Std of TFP shock Steady-state recovery fraction Equity cost parameter

Value 0.0082 0.1630 0.1040

Table 6: Calibration: JQ model with technology (TFP) shocks only. All parameters not listed here take the same values as in Table 2.

is about 0.35. I then jointly calibrate the standard deviation of the TFP shock, σz , and the equity cost parameter, κ, to match the standard deviation of output and the standard deviation of net equity payouts (as a share of output). Figure 5 presents impulse response functions to a positive, one standard deviation shock to (log) TFP in the JQ model. Net equity payouts decline on impact, while net debt repurchases increase – the opposite of the pattern in the benchmark model with TFP shocks. The key equation is the binding enforcement constraint (16). The increase in TFP directly increases output, yt , raising the value of the right hand side of the constraint. Because the firm can now “steal” more working capital, incentive compatibility requires a higher residual equity value (left hand side). This, in turn, forces the firm to reduce both its debt level and its current equity payout. Evidence for this channel appears in the bottom panel of Figure 5, which shows that the Lagrange multiplier on the enforcement constraint rises on impact. Table 7 compares moments from the TFP-calibrated JQ model with moments from the data. All variables are Hodrick-Prescott filtered with a smoothing parameter of 1600. Net equity payouts are countercylical, and net debt repurchases are slightly procyclical – a counterfactual prediction. In terms of volatilities, the JQ model is similar to the benchmark model. In particular, the volatility of net debt repurchases is close to the data, while the volatilities of consumption, investment, and hours worked are less than in the data.

5.3

Credit shocks

Jermann and Quadrini (2009b) show that credit shocks – when combined with TFP shocks – greatly improve the fit of their model to U.S. macro and financial data 23

Figure 5: Impulse responses to a positive, one standard deviation shock to log TFP (“TFP shock”) in the JQ model.

24

Variables – Standard Deviations (x100) Net Equity Payouts Net Debt Repurchases GDP Consumption Investment Hours Worked Variables – Correlations with GDP Net Equity Payouts Net Debt Repurchases Consumption Investment Hours Worked

Data 1.77 2.17 1.05 0.90 6.77 1.71 Data 0.56 -0.71 0.86 0.88 0.86

Model 1.77 2.30 1.05 0.39 3.34 0.63 Model -0.26 0.12 0.90 0.99 0.20

Table 7: Business cycle moments: Data versus JQ model with technology (TFP) shocks only. All variables are logged except for Net Equity Payouts and Net Debt Repurchases, which are expressed as shares of output in the nonfinancial business sector. I detrend all variables using a Hodrick-Prescott filter with a smoothing parameter of 1600.

from 1984.1 – 2009.1.12 In this section, I analyze the role of credit shocks in the JQ model. Following the approach in Section 4, I fix TFP, zt , at its steady-state value; and I allow the (log) recovery fraction, ξt , to be a stochastic variable. Table 8 lists only the new parameters and those that have changed (relative to the benchmark model with TFP shocks). The steady-state recovery fraction, ξ, is again calibrated to match the average debt-to-capital ratio in the data. I set the persistence of the (log) recovery fraction, ρξ , to 0.95. I then jointly calibrate the standard deviation of the credit shock, σξ , and the equity cost parameter, κ, to match the standard deviation of output and the standard deviation of net equity payouts (as a share of output). Figure 6 plots impulse response functions to a positive (expansionary), one standard deviation credit shock in the JQ model. On impact, net equity payouts rise and net debt repurchases fall. The impulse responses are similar to the responses of the benchmark model with credit shocks. The expansionary credit shock relaxes the enforcement constraint (16), as evidenced by the fall in the Lagrange multiplier 12

In a companion paper, Jermann and Quadrini (2009a) argue that credit shocks were also important drivers of the U.S. business cycle from 1952 – 2005.

25

Parameter σz ξ ρξ σξ κ

Description Std of TFP shock Steady-state recovery fraction Persistence of recovery fraction Std of credit shock Equity cost parameter

Value 0.0000 0.1630 0.9500 0.0162 0.1780

Table 8: Calibration: JQ model with credit shocks only. All parameters not listed here take the same values as in Table 2.

in the bottom panel of Figure 6. The firm can now reduce its residual equity value, and it does so by borrowing more and raising its equity payout on impact. The rise in output occurs because equity payouts are “sticky” (κ > 0), so the firm partially accommodates the relaxed constraint by hiring more labor (see Jermann and Quadrini (2009b) for an extensive discussion of this channel). As in the benchmark model with credit shocks, consumption falls on impact, though not as sharply. Table 9 compares moments from the credit-shock-calibrated JQ model with moments from the data. All variables are Hodrick-Prescott filtered with a smoothing parameter of 1600. Net equity payouts are procyclical, and net debt repurchases are countercyclical, consistent with the data. The main shortcoming of this calibration – which also afflicts the benchmark model with credit shocks – is the negative correlation between consumption and output. The model matches the volatilities of investment and hours worked fairly closely. However, it predicts too much volatility in net debt repurchases and not enough volatility in consumption. Both JQ calibrations have serious shortcomings. With TFP shocks alone, the JQ model gets the cyclicality of debt and equity flows flipped (countercyclical debt issuance and equity payouts). With credit shocks alone, the JQ model gets debt and equity right, but it predicts countercyclical consumption. The potential advantage of the benchmark model is that it gets both facts right with just one shock. On the other hand, Jermann and Quadrini (2009b) show that their model matches U.S. macro and financial data quite closely when estimated with both shocks. In their estimation, the variance of credit shocks (relative to TFP shocks) is large

26

Figure 6: Impulse responses to a positive (expansionary), one standard deviation shock to the log recovery fraction (“credit shock”) in the JQ model.

27

Variables – Standard Deviations (x100) Net Equity Payouts Net Debt Repurchases GDP Consumption Investment Hours Worked Variables – Correlations with GDP Net Equity Payouts Net Debt Repurchases Consumption Investment Hours Worked

Data 1.77 2.17 1.05 0.90 6.77 1.71 Data 0.56 -0.71 0.86 0.88 0.86

Model 1.77 3.54 1.05 0.23 4.69 1.65 Model 0.95 -0.98 -0.26 0.99 0.99

Table 9: Business cycle moments: Data versus JQ model with credit shocks only. All variables are logged except for Net Equity Payouts and Net Debt Repurchases, which are expressed as shares of output in the nonfinancial business sector. I detrend all variables using a Hodrick-Prescott filter with a smoothing parameter of 1600.

enough to make debt issuance and equity payouts procyclical, but not so large that consumption becomes countercyclical. However, JQ’s estimation does assign the larger variance to credit shocks. It is somewhat awkward that these shocks don’t produce the right dynamics for consumption on their own.

6

Conclusion

U.S. firms, as a whole, borrow more in debt markets and pay more to shareholders when aggregate output is high. This paper developed a business cycle model that can explain these cyclical patterns. The key ingredients of the model are a tax advantage on debt and a credit insurance premium that increases with the firm’s leverage ratio. The calibrated model with TFP shocks alone matches key business cycle moments in the data quite well. I then compared my model with Jermann and Quadrini (2009b) (“JQ”). With TFP shocks alone, JQ predicts counterfactual dynamics for debt and equity flows; with credit shocks alone, JQ predicts counterfactual dynamics for consumption. JQ requires both TFP and credit shocks to match U.S. macro and financial data. This paper calibrated each model with one shock at a time. I employed this 28

approach in order to highlight the economic mechanisms at work in the benchmark and JQ models. However, I did not study the models under both shocks simultaneously, as JQ do. Modeling TFP and credit shocks together is appropriate when the goal is to estimate the relative importance of each shock in U.S. data. I plan to pursue this in future work.

29

Appendix A

Full list of model equations

Firm’s first-order conditions

θ (1 − θ) zt kt−1 lt−θ = wt   n o 1 + 2κ (dt − d) 1−θ 1 = Et mt+1 θzt+1 ktθ−1 lt+1 + (1 − δ) 1 + 2κ (dt+1 − d)     1 + 2κ (dt − d) {1 + rt (1 − τ )} 1 = Et mt+1 1 + 2κ (dt+1 − d)

Household’s first-order conditions wt α = ct 1 − lt "

1 1 1+rt + µt

1 = Et mt+1

!#

   dt+1 + pt+1 1 = Et mt+1 pt

Budget constraint for firms

θ zt kt−1 lt1−θ + (1 − δ) kt−1 − wt lt +

bt = bt−1 + dt + κ (dt − d)2 + kt 1 + rt (1 − τ )

Goods market-clearing condition

θ zt kt−1 lt1−θ − µt bt − κ (dt − d)2 = ct + [kt − (1 − δ) kt−1 ]

Insurance premium  µ t = at

30

bt kt−1



Stochastic discount factor  mt = β

ct

−1

ct−1

Shocks

zˆt = ρz zˆt−1 + z,t and a ˆt = 0 (or) a ˆt = ρa a ˆt−1 + a,t and zˆt = 0 where zˆt ≡ ln(zt /z) , a ˆt ≡ ln(at /a)

Other variables of interest

θ yt = zt kt−1 lt1−θ

it = kt − (1 − δ) kt−1  dt net equity payouts = output yt   t net debt repurchases bt−1 − bt = output yt t 

Note: The household’s budget constraint is dropped due to Walras’ Law.

31

References Bernanke, Ben S., Mark Gertler, and Simon S. Gilchrist, “The Financial Accelerator in a Quantitative Business Cycle Framework,” in John B. Taylor and Michael Woodford, eds., Handbook of Macroeconomics, Amsterdam: Elsevier Science, 1999, pp. 1341–1393. Carlstrom, Charles T and Timothy S Fuerst, “Agency Costs, Net Worth, and Business Fluctuations: A Computable General Equilibrium Analysis,” American Economic Review, December 1997, 87 (5), 893–910. Christiano, Lawrence J., Roberto Motto, and Massimo V. Rostagno, “Financial factors in economic fluctuations,” Working Paper Series 1192, European Central Bank 2010. Cooley, Thomas F., Ramon Marimon, and Vincenzo Quadrini, “Aggregate Consequences of Limited Contract Enforceability,” Journal of Political Economy, 2004, 112 (4), 817–847. Covas, Francisco B. and Wouter J. den Haan, “The role of debt and equity finance over the business cycle,” Unpublished manuscript, Amsterdam School of Economics 2010. Gilchrist, Simon S., Alberto Ortiz, and Egon Zakrajsek, “Credit risk and the macroeconomy: Evidence from an estimated DSGE model,” Unpublished manuscript, Boston University 2009. Graham, John R. and Campbell R. Harvey, “The Theory and Practice of Corporate Finance: Evidence from The Field,” Journal of Financial Economics, 2001, 60, 187–243. Jermann, Urban J. and Vincenzo Quadrini, “Financial innovations and macroeconomic volatility,” Working Paper, Wharton Finance 2009. and , “Macroeconomic effects of financial shocks,” Working Paper 15338, National Bureau of Economic Research 2009. Kiyotaki, Nobuhiro and John H. Moore, “Credit Cycles,” Journal of Political Economy, 1997, 105, 211–248. and , “Liquidity, business cycles, and monetary policy,” Unpublished manuscript, Princeton University and Edinburgh University 2008. Leary, Mark T. and Michael R. Roberts, “Do Firms Rebalance Their Capital Structures?,” Journal of Finance, 2005, 60 (6), 2575–2619. Levy, Amnon and Christopher A. Hennessy, “Why Does Capital Structure Vary with Macroeconomics Conditions?,” Journal of Monetary Economics, 2007, 54, 1545–1564. Modigliani, Franco and Merton H. Miller, “The Cost of Capital, Corporation Finance and the Theory of Investment,” American Economic Review, 1958, 48, 261–297. 32

and , “Corporate Income Taxes and The Cost of Capital: A Correction,” American Economic Review, 1963, 53, 433–443. Scott, James H., “A Theory of Optimal Capital Structure,” Bell Journal of Economics, 1976, 7, 33–54.

33

Suggest Documents