Macroeconomic aspects of firm bankruptcy analysis

AMNON LEW RAN BAR-NIV Ben-Curion

University

of

Beer-Sheva,

the

Negev lsrael

Macroeconomic Aspects of Firm Bankruptcy Analysis* This study provides theoretical and empirical insights into the relationships between the probability of corporate bankruptcy and macroeconomic factors. The theoretical part hypothesizes that fluctuations in aggregate income and price level adversely affect the well-being of the business sector and links the likelihood of firm failure to structural parameters governing the business cycles. Our empirical findings for the United States indicate that the annual rate of bankruptcy is positively correlated with the variances of the GNP and the GNP deflator and negatively correlated with the covariance of these variables.

1. Introduction The purpose of this paper is to explore relationships between corporate bankruptcy and fundamental macroeconomic aspects. The research in the field of bankruptcies among firms has focused primarily on microeconomic analyses which emphasize financial aspects in explaining and predicting business failures. Stiglitz (1972, 1975) shows that market valuation of a firm is a decreasing function of its debt-equity ratio when there is a finite probability of bankruptcy, when bondholders have unambiguously more pessimistic expectations of the firm’s prospects than stockholders, and when both are risk neutral. Using the Modigliani-Miller arbitrage argument, Stapleton (1975) argues that leverage cannot reduce the value of the firm. Bulow and Shoven (1978) assume that the criterion for *The authors are indebted to the anonymous reviewer ments on the first version of the paper, and to the Phillipe Economic Research for funding the study.

Journal of Macroeconomics, Summer Copyright 0 1987 by Louisiana State 0164-0704/87/$1.50

1987, Vol. University

9, No. Press

for constructive comMonaster Center for

3, pp.

407-415

407

Amnon Levy and Ran Bar-Niv bankruptcy is the positive gain from immediate liquidation to the coalition of claimants with negotiating power, and they derive the conditions under which bankruptcy occurs where there are three asymmetrical classes of claimants on the firm’s assets and income flows. Munch and Smallwood (1980) find that minimum capital requirements appear to reduce insolvency, but other forms of regulations do not have the desired effects. Although business failure is essentially a microeconomic phenomenon reflecting a particular firm’s situation, the probability of this outcome is likely to be influenced by the overall performance of the economy that defines the environment in which firms operate. In contrast to the extensive microeconomic literature, the linkage between insolvency and macroeconomic theory appears to have attracted little attention. The study of business cycles or variations in aggregate economic variables can further enhance understanding of the determinants of the probability of firm failure. In particular, fluctuations in national income alfect the demand for the firm’s products, unless it is income inelastic, and, in the case of a normal (inferior) good, lead to lower (higher) demand in downturns and higher (lower) demand in upturns. Altman (1971) finds that the corporate failure rate in America is negatively correlated with changes in the GNP, stock prices, and money supply; and that slowdowns in economic activity increase the failure rate. Fluctuations in prices might also affect a firm’s net cash flow when payments and receipts are not fully linked to relevant price indices. Along the lines of this rationale, this paper continues with a theoretical analysis which links the underlying macroeconomic factors determining the nature of fluctuations in aggregate economic variables with the probability of business failures. In order to provide the analysis with a wide and profound theoretical basis, the model is used as a Dornbusch-Fischer (1978) macroeconomic benchmark. The reduced form of this model, incorporating the adaptive expectations’ hypothesis is presented in Section 2 by a system of first-order difference equations, and is then solved for the case of conjugate complex roots displaying oscillations in the aggregate variables. The probability of firm failure is discussed on the basis of the properties of derived business cycles. Section 3 estimates the effects of variations of aggregate variables on the annual rate of bankruptcy in post-World War II United States. The estimation’s results are statistically significant and confirm a priori expectations that the annual rate of bankruptcy increases with the variances of the real GNP and the GNP deflator. The results also 408

Macroeconomic

Aspects of Firm

indicate that the annual rate of bankruptcy variance of these variables.

2. Business

Bankruptcy declines

Analysis

with the co-

Cycles and Insolvency

The well-known (closed economy) model of Dornbusch and Fischer (1978) is a macroeconomic structure which is capable of generating cyclical fluctuations in major aggregate variables such as income and inflation rate. In this model the aggregate supply is represented by the expectations-augmented Phillips curve, IT = 7F* + 6(Y - Y,) , the aggregate demand IS/LM system,

by the time differential

Y = YeI + ya + +(m - IT), and the public’s expectations to be adaptive,

n* =

6>0;

of the solution to the

y,+>o;

about the rate of inflation

P 1 - (1 - B)L r-1 ’

(1)

(2) are assumed

o
(Cagan 1956; and Friedman 1956.) Here Y is the current level of output; Y, is the potential level of output; IT is the actual inflation rate; IT* is the expected inflation rate; a is the increase in autonomous expenditures; m is the growth rate of nominal money stock; 6 is a positive parameter reflecting the short-run trade-off, on the supply side, between inflation and GNP gap; y is the fiscal multiplier; 4 is the monetary multiplier; B is the inflationary expectations correction coefficient; and L is the lag operator. By substituting Equation (3) for n* in Equation (l), the above macroeconomic structure can be displayed by the following first-order difference equation system:

[G]

-i&[-i

1+*zk3,][cI:] 1

=i+

-I %a + +m - PY,) s+ [ WW,+ v + +m J ’

(4)

409

Amnon Levy and Ran Bar-Niv Fluctuations in Y and 71 arise from changes in the monetary and fiscal policy instruments m and a, respectively, and from changes in potential output Y,, and these changes activate further forces inherent in the system. The solution to (4) displays oscillations of the aggregate variables when [4p/(l - p)“] > SC& in which case the eigenvalues of the state transition matrix are complex conjugate pair. In any other case, the system converges to steady state along a nonspiral trajectory. The deviations of Y and n from their steadystate levels at any point of time t are given for the case where the eigenvalues of the state transition matrix in (4) are complex conjugate pair by [;;I;]

= [;;](&J5’w+

+ et).

Here the angle 0 (in radians) is the amplitude and is given by the equality

(5)

of the complex roots

(6) and the parameters bl, b2, and + are chosen to satisfy the initial conditions. Equations (4) and (5) show that the fluctuations of Y and n, which follow changes in the government policy instruments and potential output, are amplified by the modulus of the complex roots, 1 r=l+y

(7)

and by the parameters, b, and b,. The latter are directly connected to Am, Au, and AYP. Equation (5) also implies that the length of each business cycle is given by’ ‘Due to its deterministic character, the model presents cyclical symmetries and regularities, which might be viewed as a point of weakness. Mitchell (1927) and Keynes (1936) believe that business cycles are asymmetric, consisting of brief and severe downturns and longer and more gradual upturns. This belief was supported recently by Neftci (19&Q, who examine the behavior of the unemployment rate in the U.S. However, Delong and Summers (19&I), who calculate the coefficient of skewness of the distribution of GNP growth rates and industrial production growth rates for the U.S., Japan, West Germany, the U.K., and France at various time intervals, conclude that symmetry is insignificant and probably not a phenomenon of first-order importance in understanding business cycles.

410

Macroeconomic

Aspects of Firm

Bankruptcy

Analysis

We assume that the probability of firm failure during a given period increases with the intensity of the fluctuations of Y and IT (that is, with Am, Aa, and AY,, and with the modulus) and decreases with the time interval between successive troughs (that is, the cycle length). The underlying rationale is that the greater and more frequent the fluctuations of GNP, the more drastic and frequent the changes in the demand for a firm’s product. Moreover, when payments and receipts are not automatically linked to an overall price index, a firm’s net cash-flow is increasingly sensitive to fluctuations in the rate of inflation. A firm’s management, it is suggested, bears a strong analogy to sailing in rough seas where the magnitude and frequency of the waves, as well as the boat’s characteristics and crew’s skills, are the determinants of survival. Equations (6), (7), and (8) depict the relationships connecting the modulus and cycle length to the structural parameters 6, 4, and p, which represent the trade-off on the supply side between inflation and GNP gap, the monetary multiplier, and the expectations correction coefficient, respectively. These parameters may vary across economic periods and countries in correspondence to differences in the social, cultural, institutional, and political structures. For instance, 6 is related to the degree of concentration of the labor markets and to the productivity of labor; 4 to the propensity to consume (which in turn is affected by the availability of consumer credit and by the nature of the taxes and transfers systems and the like), the sensitivity of the private investment to interest rate, the velocity of money, and the population’s liquidity preferences; and p to the level of education and the technology of communication and data processing. In particular, these equations indicate the important role of the degree (p) to which the public modifies its expectations about the rate of inflation. The probability of bankruptcy increases with p due to higher frequency of the fluctuations in GNP and inflation rate. Furthermore, for sufficiently small values of p, an increment in either the monetary multiplier or the inflation-GNP gap trade-off lowers the frequency of the fluctuations of the aggregate variables as well as their magnitude (that is, lengthens the cycles and reduces the modulus) and hence reduces the likelihood of insolvency. These results and the direct relationship between the monetary multiplier and the Keynesian multiplier imply, for example, that policy measures and institutional developments which 411

Amnon Levy and Ran Bar-Niv moderate the Keynesian multiplier may affect the business sector’s stability in one direction or another, according to the intensity of the public inflationary expectations’ modification. When we modify the macroeconomic system by introducing additive random disturbances in the aggregate supply equation, (l), and the aggregate demand equation, (2), and incorporating the hypothesis that the public inflationary expectations are rather rational, we note that a greater monetary multiplier does not necessarily lead to larger variations of output and inflation rate. In fact, for a sufficiently small ratio between the variances of the disturbances in the aggregate supply and demand schedules, the greater the effectiveness of the monetary policy, the lower the likelihood of firm failure. Furthermore, the smaller the effectiveness of monetary policy, the more likely that an increment in the inflation-output tradeoff reduces the probability of insolvency.’

3. Testing the Underlying

Hypothesis

Our empirical analysis tests the paper’s basic hypothesis of direct relationship between the probability of bankruptcy and variations in the aggregate variables by estimating the parameters of the annual bankruptcy rate regression equation. The underlying rationale is that the probability of firm failure increases with the fluctuations in the demand for the firm’s product, and that the latter in turn are intensified by the variation in the public purchasing power. Our regression analysis also takes into account the effects of possible lags between payment and receipts on the firm’s net cash flow by including a measure of variation in the overall price level. It considers further the effect of covariation of these factors. Finally, the inclusion of the time index (t) on the right-hand side of the regression equation allows testing the existence of a trend. In this regard one may expect that, ceteris paribus, due to the increasing number of federal and state regulations on firm operation and improvements in managerial systems and methods, the rate of bankruptcy declines as time progresses. The estimation of bankruptcy rate regression equation parameters is carried out with post-World War II U.S. time-series data on the number of bankruptcies per ten thousand firms (Dun and 'A more detailed derivation of the effects of the structural parameters (p, +, and S) on the probability of firm failure under both the deterministic and stochastic models can be provided by the authors upon request. 412

Macroeconomic

Aspects of Firm

Bankruptcy

Analysis

Bradstreet 1984) and on the real GNP in 1972 dollars (billion) and the GNP deflator, GNPD (Gordon 1984). The best estimation results, as regards level of significance and goodness of fit, are obtained with the semilog specification: exp{BR,} = o. + ai[var(GNP)], + a,[cov(GNP,

+ a.Jvar(GNPD)],

GNPD)],

+ a$ + u, ,

(9)

where BR is the annual number of bankruptcies per ten thousand and oq are unknown parameters; and u is a ~0, al, +2, a3, random disturbance which we assume to be independently and identically distributed. The variances and the covariance of the real GNP and the GNP deflator are computed with quarterly observations of the real GNP and the GNPD according to formulas which capture the variations of these variables before and during the time of bankruptcy:

firms;

[var(GNP)],

1’ = 7 z J

[var(GNP)],

(GNP,,

- GNP)2 ;

WV

- GNPD)2 ;

(11)

0

1 J = 7 z (GNPD,, J 0

[cov(GNP,GNPD)], GNP,,

- GNP)(GNPD,,

- GNPD)

;

(12)

where GNP and GNPD are the averages of the real GNP and the GNP deflator, respectively, for the period started J quarters before the end of year t. The ordinary least squares (OLS) estimates for four reasonable choices of J (twelve, sixteen, twenty, and twenty-four quarters), which also lead to better estimation results, are summarized in Table 1 below. These estimation results are statistically significant and very robust with regard to the choice of J. The estimates of oi and cy2 confirm a priori expectations that the annual rate of bankruptcy in post-World War II U.S. increases with the degrees of dispersion of the real GNP and the GNP deflator. The results also indicate 413

Amnon Levy and Ran Bar-Niv TABLE 1. Equation* Explanatory Variable Var(GNP)

OLS Estimates of the Parameters of the Bankruptcy Value 12 quarters 0.2669

Var(GNPD)

0.1115 (2.97)

of J

16 quarters

E + 36

0.3609

(1.11)

20 quarters

E + 35

0.1997

E + 35

ww

(3.08)

E + 36

0.1242

E + 37

0.1218

24 quarters 0.1399

E + 37

0.1378

(6.26)

(6.51)

(7.54)

-0.3603

E + 36 -0.4436

E + 36 -0.3280

E + 36 -0.3398

(2.03)

(3.08)

(4.03)

(5.07)

t

-0.3719

E + 36 -0.1154 (0.81)

E + 37 -0.1933

E + 37 -0.2164

(1.37)

(1.61)

(0.19)

Constant

-0.8881 (0.W

-0.1330

E + 38

0.3094

(0.668)

(0.153)

R2

0.375

F

4.19

14.69

17.20

Durbin-Watson Statistic

1.84

1.54

1.73

*The

period

sample

0.685

is 1947-1982

and

0.725

the

t-ratios

E + 35

(2.09)

Cov(GNP, GNPD) (trend)

Rate

E + 37

0.1549

E + 37 E + 36 E + 37 E + 38

(0.82)

0.786 22.94 1.12

are

in parentheses.

that the annual rate of bankruptcy declines with the covariance of these aggregate variables. This implies further that, all other things being equal, in periods where the real GNP and the GNP deflator proceed in the same direction, the probability of firm failure is lower than in periods where they go in opposite directions. Finally, as expected, the estimated trend is negative but statistically insignificant. Note that its level of significance increases with J and reaches a peak (12%) when J is equal to twenty-four quarters.

4. Conclusion This paper examines the effects of fluctuations of macroeconomic variables on the firm’s prospects of failure. The empirical analysis indicates that variations of GNP and GNP deflator increase the probability of bankruptcy but the covariance of these variables moderates the probability of bankruptcy. It was also found that there is no significant trend in the rate of bankruptcy. The theoretical analysis of business cycles suggests further that the probability of firm failure increases with the intensity with which the public modifies its inflationary expectations (p) and that for sufficiently small 414

Macroeconomic

Aspects of Firm Bankruptcy

Analysis

values of ~3the likelihood of bankruptcy declines with the monetary multiplier and the inflation-output gap trade-off. Received: February 1986 Final version: December 1986

References Altman, E.I. Corporate Bankruptcy in America. Lexington, Mass.: Heath Lexington Books, 1971. Bulow, J.I., and J.B. Shoven. “The Bankruptcy Decision.” The Bell Journal of Economics 9 (Autumn 1978): 437-55. Cagan, P. “The Monetary Dynamics of Hyperinflation.” In Studies in the Quantity Theory of Money, edited by M. Friedman. Chicago: University of Chicago Press, 1956. Delong, B. J., and L.H. Summers. “Are Business Cycles Symmetric?” Harvard Institute of Economic Research (1984), Discussion Paper No. 1076. Dombusch, R., and S. Fischer. Macroeconomics. 2nd ed. New York: McGraw-Hill, 1978. Dun and Bradstreet. The Business Record (1984). Friedman, M. A Theory of the Consumption Function. Princeton: Princeton University Press, 1956. Gordon, R.J. Macroeconomics. 3rd ed. Boston: Little, Brown, 1984. Keynes, J.M. The General Theory of Employment, Interest and Money. London: Macmillan, 1936. Mitchell, W.C. Business Cycles: The Problem and Its Setting. New York: NBER, 1927. Munch, P., and D.E. Smallwood. “Solvency Regulation in the Property-Liability Insurance Industry: Empirical Evidence.” The Bell Journal of Economics 11 (Spring 1980): 261-79. Neftci, S.N. “Are Economic Time-Series Asymmetric Over the Business Cycle?” Journal of Political Economy 42 (April 1984): 307-28. Stapleton, R.C. “Some Aspects of the Pure Theory of Corporate Finance: Bankruptcies and Take-Overs: Comment.” The Bell Journal of Economics 6 (Autumn 1975): 708-10. Stiglitz, J.E. “Some Aspects of Pure Theory and Corporate Finance: Bankruptcy and Turnovers.” The Bell Journal of Economics 3 (Autumn 1972): 458-83. -. “Some Aspects of Pure Theory and Corporate Finance: Bankruptcy and Turnovers: Reply.” The Bell Journal of Economics 6 (Autumn 1975): 711-14. 415