What influences the number of bankruptcies?

Author:Jacobsen, Dag Henning

After having remained relatively stable from the mid-1990s, the number of bankruptcies rose sharply in 2002 and 2003, but then fell again last year and in the first six months of 2005. Using an empirical model, we analyse factors underlying developments in bankruptcies. We find that changes in profit margins, competitiveness and real interest rates, as well as cyclical fluctuations in the Norwegian and international economy, have been among the most important driving forces since 2002. The analysis indicates that deteriorating competitiveness in 2002 as a result of a strong krone exchange rate and high wage growth contributed in particular to the marked increase in the number of bankruptcies. The depreciation of the krone exchange rate in 2003 and into 2004, combined with moderate wage growth from 2003, helped to improve competitiveness in Norwegian enterprises. This explains a considerable portion of the recent fall in the number of bankruptcies.

1 Introduction

One of Norges Bank's primary responsibilities is to promote a robust and efficient financial system. Norges Bank therefore monitors trends that may threaten stability in the financial sector. A substantial increase in the number of corporate failures could constitute such a threat, as a higher number of bankruptcies normally results in higher loan losses in banks.

Although the bulk of banks' lending is to households, experience shows that banks normally incur greater losses on loans to enterprises than on loans to households. This was particularly true during the banking crisis from 1988 to 1992. From the mid-1990s until 2002, the bankruptcy rate, i.e. the number of bankruptcies in relation to the number of enterprises, was relatively low and stable (see Chart 1). In 2002, however, the bankruptcy rate rose considerably. It was substantially lower than during the banking crisis, but banks' loan losses rose markedly. There was an increase in losses on loans to the manufacturing sector in particular. (2) Loan losses continued to rise into 2003 and resulted in poorer earnings in banks. Since end-2003, the bankruptcy rate has fallen again and banks' profits have improved, primarily due to lower loan losses.


Norges Bank has previously developed an empirical model for estimating individual bankruptcy probabilities for Norwegian limited companies. (3) Among other things, the model includes idiosyncratic accounting variables as explanatory factors. The accounting variables capture changes in each limited company's profitability, financial strength and liquidity. Movements in such accounting variables will often closely follow macroeconomic developments in Norway and abroad. Furthermore, many macroeconomic variables are often published both earlier and more frequently than accounts figures. Norges Bank therefore also monitors macroeconomic variables in its assessment of banks' credit risk. The purpose of this article is to increase our understanding of the relationship between macroeconomic conditions and changes in the number of bankruptcies by means of an empirical model. The model was previously presented in Financial Stability 1/05. In this article we will look more closely at the driving forces underlying developments in bankruptcies. In particular, we will try to answer the following questions:

* What are the most important macroeconomic explanatory factors for the number of bankruptcies in the period 1991-2004?

* How swiftly and strongly do changes in these factors influence the number of bankruptcies?

* What has driven changes in the number of bankruptcies since 2002?

* What will the bankruptcy rate be in the period ahead if the Norwegian economy develops in line with the analyses in Inflation Report 2/05?

The estimated model contains effects of:

* Domestic demand and activity level

* Foreign demand and activity level

* Competitiveness

* Real interest rates

* Real labour costs

* Real material input costs

* Enterprises' real gross debt

* Real price of commercial property

* Number of enterprises

The macroeconomic factors that may influence changes in the number of bankruptcies are discussed in the next section. The empirical model is presented in section 3 and in section 4 we discuss the most important macroeconomic driving forces underlying developments in bankruptcies since 2002.

2 Changes in the number of bankruptcies and macroeconomic factors

The purpose of this empirical analysis is to identify the macroeconomic factors underlying changes in the number of bankruptcies. We will start by discussing which variables might be expected to be of importance to developments in bankruptcies on the basis of economic theory. First we will look at a profit-maximising enterprise and consider general factors that influence the probability of that enterprise going bankrupt. The presentation in this section largely follows Wadhwani (1986): (4)

(i) The enterprise produces a product using labour (L), material inputs (V) and real capital (K). The company wage level is W and the input price is Q. Real capital, K, is given in the short term, and for the sake of simplicity is excluded in the further derivation of the model.

(ii) The only source of uncertainty is the product price, which is a stochastic variable with an expected value equal to [??] and a standard deviation of [sigma]. The enterprise has to rake the product price as given.

(iii) The enterprise has borrowed the sum D to finance the real capital that is necessary for production. The enterprise has interest expenses equal to iD in each period, where i is the interest rate. (iv) NV expresses the expected present value of the enterprise's future cash flow and is therefore equal to the value of the enterprise. S expresses its equity. If the enterprise cannot meet current commitments for a period, it will be able to finance itself with the amount S = NV - D, as long as NV [greater than or equal to] D.

Under these assumptions, it is optimal for the enterprise to choose the amount of labour and material input that maximise the expected profit:

(1) max E([PI]) = [??]G(L,V) - WL- QV with respect to L and V,

where E is the expectations operator, [PI] is the profit and G( ) is the production function. An enterprise will normally be bankrupt if the value of its assets is less than its liabilities and it cannot meet its current commitments. On the basis of this definition, the enterprise we are considering would be bankrupt if the realised price, P, was such that the sum of the enterprise's profit and equity in this period was negative:

(2) PG(L,V)- WL - QV - iD + S


PG(L,V) - WL - QV - (1 + i)D + NV

However, creditor(s) will often be better served by continued operations if the costs of initiating bankruptcy proceedings are greater than the expected loss in the event of continued operations, or if there is some probability that the negative value will return to a positive value in later periods. Such assessments are probably closely linked to the cyclical situation, i.e. developments in total demand and the activity level in the economy. We can therefore express the probability of the enterprise going bankrupt as:

(3) [mu] = Pr[[??]G(L,V) - WL - QV - (1 + i)D + NV

where [mu] denotes the probability of bankruptcy and Pr[ ] is the probability function. The probability of the enterprise going bankrupt is now conditional on total demand, AD. (5) By combining (1) and (3), the amount of labour that maximises the expected profit can be expressed as:

(4) L = L(W,Q,i,D, NV, [??],[sigma]),

and similarly for material inputs:

(5) V = V(W,Q,i,D, NV,[??],[sigma])

By inserting (4) and (5) into (3), L and V can be substituted out of the equation for the probability of bankruptcy:

(3') [mu] = [mu]([??],[sigma],W,Q,i,D, NV, AD)


[[mu].sub.[??]], 0, [[mu].sub.w] > 0, [[mu].sub.Q]) >0,

[[mu].sub.i], > 0, [[mu].sub.D] > 0, [[mu].sub.NV]

[[mu].sub.i] expresses the partial derivative of [mu] ( ) with respect to factor j.

Higher demand, AD, will generally boost an enterprise's earnings through increased sales and/or a higher price, [??]. Increased earnings will improve the enterprise's ability to pay its costs, service debt and strengthen its equity. Conversely, for a given productivity level and product price, higher input prices, W and Q, will increase the enterprise's costs and thus weaken its profitability and ability to service debt. Hence, higher earnings result in a lower probability of bankruptcy for the enterprise, whereas higher costs have the opposite effect.

The probability of bankruptcy increases in step with the variation in the product price, [sigma], as higher price variation entails a greater probability that the sum of the profit and equity in a period is negative.

Higher interest rates, i, raise the enterprise's debt servicing costs. At the same time, higher interest rates reduce the value of the enterprise through a lower present value of future earnings. Higher interest rates will therefore result in a higher probability of bankruptcy. The more debt, D, an enterprise has relative to the value of its assets, NV, the more likely it is that the enterprise will go bankrupt. The probability of bankruptcy therefore increases with debt, but decreases with the value of the enterprise. (7)

Other possible explanatory factors

Equation (3') shows the probability of bankruptcy for a single, profit-maximising enterprise. An empirical model for the number of bankruptcies is presented in the next section. In the specification of the empirical model, we have used aggregated sizes of variables that are included in the function in equation (3'). We have also taken into account that other macroeconomic factors may influence the number of bankruptcies. Equation (3') is therefore extended to include competitiveness, E, commercial property prices, PN, inflation, [??], and the number of enterprises, F. [mu] is now interpreted as the average probability of bankruptcy for all enterprises:

(6) [mu] =...

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