نوسانات اقتصاد کلان و شکنندگی مالی شرکت

Using a large sample of accounting data for non-financial companies in France, this paper studies the interactions between macroeconomic shocks and companies’ financial fragility. We consider links in both directions, namely whether firms’ bankruptcies are affected by macroeconomic variables, and whether bankruptcies determine the business cycle. We estimate forecasting equations for firms’ bankruptcy using Shumway's (2001) approach and study the joint dynamics of bankruptcies and macroeconomic variables within an exogenous VAR type model estimated at the sector level. We find evidence of reciprocal links between the bankruptcy rate and the output gap and highlight significant “second round effects” of shocks to the output gap on bankruptcies. We show how taking into account the dynamic transmission of macroeconomic shocks matters in stress testing exercises.

The financial crisis that emerged in the summer of 2007, characterized by the most severe recession in the post-war period and a historical level of business bankruptcies in many countries, has highlighted the need to identify the link between bankruptcies and macroeconomic developments in a dynamic perspective. This is important for the proper implementation of “stress tests” of credit risk that are designed to assess the resilience of the financial sector, notably banks’ loan portfolios, to exceptional but plausible macroeconomic shocks. In contrast to the way stress tests are usually carried out, with a one-way impact of the macroeconomic environment on the financial sector, we highlight the need to take account of “second round” effects, namely the reverse impact of bankruptcies on the macroeconomy. To this end, we estimate a 2-equation VAR type model linking the output gap and the bankruptcy rate, also using detailed information on the financial situation of individual firms. We illustrate our methodology in the case of France and show that second round effects do matter. Fig. 1, where we report the number of corporate bankruptcies in France and a simple measure of the output gap (in inverted scale), provides prima facie evidence of the link between the two variables: in the wake of the crisis, in 2010, bankruptcies reached levels that were equivalent to those in the 1992–1993 period.1 However, taking a longer perspective, one can observe different cases: either bankruptcies led the output gap as in the early 1990s and in 2001–2002, or the output gap led bankruptcies as in the late 1990s, or the two were independent as in 1993–1994, when the increase in the number of bankruptcies outpaced that of the output gap. This was also the case in 2003–2007: more bankruptcies occurred in spite of the upward phase of the business cycle. The Banque de France (2009) stressed in particular that the higher level of business creations during the 2003–2007 period – itself correlated with the business cycle – may explain the increase in the number of bankruptcies. This calls for a more detailed analysis of the dynamic link between business bankruptcies and the business cycle.There is agreement in the financial economics literature regarding the existence of a link between bankruptcies and the business cycle. This topic has already been extensively investigated and it is now acknowledged that some interaction exists. This led the Basel Committee on Banking Supervision to recommend in 2004 a regulatory framework (commonly known as Basel II) to, inter alia, take account of the adverse effect of the macro-economy on banks’ loan portfolios, particularly in the implementation of stress tests. More recently, the Basel III framework introduced capital buffers that increase the cost of credit in the upturn, but reduce it during the downturn, highlighting the effect of capital losses on the supply of credit, hence on the business cycle. However, there is no agreement on the channels by which bankruptcies and the business cycle interact, nor on how to measure the link. Regarding the channels of interaction, the business cycle affects the environment of firms, and hence may explain, with a lag, the changes in bankruptcies over time, in addition to firm-specific variables like financial ratios. On the other hand, bankruptcies may affect the business cycle, marginally through lost capacities of production, and more significantly through credit rationing as shocks to credit supply have often been shown to be leading indicators of the business cycle (Bernanke and Gertler, 1989 and Lown and Morgan, 2006). In addition, banks may limit credit supply because they become more risk averse when they observe more bankruptcies or because larger losses constrain their ability to expand assets. As far as measurement is concerned, the approaches followed in many studies are usually partial, as they focus on one-way interactions between bankruptcies and the business cycle. As mentioned above, our study contributes to this literature by focusing on the French case, providing evidence of two-way interactions, as well as showing how taking account of the dynamic transmission of macroeconomic shocks matters in stress testing exercises. This paper attempts to merge two strands of the quantitative economic literature regarding how the macroeconomic environment affects financial fragility, and conversely how financial fragility affects the business cycle. We also consider evidence that points to two-way interactions between business bankruptcies and the macroeconomy. The first strand in the literature is the growing number of quantitative papers focusing on the impact of macroeconomic conditions on the bankruptcy of firms. The different contributions can be distinguished either according to the types of data used, or the method implemented, with overlaps between the two types of papers. First, regarding data, macroeconomic indicators have been introduced into the estimation of credit risk models for portfolio management, but we should distinguish between models that use financial market data and models that use accounting data. In the first case, we are mainly looking at large quoted companies. See Allen and Saunders (2004) for a survey of these papers.2 In the latter case, we consider a larger set of non-financial companies. Second, regarding the methods used, we should distinguish between (i) a large number of papers starting from Altman's (1968) seminal paper based on discriminant analysis that predict business failures but without introducing macroeconomic variables, (ii) papers introducing macroeconomic variables using the multi-period Logit model advocated by Allison (1982) and Shumway (2001), (iii) duration models and (iv) other econometric methods. Regarding the first group of papers, we should mention Altman and Saunders (1998), Benito et al. (2004), Bernhardsen (2001) and Bunn and Redwood (2003). Regarding the second group of papers, we refer to the methodology initiated by Allison (1982) and most notably applied by Shumway (2001), who use a particular Logit model in order to measure the dynamic relationship between macroeconomic variables and bankruptcies. In our case, we have access to a large sample of non-financial French firms (an average of 80,000 firms per year) which are observed over a sufficiently long period and make it possible to take into account the progressive deterioration of their financial conditions in predicting business failures, unlike the first generation Logit or Probit models, which only provide a static analysis, period by period, based on a cross-section of accounting ratios, hence without macroeconomic variables. Applications of this method include Chava and Jarrow (2004) and Campbell et al. (2008). In the latter paper, the macroeconomic environment is introduced through financial market variables. In addition, Beck et al. (1998) and Glennon and Nigro (2005) use dummy variables to capture the effects of the business cycle. Hillegeist et al. (2004) introduce the aggregate failure rate of US firms as a proxy for the growth rate of GDP. Nam et al. (2008) study defaults of Korean quoted companies and introduce exchange rate volatility as a macroeconomic variable. Jacobson et al. (2005) use Shumway's (2001) approach to model the default risk of Swedish companies. The third group of papers use duration models, for example Carling et al. (2007), Duffie et al. (2007), Bonfim (2009), Bhattacharjee et al. (2009) and Koopman et al. (2009). But despite the main advantages outlined above, the use of duration models remains limited due to left-censoring problems. Indeed, when the observation period is short, most firms in the dataset were created before the observation period, implying that firms’ time at risk may be much greater than the observation period. The fourth group of papers, from the point of view of methodology, use a variety of econometric techniques to estimate bankruptcies, also taking into account macroeconomic variables: Hamerle et al. (2004) estimate a random effect Logit model of bankruptcies for German companies; Bonfim (2009) uses a random effect Probit model for Portuguese firms and Qu (2008) uses a fixed-effect LSDV model. Pederzoli and Torricelli (2005) estimate a state-dependent static Probit model of default, distinguishing between expansion and recession periods. Jéminez and Saurina (2006) measure the effects of the growth of bank lending on banks’ defaults using a random effect Logit model. A second strand of the literature looks at how the financial fragility of firms affects the business cycle. Such a question is particularly relevant to macroeconomic forecasting with a view to incorporating information at the microeconomic level. Several papers investigate how financial variables, and in particular the financial position of corporate firms, affect the business cycle. In particular, Lown and Morgan (2006) provide evidence that indicators of financial fragility, as measured by business failures, together with credit standards have explanatory power for the growth of bank loans and GDP, on top of standard measures of interest rates on loans. As indicated above, our objective is to focus on the so-called “second round effects” by taking account of two-way interactions between macroeconomic developments and financial fragility. Very few papers take this approach. In the paper, in order to investigate these “second round effects”, we examine how a given initial macroeconomic shock impacts the financial position of firms, which in turn affects macroeconomic variables. Many papers in the stress testing literature design sophisticated macroeconomic scenarios. However, only a small number of them really consider the two-way interactions between bankruptcies and the macroeconomy. Regarding the first type of stress tests – i.e. one-way interaction – one should mention single equation models such as those studied by Sorge and Virolainen (2006). Simons and Rolwes (2009) also use a single equation but focus on the dynamic (autoregressive) structure of Dutch companies’ default rate, estimated in a separate Logit model. Multi-equation models can also be used in this first type of stress test. For example, VAR models are used by Alves (2005), highlighting the long-run common dynamics across sectors; Pesaran et al. (2005) as well as Castrén et al. (2010) use GVAR models for the design of the macroeconomic scenarios that affect default probabilities, but there is no feedback effect from bankruptcies to the macroeconomy. To our knowledge, only three papers really consider two-way interactions between aggregate bankruptcies and the macroeconomy. Jacobson et al. (2005) present a model in which observed bankruptcies are introduced as endogenous variables in a VAR with other macroeconomic variables. They also estimate a “micro-macro” model where estimated bankruptcies from a Logit equation with microeconomic variables are introduced as additional variables in an exogenous VAR (VARX) model. However, in the latter case, bankruptcies are no longer fully endogenous. Koopman and Lucas (2005) uncover cyclical comovements between GDP and business failures at long frequencies using a multivariate unobserved component model. Finally, Sommar and Shahnazarian (2009) use a structural credit risk model for calculating the empirical Expected Default Frequency (EDF) for listed companies, and investigate the long-run relationships between expected bankruptcies and macroeconomic developments using a Vector Error Correction Model (VECM). In comparison with the last two papers, we stress the need to use micro-data, as well as to consider a broader set of companies than only those with access to the financial market. In this paper, we follow the “micro-macro” approach of Jacobson et al. (2005) that we apply to the French case, but consider business bankruptcies as fully endogenous variables, allowing for two-way interactions at the sector level. We provide evidence of second round effects based on the persistence of the shocks to the business cycle, but also explained by the statistically and economically significant effect of bankruptcies on the output gap in our sample. The paper is organized as follows. In Section 2 we explain our modelling choices. In Section 3 we present the data and the main results we obtain regarding the bilateral effects of macroeconomic conditions on bankruptcies. Variant scenarios and stress tests are considered in Section 4. Section 5 concludes, notably regarding the trade-offs that one may need to make when implementing such a model.

This paper reports empirical evidence of the links between macroeconomic cycles and changes in financial fragility measured at the microeconomic level by focusing on corporate firms in France. We estimate a VAR type system of two equations at the sector level: the first describes an indicator of firms’ bankruptcies – measured as the Log of the odd ratio – as a linear function of financial ratios and macroeconomic variables; the second specifies the dynamics of the output gap as a linear function of firms’ bankruptcies. The first equation is estimated at the firm level and then aggregated at the sector level. This equation is derived from a multi-period Logit model in order to take account of the progressive deterioration of the financial conditions of firms in predicting their potential default. This multi-period Logit model is easily implemented through a standard Logit estimation along the lines of Shumway (2001). We show that macroeconomic conditions do have an effect on the bankruptcy rate of corporate firms, as proved by the significant impact of lagged macroeconomic variables as well as financial ratios in the multi-period Logit model estimated for each firm. Indeed, we find that the output gap included in this model with lags of two and three years has a significant negative effect on the default probability estimated at the firm level. Second, by regressing the output gap on its lagged values and the observed bankruptcy indicator at the sector level, and by using a panel GMM estimation method, we find a negative coefficient for the bankruptcy rate, which is only significant when introduced contemporaneously into the equation. It provides evidence that the financial fragility of firms does indeed have an impact on the business cycle. Third, using the system of the two previous equations, which assess the joint dynamics of the output gap and financial fragility, we highlight the importance of taking into account in stress testing exercises both the persistence of the output gap and the feedback effects of bankruptcies on the output gap. Indeed, given the statistically and economically significant effect of bankruptcies on the output gap, second round effects appear quite clearly. The fact that dynamic effects matter also implies that, following an output gap shock, the distribution of bankruptcies is expected to be more permanently affected than in standard stress testing exercises. The proper design of the macroeconomic environment of stress tests therefore requires taking account of the feedback effects that can be captured through financial fragility indicators, such as bankruptcy rates. In the course of the paper we have identified a few trade-offs associated with our approach. First, endogenising defaults through the use of accounting data, which are annual, restricts the analysis to lower frequencies. But accounting data at the micro level allow a more robust estimation of the model parameters. They also cover, in our case, a larger set of companies than only quoted firms, given the existence of many small and medium-sized firms. While quoted firms offer a larger set of indicators, notably asset prices, financial markets data may sometimes provide inadequate signals during crisis periods. Second, using a bivariate system, together with exogenous variables, instead of a larger VAR, increases the robustness of the results as well as reduces the need for additional identification assumptions. In this study, we assumed that all sectors are homogenous regarding the impact of the business cycle on the bankruptcy rate. Future research could consider estimating separate default models for the different sectors. In that case, our methodology to assess second round effects could be extended relatively easily. It would also be useful to compare our results with estimates of the impact of bankruptcies on the business cycle in other countries.