Danmarks Nationalbank's Failure-Rate Model, KIM

Danmarks Nationalbank's failure-rate model, KIM, was initially presented in Financial stability 2003. Boxes in subsequent editions of Financial stability and a working paper^[1] have described KIM further. The model is subject to ongoing development, most recently the introduction of macrovariables. This chapter describes the model tool on which the results of the analysis of Danish companies are based, and the results of the present model with macrovariables and of the former model are compared.

Scope of application
Danmarks Nationalbank's failure-rate model is used to assess the risk that Danish companies will fail. KIM estimates the probability that a company will fail within 1-2 years. The estimated failure rate can be seen as a weighted index of key financial ratios and other elements of the companies' financial statements. The estimated failure rates are also influenced by cyclical movements. The estimates are based solely on public and private limited liability companies. Agriculture and financial enterprises are not included in KIM.

Explanatory variables
The model comprises 12 explanatory variables, i.e. six quantitative variables and six dummy variables, cf. Table 9. A dummy variable is assigned the value 1 if a given criterion is fulfilled, and otherwise the value 0. Of the six quantitative variables, two are macrovariables that capture the effect of cyclical developments on the estimated failure rate.

The Sign column indicates the direction in which the variable in question affects the estimated failure rate, all other things being equal. Plus (+) means that the estimated failure rate increases, while minus (-) indicates a reduction of the estimated failure rate.

Estimation basis and definition of failure
The model is estimated on the basis of almost half a million annual financial statements presented in the period 1995-2003 by Danish public and private limited liability companies, of which almost 17,000 by failed companies.

The last financial statement presented by an active company before it fails is regarded as being presented by a failed company. The period from the presentation of the last financial statement as an active company to the time when the company is registered as having failed is 1-2 years. In KIM, a company is regarded as having failed in the following situations: compulsorily liquidated, subject to compulsory liquidation, dissolved, compulsorily dissolved, subject to compulsory dissolution, compulsory composition confirmed, or compulsory composition being negotiated. This broader definition ensures a better linkage to the time of the company's payment problems than the definition applied by Statistics Denmark.

The development in the number of failures in the model is consistent with the data from Statistics Denmark, cf. Chart 48. The broader definition increases the number of failures in KIM compared with the official statistics. On the other hand, the fact that the estimation basis solely includes public and private limited liability companies, while the data from Statistics Denmark includes all Danish enterprises, has the opposite effect.

Implementation of macrovariables
Two macrovariables have been added to KIM since Financial stability 2006. The confidence indicator reflects the companies' perception of the current situation, as well as expectations of the coming quarter in terms of employment, sales, prices, new orders and limits to production. The confidence indicator for building and construction has been chosen because this industry is more exposed to cyclical developments than other industries, e.g. manufacturing and business service.

The second macrovariable is the output gap, which indicates output in the economy in relation to the calculated potential output. A positive output gap means that output is higher than envisaged in model calculations of the economy's long-term potential.

A company's estimated failure rate is affected by company-specific factors, as well as the macroeconomic development. The macroeconomic impulses are naturally identical for all companies, but the macroeconomic scenarios have varying impacts on the companies. In an analysis of Swedish companies, Carling, Jacobson, Lindé and Roszbach[2] find that output gap, consumer expectations and the slope of the yield curve, combined with company-specific accounting data, have a significant impact on the companies' estimated failure rates.

The first step towards inclusion of macrovariables is to specify preliminary " year dummies" with a view to capturing the contribution from the cyclical development in the given year. Year dummies are specified for 1995-2003, with 1995 as the reference year. Year dummies capture the scale of the cyclical impact in relation to the reference year.

The second step is to find macroeconomic variables that follow the development in the parameter estimates for the year dummies. To some extent, both the confidence indicator for building and construction and the output gap seem to follow the development in the parameter estimates for the year dummies, cf. Charts 49 and 50. There are, however, deviations in the first couple of years of the estimation period, particularly for the confidence indicator. The two macrovariables capture effects from, respectively, changes of mood among companies and external macroeconomic factors.

Both the output gap and the confidence indicator are significant and are included in the model at the 1-per-cent significance level. The parameter estimates for the model's other explanatory variables are to a great extent unchanged after inclusion of the macrovariables.

The coefficient to the output gap is included with a positive sign. This means that a positive output gap in the current year increases the general probability that companies will experience financial difficulties in 1-2 years' time. The explanation is that periods with a positive output gap typically see the establishment of many new companies, which are generally more likely to fail.

The confidence indicator for building and construction gives an intuitively negative sign. If the confidence indicator rises, reflecting increased optimism about the immediate future, the general estimated failure rate is reduced.

The distribution of the estimated failure rates over the years changes with the inclusion of macrovariables, cf. Chart 51. The macrovariables increase the fluctuation in the estimated failure rate for the median company. At the same time, the development in the estimated failure rate for the 90th percentile since the millennium rollover is closer to the a priori expected development than in the model without macrovariables. It is certainly among the weakest 10 per cent of the companies that the vast majority of failures occur.

Since KIM is estimated over a relatively short period during which there have been no major cyclical fluctuations, the parameter estimate for the two macrovariables, which have proved to be significant, should be interpreted with caution. It should also be remembered that the output gap is a calculated entity and that its historical values are revised on an ongoing basis by recalculating the deviation between the actual and potential economic activity.