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The combination of factor and cluster analysis has been selected as a way to create firm failure processes (Laitinen, 1991; Lukason and Hoffman, 2014; Lukason and Laitinen, 2016). Factor analysis is used to summarise the firm specific- characteristics of the firms in order to reduce the number of variables that will subsequently enter the cluster analysis process. Factor analysis only uses firm- specific characteristics because the purpose of the failure process creation is to investigate which firm-specific characteristics determine the failure process of the firms. The factor analysis is used in two parts.

In the first part, the financial ratios of each firm are used for up to 7 years (lag=7; t, t-1, t-2, t-3, t-4, t-5, t-6, t-7) prior to event_failure=2, together with the age of the firm at the time of the liquidation. This is then followed by the associated cluster analysis to identify the firm failure processes.

The second part includes three directors-related variables (total number of directors, number of female directors in the board and average age of directors) in addition to the variables used in the first part. This factor analysis is then followed by the associated cluster analysis to identify the firm failure process. The rest of the section presents the results of the factor analysis without directors’ characteristics and with directors’ characteristics as determinants in the failure process formation; it then compares findings with the literature.

5.3.1 Factor Analysis without Directors’ Characteristics

The first stage of the factor analysis (hereafter factor analysis without directors’ characteristics) examines the financial ratios from the 5,195 event_failure=2 (liquidated/bankrupt) firms for up to 7 years prior to the failure event. That is, the financial ratios are lagged up to lag 7. Additionally, the factor analysis includes the firm age at the last year with available data before it entered liquidation. The age of the firm is not lagged as any such attempt would create a completely linear result. This part of the analysis aims to use metrics that have been previously used in the quantitative firm failure process literature, in order to offer a basis of comparison for the analysis with directors’ characteristics that follows.

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An eigenvalue criterion by means of the Kaiser test (Kaiser, 1960), has been applied to factor analysis. Only factors with eigenvalues above 1 are allowed to return to the second step of the factor analysis which is the VARIMAX rotation. The first part of the factor analysis shows (Appendix A, Table A.9) that there are 12 factors with an eigenvalue >1. These initial factors explain the 89% of the total variation of the initial variables, higher than previous studies where Factor Analysis explained 80% of the variables’ variation for Lukason and Laitinen (2016), 69% for Laitinen et al., (2014) and 52% for Laitinen (1991). This potentially indicates that the additional time periods that this study uses add value to the failure process extraction given that Laitinen (1991) used a six year period in his analysis but with two-year intervals while Laitinen et al., (2014) used a four year period (with yearly intervals) and Lukason and Laitinen (2016) used a five year period (with yearly intervals).

The VARIMAX orthogonal rotation is then applied to the 12 factors in order for factors to be uncorrelated throughout the rotation process. VARIMAX rotation is perceived as the most popular (Hair et al., 2006) and best orthogonal rotation (Fabrigar, et al., 1999) to assist the interpretation of factors. Initial factors have cross-loadings and therefore the rotation technique should assist to develop a clear set of factor loadings. Consequently that would assist the development of reasonably separate failure processes. Table A.11 (Appendix A) presents the loadings of the factor analysis after the VARIMAX rotation. The interpretation of the first round of factor analysis is as follows:

o The first factor is associated with the time series development of the trade credit to total liabilities ratio (TCTL).

o The second factor is associated with the time series development of the Quick assets to current assets (QACA) ratio.

o The third factor is associated with the total liabilities to total assets (TLTA) ratio between the 4th _{and the 7}th _{year prior to failure. The same factor is}

also correlated with the return on investment (ROI) on the 7th _{year before}

the failure (Lag=7).

o The fourth factor is associated with the net sales to total assets (NSTA) ratio between the years 4 and 7 before failure.

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o The fifth factor is associated with QACA ratio between years 4 and 7 and with the TCTL ratio between years 5 and 7 prior to the failure event.

o The sixth factor is correlated with TLTA on the 3rd year prior to failure and with ROI at the same time period.

o The seventh factor is associated with the growth rate of the firm, 3 years prior to failure and with the NSTA (same as what you have done with in previous sentences, put full name here) ratio, also 3 years prior to failure. o The eighth factor is associated with ROI 1 and 2 years prior to failure, TLTA

up to 2 years prior to failure and with NSTA just on the failure time.

o The ninth factor is associated with the time series development of ROI and with TLTA on year 5.

o The tenth factor is associated with the development of the quick ratio between years 2 and 5 from the time of failure.

o The eleventh factor is associated with the development of NSTA ratio up to 4 years before and up to the time of failure.

o The twelfth factor is associated with the development of cash flow to total sales ratio (CFTS) between years 7 and 3 prior to the failure event.

5.3.2 Factor Analysis with Directors’ Characteristics

The second part of the factor analysis (hereafter factor analysis with directors’ characteristics) includes directors’ characteristics in addition to the previous analysis. The inclusion of director characteristics aims to capture some of the observations of the qualitative firm failure process literature within a quantitative approach. As such, the directors’ characteristics include a proxy for gender heterogeneity in the board as measured by the number of female directors. In addition, a proxy for the breadth of social capital that directors bring to the board is captured by the total number of directors. Finally, the experience of the board is captured by using the average age of directors as a proxy.

The financial ratios were treated in the same way as in the first round of factor analysis. Firm age was also treated on the same way with the only the age of the firm at the year of failure entering the data. The directors’ characteristics were included at the time of failure and were not lagged. A specification with lagged directors’ characteristics was tested and returned broadly similar results. This is

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because there was very limited variation in the structure of the board in the 7 years prior to failure. In many firms there was no variation while the average age of directors had a linear relationship across the years. Therefore, only the results with directors’ characteristics that do not include lags in the directors are reported. The results demonstrate that there are again 12 factors with an eigenvalue above 1 (Appendix A, Table A.13). With the inclusion of the directors’ variables the 12 factors explain 87.67% of the total variance, slightly less than the 89% that was achieved without the directors’ variables. However the difference is relatively small to be a reason for not proceeding further with this classification. Therefore, we proceed to analyse the factors after the VARIMAX rotation is performed. Following the VARIMAX rotation the factors are presented in Table A.15 (Appendix A) and can be explained as follows:

o The first factor is characterized by the time-series development of the trade credit to total liabilities ratio (TCTL). This is similar to the first factor without the directors’ characteristics.

o The second factor is associated with the time series development of the Quick assets to current assets (QACA) ratio. This is also similar to the second factor on the factor analysis without directors’ characteristics. o The third factor is partly associated with the total liabilities to total assets

(TLTA) ratio between the 4th _{and the 7}th _{year prior to failure. It is also}

associated to some extend with the return on investment (ROI) on the 7th

year before the failure (Lag=7) and it is broadly similar to the factor analysis without director characteristics.

o The fourth factor is associated with the net sales to total assets (TLTA) ratio between the years 4 and 7 before failure. There is a weak association with the same ratio in years 0 to 3. The factor is similar to the one without the director characteristics.

o The fifth factor is associated with QACA ratio between years 4 and 7 and has a weaker association with the TCTL ratio between years 6 and 7 prior to the failure event. In terms of the financial ratios this factor is broadly similar to the one in the analysis without the directors’ characteristics. Moreover, the firm age is more significant in factor 5 when the directors’ characteristics are included (-46.8% against -24.8% in the non-directors’ analysis). However, this factor is differentiated from its non-directors

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characteristics counterpart because of its association with the number of female directors and the total number of directors.

o The sixth factor is correlated with TLTA on the 3rd year prior to failure and with ROI at the same time period; similar to the 6th _{factor from the analysis}

without the directors’ characteristics.

o The seventh factor is associated with the growth rate of the firm, 3 years prior to failure and with the NSTA ratio, similar to the 7th _{factor from the}

analysis without the directors’ characteristics.

o The eighth factor is associated with ROI 1 and 2 years prior to failure, TLTA up to 2 years prior to failure and a weaker association with NSTA just on the failure time; broadly similar to the eighth factor in the analysis without directors’ characteristics.

o The ninth factor is associated with the time series development of ROI (although not in lag 3) and with the growth rate at lag 6. In the case of ROI, there are similarities with the ninth factor in the analysis without the directors’ characteristics but here, there is evidence of an association with growth rate (6 years before failure) as opposed to the TLTA (5 years before failure) in the analysis without directors’ characteristics.

o The tenth factor is associated with the development of the quick ratio between years 2 and 5 from the time of failure; similar to the tenth factor in the analysis without directors’ characteristics.

o The eleventh factor is associated with the development of NSTA ratio up to 4 years before and up to the time of failure, broadly similar to the eleventh factor in the analysis without directors’ characteristics.

o The twelfth factor is associated with the development of CFTS between years 7 and 3 prior to the failure event, broadly similar to the eleventh factor in the analysis without directors’ characteristics.

One can conclude that the inclusion of directors’ characteristics has modified the fifth factor by adding the board dimension to some of them. In particular, the fifth factor (with directors’ characteristics) is associated with the number of female directors and the total number of directors in firms and therefore captures most of the effects of the board variables.

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