Hypothesis Testing on Clusters

Having developed the clusters of the firm failure processes (with and without directors’ characteristics) and having discussed some observable differences in the concentration of firms among different clusters, the chapter proceeds to analyze

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whether there are any statistically significant differences between the failure processes as expressed in the two versions of the clusters. These tests include both the firm-specific (financial ratios, firm age and directors’ characteristics) characteristics that were used in order to identify the alternative firm failure processes as well as a number of additional characteristics, associated with the economic and business environment. The latter have been discussed in the development of the Hypotheses (Chapter 2).

The approach undertaken to test the Hypotheses relating to the cross-country comparison of the firm failure processes applies the median test for continuous variables. For categorical variables, the Pearson chi square test of the independence of rows and columns in a two-way distribution table is employed. Table 5.4 presents the results of the chi-square tests and Table 5.5 the results of the median test

Table 5.4: Pearson Chi-Square on Differences in Firms’ Characteristics between Firm- Clusters

Table 5.5: Median test - Pearson Chi-Square values on Differences in Financial Ratios between Firm-Clusters

The first step, is to ascertain whether the firm failure processes are independent to the countries. In addition, it is tested whether the (mainly) business environment characteristics that are categorical variables in nature differ between the alternative firm failure processes (with and without directors’ characteristics). The results for the independence between countries and firm failure processes are assessed with a Pearson chi-square test (Table 5.4). The null hypothesis of the Pearson Chi-square is that there is no difference in the distribution of firms between the rows (countries) and the columns (firm failure processes).

Firm Clusters

(Failure Processes) Legal Origins Industry Countries SGR

Clusters without Directors' characteristics 705.17 / 0.000 122.45 / 0.000 189.16 / 0.000 13.93 / 0.003 Clusters with Directors' characteristics 429.32 / 0.000 875.81 / 0.000 125.97 / 0.000 9.32 / 0.025

Chi-Squared statistic/p-value

Firm Clusters

(Failure Processes) ROI

GROWTH

RATE NSTA CFTS QUICK

RATIO TLTA QACA TCTL FIRM AGE GDP Growth Credit Availability Women Age of Directors Nr. Of Directors

Clusters without Directors' characteristics 245.79 / 0.000 221.49 / 0.000 308.79 / 0.000 283.39 / 0.000 647.04 / 0.000 192.82 / 0.000 887.37 / 0.000 111.03 / 0.000 284.84 / 0.000 338.88 / 0.000 560.70 / 0.000 88.80 / 0.000 102.95 / 0.000 343.76 / 0.000 Clusters with Directors' characteristics

391.99 / 0.000 445.78 / 0.000 343.78 / 0.000 491.94 / 0.000 561.72 / 0.000 414.93 / 0.000 608.86 / 0.000 697.95 / 0.000 343.08 / 0.000 500.07 / 0.000 579.62 / 0.000 140.00 / 0.000 13.08 / 0.004 120.02 / 0.000 Chi-Squared statistic/p-value

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Consequently, the alternative hypothesis is that there is a difference in the distribution between firm failure processes and countries and as a result firm failure processes differ between countries. The results, reported in Table 5.4, show the chi-square test is significant at the Sig. <0.01 level. Therefore one can reject the null hypothesis. This applies to both analyses with and without directors’ characteristics. In addition, a number of hypotheses that were set in earlier chapters are tested.

Hypothesis 1: Countries’ legal origins differ between firms in the alternative

failure processes in the EU countries under consideration; they are also determinants of firms’ transition to failure.

In the context of the Chi-square test, the null hypothesis is that the rows (legal origins) and columns (failure process clusters) do not differ in the distribution of firms. The alternative hypothesis is that there is a difference in the distribution of firms between failure processes and legal origins and therefore that countries’ legal origins differ between firms in the alternative firm failure processes.

The Pearson Chi-square is significant (at p level<0.01), confirming that the null hypothesis is rejected and therefore there are statistically significant differences in the distribution of firms’ legal origins in the failure clusters (Table 5.4). Therefore, this part of the analysis accepts the first part of Hypothesis 1 that countries’ legal origins differ between the alternative failure processes in the European countries under consideration. The results are consistent irrespective of whether the clustering has been with or without directors’ characteristics.

Hypothesis 2: Industry classification differs between firms in the alternative firm

failure processes in EU firms; it also differs as a determinant of firms’ transition to failure in the alternative firm failure processes.

In the context of the Chi-square test, the null hypothesis is that the rows (industries) and columns (failure process clusters) have no difference in the distribution of firms.

The alternative hypothesis is that there is a difference in the distribution of firms between failure processes and the industries they belong to. The Pearson Chi- square is significant (Table 5.4) with 27 degrees of freedom (p-value <0.01),

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rejecting the null hypothesis. Therefore one can conclude that there is a statistically significant difference in the industry distribution across the failure clusters. As such the first part of Hypothesis 2 is accepted: Industry classification

differs between firms in the alternative firm failure processes in EU firms. The

results are consistent for both sets of clusters, with and without directors’ characteristics.

Hypothesis 3: Financial performance represented by key financial ratios and the

age of the firm, differ in the alternative firm failure processes of EU firms; they also differ as determinants of firms’ transition to failure in the alternative firm failure processes.

The financial ratios and the age of the firm are firm specific characteristics that were used to identify the alternative firm failure processes. As such one would expect that these will differ in the alternative firm failure processes. The median test (using a Pearson chi square statistic) has been applied to compare the medians of all financial ratios across the different clusters. In the context of the median test, the null hypothesis is that there is no statistical difference in the medians of the financial ratios and of the firms’ age between failure clusters. The alternative hypothesis suggests there is a difference in the medians of the financial ratios and of the firms’ age in the alternative firm failure processes. The results (Table 5.5) for both failure clusters (with and without directors’ characteristics) reject the null hypothesis and therefore they indicate that there are statistically significant differences between firm failure clusters’ in all financial ratios’ and the firm age medians. Therefore, the medians of financial ratios and of the age of the firms are not the same across firm failure clusters. As such, this part of the analysis accepts the first part of Hypothesis 3: Financial performance represented by key

financial ratios and the age of the firm, differ in the alternative firm failure processes of EU firms. The results are consistent for both sets of clusters, with and

without directors’ characteristics.

Hypothesis 4: In a cross country context, macroeconomic conditions differ

between firms in the alternative firm failure processes in EU firms; they also differ as determinants of firms’ transition to failure in the alternative firm failure processes.

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GDP growth and the credit availability are both continuous variables. The median test (Pearson chi square) has been applied to compare the median GDP growth and credit availability between difference clusters. The null hypothesis of the median test suggests that there is no statistical difference in the medians of GDP growth and credit availability between failure clusters. The alternative hypothesis suggest that there is a difference in the medians in the alternative firm failure process clusters. The results (Table 5.5) in both failure clusters (with and without directors’ characteristics) indicate that there is statistically significant difference between firm clusters’ in both the GDP growth and the credit availability as the null hypothesis is rejected for both economic metrics. Therefore, the first part of Hypothesis 4 is accepted: In a cross country context, macroeconomic conditions

differ between firms in the alternative firm failure processes in EU firms.

Hypothesis 5: Directors’ Characteristics such as the presence of women in SMEs’

management, director age as a proxy of director experience and the number of directors, differ in the alternative EU firm failure processes; they also differ as determinants of firms’ transition to failure in the alternative firm failure processes.

The directors’ characteristics are firm specific characteristics that were used to identify the alternative firm failure processes. As such one would expect that these will differ in the alternative firm failure processes. The median test (Pearson chi square) has been applied to compare the median number of women in the board, median age of directors and median number of directors across the 4 different failure clusters (with and without directors’ characteristics). The null hypothesis of the median test suggests that there is no statistical difference in the medians of the director characteristics between failure clusters. The alternative hypothesis suggests that there is a difference in the medians of the director characteristics in the alternative firm failure process clusters.

The result (Table 5.5) in both failure clusters (with and without directors’ characteristics) indicate that firm failure clusters have statistically different median number of women in the board, age of directors and total number of directors. Therefore, the first part of Hypothesis 5 is accepted: Directors’ Characteristics such

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director experience and the number of directors, differ in the alternative EU firm failure processes. The results are consistent for both sets of clusters, with and

without directors’ characteristics. This is a further indication that the inclusion of directors’ characteristics is important in the identification of firm failure processes in the quantitative failure process literature and confirms the evidence from the qualitative failure process literature (see for example Argenti, 1976; Richardson et al., 1994; Ooghe and DePrijcker, 2008).

Hypothesis 6: The distribution of firms with unsustainable levels of growth differs

between the alternative firm failure processes in EU firms; unsustainable levels of growth are also determinants of firms’ transition to failure.

The Sustainable growth variable (SGR) has been developed by employing the formulae presented in Chapter 4. The SGR takes the value of 1 if a firm’s annual growth in sales exceeds the calculated sustainable growth level and 0 otherwise. A rapid increase of a firm’s sales, beyond the sustainable levels has been associated with firm failure (Argenti, 1976; Richardson et al., 1994; Higgins, 1977). The null hypothesis of the chi square is that there is no difference in the distribution of firms in the rows (SGR) and columns (failure clusters). The alternative hypothesis is that there is a difference in the distribution of firms between failure processes and the SGR.

The results (Table 5.4) demonstrate that the Pearson Chi-square is significant with 3 degrees of freedom (p-value <0.01). Therefore, one can accept hypothesis 6:

The distribution of firms with unsustainable levels of growth differs between the alternative firm failure processes in EU firms. This is because there is a statistically

significant difference in the distribution of firms where SGR=1 and therefore with unsustainable levels of growth across the failure clusters.

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