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ƒ Panel analysis: Modeling the thresholds as depending on the level of business confidence, a measure of uncertainty and company size

To test the hypothesis whether the indifference thresholds vary across respondents, in the next step the thresholds are modeled as depending on the company size. The model is estimated at the micro-data level. To test for robustness of the above discussed results with respect to the model specification also the measure of uncertainty and the level of business confidence were included in the model.

The independent variables that entered the model were the proxy for uncertainty in form of the standard deviation of business expectations at each month, the level of aggregate business situation, the level of aggregate business expectations, company size (measured by the number of employees) and the time dummies to control for the variation of the indifference thresholds over time. The proxy of uncertainty and the level of business situation and business expectations vary only over time, but not across respondents. The company size varies both, within and across respondents. The company size was defined by the number of employees. To avoid that outlier (companies with more than 100,000 employees bias the regression results), eleven company size classes3 were generated.

The model was estimated by the fixed effects (FE) panel regression. Although the FE estimator ignores the between subjects variation, estimating the within subjects variation and is not as efficient as the random effect estimator, it was selected for several reasons: The random effects estimator would be biased a soon as one of the explanatory variables is correlated with the composite error term. The composite error term is unknown. It can include some characteristics of the respondent or the respondent’s firm characteristics. So, for example the firm growth may be related to some unobserved firm characteristics or to respondent specific loss aversion. The F- test following the fixed effects panel regression indicates that there are significant

3 _{The 11 company size classes were generated according to the number of employees: (1/49 = 1)} (50/99 = 2) (100/149 = 3) (150/199 = 4) (200/249 = 5) (250/349 = 6) (350/499 = 7) (500/649 = 8) (650/999 = 9) (1,000/1,999 = 10) (2,000/200,000 = 11).

individual (firm level) effects (Table 3.14 and Table 3.15). Whether the random effects model can be used, was evaluated with the Hausman4 test that checks whether the random effects estimate is insignificantly different from the fixed effects estimate. The results of the Hausman test indicated that there may be an omitted variable that is correlated with one of the explanatory variables. Consequently the FE estimator was used. An advantage of the FE estimator is, however, that it controls for all time-invariant variables not just those that were in the model.

The results of the FE panel regression of the indifference threshold on company size, a measure of uncertainty and the aggregate level of business situation and business expectations confirm previous findings (Table 3.14 and Table 3.15).

The level of uncertainty increases the upper bound and decreases the lower bound in both variables. The aggregate level of business situation seems to be positively related to the upper threshold (see Table 3.14). The same pattern applies to business expectations, the higher the level of business expectations the expected changes of business conditions have to exceed a considerably higher threshold before firms report that they expect an improvement. For the lower threshold, in contrast, the higher the aggregate level of business expectations, the smaller the negative changes have to be to make firms report that they expect a deterioration.

Although the company size varies weakly within the companies it was found to be significantly related to the width of the indifference threshold in the variable “present business situation” (see Table 3.14). Increasing number of employees appears to narrow the indifference interval of the variable “present business situation”, meaning that for larger companies a smaller percentage change in output or profits, results in reporting a fall on the three-category scale, than for small-scale enterprises. These results are inline with theoretical considerations reported in the literature (Ronning, 1990). In the variable “business expectations” company size was not significantly related to the width or the form of the indifference interval.

4 _{The Hausman test tests the null hypothesis that the coefficients estimated by the efficient random} effects estimator are the same as the ones estimated by the consistent fixed effects estimator. According to the results of the Hausman test the coefficients were jointly significant (Prob>chi² smaller than 0.05) indicating that there may be an omitted variable that is correlated with one of the explanatory variables.

ƒ Cross-sectional analysis: Modeling the thresholds as depending on the level of business confidence and company size

To test whether these results hold also at the cross-sectional level the upper and the lower thresholds were modeled as depending on the company size, the firm’s business situation appraisal and the firm’s business expectations. The uncertainty proxy could not be added to the model as this variable does not vary within months only across months. Company size is expected to have rather a negative sing in the regression of the upper threshold and a positive sing in the regression of the lower threshold.

The results appear to be robust and consistent with the above findings. In the regression of the upper threshold of the variable “business situation” company size has a negative sign in most months and is in two months significant (see Table 3.16). In the regression of the lower threshold of the variable “business situation” company size was found to be three times significantly positive (see Table 3.17). Somewhat contradictory are the results of the regressions of the upper threshold of business expectations on company size and controls (see Table 3.18). Although in the majority of months company size has a negative sign, it is twice significantly positive and only once significantly negative. However, in the regression of the lower threshold of the variable “business expectations” company size was found to be a significant predictor twice, both times with a positive sign (see Table 3.19). The overall results justify the conclusion that for larger companies a smaller expected change may result in choosing the positive or the negative category than for smaller companies.