4.1. Revenue Changes as a Dependent Variable
Model A in
Table 5 includes revenue changes as an ordinal dependent variable, i.e., it takes the three different values: (1) reduced revenues, (2) unchanged revenues, or (3) increased revenues, cf. our previous explanation and discussion. We observe that the effects on the dependent variable are significant and positive for both the manufacturing industry and the consulting, finance, and insurance industry. As these are compared to the hospitality, tourism, and culture industry as a baseline or reference category, it indicates that the latter has experienced a negative revenue change compared to the two other industries. Thus, the probability of a negative change in revenues is higher for firms in the hospitality, tourism, and culture industry than in the others.
Table 6 gives more detailed information concerning the industry effect as it displays logit prediction probabilities in percent from the estimates in Model A. The table shows that the percentage of firms experiencing decreased revenues is roughly twice as high in the hospitality, tourism, and culture industry (78.2%) compared to the others (37.7% and 43.1%). The percentage experiencing unchanged revenues is about half in the hospitality, tourism, and culture industry (16.3%) compared to the others (36.4% and 35.2%). Finally, the percentage experiencing increased revenues is about one-fifth in the hospitality, tourism, and culture industry (5.50%) compared to the manufacturing industry (25.8%) and about one-fourth compared to the consulting, finance, and insurance industry (21.8%).
Figure 1, also based on the estimates in Model A (
Table 5), provides information similar to
Table 6 but also gives a graphic display of 95% confidence intervals (CIs) in brackets. For the manufacturing industry, the figure shows that revenues have not changed significantly in either direction. The percentage or probability of firms reporting decreased and unchanged revenues is higher than for those reporting increased revenues, but the difference is non-significant (as illustrated by the overlap in the brackets displaying 95% CIs). Moreover, the percentage or probability of firms reporting decreased vs. unchanged revenues is practically identical in the manufacturing industry.
For the consulting, finance, and insurance industry,
Figure 1 shows that the probability or percentage of firms reporting decreased revenues is higher than for those reporting unchanged revenues, but the difference is non-significant (as illustrated by the overlap in the brackets displaying 95% CIs). However, the probability or percentage of firms reporting increased revenues is lower than for those reporting both unchanged and increased revenues, and here, the difference is significant (as illustrated by the absence of overlap in the brackets displaying 95% CIs).
For the hospitality, tourism, and culture industry,
Figure 1 shows that the percentage or probability of firms reporting decreased revenues is higher than for those reporting both unchanged and increased revenues, and the differences are strongly significant (as illustrated by the “widely” absent overlap in the brackets displaying 95% CIs). Also, the probability or percentage of firms reporting unchanged revenues is significantly higher than for those reporting increased revenues (as illustrated by the absence of overlap in the brackets displaying 95% CIs).
More interestingly, however, is perhaps the observation in
Figure 1 that the percentage or proportion of firms reporting unchanged or increased revenues is significantly lower in the hospitality, tourism, and culture industry than in the two others, while the opposite is the case concerning the proportion or percentage of firms reporting decreased revenues. In other words, the percentage or proportion reporting decreased revenues is significantly higher in the hospitality, tourism, and culture industry than in the two others. Altogether, we conclude that revenue losses are significantly more prevalent in the hospitality, tourism, and culture industry than in the others.
Returning to
Table 5, none of the other variables in Model A significantly affect the dependent variable. The likelihood ratio χ
2 is strongly significant, implying a robust model fit (the following models will also show robust and significant model fits). Maximum and average variance inflation factors (VIFs) taking relatively low values concerning the independent variables indicate that multicollinearity is not a problem (the following models will also show relatively low VIFs). Theoretically, the lowest value the VIF can take is 1, implying that an independent variable is not correlated with any of the other independent variables in the model. The more an independent variable is correlated with other independent variables in a model, the higher the VIF. The literature suggests that VIFs taking values higher than 4, sometimes 10, can be problematic, creating unstable standard errors and regression estimates [
36]. Thus, the VIFs that we report are far below these critical values.
4.2. Received Revenue Compensation (or Not) as a Dependent Variable
In Model B1,
Table 5, we include the binary dependent variable that indicates whether a firm has received revenue compensation and observe that firm size in employees has a significant positive effect. Based on the model,
Figure 2 displays the proportion or percentage of firms receiving compensation as a function of firm size. Also, it includes 95% CIs. A tiny firm with one employee has a probability little higher than 0.2 (i.e., 20%) of receiving compensation, a small firm with ten employees a probability of about 0.35 (i.e., 35%), a medium-sized firm with 100 employees a probability of more than 0.5 (i.e., 50%), and a large with 1000 employees a probability of about 0.7 (i.e., 70%). I.e., firm size in employees strongly predicts the probability of revenue compensation, and the results are particularly interesting as large firms did not report a significantly higher probability of revenue losses than small firms (cf. Model A). Moreover, the firm size effect on the probability of revenue compensation in Model B1 is conservative as it is stronger in all the later models
Table 5 reports on.
Also, Model B1,
Table 5, shows that the probability of revenue compensation is significant and negative for both the manufacturing industry and the consulting, finance, and insurance industry. As these two industries are compared to the hospitality, tourism, and culture industry as a baseline or reference group, it indicates that the latter had a higher probability of receiving compensation than the others. Similarly, the odds ratios in brackets reveal that the hospitality, tourism, and culture industry had a much higher probability of receiving compensation than the others. Specifically, the odds of receiving revenue compensation were 11.6 times higher for a firm in the hospitality, tourism, and culture industry than for a firm in the manufacturing industry. Similarly, the odds of receiving revenue compensation were 11.9 times higher for a firm in the hospitality, tourism, and culture industry than for a firm in the consulting, finance, and insurance industry. (Note that the odds ratios we report are related to the hospitality, tourism, and culture industry compared to the others.)
The high probability of revenue compensation in the hospitality, tourism, and culture industry (Model B1) coincides with the high probability of revenue losses, as shown in the previous model (Model A). However, when controlling for revenue changes as a nominal dummy variable in Model B2, taking the three different values of revenues increased, decreased, or reduced, we still observe that the industry effects are significantly robust. Nonetheless, the absolute value of the estimates and the odds ratios are lower in Model B2 than in B1 (which does not control for revenue changes). It indicates that revenue changes in the hospitality, tourism, and culture industry partly explain the probability of revenue compensation (due to the lower absolute value of regression estimates and odds ratios in Model B2 compared to Model B1). Yet, still observing significantly robust industry estimates nonetheless indicates a relatively high probability of receiving revenue compensation in the hospitality, tourism, and culture industry independent of whether firms had revenue losses.
Expectedly, the nominal dummy variable of revenue changes shows a lower probability of revenue compensation for firms experiencing unchanged or increased revenues than those observing decreased revenues as a baseline or reference category and, therefore, not visible (Model B2). Interestingly, firms with increased revenues have a slightly higher probability of revenue compensation than firms with unchanged revenues (as the regression estimate is lower for the latter group). It may indicate that firms with increased revenues are in a more favorable position to apply for and negotiate compensation than firms with unchanged revenues, but we emphasize that the difference is marginal. The control variables have non-significant effects on the probability of revenue compensation (which is also the case in the following models).
Models B3 and B4 replicate the two previous models, except that the manufacturing industry (MI) and the consulting, finance, and insurance industry (CI) are merged into one group that we compare with the hospitality, tourism, and culture industry. None of the statistical conclusions are altered compared to the two previous models.
Models B5 and B6 replicate the two previous models, except that we balance firm observations in the merged industries with firm observations in the hospitality, tourism, and culture industry using the coarsened exact matching (CEM) procedure [
37]. CEM “prunes” two different groups—in our case, the merged industries and the hospitality, culture, and tourism industry—to become as similar as possible, and King and Nielsen demonstrate that it has better properties than propensity score matching [
38]. In our study, we balanced the groups according to firm size and revenue changes, as they were the only significant predictors except for the industry variables. Thus, we divide the firms into five groups according to size, from the smallest to the largest, each including the same number of firms. Also, we divide the firms into three groups according to whether they reported decreased, unchanged, or increased revenues. Altogether, the divisions generate 15 bins or strata (5 * 3 = 15). If a bin or stratum were to include observations from one industry only, they would be excluded as the observations cannot be matched with the observations from the other industry due to their very absence in the stratum (but in our data, all 15 strata included observations from both industries). Next, observations in the 15 strata were weighed according to the number of firms in each industry. For instance, if observations in a stratum are seven for firms in the merged industries and three in the other as the baseline group, each observation in the merged industries is given a weight of 0.43 (3/7). If the opposite is the case in another stratum, each firm in the merged industry is given a 2.3 (7/3) weight. We used the algorithm by Blackwell et al. [
39] to execute the CEM, and the weighted regression estimates in Models B5 and B6 based on the “pruned” strata do not alter the statistical conclusions from the previous models. The only exception is that the probability of revenue compensation in the hospitality, tourism, and culture industry is somewhat lower when the sample is matched. We conclude that the probability of receiving revenue compensation is higher in the hospitality, tourism, and culture industry than in the other industries, regardless of revenue losses. (Based on Greene’s [
40] limited dependent (LIMDEP) variable model, we also carried out unreported seemingly unrelated probit regression analyses by simultaneously adding and estimating separate models where revenues unchanged and revenues increased are also dependent variables. The independent variables in these unreported analyses were the same as in Models A and B1 (
Table 5), and no statistical conclusion was altered concerning the study’s research questions).