Appendix A The historical distribution of Return on Capital Employed (ROCE) was studied between 2003 and 2012 for a sample of Italian firms with revenues between euro 10 million and euro 50 million. 1 As well as observing the behaviour of ROCE for different sectors, we studied the distribution behaviour changes along with changes in some determining factors of the ROCE such as profitability ratios and turnover ratios. Descriptive analysis: definition of the sample of reference. To make the analysis as robust as possible, we will immediately eliminate firms with missing data, maintaining only those with complete data. In particular, the cleaning of the data has the following steps: The number of values missing is: 53,296 for Return on Capital Employed; 53,616 for Return on Sales; 87,207 for Monetary cycle; 50,135 for Lease to Sales; 48,026 for Fixed Assets to Total Assets; 48,800 for Fixed Asset Turnover; 17,140 for type of company (in this case the missing data is due to the difficulty of automatically identifying the company organisation from the name provided in the archive); 550 for the Ateco code; The total number of lost observations due to missing values is 102,062 2. As well as eliminating the missing data, we have considered the presence of irregular values below. In particular, we have observed: 214 values of the variable costs for leasing of assets (rents and so on) less than 0 or greater than 1 (limits placed to eliminate values such as 12,000 and 2,389,000 respectively the minimum and maximum observed); 953 values of the variable Fixed Asset Turnover less than 0 or greater than 25,000 (also in this case these limits are placed to eliminate values that are obviously incorrect); 167
168 Appendix A 5 observations of the variable Fixed Assets to Total Assets greater than 1. The overall effect of the data cleaning provides a dataset of 134,139 observations (more than sufficient to be able to evaluate the distributive ownership of the index we are interested in). The distribution of the Return on Capital Employed (ROCE) ROCE distribution is asymmetrical with a very high proportion of irregular observations (Figure A.1). In particular we observe a very high number of positive as opposed to negative irregular values. Figure A.2 provides the ROCE box and whiskers plot diagrams for the Ateco sectors. The graphs indicate that the individual Ateco categories have distributions that can be significantly different in terms of average. In general, all the conditional (and unconditional) distributions are asymmetrical with a significant number of irregular values, mainly positive. An alternative representation of the distributions of conditional frequency is based on violin plots. Figure A.3 provides an example of Histogram of ROCE Frequency 0 5000 10000 15000 20000 100 0 100 200 300 400 500 ROCE values Figure A.1 Historical distribution of ROCE Source : Aida Amadeus data.
500 400 300 200 100 0 100 10 13 16 19 22 25 28 31 35 38 42 46 50 53 58 61 64 68 71 74 79 82 87 90 93 96 Figure A. 2 code Distributions of the conditional ROCE observed on the Ateco Source: Aida Amadeus data. 100 0 100 200 300 400 500 ROCE distribution by observed industry classification 22 25 31 46 47 Figure A. 3 Distributions of frequency of the conditional ROCE for the five Ateco codes chosen. Source: Aida Amadeus data. the distributions of frequency for some sectors of interest for which we analysed three firms in the Chapter 5. The width of the graphs represents the numbers of the sub-groups whereas the thin shape identifies the ROCE distribution asymmetry. The same solution has also been adopted to represent conditional ROCE distribution according to the type of company: cooperatives (COOP), limited companies with Account Equity greater than euro
170 Appendix A 120,000 (SPA) and limited companies with Account Equity greater than euro 10,000 (SRL) (see Figure A.4). Nonetheless, we can observe that the difference between the average levels of the ratio in the three sub-groups for the distributions of frequency observed are not significantly different. The same investigation has also been undertaken for years of observation (see Figure A.5). Also in this case the distributions are ROCE distribution by observed legal types 100 0 100 200 300 400 500 COOP SPA SRL Figure A.4 Distributions of frequency of the conditional ROCE for the three types of companies identified in the dataset. Source : Aida Amadeus data. 100 0 100 200 300 400 500 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Figure A.5 Distribution of the conditional ROCE for the year of observation. Source : Aida Amadeus data.
Appendix A 171 not significantly different. Nonetheless, we can identify an average negative trend for the beginning of the current period of economic crisis that carries on until the latest data available to us. The formalisation of this graph is summarised in Table A.1 where the principal indices of position (minimum, first quartile, medium, average, second quartile and maximum) are provided together with the indices of variability (standard deviation and interquartile range). The analysis of the descriptive statistics provided in Tables A.1 and A.2 allows us to identify a certain difference in the distribution of the economic ratio compared to the three classifications considered. In particular, we can observe an average difference between the values observed in the three types of company. The analysis of the indices of variability (standard deviation and interquartile difference) allows us to identify the presence of heteroscedasticity in the dataset. The maximum average value and the maximum variability are observed for the SRLs whereas the minimum values of average and variability correspond to the COOP. The analysis conditional on the Ateco classification allows us to identify by business sectors (46 and 47) the average values and also the variability greater than that of the industrial production sectors (22, 25 and 31). With regard to the analysis of the phenomenon conditional on the year of observation, we can see that the average values have a performance which could plausibly be associated with the general climate of economic deterioration. The study of ROCE determining factors When describing the context of analysis, we must also investigate the distribution of the co-variables or control variables for the system. In particular, we can identify the following variables in this dataset: Profitability ratios: Return on Sales and Lease to Sales (ROS and MC): the first is the relationship between EBIT and sales and allows us to understand the firm s unitary margin; the second identifies the incidence of the costs of rent and of leasing on sales, profit achieved if comparable firms have some productive units rented; Turnover and incidence ratios: Monetary cycle, Fixed Asset Turnover and Fixed Assets to Total Assets (LOS, FA% and FAT). The first represents the space of time between payments and
Table A.1 Conditional descriptive statistics for the ROCE Mean Minimum 1st quartile Average 3rd quartile Maximum Standard deviation Interquartile difference Kurtosis Skewness ROCE 26.015 99.850 7.380 16.520 32.990 499.630 38.910 25.610 26.778 3.823 Legal type COOP 22.828 92.530 3.740 8.310 19.738 489.770 51.932 15.998 30.117 4.965 SPA 20.034 99.820 6.310 14.160 27.250 499.630 28.266 20.940 28.821 3.277 SRL 32.217 99.850 9.150 20.060 40.500 498.950 45.834 31.350 19.940 3.434 Ateco Industry Classification Year of observation 22 16.868 93.730 6.103 13.045 23.618 314.520 22.930 17.515 22.275 2.493 25 21.989 97.950 7.803 15.700 28.430 473.810 29.460 20.628 44.345 4.323 31 19.543 97.880 5.770 12.500 25.893 328.590 30.099 20.123 18.639 2.994 46 32.323 99.850 10.230 21.380 40.970 495.620 42.378 30.740 20.611 3.409 47 32.742 99.360 7.470 17.830 39.110 494.020 51.396 31.640 14.790 3.032 2003 34.980 98.990 10.520 21.600 43.570 496.050 47.829 33.050 18.159 3.372 2004 30.115 99.850 9.830 19.870 37.110 494.020 40.350 27.280 23.579 3.692 2005 28.635 98.940 9.110 18.610 35.560 484.100 38.989 26.450 22.511 3.536 2006 30.733 99.180 9.990 20.090 38.078 498.370 41.824 28.088 25.836 3.890 2007 31.517 97.880 10.870 21.150 39.210 498.950 40.779 28.340 24.239 3.722 2008 25.423 99.360 7.540 16.250 32.590 486.710 36.889 25.050 25.909 3.656 2009 19.072 99.820 4.320 11.730 25.380 490.040 34.735 21.060 32.165 3.880 2010 20.004 97.950 5.160 12.130 25.618 482.970 33.741 20.458 37.870 4.374 2011 20.515 98.720 5.460 12.905 26.550 499.630 35.244 21.090 36.694 4.324 2012 21.027 98.460 5.730 13.775 27.968 458.910 33.632 22.238 33.321 3.920 Source : Aida Amadeus data.
Table A.2 Conditional empirical quartiles for the ROCE Empirical quantiles 0% 0.10% 1% 5% 10% 90% 95% 99% 99.90% 100% ROCE 99.850 87.746 38.170 5.190 1.560 60.944 89.640 177.439 391.548 499.630 COOP 92.530 74.432 18.642 0.798 1.169 50.528 91.111 306.497 457.367 489.770 SPA 99.820 87.464 36.857 6.142 0.700 47.550 66.124 123.016 261.454 499.630 SRL 99.850 88.117 40.893 4.176 2.630 76.260 111.540 222.003 422.679 498.950 Ateco 22 93.730 81.688 37.927 7.104 0.291 40.119 53.301 92.474 208.828 314.520 Ateco 25 97.950 81.589 30.435 3.404 2.353 49.254 69.621 126.180 300.396 473.810 Ateco 31 97.880 90.535 42.960 7.157 0.279 46.456 68.857 145.142 262.421 328.590 Ateco 46 99.850 88.580 34.088 0.813 3.808 74.072 105.221 203.275 402.981 495.620 Ateco 47 99.360 94.890 56.806 6.960 1.238 86.480 134.066 238.750 435.687 494.020 Year 2003 98.990 84.480 35.235 0.912 3.969 79.795 118.421 239.030 427.509 496.050 Year 2004 99.850 84.530 28.912 1.090 3.600 65.939 98.402 199.767 373.943 494.020 Year 2005 98.940 86.058 31.624 2.190 3.156 65.044 96.318 184.636 380.607 484.100 Year 2006 99.180 86.799 29.175 1.140 3.647 68.546 99.614 197.120 413.985 498.370 Year 2007 97.880 80.404 27.272 0.194 4.340 69.562 98.418 193.100 401.791 498.950 Year 2008 99.360 87.720 37.284 4.740 1.800 59.717 86.666 166.590 349.343 486.710 Year 2009 99.820 91.703 50.742 13.082 3.054 49.542 72.792 149.127 367.201 490.040 Year 2010 97.950 87.537 41.066 7.381 0.240 49.034 73.234 144.774 391.493 482.970 Year 2011 98.720 90.204 47.317 9.130 0.450 49.968 74.184 146.713 393.791 499.630 Year 2012 98.460 88.086 47.795 8.620 0.048 51.330 74.998 140.793 364.646 458.910 Source : Aida Amadeus data.
174 Appendix A collections and calculated as sale times plus collection times less payment times; the second is the relationship between sales and total assets, expressing how many times the fixed investments are recovered through sales, the last is the relationship between the assets and the total assets, profit to be determined based on the weight of the multi-year costs compared to the needs of working capital; Basic details: company organisation, Ateco code of activity and year of observation (LType, IndClass and Year respectively); Whereas the last three variables can easily be studied with the tables of frequency (Tables A.3 and A.4) the other variables are numerical and require a numerical synthesis (similar to that observed in Table A.1 see the results provided in Table A.5). With regard to the results in Tables A.3 and A.4, we observe that the distributions of frequency of the observations are not strongly conditioned by the year of observation. The analysis of the results provided in Tables A.5 and A.6 mainly allows us to identify the presence of outliers in the data and in particular for the FAT and MC variables. After having studied the summary descriptive indices of ROCE distribution and of the other quantitative variables we must study the relationship between these variables. To this end, in Tables A.6 and A.7 respectively we provide the matrixes of the Spearman and Pearson indexes of co-relationship and the results of the theoretical test on the linear independence between variables. We can note that all the linear co-relationships studied are statistically significant. However, this result is associated more with the many samples considered than the real relationship existing between variables. Empirical evidence in confirmation of this statement is given by the results provided in Figure A.5. We can see that relationships existing between the variables (the results of the non-linear regressions obtained using the generalised additional model based on the spline are provided in red) are not very evident from the dispersion graphs. In Table A.6, the co-relationships between the variables have been calculated both through Pearson s index of linear co-relationship and considering the index of co-relationship between Spearman s levels. In both cases, we can see that there is no cause for concern regarding the co-linear variables as we do not see any high co-relationships between the
Appendix A 175 Table A.3 Distribution of frequency of the observations for years (2003 2007), type of company and Ateco code (to simplify reading of the results, we have provided in this table only the frequencies of the categories most represented in the dataset) Year of observation 2003 2004 2005 2006 2007 COOP 307 2.54% 305 2.55% 332 2.58% 354 2.57% 352 2.45% SPA 5938 49.16% 6380 53.44% 6610 51.33% 6918 50.21% 7125 49.50% SRL 5835 48.30% 5253 44.00% 5935 46.09% 6506 47.22% 6916 48.05% 10 674 5.58% 656 5.50% 688 5.34% 715 5.19% 739 5.13% 11 118 0.98% 124 1.04% 131 1.02% 132 0.96% 136 0.94% 13 282 2.33% 282 2.36% 287 2.23% 294 2.13% 300 2.08% 14 211 1.75% 204 1.71% 218 1.69% 228 1.65% 238 1.65% 15 212 1.75% 211 1.77% 225 1.75% 235 1.71% 252 1.75% 16 142 1.18% 144 1.21% 152 1.18% 164 1.19% 165 1.15% 17 187 1.55% 187 1.57% 190 1.48% 201 1.46% 200 1.39% 20 333 2.76% 323 2.71% 347 2.69% 358 2.60% 374 2.60% 22 437 3.62% 426 3.57% 448 3.48% 470 3.41% 488 3.39% 23 248 2.05% 264 2.21% 265 2.06% 276 2.00% 280 1.95% 24 245 2.03% 237 1.99% 253 1.96% 263 1.91% 268 1.86% 25 781 6.47% 795 6.66% 827 6.42% 880 6.39% 930 6.46% 26 148 1.23% 153 1.28% 157 1.22% 166 1.20% 181 1.26% 27 277 2.29% 271 2.27% 279 2.17% 293 2.13% 307 2.13% 28 849 7.03% 847 7.09% 881 6.84% 917 6.66% 961 6.68% 29 116 0.96% 122 1.02% 129 1.00% 133 0.97% 139 0.97% 31 192 1.59% 195 1.63% 204 1.58% 220 1.60% 227 1.58% 32 133 1.10% 120 1.01% 127 0.99% 131 0.95% 134 0.93% 38 145 1.20% 160 1.34% 175 1.36% 183 1.33% 174 1.21% 41 149 1.23% 145 1.21% 154 1.20% 166 1.20% 183 1.27% 43 226 1.87% 195 1.63% 224 1.74% 232 1.68% 254 1.76% 45 790 6.54% 840 7.04% 909 7.06% 947 6.87% 983 6.83% 46 2481 20.54% 2222 18.61% 2410 18.72% 2627 19.07% 2750 19.11% 47 563 4.66% 561 4.70% 608 4.72% 673 4.88% 709 4.93% 49 270 2.24% 263 2.20% 301 2.34% 318 2.31% 340 2.36% 52 224 1.85% 223 1.87% 279 2.17% 297 2.16% 293 2.04% 62 110 0.91% 104 0.87% 123 0.96% 134 0.97% 139 0.97% 86 145 1.20% 159 1.33% 160 1.24% 177 1.28% 179 1.24% Totals 12080 100.00% 11938 100.00% 12877 100.00% 13778 100.00% 14393 100.00% Source : Aida Amadeus data.
176 Appendix A Table A.4 Distribution of frequency of the observations for years (2008 2012), type of company and Ateco code (to simplify reading of the results we have provided in this table only the frequencies of the Ateco categories most represented in the dataset) Year of observation 2008 2009 2010 2011 2012 COOP 357 2.41% 368 2.44% 383 2.44% 381 2.35% 191 2.50% SPA 7245 48.81% 7261 48.19% 7471 47.60% 7561 46.55% 3428 44.86% SRL 7242 48.79% 7440 49.37% 7840 49.96% 8300 51.10% 4023 52.64% 10 774 5.21% 804 5.34% 823 5.24% 853 5.25% 395 5.17% 11 144 0.97% 138 0.92% 141 0.90% 142 0.87% 66 0.86% 13 297 2.00% 286 1.90% 311 1.98% 336 2.07% 158 2.07% 14 240 1.62% 240 1.59% 253 1.61% 262 1.61% 132 1.73% 15 260 1.75% 256 1.70% 273 1.74% 292 1.80% 157 2.05% 16 169 1.14% 174 1.15% 177 1.13% 181 1.11% 82 1.07% 17 206 1.39% 220 1.46% 226 1.44% 227 1.40% 103 1.35% 20 374 2.52% 388 2.57% 408 2.60% 414 2.55% 228 2.98% 22 491 3.31% 495 3.28% 515 3.28% 540 3.32% 268 3.51% 23 280 1.89% 274 1.82% 279 1.78% 278 1.71% 116 1.52% 24 280 1.89% 279 1.85% 299 1.91% 309 1.90% 170 2.22% 25 972 6.55% 932 6.18% 988 6.30% 1004 6.18% 485 6.35% 26 180 1.21% 185 1.23% 195 1.24% 200 1.23% 100 1.31% 27 331 2.23% 323 2.14% 350 2.23% 385 2.37% 183 2.39% 28 999 6.73% 947 6.28% 1002 6.38% 1062 6.54% 532 6.96% 29 140 0.94% 140 0.93% 156 0.99% 157 0.97% 57 0.75% 31 232 1.56% 229 1.52% 228 1.45% 226 1.39% 95 1.24% 32 137 0.92% 136 0.90% 143 0.91% 151 0.93% 75 0.98% 38 196 1.32% 204 1.35% 218 1.39% 225 1.39% 88 1.15% 41 186 1.25% 175 1.16% 185 1.18% 189 1.16% 70 0.92% 43 260 1.75% 264 1.75% 286 1.82% 307 1.89% 142 1.86% 45 988 6.66% 1028 6.82% 1037 6.61% 1033 6.36% 367 4.80% 46 2819 18.99% 2891 19.19% 2993 19.07% 3151 19.40% 1635 21.39% 47 732 4.93% 764 5.07% 796 5.07% 807 4.97% 372 4.87% 49 340 2.29% 362 2.40% 383 2.44% 387 2.38% 159 2.08% 52 298 2.01% 315 2.09% 334 2.13% 359 2.21% 159 2.08% 62 142 0.96% 154 1.02% 162 1.03% 163 1.00% 90 1.18% 86 182 1.23% 191 1.27% 185 1.18% 192 1.18% 71 0.93% Totals 14844 100.00% 15069 100.00% 15694 100.00% 16242 100.00% 7642 100.00% Source : Aida Amadeus data
Table A. 5 Statistics describing the explanation variables Mean Minimum 1st quartile Average 3rd quartile Maximum Standard deviation Interquartile difference Kurtosis Skewness ROS 4.124 49.610 1.350 3.200 6.140 30.000 5.932 4.790 7.803 0.083 MC 104.599 486.700 27.450 85.070 163.010 1851.990 117.622 135.560 2.689 0.905 LOS 0.028 0.000 0.006 0.015 0.034 0.996 0.049 0.028 82.834 7.176 FA% 0.257 0.000 0.090 0.215 0.380 0.999 0.202 0.290 0.314 0.902 FAT 2483.449 0.001 2.883 6.601 19.334 136025675.000 432440.105 16.451 75696.127 258.758 Source: Aida Amadeus data. Table A.6 Empirical quantiles of the explanation variables Empirical quantiles 0.10% 1% 5% 10% 90% 95% 99% 99.90% ROS 33.643 12.784 2.510 0.110 10.920 14.850 23.450 29.014 MC 297.680 135.862 44.610 14.344 258.450 330.312 458.309 616.716 LOS 0.000 0.000 0.000 0.001 0.063 0.094 0.214 0.646 FA% 0.000 0.003 0.016 0.032 0.544 0.651 0.841 0.958 FAT 0.082 0.361 0.976 1.487 61.394 129.394 841.449 25549.406 Source: Aida Amadeus data.
178 Appendix A Table A.7 Co-relationships between variables considered in the study ROCE ROS MC LOS FA% FAT Table A.8 Test for the absence of linear co-relationship Relationship Correlation P.value ROCE ROS 0.276 0.000 ROCE-MC 0.149 0.000 ROCE-LOS 0.008 0.004 ROCE-FA% 0.294 0.000 ROCE-FAT 0.002 0.415 Source : Aida Amadeus data. Spearman correlation indexes ROCE 1.000 0.485 0.164 0.011 0.426 0.481 ROS 0.485 1.000 0.154 0.055 0.029 0.103 MS 0.164 0.154 1.000 0.038 0.082 0.113 LOS 0.011 0.055 0.038 1.000 0.055 0.097 FA% 0.426 0.029 0.082 0.055 1.000 0.932 FAT 0.481 0.103 0.113 0.097 0.932 1.000 Pearson correlation indexes ROCE 1.000 0.276 0.149 0.008 0.294 0.002 ROS 0.276 1.000 0.061 0.046 0.022 0.001 MS 0.149 0.061 1.000 0.035 0.130 0.004 LOS 0.008 0.046 0.035 1.000 0.118 0.003 FA% 0.294 0.022 0.130 0.118 1.000 0.007 FAT 0.002 0.001 0.004 0.003 0.007 1.000 Source: Aida Amadeus data explanation variables (except for the relationship between fixed asset to total assets and fixed asset to turnover identified with the co-relationship coefficient between levels). The only co-relationships worthy of note are those that can be observed between the ROCE and the other variables included in the study. The results provided in Table A.8 allow us to state that there is a statistically significant linear relationship between the ROCE and the other ratios. This relationship will also be investigated with the
Appendix A 179 help of the models of regression for panel data as it is possible to see in the next section. The significance of the relationship (that it is not very intense) presents a maximum value of the index of co-relationship 0.294. The same relationships can be studied with the help of the dispersion graphs provided in Figure A.6 (where we also find the non-linear regressions obtained through smoothing). ROCE Local polynomial smooth 0 200 400 600 200 60 40 20 0 ROS kernel = epanechnikov, degree = 0, bandwidth =.88 20 40 ROCE 200 400 600 Local polynomial smooth 200 0 500 0 500 1000 MC kernel = epanechnikov, degree = 0, bandwidth = 9.23 1500 2000 Figure A.6 Continued
180 Appendix A Local polynomial smooth 0 ROCE 200 400 600 200 0.2.4.6 LOS kernel = epanechnikov, degree = 0, bandwidth =.07.8 1 ROCE 200 400 600 Local polynomial smooth 0 200 0.2.4.6 FA% kernel = epanechnikov, degree = 0, bandwidth =.06.8 1
Appendix A 181 ROCE 200 400 600 Local polynomial smooth 0 200 0 50 100 150 FAT kernel = epanechnikov, degree = 0, bandwidth = 2.47 200 Figure A.6 Study of the relationship between quantitative variables Source : Aida Amadeus data. Models of regression dynamic panels and regression with autoregressive residuals To study the relationship between the ROCE and the variables that we have already listed in the previous section, we have used specific models for the data structure. Therefore, the models used in this context consider all the presence of temporal self-relationship of the residuals (see Baltagi, 2008 for more details on the models adopted) and to take into account this self-relationship we have used dynamic panel models in which the variable response becomes a delayed part of the regressors (using a logic similar to that of the models for simple time sequences, see Arellano and Bover, 1995; and Arrelano and Bond, 1991 for more details). The estimated results provided in Table A.9 allow us to confirm that, except for the variable fixed assets turnover, we can identify a relationship between the ROCE values and the context variables chosen for the study. The estimated coefficients of the regressions represent the net effect of each variable on the value of the ROCE and given the substantial coherency of the results between the various models estimated, we can state that: the increase of the fixed assets to total assets and the monetary cycle has negative effects on the estimated value of the ROCE;
Table A.9 Results of linear regression on the panel data (considering both static first model and dynamic models) Random Effects GLS regression with AR(1) Arellano-Bond dynamic disturbances System dynamic panel-data panel-data Dynamic Random Effects GLS regression with AR(1) disturbances Full model Full model Null model Full model Null model Full model Null model Explicative variables Est. values Std. Errors Est. Values Std. Errors Est. values Std. Errors Est. Values Std. Errors Est. values Std. Errors Est. values Std. Errors Est. values Std. Errors Constant Lagged ROCE FA% FAT MC ROS LOS SRL Dummy COOP Dummy Autocorrelation Index RE standard deviation Errors standard deviation Goodness of fit index 33.558 0.402 57.075 >0.001 0.048 2.049 9.991 9.879 10.253 32.258 9.850 11.145 0.349 19.355 0.814 10.152 0.352 15.313 0.243 9.268 0.111 0.430 0.014 0.484 0.013 0.435 0.013 0.521 0.013 0.463 0.002 0.561 0.002 0.706 53.106 53.105 1.967 29.533 0.462 >0.001 >0.001 >0.001 >0.001 >0.001 >0.001 >0.001 0.001 0.026 0.002 0.026 0.002 0.032 0.001 0.017 2.479 0.047 2.482 0.047 1.469 0.014 2.841 25.840 9.075 26.670 9.034 6.900 1.873 0.398 102.483 17.715 2.752 0.196 1.282 132.258 96.726 3.646 0.619 0.023 0.067 0.179 Sign. AR(1) Sign. AR(1) Sign. AR(1) 23.679 8.064 6.394 24.609 21.271 23.251 0.207 0.546 0.502 Sign. AR(1) Source: Author s analysis of Aida Amadeus data.
Table A.10 Statistics describing regression residuals for dynamic models (these residuals must be interpreted as measuring the purely irregular component of the ROCE) Mean Minimum 1st quartile Average 3rd quartile Maximum Standard deviation Interquartile difference Kurtosis Skewness System Dynamic Full Model System Dynamic Null Model A-B Dynamic Full Model A-B Dynamic Null Model RE model with AR(1) residuals Full Model RE model with AR(1) residuals Null Model 0.000 274.377 53.504 17.587 49.701 481.649 56.596 103.206 0.608 0.075 0.000 247.786 9.562 3.990 5.457 466.491 24.908 15.019 37.475 3.316 0.000 225.901 11.020 2.172 7.451 463.876 24.814 18.471 37.646 3.488 0.000 265.551 9.039 3.655 5.448 467.067 24.595 14.487 37.948 3.138 0.015 297.701 4.658 0.122 4.197 373.882 16.524 8.855 39.375 0.881 0.054 319.005 5.469 0.170 5.249 399.002 18.386 10.718 31.099 0.441 Source: Author s analysis of Aida Amadeus data.
184 Appendix A however, there is a positive correspondence between the ROS and the identification variables of the SRL and of the COOP; the lagged ROCE delayed variable has a positive value and indeed its inclusion in the model allows us to explain the residual self-relationship present in the first model (the only non-dynamic). This is highlighted by the very reduced value assumed by the self-relationship coefficient of the residuals in the last model estimated. For all the dynamic models, we have attempted to verify the actual weight of the explanation variables by estimating the complete models (full model) and the void models (null model) and comparing the estimated results. These comparisons have been made for all three specifications adopted but from a purely descriptive point of view, it is much simpler to stop at the comparison between the coefficients of linear determination calculated automatically by the Stata software for the latest model. By comparing two values of R 2 it is reasonable to conclude that the support for the explanation variables (7 variables) at the model s explanation capacity is very limited. The objective of this analysis is to clean the phenomenon observed (ROCE) by removing the co-variation effects and taking into account their temporal dependence. The residuals of the regressions considered can be studied to understand if, net of the variables considered, the phenomenon assumes more regular performance specifics, compared to the pure phenomenon. As we can observe, also after having considered the dynamic component in the model, the self-relationship of the residuals is still significant from a statistical point of view even if its size is significantly reduced. Table A.9 provides statistics describing the residuals of the models. The best indices of asymmetry and kurtosis correspond to the first complete dynamic model but this has a higher standard deviation and interquartile difference. The model with the least residual variation is the complete model with casual effects, variable delayed response and self-regressive residuals. In general, all the models have a very high index of kurtosis (that corresponds to the presence of very irregular values already in the original data) and a positive asymmetry. The diagnostics of the models and the descriptions of the distributions of the regression residuals are very similar between the models considered. Therefore, we provide below analysis of only the residuals of the GLS random effects regression with AR(1) disturbances model.
Residuals 0 Distance above median 100 200 300 400 0 100 200 Distance below median 300 27.19397.0145904 27.16479 Residuals 200 0 200 400 20.73201.1215139 20.19784 400 100 50 0 50 Inverse Normal 100 Empirical distribution of model residuals Density.02.04.06.08 0 400 200 0 200 400 Residuals Figure A.7 Diagnostic plot for model residuals. Source : Author s analysis of Aida Amadeus data.
Appendix B With reference to the statistical analysis, other descriptive analysis can be used considering the various classifications examined together. Table B.1 Empirical quantiles for the context variables according to Ateco code Empirical quantiles 0.10% 1% 5% 10% 90% 95% 99% 99.90% ROS Ateco 22 30.127 12.688 3.335 0.513 10.465 14.285 22.567 27.936 MC Ateco 22 161.876 60.409 12.037 13.166 207.411 260.104 387.510 490.497 LOS Ateco 22 0.000 0.000 0.000 0.002 0.060 0.075 0.124 0.195 FA% Ateco 22 0.002 0.018 0.078 0.118 0.533 0.597 0.715 0.833 FAT Ateco 22 0.319 0.760 1.172 1.486 13.293 20.564 95.737 1004.408 ROS Ateco 25 25.434 10.620 1.924 0.430 12.197 15.914 23.641 29.067 MC Ateco 25 255.564 77.155 8.708 17.819 294.612 370.247 482.499 585.511 LOS Ateco 25 0.000 0.000 0.001 0.002 0.068 0.087 0.149 0.419 FA% Ateco 25 0.002 0.013 0.048 0.076 0.501 0.571 0.695 0.866 FAT Ateco 25 0.285 0.687 1.181 1.544 18.959 32.578 107.752 876.071 ROS Ateco 31 33.205 12.298 4.112 0.813 8.546 11.546 19.289 28.205 MC Ateco 31 71.432 47.180 1.514 24.666 281.461 334.956 450.899 500.017 LOS Ateco 31 0.000 0.000 0.001 0.002 0.056 0.072 0.109 0.160 FA% Ateco 31 0.003 0.019 0.046 0.070 0.528 0.590 0.680 0.827 FAT Ateco 31 0.638 0.815 1.246 1.540 21.931 33.010 97.880 554.407 ROS Ateco 46 24.181 6.524 0.760 0.250 8.960 12.351 20.192 27.914 MC Ateco 46 205.875 72.550 19.060 1.954 224.684 286.985 416.771 623.047 LOS Ateco 46 0.000 0.000 0.000 0.001 0.037 0.053 0.121 0.277 FA% Ateco 46 0.000 0.001 0.006 0.012 0.403 0.512 0.717 0.859 FAT Ateco 46 0.358 0.914 1.931 3.022 177.642 398.675 3626.819 94831.216 ROS Ateco 47 31.374 15.408 2.540 0.430 7.110 9.666 17.968 27.067 MC Ateco 47 246.585 131.004 69.496 46.072 160.936 215.486 365.455 469.463 LOS Ateco 47 0.000 0.000 0.001 0.003 0.099 0.135 0.226 0.454 FA% Ateco 47 0.000 0.006 0.027 0.048 0.674 0.749 0.847 0.936 FAT Ateco 47 0.179 0.549 1.118 1.686 54.748 105.734 676.019 5856.836 Source : Dati Aida Amadeus. 186
Table B.2 Empirical quantiles for the ROI for year and type of company (at the same time) Empirical quantiles 0% 0.10% 1% 5% 10% 25% 50% 75% 90% 95% 99% 99.90% 100% Year 2003 ROCE 98.990 84.480 35.235 0.912 3.969 10.520 21.600 43.570 79.795 118.421 239.030 427.509 496.050 Year 2003 COOP 29.150 28.394 23.573 0.771 2.054 4.515 10.480 23.215 55.226 88.165 360.821 455.381 457.630 Year 2003 SPA 98.950 88.131 38.871 2.590 2.881 8.855 17.910 34.158 60.610 85.509 159.818 359.800 482.800 Year 2003 SRL 98.990 83.808 29.967 0.840 5.818 13.505 27.510 54.480 101.260 148.662 288.122 442.280 496.050 Year 2004 ROCE 99.850 84.530 28.912 1.090 3.600 9.830 19.870 37.110 65.939 98.402 199.767 373.943 494.020 Year 2004 COOP 16.710 13.418 3.306 0.836 1.828 3.910 8.660 18.940 41.840 91.372 281.085 346.646 354.100 Year 2004 SPA 99.810 86.758 28.663 1.811 2.999 8.810 17.555 31.718 52.972 71.761 136.326 358.689 463.030 Year 2004 SRL 99.850 81.410 30.559 0.188 5.082 12.100 24.270 47.140 86.510 126.034 238.920 427.929 494.020 Year 2005 ROCE 98.940 86.058 31.624 2.190 3.156 9.110 18.610 35.560 65.044 96.318 184.636 380.607 484.100 Year 2005 COOP 92.530 88.528 12.786 0.285 1.381 4.170 9.375 19.640 48.841 101.262 241.000 352.259 382.890 Year 2005 SPA 98.940 84.782 30.602 3.197 2.590 8.223 16.685 29.620 50.284 71.298 135.212 234.998 395.520 Year 2005 SRL 90.060 85.993 32.568 1.483 4.100 10.915 22.690 44.565 84.268 118.040 227.003 407.708 484.100 Year 2006 ROCE 99.180 86.799 29.175 1.140 3.647 9.990 20.090 38.078 68.546 99.614 197.120 413.985 498.370 Year 2006 COOP 53.830 52.199 17.138 0.257 1.374 4.025 9.790 21.353 54.527 117.157 260.509 375.513 380.430 Year 2006 SPA 97.460 79.546 27.939 1.810 3.178 8.930 17.570 31.678 54.276 72.878 133.976 282.749 485.850 Year 2006 SRL 99.180 89.214 29.893 0.410 4.830 12.213 24.135 46.348 87.220 126.035 263.007 457.219 498.370 Year 2007 ROCE 97.880 80.404 27.272 0.194 4.340 10.870 21.150 39.210 69.562 98.418 193.100 401.791 498.950 Year 2007 COOP 21.970 20.008 10.722 0.025 1.595 4.623 9.560 21.875 48.078 83.178 213.210 443.800 489.770 Year 2007 SPA 93.340 78.481 27.558 0.916 3.860 9.950 18.650 33.180 54.684 74.122 132.125 291.109 446.900 Year 2007 SRL 97.880 82.659 27.360 0.733 5.505 12.750 25.195 47.450 86.085 122.940 245.920 418.945 498.950 Year 2008 ROCE 99.360 87.720 37.284 4.740 1.800 7.540 16.250 32.590 59.717 86.666 166.590 349.343 486.710 Year 2008 COOP 74.610 67.686 24.223 1.048 1.426 4.350 8.590 19.850 53.352 94.144 237.742 317.574 327.880 Year 2008 SPA 99.360 84.847 33.686 5.902 0.674 6.370 13.790 26.340 45.920 63.716 113.909 259.243 348.440 Continued
Table B.2 Continued Empirical quantiles 0% 0.10% 1% 5% 10% 25% 50% 75% 90% 95% 99% 99.90% 100% Year 2008 SRL 96.880 88.334 42.296 3.159 2.981 9.100 19.825 40.518 74.657 107.668 203.982 413.113 486.710 Year 2009 ROCE 99.820 91.703 50.742 13.082 3.054 4.320 11.730 25.380 49.542 72.792 149.127 367.201 490.040 Year 2009 COOP 74.070 58.594 18.888 2.425 0.748 3.218 7.365 17.348 47.303 83.325 265.767 454.184 456.830 Year 2009 SPA 99.820 90.972 51.230 13.990 4.970 3.280 9.380 20.170 37.420 52.480 104.444 210.049 379.200 Year 2009 SRL 99.300 91.741 50.552 12.230 1.031 5.998 14.940 32.165 61.900 92.324 172.927 396.438 490.040 Year 2010 ROCE 97.950 87.537 41.066 7.381 0.240 5.160 12.130 25.618 49.034 73.234 144.774 391.493 482.970 Year 2010 COOP 90.860 81.864 20.388 2.713 0.628 2.450 6.560 17.910 61.094 102.934 399.395 480.705 482.970 Year 2010 SPA 96.570 87.593 42.452 8.605 0.900 4.170 9.990 20.290 37.010 52.015 99.656 167.542 364.910 Year 2010 SRL 97.950 85.918 40.709 6.101 1.509 6.790 15.245 31.623 60.604 89.124 165.431 402.285 461.380 Year 2011 ROCE 98.720 90.204 47.317 9.130 0.450 5.460 12.905 26.550 49.968 74.184 146.713 393.791 499.630 Year 2011 COOP 40.780 40.324 17.168 4.180 0.610 2.980 6.740 17.620 54.740 87.230 320.502 443.407 446.930 Year 2011 SPA 98.120 90.380 41.550 9.130 1.230 4.490 10.480 21.060 37.600 52.650 99.544 183.102 499.630 Year 2011 SRL 98.720 89.285 50.721 9.345 0.449 6.850 15.965 32.523 61.157 93.171 184.149 413.742 460.050 Year 2012 ROCE 98.460 88.086 47.795 8.620 0.048 5.730 13.775 27.968 51.330 74.998 140.793 364.646 458.910 Year 2012 COOP 38.170 35.660 21.945 2.375 1.070 3.510 7.090 15.960 41.770 76.985 302.281 370.739 377.210 Year 2012 SPA 98.460 88.161 43.649 9.203 1.211 4.670 11.400 22.630 39.095 54.871 98.760 174.690 431.340 Year 2012 SRL 93.730 85.285 51.846 8.539 0.912 7.460 17.060 33.750 62.056 90.554 164.406 399.564 458.910 Source : Aida Amadeus data.
Table B.3 Empirical quantiles for the variables of context by year Empirical quantiles 0.10% 1% 5% 10% 90% 95% 99% 99.90% Year 2003 ROS 32.058 11.363 1.481 0.240 10.550 14.290 22.498 28.399 Year 2003 MC 292.661 129.939 39.681 10.250 246.872 317.449 450.321 597.586 Year 2003 LOS 0.000 0.000 0.000 0.001 0.062 0.091 0.193 0.605 Year 2003 FA% 0.000 0.004 0.018 0.036 0.512 0.615 0.818 0.941 Year 2003 FAT 0.125 0.438 1.222 1.781 58.917 112.547 559.259 5840.699 Year 2004 ROS 32.796 10.478 1.510 0.327 11.170 14.820 23.440 28.653 Year 2004 MC 290.614 128.952 44.725 13.943 251.044 316.742 452.005 635.190 Year 2004 LOS 0.000 0.000 0.000 0.001 0.062 0.089 0.200 0.524 Year 2004 FA% 0.000 0.004 0.019 0.036 0.520 0.630 0.831 0.950 Year 2004 FAT 0.094 0.391 1.091 1.712 54.880 107.522 528.914 6849.739 Year 2005 ROS 33.060 10.419 1.680 0.176 10.908 14.782 23.332 29.062 Year 2005 MC 304.873 146.663 46.366 15.494 250.228 316.710 447.236 592.480 Year 2005 LOS 0.000 0.000 0.000 0.001 0.063 0.092 0.203 0.646 Year 2005 FA% 0.000 0.004 0.018 0.033 0.516 0.628 0.837 0.955 Year 2005 FAT 0.068 0.365 1.080 1.687 58.196 116.314 578.840 9694.472 Year 2006 ROS 33.962 10.122 1.220 0.320 11.070 15.260 23.710 28.657 Year 2006 MC 299.881 140.953 44.940 15.643 249.221 318.701 455.065 611.646 Year 2006 LOS 0.000 0.000 0.000 0.001 0.062 0.092 0.207 0.636 Year 2006 FA% 0.000 0.003 0.017 0.032 0.507 0.620 0.820 0.953 Year 2006 FAT 0.075 0.356 1.113 1.735 61.585 127.562 700.054 11972.374 Year 2007 ROS 31.214 10.246 0.968 0.410 11.570 15.550 23.801 28.867 Year 2007 MC 279.732 133.961 43.322 14.802 250.346 321.962 448.696 629.965 Year 2007 LOS 0.000 0.000 0.000 0.001 0.061 0.090 0.215 0.624 Year 2007 FA% 0.000 0.003 0.015 0.031 0.505 0.617 0.826 0.952 Year 2007 FAT 0.108 0.389 1.151 1.783 64.223 135.248 879.694 21497.624 Continued
Table B.3 Continued Empirical quantiles 0.10% 1% 5% 10% 90% 95% 99% 99.90% Year 2008 ROS 31.568 12.334 2.340 0.050 10.960 14.860 23.350 29.350 Year 2008 MC 305.727 137.388 43.920 12.919 258.524 328.884 454.311 586.426 Year 2008 LOS 0.000 0.000 0.000 0.001 0.063 0.094 0.213 0.669 Year 2008 FA% 0.000 0.003 0.016 0.033 0.565 0.672 0.840 0.965 Year 2008 FAT 0.085 0.360 0.922 1.380 61.096 131.566 844.496 37046.907 Year 2009 ROS 35.910 18.056 5.690 1.812 10.470 14.890 23.490 29.086 Year 2009 MC 296.387 138.712 50.352 16.700 284.026 358.984 477.389 617.920 Year 2009 LOS 0.000 0.000 0.000 0.001 0.070 0.105 0.240 0.653 Year 2009 FA% 0.000 0.002 0.015 0.032 0.585 0.683 0.853 0.966 Year 2009 FAT 0.056 0.305 0.801 1.195 59.102 124.172 930.923 40767.911 Year 2010 ROS 36.844 13.798 3.194 0.420 10.657 14.544 23.701 28.959 Year 2010 MC 281.048 138.332 46.634 15.690 269.887 341.754 463.761 637.432 Year 2010 LOS 0.000 0.000 0.000 0.001 0.064 0.096 0.228 0.637 Year 2010 FA% 0.000 0.002 0.014 0.030 0.569 0.671 0.858 0.965 Year 2010 FAT 0.071 0.327 0.861 1.283 62.936 139.907 1058.927 39443.191 Year 2011 ROS 31.420 13.392 3.230 0.600 10.580 14.470 23.170 29.030 Year 2011 MC 297.152 127.711 44.130 13.589 261.623 339.780 462.551 624.315 Year 2011 LOS 0.000 0.000 0.000 0.001 0.062 0.092 0.217 0.673 Year 2011 FA% 0.000 0.002 0.014 0.029 0.563 0.667 0.850 0.957 Year 2011 FAT 0.090 0.351 0.913 1.383 64.837 145.411 1261.456 36094.546 Year 2012 ROS 34.148 12.361 2.880 0.700 11.069 15.140 23.830 29.079 Year 2012 MC 310.148 130.177 40.220 12.007 257.820 324.537 452.417 566.212 Year 2012 LOS 0.000 0.000 0.000 0.001 0.060 0.091 0.217 0.635 Year 2012 FA% 0.000 0.002 0.011 0.025 0.556 0.658 0.844 0.961 Year 2012 FAT 0.091 0.424 1.018 1.506 77.019 177.422 1862.585 224257.614 Source : Aida Amadeus data.
Table B.4 Empirical quantiles of the ROCE for year and Ateco code Empirical Quantiles 0% 0.10% 1% 5% 10% 25% 50% 75% 90% 95% 99% 99.90% 100% Year 2003 ATECO 22 78.730 75.242 24.164 1.264 3.328 8.640 17.610 31.600 52.310 67.946 111.314 190.704 244.210 Year 2003 ATECO 25 68.500 61.137 14.732 0.370 4.530 9.470 16.700 32.310 61.310 84.270 169.712 330.887 443.940 Year 2003 ATECO 31 73.090 62.264 12.297 0.097 4.512 10.233 17.565 31.153 59.120 75.711 148.629 155.872 157.010 Year 2003 ATECO 46 97.830 84.123 26.128 2.430 6.860 15.160 30.350 57.410 106.060 149.740 277.206 409.713 459.300 Year 2003 ATECO 47 98.990 86.592 50.959 1.431 3.032 12.290 26.520 54.620 114.528 164.000 264.407 448.400 459.870 Year 2004 ATECO 22 89.630 74.730 35.385 5.920 2.165 7.468 15.905 29.315 45.625 62.683 96.558 203.143 225.740 Year 2004 ATECO 25 40.120 39.477 11.131 2.638 5.268 10.065 17.810 31.590 56.806 84.356 162.002 452.793 460.590 Year 2004 ATECO 31 88.210 82.347 52.547 4.373 3.664 7.850 14.000 25.690 43.026 59.512 128.951 147.373 150.710 Year 2004 ATECO 46 99.850 87.236 27.114 0.536 5.584 13.310 25.810 47.750 84.808 113.492 206.707 331.822 361.640 Year 2004 ATECO 47 81.710 79.397 35.664 1.710 3.460 9.970 21.840 44.940 103.380 170.130 276.092 464.133 494.020 Year 2005 ATECO 22 53.350 51.093 23.666 3.217 2.227 7.085 14.910 23.653 37.062 48.628 96.503 156.526 159.780 Year 2005 ATECO 25 88.300 44.472 19.945 0.554 4.318 10.070 17.920 30.290 51.426 78.402 126.375 197.748 281.570 Year 2005 ATECO 31 48.830 42.044 14.427 2.314 5.071 9.290 16.735 28.730 46.408 71.473 143.450 191.109 202.380 Year 2005 ATECO 46 87.790 74.743 21.257 0.729 5.306 12.240 24.055 43.090 76.458 107.936 181.857 408.278 463.540 Year 2005 ATECO 47 92.490 78.960 29.988 1.170 3.115 9.620 21.270 47.325 101.367 145.992 240.520 354.438 366.590 Year 2006 ATECO 22 92.410 83.279 30.361 5.305 0.358 7.573 14.655 26.803 46.010 57.516 111.978 162.530 185.520 Year 2006 ATECO 25 44.700 33.880 14.155 2.541 6.507 12.195 20.120 35.155 59.387 80.644 136.263 282.714 321.610 Year 2006 ATECO 31 51.390 45.449 17.631 0.524 4.384 9.530 16.505 31.083 48.106 74.304 167.027 220.240 230.750 Year 2006 ATECO 46 99.060 90.165 24.274 1.620 6.246 13.805 25.960 46.540 82.946 115.702 231.890 421.954 495.620 Year 2006 ATECO 47 95.170 80.917 25.807 0.944 3.882 9.700 21.110 43.850 106.340 152.536 276.933 448.234 450.640 Year 2007 ATECO 22 77.690 58.278 25.294 3.556 2.729 8.458 15.730 27.115 47.110 60.156 95.234 249.972 291.620 Year 2007 ATECO 25 93.340 93.294 28.624 4.024 7.752 13.430 23.395 37.723 59.072 80.362 143.054 201.521 213.570 Year 2007 ATECO 31 97.880 91.911 50.079 0.128 4.832 10.410 17.920 33.045 59.260 82.451 160.729 262.658 265.980 Year 2007 ATECO 46 89.190 78.046 26.136 2.922 7.547 14.433 26.510 46.925 82.430 113.281 229.505 390.899 420.510 Year 2007 ATECO 47 95.250 88.715 59.924 0.590 4.140 9.830 20.300 42.820 94.332 150.336 353.732 412.964 433.000 Year 2008 ATECO 22 85.640 79.079 41.514 6.275 2.220 6.240 12.420 21.180 36.510 54.740 107.267 252.765 314.520 Year 2008 ATECO 25 70.040 64.146 28.237 1.610 2.887 8.545 16.590 29.595 51.479 69.636 125.186 184.870 473.810 Year 2008 ATECO 31 52.740 51.892 36.062 12.330 0.495 5.863 13.040 26.235 54.355 77.593 148.108 298.010 328.590 Continued
Table B.4 Continued Empirical Quantiles 0% 0.10% 1% 5% 10% 25% 50% 75% 90% 95% 99% 99.90% 100% Year 2008 ATECO 46 97.690 82.789 34.369 0.571 4.702 10.940 21.780 41.270 74.678 104.877 216.194 398.877 486.710 Year 2008 ATECO 47 99.360 92.174 58.042 7.981 2.025 7.608 16.355 36.548 75.410 114.118 216.651 443.137 482.150 Year 2009 ATECO 22 75.840 71.073 53.806 10.246 3.356 3.600 9.010 18.690 31.668 43.096 65.874 152.089 212.550 Year 2009 ATECO 25 84.520 77.696 39.152 17.657 9.206 2.343 8.315 18.205 35.036 53.439 84.647 157.937 463.370 Year 2009 ATECO 31 64.120 63.292 27.169 12.714 5.982 1.520 8.080 16.450 32.136 57.540 85.588 223.542 262.970 Year 2009 ATECO 46 99.820 93.468 51.663 8.475 0.580 6.755 15.020 31.575 58.570 83.785 156.364 299.035 419.740 Year 2009 ATECO 47 99.300 87.985 56.566 11.622 1.268 5.658 14.075 34.165 72.686 129.316 222.308 348.656 388.210 Year 2010 ATECO 22 65.630 59.215 47.161 8.161 0.418 4.210 10.190 18.625 31.836 41.646 81.944 124.980 126.450 Year 2010 ATECO 25 97.950 96.351 38.338 7.378 0.087 5.048 11.265 21.220 37.464 47.963 85.906 144.078 336.770 Year 2010 ATECO 31 48.960 47.845 41.296 11.919 3.403 2.768 7.685 15.648 32.373 46.209 76.664 207.063 225.030 Year 2010 ATECO 46 94.530 78.649 24.116 0.474 2.782 7.230 15.610 30.850 59.736 86.876 144.799 389.515 401.560 Year 2010 ATECO 47 94.690 93.140 51.818 12.950 1.065 5.610 13.185 32.195 66.860 107.243 173.438 258.925 272.440 Year 2011 ATECO 22 84.290 75.688 37.795 11.247 0.950 4.943 11.205 21.400 34.096 41.831 70.050 144.004 144.430 Year 2011 ATECO 25 84.240 78.051 42.537 4.311 1.539 6.580 12.790 23.850 39.975 52.976 100.336 298.515 417.980 Year 2011 ATECO 31 90.650 83.662 55.158 10.443 3.855 3.188 7.920 19.728 41.580 68.443 134.385 193.114 202.730 Year 2011 ATECO 46 96.170 87.849 43.085 4.135 2.410 7.690 16.870 31.895 57.520 84.095 143.445 394.512 454.410 Year 2011 ATECO 47 95.620 95.427 63.320 14.698 1.614 5.190 13.460 31.390 66.394 102.763 175.927 267.480 387.550 Year 2012 ATECO 22 93.730 90.005 49.207 6.725 0.525 5.168 12.330 21.573 31.502 41.555 62.712 77.203 79.040 Year 2012 ATECO 25 57.940 54.291 30.878 1.994 2.134 6.000 12.640 23.330 37.184 49.442 97.327 187.602 219.410 Year 2012 ATECO 31 90.790 86.244 45.332 10.558 3.406 3.375 10.000 25.500 41.166 54.364 70.309 78.473 79.380 Year 2012 ATECO 46 93.380 78.678 40.991 5.097 2.286 8.050 17.450 31.315 58.232 82.940 201.067 440.124 458.910 Year 2012 ATECO 47 90.560 87.863 76.754 24.702 8.446 4.115 13.455 34.640 65.476 107.641 147.399 218.190 232.900 Source : Aida Amadeus data.
Table B.5 Descriptive statistics for the conditional ROCE at the Ateco codes observed Ateco Classification Mean Standard deviation Empirical quantiles 0.10% 1% 5% 10% 25% 50% 75% 90% 95% 99% 99.90% 10 16.717 26.957 77.667 31.926 3.400 1.530 5.740 11.150 21.250 37.170 52.990 114.398 336.975 41 31.261 42.251 63.756 20.896 0.691 3.894 9.550 19.680 39.770 69.377 97.545 183.634 424.381 25 21.989 29.460 81.589 30.435 3.404 2.353 7.803 15.700 28.430 49.254 69.621 126.180 300.396 46 32.323 42.378 88.580 34.088 0.813 3.808 10.230 21.380 40.970 74.072 105.221 203.275 402.981 22 16.868 22.930 81.688 37.927 7.104 0.291 6.103 13.045 23.618 40.119 53.301 92.474 208.828 14 24.258 30.644 67.007 22.708 0.768 2.705 7.780 16.630 32.228 56.075 76.083 145.688 283.580 20 18.651 28.646 84.786 47.428 9.304 0.548 6.015 13.630 26.710 44.618 58.788 114.922 327.245 47 32.742 51.396 94.890 56.806 6.960 1.238 7.470 17.830 39.110 86.480 134.066 238.750 435.687 29 19.815 35.464 88.018 52.000 12.970 3.344 5.710 14.260 28.000 47.094 66.548 128.814 415.848 21 23.564 38.369 84.717 44.914 13.080 2.798 6.630 16.240 31.880 54.962 71.558 191.370 320.701 28 24.078 30.633 89.914 42.368 6.024 2.326 8.750 17.960 32.730 54.022 74.000 135.188 295.765 31 19.543 30.099 90.535 42.960 7.157 0.279 5.770 12.500 25.893 46.456 68.857 145.142 262.421 82 41.910 54.662 76.699 43.443 4.117 1.394 7.675 26.410 61.765 102.726 140.239 245.730 418.123 17 16.813 24.501 68.591 25.614 4.383 0.920 5.375 12.040 22.530 38.346 51.572 111.056 289.047 12 11.040 37.254 53.712 14.308 0.722 1.550 2.800 4.640 7.950 21.002 29.260 98.936 430.746 55 12.032 27.105 86.519 60.570 14.951 5.742 1.395 6.710 19.315 38.212 50.187 114.652 208.271 79 45.101 67.420 87.994 61.877 18.161 1.969 8.510 25.345 64.850 117.217 151.094 353.398 465.759 43 36.328 44.028 82.476 25.829 1.740 5.418 12.113 24.990 46.188 80.713 112.201 232.197 368.714 33 32.930 39.274 68.794 33.214 0.432 4.904 12.340 23.690 42.980 69.774 97.004 172.874 385.535 61 37.157 52.126 88.738 43.120 13.508 1.435 7.603 21.140 49.425 110.535 143.003 208.308 306.737 16 19.183 35.358 68.395 22.335 4.202 0.619 4.138 10.615 21.778 45.954 66.968 169.764 373.943 13 15.937 27.107 80.621 38.494 10.408 2.870 4.040 10.680 21.960 40.190 58.102 118.660 275.479 26 25.986 30.462 77.308 37.907 4.512 2.670 9.320 20.300 36.830 58.746 75.474 136.650 285.078 58 32.108 46.517 81.015 47.138 18.765 4.680 7.140 17.570 43.125 100.780 137.940 172.431 262.824 15 25.860 33.169 66.900 27.230 2.378 3.280 8.280 17.580 34.560 57.180 82.366 142.896 291.412 52 39.582 60.051 90.498 46.738 10.290 1.150 8.760 22.510 48.940 99.690 146.880 309.466 482.713 Continued
Table B.5 Continued Ateco Classification Mean Standard deviation Empirical quantiles 0.10% 1% 5% 10% 25% 50% 75% 90% 95% 99% 99.90% 30 24.492 33.381 88.763 59.106 9.919 0.184 8.050 17.730 34.375 59.514 76.391 133.997 316.247 45 21.826 27.208 89.946 34.808 4.278 1.651 8.143 16.695 29.378 48.419 64.905 118.104 258.848 62 46.854 61.723 91.640 61.992 13.550 2.590 13.600 32.410 65.400 109.050 148.620 292.214 477.227 11 18.086 32.594 69.731 27.332 0.818 2.171 5.418 11.120 21.135 38.072 55.074 163.642 348.837 63 44.354 50.936 87.719 40.421 4.844 4.384 13.710 30.740 57.710 113.250 155.476 207.357 313.146 23 15.516 25.940 82.150 35.160 7.132 0.603 4.505 10.540 21.233 38.371 52.182 108.267 272.423 86 24.920 41.136 67.924 28.590 5.230 1.120 6.850 15.500 30.180 54.070 83.950 192.446 437.783 73 55.552 63.400 90.898 75.736 7.420 3.650 17.340 40.160 77.510 134.350 179.895 262.891 442.010 38 27.216 38.103 64.991 21.368 0.204 2.834 7.970 16.150 33.888 65.693 88.135 174.681 371.725 49 25.178 41.275 86.368 34.833 7.081 0.592 5.915 14.330 31.110 64.452 93.263 179.341 426.290 42 31.891 52.993 42.560 18.392 0.440 2.608 8.385 17.780 35.575 61.032 102.838 317.639 384.092 24 18.976 26.373 71.612 34.930 6.842 0.736 6.605 13.680 25.345 45.686 62.170 115.026 227.000 50 12.200 27.001 76.808 46.682 11.458 4.342 1.708 6.540 15.508 31.997 59.808 134.492 158.297 27 23.261 31.552 93.618 47.505 9.983 0.002 7.795 17.490 33.155 56.182 73.165 136.095 250.652 32 20.872 27.141 73.339 28.014 5.459 1.680 7.460 14.470 27.590 51.806 69.766 110.986 203.741 90 56.481 60.601 20.127 3.817 1.172 4.758 13.770 41.870 79.205 136.560 161.978 259.099 299.614 35 26.026 39.263 79.889 26.192 3.155 1.326 5.408 13.090 31.535 69.374 111.326 170.726 258.363 69 64.561 64.882 83.942 42.237 1.694 7.756 16.870 46.020 98.715 156.574 177.602 264.208 370.222 80 56.703 68.887 61.625 19.372 5.678 8.350 17.468 35.015 66.238 122.398 173.989 371.370 406.454 70 25.555 47.487 86.751 43.625 11.430 2.353 4.183 12.975 29.160 67.325 112.861 219.982 407.320 77 24.520 32.086 92.414 43.222 9.175 0.421 7.383 17.340 34.625 59.159 95.169 131.017 188.500 68 19.200 31.797 84.582 38.541 10.538 1.330 3.770 11.670 25.205 50.298 76.953 141.351 280.389 71 41.570 50.482 59.895 34.716 5.799 3.270 12.838 27.915 57.475 96.100 134.323 237.097 389.694 78 27.300 34.018 78.969 56.641 25.566 3.738 8.230 23.120 46.600 73.590 89.276 105.701 125.489 53 50.442 68.027 83.580 83.042 30.398 8.134 19.860 33.680 72.220 103.678 170.322 257.309 261.756 74 38.149 48.051 54.649 28.003 4.058 2.361 8.373 20.280 56.165 105.864 129.406 210.919 267.349
18 15.767 28.899 85.763 56.986 16.091 4.462 4.688 11.505 22.420 40.950 57.268 127.797 232.086 93 21.310 40.910 76.500 49.631 15.598 6.157 3.285 10.240 22.413 67.108 113.560 178.941 202.400 85 55.434 71.444 40.673 25.128 2.605 4.405 20.388 31.675 63.403 144.010 166.523 350.432 361.608 88 20.602 25.097 41.461 10.387 0.873 3.409 7.648 15.965 25.455 46.596 61.024 124.588 201.859 87 23.390 35.821 63.060 48.706 10.695 1.645 7.143 17.755 31.110 53.820 62.095 120.471 278.151 60 17.297 32.116 77.220 55.141 25.762 14.092 1.700 14.930 29.610 45.296 71.086 131.577 203.035 56 36.628 64.008 87.242 72.316 25.325 8.320 7.800 20.720 44.118 107.178 171.891 328.991 398.818 96 31.966 63.991 89.422 46.545 17.280 4.318 5.595 15.280 42.315 76.182 96.744 301.009 467.955 81 45.080 68.433 62.687 33.555 1.774 3.222 10.400 22.610 56.390 105.590 158.130 373.003 484.089 95 42.810 49.758 90.636 50.141 4.812 3.039 18.830 33.830 56.105 93.551 111.036 210.280 315.534 99 24.904 29.755 3.172 2.741 0.824 1.572 2.810 20.590 25.820 60.194 75.382 87.532 90.266 39 40.709 68.148 23.137 9.702 0.386 3.740 9.250 20.750 42.760 89.536 123.664 328.956 463.438 36 10.040 22.894 75.146 21.567 4.388 0.916 1.690 4.450 10.050 23.406 45.374 121.304 138.633 66 40.201 47.541 68.045 49.894 0.336 1.104 15.625 25.570 53.770 125.784 143.276 168.390 170.710 72 30.483 28.492 78.033 44.216 0.075 6.790 12.925 27.920 41.145 65.490 78.815 111.457 138.566 59 44.850 80.252 94.860 80.151 22.548 2.720 6.990 21.200 52.030 135.308 188.442 397.718 451.862 89 7.630 11.606 24.469 22.116 15.275 5.397 2.948 7.620 13.485 22.450 26.226 30.284 32.629 19 21.997 32.178 27.690 22.209 3.227 1.541 5.545 14.265 29.725 50.958 71.148 138.375 315.188 65 30.295 28.035 10.540 9.914 7.130 4.184 10.730 20.910 53.270 64.426 68.002 69.744 70.136 51 15.008 38.523 78.558 69.265 37.670 13.140 1.290 10.360 24.565 45.440 62.690 159.614 207.229 64 12.437 21.384 68.023 30.320 8.468 1.694 2.860 8.770 17.070 31.554 47.558 104.541 152.598 37 20.439 39.955 16.638 11.890 5.445 0.938 3.145 7.900 21.895 48.012 92.895 190.162 279.342 91 33.950 40.732 30.124 21.429 6.683 2.158 7.673 18.715 54.573 92.397 129.055 134.310 136.290 92 38.923 58.624 87.953 87.077 42.058 10.632 4.950 30.520 65.450 101.330 136.888 248.215 255.581 94 22.456 13.568 6.428 6.766 8.270 10.149 13.388 18.575 30.003 40.060 42.615 44.659 45.119 Source : Aida Amadeus data.