Endeavor

For the set of entrepreneurial performance indicators chosen for this study, the first three components alone explain approximately 85% of the total variation of the set. That is, with the application of Principal Component Analysis we obtain three variables completely uncor- related with each other and that summarize adequate- ly the performance indicators. The final performance measure adopted in the preparation of the final ranking, therefore, is the simple combination of these three stan- dard components: Performance_x = Component_1' + Component_2' + ... + Component_k' Performance_x' = (Performance_x – Average (Performances) / Stand.dev (Performances)) + 6 This way, the entire set of performance variables is con - densed into a single statistical analysis, which has the advantage of not using a specific conceptual framework for its development — which, unlike determinants, is still not widely discussed in today's existing literature on the subject. It's worth noting that, for the data used, the en- trepreneurial performance indicator obtained is highly correlated to an indicator created by the simple sum of all the contemplated variables. FInal CItY's IndExEs and WEIgHt oF dEtErmInants A complex and controversial aspect in the development of rankings is to establish weights for each of its elements. There are rankings in which variables aren't attributed any weight at all. There are others in which experts are con- sulted, based on their experience, in order to establishing arbitrary weights to the indicators. The decision adopted for this study was to use weights obtained from the cor- relation between entrepreneurial performance and its de- terminants. The adopted weights are therefore the result of empirical evaluation. The arbitrariness stays limited to how they're calculated and doesn't depend on Endeavor's vision, specialists, or previous records on the correlation between determinants and entrepreneurial performance, even having produced widespread and defensible results in the literature. The fundamental assumption of this operation is that there is a cause and effect relationship between entrepreneurial performance and its determinants. This is the starting point of the Endeavor Brazil's framework and of other tools adopted by organizations and international con - sulting firms. Cities with good performance determinants should, hopefully, have a positive effect on entrepreneurial performance. Ideally, there would be information about several Brazilian cities and it would be possible to estimate more accurately the relationship between determinants and entrepreneur- ial performance. However, when choosing only 14, you limit the capacity to obtain, from the data, a precise measure- ment. you cannot, for example, apply basic techniques of linear regression to estimate partial coefficients that represent the correlation between entrepreneurial perfor- mance and their causes. Given the limiting number of cities, the option was to build weights directly in correlations with each of the seven de- terminants presented in the framework and the measured performance obtained through the Principal Component Analysis. The risk in this procedure is to obtain a negative correlation between -1 and 0, or even zero weights, and wrongfully representing connections that, at least in the- ory, should be positive. During the stipulation of weights for each determinant, it was decided, therefore, to build measurements that would vary in a positive range, larger than 1 and smaller than 2, and to be a function of the correlation with the measured performance. The linear transformation of the correlation between 1 and 2 produces weights that meet these criteria. The calculation of the weights is thus quite simple: subtract from each correlation the lesser amount of all correlations and divide the result by the difference between the highest and the lowest correlation, according to the formula below: Weight = corr(determinant, performance) — min (corr) / max( - corr) — min (corr) The weights obtained in this manner are rational numbers and, in most cases, contains a number of decimal places. Since the correlations are estimated based on data from few cities, it is undesirable, for example, to have unsta - ble measurements. To make the most stable weights and hence reduce the sensitivity of the ranking, it was decided in the end to limit the weights to only three possible values — 1, 1.5 and 2 — obtained by a conventional rounding rule. 93

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