Empirical Results. We implemented our algorithm and experiments in Python 2.7, using the Glop linear programming solver1 to compute the liquid welfare within our algorithm. Each run of the ex- periment takes roughly 30 seconds on a single CPU. Figure 1 demonstrates the revenue and welfare trends for a single in- ventory unit as the budget ratio r is varied (trends were very similar across all inventory units), and Table 1 summarizes the results for r = 1. From Figure 1 we see that our algo- rithm’s (AAGBudget) revenue performance closely tracks the optimal revenue achievable as captured by the liquid welfare for all values of r. The original AAG algorithm that does not take budget into account (AAGNoBudget) performs poorly especially when the budgets are small, and improves as the budgets increase. This is because, when the budget is small, the AAGNoBudget algorithm might offer a deal that violates buyer’s budget. Given such a deal, the buyer may reject the deal, resulting in 0 revenue. This is why AAGBudget shows 0 revenue up to r = 0.5. Recall that for AAGBudget and AAGNoBudget, revenue is equivalent to welfare. An opposite revenue trend holds for the second-price auc- tion benchmarks: their revenue performance decreases as r increases. This is because when the budget is small, the second price auction may be able to exhaust all the budgets within 100K auctions and therefore approach the liquid wel- fare optimum. For second-price auctions, especially the one with optimal reserves, there is a trade-off between revenue and efficiency. To understand why welfare can be higher than liquid welfare for the second-price auctions, recall that liquid 1See xxxxx://xxxxxxxxxx.xxxxxx.xxx/optimization/lp/glop. welfare only provides an upper bound on the revenue but not the welfare. If auction prices are consistently low but values are high, it is possible to achieve a high total welfare beyond the available budget, while respecting budget constraints. Table 1 provides results, indexed against the optimal so- cial welfare (unconstrained by budget) to interpret both the revenue and social welfare levels together. When compar- ing revenue directly against liquid welfare (the revenue op- timum), AAGBudget’s performance ranges from 94–99% of the optimum across inventory units, whereas AAGNoBudget ranges from 54–65% and Optimal SPA from 60–90%. Our algorithm’s revenue performance is consistently close to the liquid welfare benchmark across all values of r and outper- forms all other algorithm...
Empirical Results. The data used to measure the variables defined above were all obtained from the SIS database. The non-trade data are based on their annual Census of Industrial Production. This data was only available for the period 1974-1999; hence, we considered it in the estimations. This, however, is not an important shortcoming since the rate of IIT starts reaching meaningful levels after 1980. All data have been deflated using the 1987- based WPI. We used three proxies for the IIT variable. These are, the A-index for MIIT, the change in the GL index, ∆GL, and the GL index itself. The A index and ∆GL have been calculated as yearly changes. It has been shown by Xxxxxxxx and Terra (1997) that A-indexes calculated for subintervals of a given interval cannot be aggregated to the A index for the parent interval unless the net balance of trade changes has the same sign in all subintervals. Since this situation may be the exception rather than the rule, choice of interval in calculating the A index is important. Brulhart (1999) has investigated this question within the context of testing the SAH and has reached the conclusion that A indexes based on yearly changes give the best results.3 The estimates are given in Table 1. We find that (a) the coefficient of IIT is positive in all specifications and for all proxies except for the coefficient of GLxLTREX; this estimate, however, is not statistically significant, (b) the coefficient of the A-index, even though positive, is statistically significant in the specification with the interaction term and so is the coefficient of the interaction term, (c) the coefficients of ∆GL and ∆GLxLTREX are positive but statistically insignificant, while the coefficient of GL in the model without an interaction term is positive and significant, but becomes insignificant when GLxLTREX is introduced. These results are the reverse of what is expected when testing the SAH and appear to be closer to what Brulhart and Xxxxxx (2000) found for Malaysia. They call their findings for Malaysia “puzzling” but, in view of Xxxxxxxx and Calfat (1999) and Xxxxxxxxx et al. (2002)’s Table 1 Panel Data Estimates For Yearly Changes
Empirical Results. We start by presenting the unit root tests on the individual series. The tests are the ADF and KPSS tests. The equations needed for both tests contain an intercept and a linear time trend. In this and future applications of the ADF statistic, the lag length, pi, was chosen using three criteria: AIC, Xxxxxxxx Information Criterion (SIC) and the t-ratio for the coefficient of the last lag. A general-to-specific procedure was implemented, starting with an equation for which a large enough lag length, pmax, was specified. In all applications, pmax was chosen to be 13. Following Erlat (2002), we initially sought agreement between, at least, two of the criteria. If there was no agreement, then the result of the criterion indicating the largest lag was chosen. For this choice of pi, autocorrelation in the residuals was tested using the Ljung-Box statistic and if significant autocorrelation was found, pi was increased until it was eliminated. For the KPSS statistic, the number of weights, , (see equation (3) above) was decided upon by using a procedure suggested in Mayadune et al. (1995). We took the residuals obtained from equation (2), calculated their autocorrelations and compared them with twice their standard errors, which were estimated as T-1/2. We chose to be equal to the degree of the last significant autocorrelation. The results of the ADF and KPSS tests are given in Table 1. We note that only for four series is the unit root null rejected in the case of the ADF tests; Italy, Norway, Sweden and the UK. The rejection for the first three is only at the 10% level while the rejection for the UK series is very strong, at 1%. On the other hand, the KPSS results indicate that the stationarity null is not rejected only for Japan, the Netherlands and the UK. The KPSS results appear to confirm the ADF results only for the UK series. They do, however, indicate stationarity for series not picked up by the ADF statistic. Given that the power of the ADF statistic is low, this may be viewed as a useful result. On the other hand, the fact that the KPSS statistic does not offer collaboration of the ADF results for Italy, Norway and Sweden is not that surprising in view of Caner and Xxxxxx (2001) where they show that the KPSS statistic tends to reject the stationarity null more often than it should. Table 1 ADF and KPSS Test Results P ADF LB KPSS Austri a 2 -2.189 13.325 (0.960) 20 0.132* Belgium 1 -2.689 16.904 (0.853) 19 0.135* Denmark 1 -2.714 15.218 (0.914) 18 0.135* ...
Empirical Results. We implemented our algorithm and experiments in Python 2.7, using the Glop linear programming solver [Google, 2018] to compute the liquid welfare within our algorithm. Each run of the experiment takes roughly 30 seconds on a single CPU. Figure 1 demonstrates the revenue and welfare trends for a single inventory unit as the budget ratio r is var- ied (trends were very similar across all inventory units), and Table 1 summarizes the results for r = 1. From Figure 1 we see that our algorithm’s (AAGBud- get) revenue performance closely tracks the optimal revenue achievable as captured by the liquid welfare for all values of
Empirical Results. 5.2.1 Pooled sample results
Empirical Results. 4.1. Firm growth as dependent variable As mentioned earlier, three business growth measures are used to examine whether they are affected by B Corp certification. Xxxxxx et al. (2003) stated that implementing different growth measures in an empirical research is valuable to assess the model’s robustness. Table 1 shows the correlations between the different measures of firm growth used in this study. No strong correlations are observed between these different growth measures. Consequently, three regression models are estimated, namely total asset growth, turnover growth and employee growth.
Empirical Results
