satisfactory way of assessing the accuracy of estimated multipliers and coefficients (see, for example, Bonfiglio and Chelli, 2008; Sawyer and Miller, 1983). What is more, the negligible difference of 0.053 in the mean values of for = 0.25 and = 0.3 may mask some useful μ5 δ δ information. Hence a set of disaggregated results is presented in Table 4. Table 4 near here Table 4 strongly confirms the earlier finding that the optimal tends to rise with regional δ size. Indeed, five of the largest regions require = 0.35, whereas two of the smallest require δ = 0.15. Furthermore, compared with Table 3, there has been a shift towards the right in the δ distribution of results, with 14 of the 20 regions now clustered in the range 0.3 ± 0.05. However, only three regions are located in the centre of this range. One might ask whether this rightward shift is explicable in terms of the characteristics of the FLQ. To explore this issue, we examined the sectoral distribution of errors for each region when 0. We then increased by 0.025 to create a new distribution of errors. μ1 ≈ δ A fundamental property of the FLQ is that a rise in the value of decreases the extent to δ which any multipliers are overestimated, while increasing the amount of any underestimation. When is used as the criterion, overestimates can be offset by underestimates but this is not μ1 possible with as all errors of a given size are treated equally. We identified nine regions μ5, where the rise in the value of decreased the degree of overestimation by considerably more δ than it increased the degree of underestimation. For these regions, typically reached a μ5 minimum at a somewhat higher than it did for On the other hand, there were only two δ μ1. regions where there was a noticeable movement in the opposite direction. The overall shift rightwards in the distribution of results is, therefore, unsurprising. In the light of the above results, should we accept 0.3 as the best single value of We δ? would suggest not. Our justification for this view is that raising from 0.25 to 0.3 would δ introduce bias that was not previously there, yet yield only a minimal gain in terms of
satisfactory way of assessing the accuracy of estimated multipliers and coefficients (see, for example, Bonfiglio and Chelli, 2008; Sawyer and Miller, 1983). What is more, the negligible difference of 0.053 in the mean values of μ5 for δ = 0.25 and δ = 0.3 may mask some useful information. Hence a set of disaggregated results is presented in Table 4. Table 4 near here Table 4 strongly confirms the earlier finding that the optimal δ tends to rise with regional size. Indeed, five of the largest regions require δ = 0.35, whereas two of the smallest require δ = 0.15. Furthermore, compared with Table 3, there has been a shift towards the right in the distribution of results, with 14 of the 20 regions now clustered in the range 0.3 ± 0.05. However, only three regions are located in the centre of this range. One might ask whether this rightward shift is explicable in terms of the characteristics of the FLQ. To explore this issue, we examined the sectoral distribution of errors for each region when μ1 ≈ 0. We then increased δ by 0.025 to create a new distribution of errors. A fundamental property of the FLQ is that a rise in the value of δ decreases the extent to which any multipliers are overestimated, while increasing the amount of any underestimation. When μ1 is used as the criterion, overestimates can be offset by underestimates but this is not possible with μ5, as all errors of a given size are treated equally. We identified nine regions where the rise in the value of δ decreased the degree of overestimation by considerably more than it increased the degree of underestimation. For these regions, μ5 typically reached a minimum at a somewhat higher δ than it did for μ1. On the other hand, there were only two regions where there was a noticeable movement in the opposite direction. The overall shift rightwards in the distribution of results is, therefore, unsurprising. In the light of the above results, should we accept 0.3 as the best single value of δ? We would suggest not. Our justification for this view is that raising δ from 0.25 to 0.3 would introduce bias that was not previously there, yet yield only a minimal gain in terms of
RegStudies_V6_wpaper.docx