inputoutput tables for 1995, which identify 37 separate sectors, as a benchmark to evaluate the relative performance of the FLQ and other LQ-based adjustment formulae in estimating input coefficients and type I sectoral output multipliers. We employed a wide range of statistical criteria to assess the results. As expected, the FLQ outperformed the conventional LQs by a wide margin, regardless of which criterion was used. Moreover, an analysis using Theil’s index of inequality revealed that the FLQ produced a much closer match between the estimated and survey-based input coefficients. This was true irrespective of whether one measured this match in terms of bias, variance or covariance. Using the mean proportional difference, as the criterion, we found that = 0.25 was μ1, δ the best single value for estimating multipliers. This criterion has the desirable property that it minimizes bias. When averaged across regions, the unweighted mean value of was μ1 0.4%, compared with 1.9% for = 0.3. By contrast, when the results were weighted by size δ of region, = 0.3 gave the best outcome. There was a discernible tendency for the optimal δ value of to rise with regional size. It is also worth noting that the use of absolute values δ suggested that 0.3 rather than 0.25 might be the best single value of Nevertheless, when δ. averaged across regions, the outcomes for these two values of were very similar indeed. δ It is interesting that our findings are broadly consistent with of Bonfiglio and Chelli (2008), who used a Monte Carlo approach to generate 400,000 sectoral output multipliers. Their study indicated an optimal 0.3. On the other hand, using Scottish data, Flegg and δ ≈ Webber (2000) found that the FLQ with 0.15 yielded µ1 0. This relatively low value of δ ≈ ≈ can probably be explained by the fact that almost half of the Scottish survey-based δ coefficients were larger than those in the parent table that was being used in the simulation. Although the FLQ was demonstrably better than the conventional LQs, its performance was not as good as we have wished. For instance, the unweighted mean absolute proportional error, with = 0.3, was 8.1% for multipliers. The weighted mean was 7.6%. As δ
inputoutput tables for 1995, which identify 37 separate sectors, as a benchmark to evaluate the relative performance of the FLQ and other LQ-based adjustment formulae in estimating input coefficients and type I sectoral output multipliers. We employed a wide range of statistical criteria to assess the results. As expected, the FLQ outperformed the conventional LQs by a wide margin, regardless of which criterion was used. Moreover, an analysis using Theil’s index of inequality revealed that the FLQ produced a much closer match between the estimated and survey-based input coefficients. This was true irrespective of whether one measured this match in terms of bias, variance or covariance. Using the mean proportional difference, μ1, as the criterion, we found that δ = 0.25 was the best single value for estimating multipliers. This criterion has the desirable property that it minimizes bias. When averaged across regions, the unweighted mean value of μ1 was 0.4%, compared with 1.9% for δ = 0.3. By contrast, when the results were weighted by size of region, δ = 0.3 gave the best outcome. There was a discernible tendency for the optimal value of δ to rise with regional size. It is also worth noting that the use of absolute values suggested that 0.3 rather than 0.25 might be the best single value of δ. Nevertheless, when averaged across regions, the outcomes for these two values of δ were very similar indeed. It is interesting that our findings are broadly consistent with of Bonfiglio and Chelli (2008), who used a Monte Carlo approach to generate 400,000 sectoral output multipliers. Their study indicated an optimal δ ≈ 0.3. On the other hand, using Scottish data, Flegg and Webber (2000) found that the FLQ with δ ≈ 0.15 yielded µ1 ≈ 0. This relatively low value of δ can probably be explained by the fact that almost half of the Scottish survey-based coefficients were larger than those in the parent table that was being used in the simulation. Although the FLQ was demonstrably better than the conventional LQs, its performance was not as good as we have wished. For instance, the unweighted mean absolute proportional error, with δ = 0.3, was 8.1% for multipliers. The weighted mean was 7.6%. As
RegStudies_V6_wpaper.docx