Tony Flegg University of the West of England, Bristol Timo Tohmo University of Jyväskylä, Finland

1. Can Formulae based on Location Quotients Yield Adequate Estimates of Regional Output Multipliers? A Study of South Korean Regions Tony Flegg University of the West of England, Bristol Timo Tohmo University of Jyväskylä, Finland

2. Applying LQ-based adjustments The regional input coefficients, the rij, are estimated by multiplying the corresponding national input coefficients, the aij, by a location quotient: = LQij × aij where is the estimated number of units of regional input i required to produce one unit of gross output of regional purchasing sector j. The aij exclude imports. This scaling is only applied if LQij < 1. An allowance of (1  LQij) × aij is then made for imports of input i from other regions.

3. The FLQ formula FLQij CILQij* for i  j FLQij SLQi* for i = j * = [log2(1 + TRE/TNE)] SLQi CILQij

4. Properties of the FLQ When determining the adjustment for interregional trade, the FLQ explicitly takes into account: 1. the relative size of regional supplying sector i, REi/TRE; 2. the relative size of regional purchasing sector j, REj/TRE; 3. the relative size of a region, TRE/TNE. The CILQ recognizes factors 1 & 2 but not 3; the SLQ allows for 1 (correctly) & 3 (wrongly), yet ignores 2.

5. Why use the FLQ? Analysts rarely have the data they need to construct regional input-output tables directly. Normally, employment data for individual regional sectors are readily available but not much else. Extensive surveys cost too much and take too long. We would argue that the FLQ offers a cost-effective way of adjusting national data to yield an initial set of regional input coefficients. These coefficients can then be refined via hybrid methods.

6. The role of  The inclusion of  makes it possible to refine the function * = log2(1 + TRE/TNE) by altering its degree of convexity. 0  < 1; as  rises, so too does the allowance for interregional imports.  = 0 is a special case where FLQij = CILQij.

7. Figure 1. How * varies with  and TRE/TNE λ* δ = 0.2 δ = 0.3 δ = 0.5 δ = 1 TRE/TNE

8. Reconciling the national and regional tables Our starting point was a national 28 × 28 survey-based transactions matrix constructed by the Bank of Korea for 2005. This type B matrix excluded foreign imports. For each region, the Bank built a 78 × 78 survey-based transactions table of type B. We aggregated these regional tables to be consistent with the national table. We then computed regional input coefficients and type I sectoral output multipliers for each of the 16 regions. We used different LQ-based formulae to regionalize the national coefficient matrix and evaluated the methods in terms of their relative accuracy in matching the benchmark regional multipliers.

9. Criteria for evaluating estimated multipliers

10. Table 1. Accuracy of different methods: sectoral output multipliers (28 sectors and 16 regions)

11. Refining the FLQ: Kowalewski’s SFLQ Kowalewski’s sector-specific (SFLQ) approach aims to enhance the accuracy of the FLQ by permitting to vary across sectors. The SFLQ is based on a regression model, which we re-estimated for two Korean regions. The regressors were SLQj plus three other variables requiring only national data. R2 = 0.63 for one region and 0.41 for the other. The SFLQ gave encouraging results but more work needs to be done to refine the underlying regression model. Relative to the FLQ with  = 0.3, MAPE was cut by 1.5 and 0.3 percentage points in the two regions.

12. A regression model to estimate  ln* = intercept + 0.168lnR + 0.325lnP + 0.317lnF + e * is the optimal  for each region; R is regional size measured in terms of output (%); P is each region’s propensity to import from other regions, as a proportion of gross output; Fis each region’s average use of foreign intermediate inputs, as a proportion of gross output; e is a residual. R2 = 0.934; t ratios = 4.80, 2.37, 6.64; excellent 2 statistics for heteroscedasticity, functional form and normality.

13. Using our regression to estimate  Unlike the SFLQ, our approach aims to determine a value of for each region by using region-specific data. Interregional variation in the propensity to import from abroad plays a key role in determining the value of . Compared with using a common  = 0.4 for all regions, the method lowers MAPE by 0.7 percentage points on average. However, its use is limited by the availability of data.

14. Conclusion The FLQ gave far more accurate estimates of type I output multipliers than the SLQ and CILQ. On average across the 16 regions, the FLQ gave a mean absolute percentage error of 8.0% with  = 0.4 ± 0.025. Flegg and Tohmo’s regression model, as reformulated here, can be used to find an approximate initial value of  for each region. However, the model makes use of region-specific data that may be unavailable. Kowalewski’s sector-specific (SFLQ) approach, which aims to enhance the accuracy of the FLQ by permitting to vary across sectors, gave encouraging results but more work needs to be done to refine the underlying regression model.

15. Conclusion continued The FLQ can only be relied upon to give a satisfactory initial set of regional input coefficients. Analysts should always try to refine these estimates by using informed judgement, any available superior data, surveys of key sectors and so on.