A note on distortions from estimating the regional impacts of exogenous changes in output

ABSTRACT

This paper demonstrates both theoretically and empirically that when outputs instead of final demands are exogenously predetermined, the traditional Leontief final demand model overestimates economic impact, and even more so in a multiregional context. We assess this premise vis-à-vis the Leontief output model using the 2013 interregional input–output table of the Republic of Korea. We find that from a multiregional perspective the standard Leontief final demand model yields substantially biased output multipliers for Chungbuk Province.

KEYWORDS:

• Leontief final demand model
• Leontief output-based model
• exogenous output shocks
• estimation biases
• interregional feedback

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 In Equations 2 and 3, ${\mathbf{\text{I}}}_{11}$ represents a 1 × 1 identity matrix, while ${\mathbf{\text{I}}}_{22}$ indicates an (n − 1) × (n − 1) identity matrix.

2 Derivations of Equations 5 and 6 are detailed in the supplementary material.

3 In fact, that $\mathrm{\Delta }{\mathbf{\text{f}}}_1$ equals 1.0 in Equation 3 means that $\mathrm{\Delta }{\mathbf{\text{f}}}_1$ is replaced with $\mathrm{\Delta }{\mathbf{\text{x}}}_1$, the value of which is assumed to be 1.0.

4 The condition that $\mathrm{\Delta }{\mathbf{\text{f}}}_1^{\mathrm{r}}$ is set to 1.0 implies that $\mathrm{\Delta }{\mathbf{\text{f}}}_1^{\mathrm{r}}$ in Equation 6 is replaced with $\mathrm{\Delta }{\mathbf{\text{x}}}_1^{\mathrm{r}}$, which is equal to 1.0.

5 Miller (1969) reports average error between a single-region and two-region model experiment as between 5% and 8% over a wide range of experiments. The magnitudes of percentage error in the Chungbuk case are consistent with the results of Miller's experiments.