Calibration of incomplete demand systems in quantitative analysis

Abstract

An easily implemented and flexible calibration technique for partial demand systems is introduced, combining recent developments in incomplete demand systems and a set of restrictions conditioned on the available elasticity estimates. The technique accommodates various degrees of knowledge on cross-price elasticities, satisfies curvature restrictions, and allows the recovery of an exact welfare measure for policy analysis. The technique is illustrated with a partial demand system for food consumption in Korea for different states of knowledge on cross-price effects. The consumer welfare impact of food and agricultural trade liberalization is measured.

Acknowledgements

We thank Georgeanne Artz and participants at the 2003 International Conference of Agricultural Economists for their comments.

Notes

¹ For n goods, the number of price elasticities to estimate is equal to {n(n + 1)/2}, assuming symmetry is imposed in a calibration using deflated prices; n income elasticities have to be found as well.

² Concavity (quasi-concavity) of utility is defined with the condition that the Slutsky matrix of compensated price responses of the demand system is negative definite (negative semi-definite).

³ If only expenditures are known, quantity units for each good are redefined such that the associated price is equal to 1 per unit.

⁴ Giffen goods are ruled out (income term smaller in absolute value to the Hicksian price term in absolute value in the Slutsky decomposition).

⁵ The sensitivity of EV with respect to δ( q _z ) (dEV/d δ( q _z )) is 0.007 (an additional 1 million won in the income argument via δ( q _z ) induces 7 million won of variation in EV, which is of the order of 14 trillion won for the price change considered in the illustration).

⁶ The Cholesky factorization decomposes minus the Slutsky matrix - S into - S = L _l DL _h , where D is a diagonal matrix constrained to have nonnegative elements D _ii for quasi-concavity of the utility function, L _l is a unit lower triangular matrix, and L _h is the transpose of L _l (Lau). A similar scaling approach is used for the Cholesky factorization as for the diagonal-dominance approach. Scaling factors are applied to the slope estimates of the Marshallian cross-price effects to satisfy curvature restrictions (D _ii ) positive.