Time-varying parameters in the almost ideal demand system and the Rotterdam model: will the best specification please stand up?

Abstract

This article assesses the ability of the Rotterdam Model (RM) and of three versions of the Almost Ideal Demand System (AIDS) to recover the time-varying elasticities of a true demand system and to satisfy theoretical regularity. Using Monte Carlo simulations, we find that the RM performs better than the linear-approximate AIDS at recovering the signs of all the time-varying elasticities. More importantly, the RM has the ability to track the paths of time-varying income elasticities, even when the true values are very high. The linear-approximate AIDS, not only performs poorly at recovering the time-varying elasticities but also badly approximates the nonlinear AIDS.

Keywords:

• AIDS
• Rotterdam model
• structural time series models
• Monte Carlo experiment
• theoretical regularity

JEL Classification::

• D12
• C51
• C52

Acknowledgements

Isaac Kanyama acknowledges the support from the Economic Research Southern Africa (ERSA).

Notes

¹ The formulae for the Divisia quantity and price indexes are and , respectively, where m is the total consumer expenditure.

² Although we shall only consider two specifications of the parameters' time-varying structure, other stochastic processes can be specified for the time-varying coefficients as well, such as the autoregressive structure suggested by Chavas (1983).

³ The autoregressive models for the supernumerary quantities and income are the following: y _1t  = 2 + 0.75y _1,t−1 + e _1t ; y _2t  = 1 + 0.739y _2,t−1 + e _2t ; m _1t  = 125 + 0.98m _1,t−1 + e _3t where e _1t , e _2t and e _3t are zero mean and serially uncorrelated normal error terms with variance 1.

⁴ See Barnett and Choi (1989).

⁵  y _3t  = 3 + 0.69y _3,t−1 + e _4t .

⁶ See Barnett and Choi (1989) for the specification of this utility maximization problem.

⁷ The values used to generate the data are: α₁ = 1, α₂ = 10 and α₃ = 4. This specification is used for the RWM. For the LTM, each of the α _i 's is specified as a random walk plus a shift, where the shift itself follows a random walk process.

⁸ A regular cost function is continuous, nondecreasing, linearly homogeneous and concave in p, increasing in u and twice continuously differentiable.