A note on the estimation of the PD-GEV models

Abstract

This note provides a formula to compute the value of the mean utilities as a function of market shares in Bresnahan et al.'s (1997) production differentiation models (PD-GEV) (1997). Such a formula avoids the time consuming contraction mapping procedure suggested by Berry et al. (1995).

Acknowledgement

I am grateful to Professor Steinar Str⊘m for very helpful comments and discussions.

Notes

¹ See for instance Goldberg and Verboven (2001), Peters (2003), Tovar (2004).

² This procedure is of course fundamental when closed forms do not exist.

³ The correlation coefficients are the complement of logsum coefficients.

⁴ The inequality on cross elasticity of substitution when dimension B and D competes simultaneously and symmetrically according to PD-GEV model is ε_{BD, BD} ≥ (ε_{NBD, BD}, ε_{BND, BD}) ≥ ε_{NBND, BD} with ε_{NBD, BD} ≥ or ≤ε_{BND, BD}

⁵ See for instance Moul (2003). In this case mean utilities could be expressed as:

(18)

where m represents the dimension at the top of nesting, and s and r the dimensions at the bottom.