Using a multinomial probit to test for complementarity

Abstract

This note shows that the structural parameter estimate of complementarity among innovation strategies can be recovered when the strategies are dichotomous if we use a multinomial probit model. That is, we can separate the complementarity between the innovation strategies from the unobserved heterogeneity, by estimating both the parameter of complementarity and the correlation coefficients in the error terms. This result holds because the multinomial probit, in contrast to the bivariate probit, is not an incoherent model.

Keywords:

• complementarity
• innovations
• multinomial probit

JEL Classification:

• C25
• C35
• 032
• 033

Notes

¹ Much of the intuition presented here extends to cases of three or more innovations; however, the analysis becomes far more cumbersome.

² The only difference is that the estimated parameter in the MNP are normalized.

³ See Train (2007) for an extensive discussion.

⁴ Note that we have the symmetric case in the bivariate probit model, when and only the correlation coefficients can be estimated due to the incoherence problem.