Information Structure and Statistical Information in Discrete Response Models
Discrete response models are of high interest in economics and econometrics as they encompass treatment effects, social interaction and peer effect models, and discrete games. We study the impact of the structure of information sets of economic agents on the Fisher information of (strategic) interaction parameters in such models. While in complete information models the information sets of participating economic agents coincide, in incomplete information models each agent has a type, which we model as a payoff shock, that is not observed by other agents. We allow for the presence of a payoff component that is common knowledge to economic agents but is not observed by the econometrician (representing unobserved heterogeneity) and have the agents' payoffs in the incomplete information model approach their payoff in the complete information model as the heterogeneity term approaches 0. We find that in the complete information models, there is zero Fisher information for interaction parameters, implying that estimation and inference become nonstandard. In contrast, positive Fisher information can be attained in the incomplete information models with any non-zero variance of player types, and for those we can also find the semiparametric efficiency bound with unknown distribution of unobserved heterogeneity. The contrast in Fisher information is illustrated in two important cases: treatment effect models, which we model as a triangular system of equations, and static game models. In static game models we show this result is not due to equilibrium refinement with an increase in incomplete information, as our model has a fixed equilibrium selection mechanism. We find that the key factor in these models is the relative tail behavior of the unobserved component in the economic agents' payoffs and that of the observable covariates.
|Date of creation:||2011|
|Date of revision:|
|Contact details of provider:|| Postal: Department of Economics Duke University 213 Social Sciences Building Box 90097 Durham, NC 27708-0097|
Phone: (919) 660-1800
Fax: (919) 684-8974
Web page: http://econ.duke.edu/
When requesting a correction, please mention this item's handle: RePEc:duk:dukeec:11-19. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Department of Economics Webmaster)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.