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st: disequilibrium model

From   Matt <>
Subject   st: disequilibrium model
Date   Mon, 22 Apr 2013 11:04:31 +0100


I'm current working on the disequilibrium model as in the Maddala and Nelson (1974). 

Quantity of demand (qDt) = B1X'1t + u1t
Quantity of supply (qSt) = B2X'2t + u2t
Quantity observed (qt) = min (qDt, qSt)

the model consists of a demand equation qDt, a supply equation qSt, and a transaction equation qt. 
the vectors X'1t and X'2t are exogenous, independent variables, B1 B2 are their coefficients, u1t and u2t are their disturbances.

qDt and qSt in this model are the amount of bank debt demanded and supplied, but they are not observed by any external party. 
Only the amount of bank debt which was actually received, the transaction amount qt can be perceived. 
But we don't know if this transaction amount of debt is the agrees to the amount demanded by the firm or whether it is limited by bank. We don't know whether the firms in the sample face credit rationing - unknown sample separation.

So, to avoid writing the complicated ML programme, i uses 3-stage least square to estimate the demand and supply model, but i'm confused about the dependent variable should be used for estimation of demand and supply equation. Indeed, for the quantity observed (qt) is the short-term bank loans of the firm as in the balance sheet. But what should be the dependent variable for qDt and qSt?

Also, how can i do conditional probability in stata?

Many thanks if you can answer my query. 

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