The interpretation of instrumental variables estimators in simultaneous equations models with an application to the demand for fish

In markets where prices are determined by the intersection of supply and de mand curves, standard identification results require the presence of instru ments that shift one curve but not the other. These results are typically p resented in the context of linear models with fixed coefficients and additi ve residuals. The first contribution of this paper is an investigation of t he consequences of relaxing both the linearity and the additivity assumptio n for the interpretation of linear instrumental variables estimators. Witho ut these assumptions, the standard linear instrumental variables estimator identifies a weighted average of the derivative of the behavioural relation ship of interest. A second contribution is the formulation of critical iden tifying assumptions in terms of demand and supply at different prices and i nstruments, rather than in terms of functional-form specific residuals. Our approach to the simultaneous equations problem and the average-derivative interpretation of instrumental variables estimates is illustrated by estima ting the demand for fresh whiting at the Fulton fish market. Strong and cre dible instruments for identification of this demand function are available in the form of weather conditions at sea.