  This paper considers the nonparametric regression model with an additive
error that is dependent on the explanatory variables. As is common in empirical
studies in epidemiology and economics, it also supposes that valid instrumental
variables are observed. A classical example in microeconomics considers the
consumer demand function as a function of the price of goods and the income,
both variables often considered as endogenous. In this framework, the economic
theory also imposes shape restrictions on the demand function, like
integrability conditions. Motivated by this illustration in microeconomics, we
study an estimator of a nonparametric constrained regression function using
instrumental variables by means of Tikhonov regularization. We derive rates of
convergence for the regularized model both in a deterministic and stochastic
setting under the assumption that the true regression function satisfies a
projected source condition including, because of the non-convexity of the
imposed constraints, an additional smallness condition.
