Estimation and Inference for Linear Models in Which Subsets of the Dependent Variable are Constrained

Subsets of the dependent variable of a linear model often conform to known constraints; for example, this situation arises with Engel curves and with models which estimate transition probabilities, market shares, or other classes of proportions. These models imply a variety of restrictions on the parameters, explanatory variables and residuals which must be treated explicitly in estimating and testing hypotheses about the parameters. This paper discusses these restrictions and develops an estimating procedure which yields consistent estimates which are asymptotically efficient, unbiased and normal.