Aggregation of Variables in Least-Squares Regression

I consider the properties of the estimator when the true model is y = .1 x 1 + .2 x 2 + u, but the restriction .1 = .2 = . is incorrectly imposed.I show that the probability limit of is a weighted sum of .1 and .2; the weights sum to 1 but do not necessarily lie in the unit interval, so plim need not be bounded by .1 and .2.Sufficient conditions for such bounding are derived.Certain changes in the moments of x 1 and x 2 have .perverse. effects on the weights.I illustrate the consequences of inappropriate aggregation of variables with an empirical example of the effect of research and development investment on productivity.