where R = is a known matrix of order qxk (q < k) and r is a known vector of q elements. To illustrate, suppose our model is

Yi = 01 + 02 X2i + 03 X3i + 04 X4i + 05 X5i + û (3)

and suppose we want to estimate this model subject to these restrictions:

We can use some of the techniques discussed in Chapter 8 to incorporate these restrictions (e.g., 02 = 03 and 04 = 1 — 05, thus removing 02 and 04 from the model) and test for the validity of these restrictions by the F test discussed there. But a more direct way of estimating (3) incorporating the restrictions (4) directly in the estimating procedure is first to express the restrictions in the form of Eq. (2), which in the present case becomes

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