Use the same model for the Patents-R\&D data as in Section 23.3, except vary the dependent variable and model as suggested in the following. In each case estimate random effects models and, if theoretically feasible, a fixed effects model.

(a) Use a logit model of whether or not the firm has a patent.

(b) Use a truncated tobit model of number of \(\log\) (Patents) with observations of firms with zero patents dropped.

(c) Use a Poisson model for number of patents.

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23.3. Nonlinear Panel Example: Patents and R&D We model the relationship between patents and R&D expenditures, using U.S. data on 346 firms for each of the five years 1975-1979 from Hall, Griliches, and Hausman (1986). The dependent variable yit is Patents, defined as the number of patents applied for during the year that were eventually granted. For simplicity we consider just one explanatory variable xit, real R&D spending during the year (in 1972 dollars).