Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 10

(Requires calculus) Let patents be the number of patents applied for by a firm during a given year. Assume that the conditional expectation of patents given sales and RD is E(patents|sales,RD) = exp[?0 + ?1log(sales) + (?2RD + ?3RD2],

where sales is annual firm sales and RD is total spending on research and development over the past 10 years.

(i) How would you estimate the ?j? Justify your answer by discussing the nature of patents.

(ii) How do you interpret ?1?

(iii) Find the partial effect of RD on E(patents|sales, RD).

Step 1 of 3

Given that:

Where, = Number of patents applied by the firm annually

=annual firm sales

=annual firm’s spending on Research and Development over the past 10 years

(i)

The coefficients is estimated by Poisson Regression model

The variable is a non-negative dependent variable, which can suitably be termed as count variable, which could take only the non-negative integer values.

The Logit or Probit model could not be used because, can take values beyond 0 and 1.

Even the Tobit model could not be used as can take zero as a value and it is not possible to obtain the logarithm of zero.

The coefficients is suitably estimated by Poisson Regression model