In Exercise 9.26 , you estimated a cost function on a cross-section of electric companies. Consider the nonlinear specification logTC 1 2 logQ 3

In Exercise 9.26

, you estimated a cost function on a cross-section of electric companies.

Consider the nonlinear specification logTC Æ ¯1 ů2 logQ ů3

¡

logPLÅlogPK ÅlogPF

¢

ů4 logQ 1Åexp

¡

¡

¡

logQ ¡°

¢¢ Åe. (23.11)

This model is called a smooth threshold model. For values of logQ much below °, the variable logQ has a regression slope of ¯2. For valuesmuch above ¯7, the regression slope is ¯2ů4. Themodel imposes a smooth transition between these regimes.

(a) The model works best when ° is selected so that several values (in this example, at least 10 to 15)

of logQi are both below and above °. Examine the data and pick an appropriate range for °.

(b) Estimate the model by NLLS using a global numerical search over (¯1,¯2,¯3,¯4,°).

(c) Estimate the model by NLLS using a concentrated numerical search over °. Do you obtain the same results?

(d) Calculate standard errors for all the parameters estimates (¯1,¯2,¯3,¯4,°).