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What is meant by intrinsically linear and intrinsically nonlinear regression models? Give some examples.

Since the error term in the Cobb-Douglas production function can be entered multiplicatively or additively, how would you decide between the two?

What is the difference between OLS and nonlinear least-squares (NLLS) estimation?

The relationship between pressure and temperature in saturated steam can be expressed as9:

574 PART THREE: TOPICS IN ECONOMETRICS

Problems where Y = pressure and t = temperature. Using the method of nonlinear least squares (NLLS), obtain the normal equations for this model.

14.5. State whether the following statements are true or false. Give your reasoning.

a. Statistical inference in NLLS regression cannot be made on the basis of the usual t, F, and x2 tests even if the error term is assumed to be normally distributed.

b. The coefficient of determination (R2) is not a particularly meaningful number for an NLRM.

14.6. How would you linearize the CES production function discussed in the chapter? Show the necessary steps.

14.7. Models that describe the behavior of a variable over time are called growth models. Such models are used in a variety of fields, such as economics, biology, botany, ecology, and demography. Growth models can take a variety of forms, both linear and nonlinear. Consider the following models, where Y is the variable whose growth we want to measure; t is time, measured chronologically; and ut is the stochastic error term.

a. Yt = 01 + 021 + ut b. ln Yt = 01 + 021 + ut c. Logistic growth model: Yt = ^^ + ut d. Gompertz growth model: Yt = 01 e-foe + ut

Find out the properties of these models by considering the growth of Y in relation to time.

14.8. The data in Table 14.2 gives U.S. population, in millions of persons, for the period 1970-1999. Fit the growth models given in exercise 14.7 and decide which model gives a better fit. Interpret the parameters of the model.

Observation

U.S. population

Time

Observation

U.S. population

Time

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