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. Y_t = β₁ + β_2t + u_t

b. ln Y_t = β₁ + β_2t + u_t

c. Logistic growth model:

d. Gompertz growth model:

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

Transcribed Image Text:

+U; I+ Be P3T Y, = Bje-B2e¬B3t + Uj -Be#3t