Consider the following model:

Y_t = α + βX_t + u_t

Assume that ut follows the Markov first-order autoregressive scheme given in Chapter 12, namely,

u_t = pu_t-1 + ε_t

where ρ is the coefficient of (first-order) autocorrelation and where εt satisfies all the assumptions of the classical OLS. Then, as shown in Chapter 12, the model

will have a serially independent error term, making OLS estimation possible. But this model, called the serial correlation model, very much resembles the Koyck, adaptive expectations, and partial adjustment models. How would you know in any given situation which of the preceding models is appropriate?*

Y, = a(1 p) + B(X, pX,-1) + pY,1 +