Least squares estimation in a simple random coefficient autoregressive model

The question we discuss is whether a simple random coefficient autoregressive model with infinite variance can create the long swings, or persistence, which are observed in many macroeconomic variables. The model is defined by yt=stρyt−1+εt,t=1,…,n, where st is an i.i.d. binary variable with p=P(st=1), independent of εt i.i.d. with mean zero and finite variance. We say that the process yt is persistent if the autoregressive coefficient ρˆn of yt on yt−1 is close to one. We take p<1