I wish to estimate the following model: y=b0+b1*x1+b2*X2+mu if X2>= f(x1) and y=a0+a1*x1+epsilon if X2>= f(x1), where f() is continuous unknown function. The theoretical model ensuresthat this exits and it is well behaved. The problem is that X2 is a continuous variable in the set [0,1]. If X2 were to be dichotomic, then I think the way of estimating this will be by mean of a switching regression. This model comes out of theoretical repeated game model. y=cooperation and X2=discount factor. Thanks a lot