Regime switching in the present value models: A backward-solving method

We develop a new method for incorporating regime shifts in the present value models. Existing studies solve the present value problem forward by projecting the expectations of investors and regimes into the infinite future. Representing the problem in a recursive form, we propose a backward-solving approach in which the initially guessed formulation of the present value is verified by the undetermined coefficients method. Unlike the forward-solving methods, ours does not resort to unnecessary approximations or overly restricted forms of regime switching. Applied to the Korean housing market, our regime-switching present value model sharply detects two distinctive regimes in the behaviour of the price-rent ratio.