02119cam a22002417 4500001000600000003000500006005001700011008004100028100002200069245011500091260006600206490004100272500001600313520116500329530006101494538007201555538003601627700002301663710004201686830007601728856003701804856003601841w1885NBER20180522175108.0180522s1986 mau||||fs|||| 000 0 eng d1 aCampbell, John Y.10aCointegration and Tests of Present Value Modelsh[electronic resource] /cJohn Y. Campbell, Robert J. Shiller. aCambridge, Mass.bNational Bureau of Economic Researchc1986.1 aNBER working paper seriesvno. w1885 aApril 1986.3 aIn a model where a variable Y[sub t] is proportional to the present value, with constant discount rate, of expected future values of a variable y[sub t] the "spread" S[sub t]= Y[sub t] - [theta sub t] will be stationary for some [theta] whether or not y[sub t]must be differenced to induce stationarity. Thus, Y[sub t] and y[sub t] are cointegrated. The model implies that S[sub t] is proportional to the optimal forecast of [delta Y{sub t+1}] and also to the optimal forecast of S*[sub t], the present value of future [delta y{sub t}]. We use vector autoregressive methods, and recent literature on cointegrated processes, to test the model. When Y[sub t] is the long-term interest rate and y[sub t] the short-term interest rate, we find in postwar U.S. data that S[sub t] behaves much like an optimal forecast of S*[sub t] even though as earlier research has shown it is negatively correlated with [delta Y{sub t+1}]. When Y[sub t] is a real stock price index and y[sub t] the corresponding real dividend, using annual U.S. data for 1871-1986 we obtain less encouraging results for the model, al-though the results are sensitive to the assumed discount rate. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web.1 aShiller, Robert J.2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w1885.4 uhttp://www.nber.org/papers/w188541uhttp://dx.doi.org/10.3386/w1885