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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Review of Financial Economics, Volume 13, Issue 3, 2004, Pages 245–258
This paper tests the validity of present value (PV) models of stock prices by employing a two-step strategy for testing the null hypothesis of no cointegration against alternatives which are fractionally cointegrated. Monte Carlo simulations are conducted to evaluate the power and size properties of this test, which is shown to outperform existing ones, and to compute appropriate critical values for finite samples. It is found that stock prices and dividends are both I(1) nonstationary series, but they are fractionally cointegrated. This implies that, although there exists a long-run relationship, which is consistent with PV models, the equilibrium errors exhibit slow mean reversion. As the error correction term possesses long memory, deviations from equilibrium are highly persistent.
One of the central propositions of modern finance theory is the efficient markets hypothesis (EMH), which in its simplest formulation states that the price of an asset at time t should fully reflect all the available information at time t. This has often been tested by using the present value (PV) model of stock prices, since, if stock market returns are not forecastable, as implied by the EMH, stock prices should equal the present value of expected future dividends. As pointed out by Campbell and Shiller (1987) in their seminal paper, this implies that stock prices and dividends should be cointegrated, and recent studies of PV models have mainly used cointegration techniques. However, the discrete options I(1) and I(0) offered by classical cointegration analysis are rather restrictive, which might explain why the available empirical evidence is inconclusive. Adjustment to equilibrium might in fact take a longer time than suggested by standard cointegration tests. In other words, stock prices and dividends might be tied together through a fractionally integrated I(d)-type process such that the equilibrium errors exhibit slow mean reversion. The contribution of the present paper is twofold. First, we propose a two-step strategy for testing the null of no cointegration against alternatives, which are fractionally cointegrated. We conduct Monte Carlo simulations to evaluate the size and power properties of this test, which is shown to outperform existing ones, and to compute appropriate critical values for finite samples. Second, we apply the new methodology to an updated version of the Campbell and Shiller's (1987) dataset to test the adequacy of PV models of stock prices. We find that stock prices and dividends are both I(1) nonstationary series, but they are fractionally cointegrated. This implies that, although there exists a long-run relationship, which is consistent with PV models, the error correction term possesses long memory, and hence, deviations from equilibrium are highly persistent. The layout of the paper is the following. Section 2 briefly reviews the existing literature on PV models. Section 3 starts by describing the concepts of fractional integration and cointegration, and then introduces a procedure for testing the null hypothesis of no cointegration against fractionally cointegrated alternatives, and its properties are investigated by conducting Monte Carlo experiments. This methodology is applied in Section 4 to test PV models, and Section 5 offers some concluding remarks.
نتیجه گیری انگلیسی
We have shown in this paper that the cointegrating relationship between stock prices and dividends possesses long memory. This is an important finding, as it means that, although these two variables are linked in the long run, adjustment to equilibrium takes a long time. Thus, the validity of PV models of stock prices is confirmed, but only over a long horizon. Failure to take into account this slow adjustment process explains why the evidence from standard cointegration tests is often contradictory. An implication of our results is that investment strategies should allow for the slow response to shocks and the persistence of deviations from equilibrium. We have also made a methodological contribution by proposing a two-step strategy for fractional cointegration. It is based on Robinson (1994), and involves initially testing the order of integration of the individual series, testing then the degree of integration of the estimated residuals from the cointegrating regression. As the Monte Carlo analysis shows, the test has higher power than alternative tests for the null of cointegration against fractional alternatives. It should also be mentioned that we did not attempt in this paper to select a specific model for the residuals from the cointegrating regression. In fact, our approach generates simply computed diagnostics for departures from any real d. Thus, given the continuity of d on the real line, it is not surprising that, when fractional hypotheses are considered, the evidence should appear to be supportive. Other methods for estimating d, based on semiparametric approaches, have been recently proposed (see, e.g., Robinson, 1995a and Robinson, 1995b), and they could also be usefully employed for analysing financial or macroeconomic series. However, these methods may be too sensitive to the choice of the bandwidth parameter and, in that respect, a fully parametric model such as the one selected in this paper may be more appropriate. Extensions of the multivariate version of the tests of Robinson (1994) which are suitable to test fractional cointegration in a system-based model is also of interest. There exists a reduced-rank procedure suggested by Robinson and Yajima (2000), However, it is not directly applicable here, neither in the simulation study nor in the empirical application, since that method assumes I(d) stationarity (d<0.5) for the individual series, while we consider I(1) nonstationary processes.