What drives stock prices? Identifying the determinants of stock price movements.

• Author: Balke, Nathan S.

1. Introduction

   Before 1981, much of the finance literature viewed the present value of dividends to be the principal determinant of the level of stock prices. However, LeRoy and Porter (1981) and Shiller (1981) found that, under the assumption of a constant discount factor, stock prices were too volatile to be consistent with movements in future dividends. This conclusion, known as the excess volatility hypothesis, argues that stock prices exhibit too much volatility to be justified by fundamental variables. Several papers (Flavin 1983; Kleidon 1986; Marsh and Merton 1986; Mankiw, Romer, and Shapiro 1991) challenged the statistical validity of the variance bounds tests of LeRoy and Porter and Shiller, on the grounds that stock prices and dividends were nonstationary processes; however, much of the subsequent literature found that stock price movements could not be explained solely by dividend variability, as suggested by the present value model with constant discounting (Campbell and Shiller 1987; West 1988a). (1)

   By relaxing the assumption of constant discounting, Campbell and Shiller (1988, 1989) and Campbell (1991) attempted to break up stock price movements (returns) into the contributions of changes in expectations about future dividends and future returns. They employed a log-linear approximation of stock returns and derived a linear relationship between the log price-dividend ratio and expectations of future dividends and stock returns. They further assumed that the data- generating process of dividend growth and the log price-dividend ratio could be adequately characterized by a low-order vector autoregression (VAR). By using the VAR to forecast future dividend growth and future stock returns, they were able to decompose the variability of current stock returns into the variability of future dividend growth and future stock returns. They attributed most of the movements in stock prices to revisions in expectations about future stock returns rather than to future dividend growth. Campbell and Ammer (1993) extended the log-linear approximation and the VAR approach to an examination of bond returns as well as stock returns. They found that expectations of future excess returns contributed more to the volatility of stock returns than did movements in expected future dividends. (2)

   In this paper, we argue that there is a fundamental problem in identifying the sources of stock price movements. The problem lies in the fact that stock prices (or, more specifically, price-dividend ratios) are very persistent but real dividend growth and excess returns are not. Figure 1 plots the log price-dividend ratio from 1953:II to 2001:IV. This figure clearly indicates that the log price-dividend ratio shows substantial persistence. Standard Dickey-Fuller tests fail to reject the null hypothesis of a unit root in the log price-dividend ratio. (3) In the standard market fundamentals stock price valuation model, movements in the expected values of real dividend growth, real interest rates, and excess returns (the latter two making up required return) explain movements in the price-dividend ratio. Real interest rates, which have a substantial low-frequency component, do not move over time in a manner that would explain the low-frequency movements in the price-dividend ratio. Thus, a market fundamentals explanation of persistent stock price movements also requires movements in excess returns or real dividend growth to persist. However, if we look at movements in real dividend growth and excess returns over time (Figure 2, Panels A and B), we find that these are very volatile, containing little discernable low-frequency movement. Therefore, the log price-dividend ratio exhibits substantial persistence but its market fundamental components do not.

   [FIGURES 1-2 OMITTED]

   Because of the apparent lack of low-frequency movements in either excess returns or real dividend growth, it is not possible to identify which of these is more important in producing long swings in the price-dividend ratio. More formally, we show that the data cannot distinguish a model in which there are small permanent changes in dividend growth from one in which there are small permanent changes in excess returns. In a five-variable system that includes log price-dividend ratio, real dividend growth, short- and long-term interest rates, and inflation, we find that we cannot reject two alternative vector error correction models (VECMs) that each contain two cointegrating vectors: one corresponding to stationary real dividend growth and stationary term premium and the other corresponding to stationary excess returns and stationary term premium.

   The inability of the data to distinguish between these alternative models has enormous consequences for VAR stock price decompositions. We show that the relative importance of dividends and excess returns for explaining stock price volatility is very sensitive to the specification of the long-run properties of the estimated VAR. For the model in which excess returns are assumed to be stationary but real dividend growth is assumed to be nonstationary, real dividend growth (not excess returns) is the key contributor to stock price movements. The relative contributions reverse when we reverse the assumptions about stationarity. Thus, in contrast to much of the previous literature, we argue that the data cannot distinguish between a decomposition in which expectations about future real dividend growth are substantially more important than expectations about future excess returns and a decomposition in which the reverse is true.

   The remainder of this paper is organized as follows. In section 2, we review the log-linear, VAR approach to stock price decomposition pioneered by Campbell and Shiller and used in many subsequent studies. In section 3, we show how alternative assumptions about low-frequency movements in stock market fundamentals can be described in terms of restrictions on cointegrating vectors in a VECM. In section 4, we test alternative specifications of the VECM/VAR used to describe the time-series properties of the data and, therefore, to calculate expectations of future stock market fundamentals. These tests include the Johansen (1991) test for cointegration and tests in which the cointegrating vector is prespecified (Horvath and Watson 1995). Section 5 presents stock price decompositions for alternative models and demonstrates how sensitive these are to the specification of the VECM. In section 6, we discuss whether low-frequency movements in real dividend growth or excess returns are plausible, at least on statistical grounds, and discuss why our results differ from much of the previous literature. In section 7, we examine whether our findings could be the consequence of poor power and size properties of our statistical approach. In section 8, we discuss whether our results reflect the existence of a rational bubble in stock prices. We find, however, that the data do not appear to support the existence of a rational bubble. Section 9 provides a summary and conclusion.

2. Stock Price Decompositions

   The stock price (returns) decompositions of Campbell and Shiller (1988, 1989), Campbell (1991), and Campbell and Ammer (1993) start with a log-linear approximation of the accounting identity: 1 [equivalent to] [([R.sub.t+1]).sup.-1]([P.sub.t+1]/[D.sub.t+1] + 1)([D.sub.t+1]/[D.sub.t])/([P.sub.t]/[D.sub.t]) where [R.sub.t+1] is gross stock returns, [P.sub.t]/[D.sub.t] is price-dividend ratio, and [D.sub.t+1]/[D.sub.t] is one plus real dividend growth. Log linearizing and breaking the rate of return on stocks into the real return on short-term bonds (the ex-post real interest rate), [r.sub.t], and the excess return of equity over short-term bonds, et, yields:

   [p.sub.t] = [E.sub.t][[rho][p.sub.t+1] + [d.sub.t+1] - ([r.sub.t+1] + [e.sub.t+1]) + k], (1)

   where [p.sub.t] is the log price-dividend ratio, [d.sub.t] is real dividend growth and [rho] = exp([bar.p])/(1 + exp([bar.p])), and k = log(1 + exp([bar.p])) - [rho][bar.p] where [bar.p] is the average log price-dividend ratio over the sample. Recursively substituting, we obtain:

   [p.sub.t] = [[infinity].summation over (j=0)][[rho].sup.j]([E.sub.t][d.sub.t+1+j] - [E.sub.t][r.sub.t+1+j] - [E.sub.t][e.sub.t+1+j]) + [k/[1 - [rho]]]. (2)

   Thus, stock prices are a function of expectations of future real dividend growth, future real interest rates, and future excess returns. Similarly, surprises in excess returns can be written as:

   [e.sub.t] - [E.sub.t-1][e.sub.t] = [[infinity].summation over (j=1)][[rho].sup.j][([E.sub.t] - [E.sub.t-1]) [d.sub.t+j] - ([E.sub.t] - [E.sub.t-1])[r.sub.t+j] - ([E.sub.t] - [E.sub.t-1])[e.sub.t+j]]. (3)

   Surprises in excess returns are a function of revisions in expectations about future real dividend growth, future real interest rates, and future excess returns. One can construct similar decompositions of bond yields and returns (see Campbell and Ammer 1993).

   In order to evaluate the above expressions, Campbell and Shiller (1988, 1989), Campbell (1991), and Campbell and Ammer (1993) propose estimating a VAR to calculate expectations of future real dividend growth, real interest rates, and excess returns. We extend their framework to allow for cointegration among the variables and consider a vector error correction model (VECM). Let the vector of time series given by [y.sub.t] = ([p.sub.t], [d.sub.t], [i.sub.t], [l.sub.t], [[pi].sub.t])', where [p.sub.t] is log price-dividend ratio, [d.sub.t] is real dividend growth, [i.sub.t] is the yield on short-term bonds, [l.sub.t] is the yield on long-term bonds, and [[pi].sub.t] is the inflation rate. Consider the following vector error correction model:

   [DELTA][y.sub.t] = [mu] + [alpha][beta]'[y.sub.t-1] + [[m-1].summation over (i=1)][C.sub.i][DELTA][y.sub.t-i] + [v.sub.t], (4)

   where [y.sub.t] is the 5 x 1 vector of possibly I(1) variables as defined, [beta] is a 5 x r matrix whose r columns...