Permanent and Transitory Components of GNP and Stock Prices

“A recent voluminous literature has examined the long-run properties of GNP and stock prices, with surprising results. One would expect that GNP reverts to ‘potential GNP’ or some other trend following a shock. Yet many studies have found no mean-reversion, especially in postwar U.S. GNP” – a finding that “obviously challenges a broad spectrum of macroeconomic theories designed to produce and understand transitory fluctuations” (Introduction, p. 241). Cochrane notes a parallel reversal in the finance literature: “conventional wisdom once held that stock prices are random walks…that display no mean-reversion. Yet a large number of recent studies have instead found mean-reversion,” interpreted by different authors as evidence of irrational “fads” or of unmodeled time-variation in investment opportunities.

“Most of the GNP literature is based on univariate forecasts. It documents that lagged GNP growth forecasts future GNP growth poorly. The consumption/GNP ratio is a much more potent forecaster of long-horizon GNP growth. Thus, it can imply much larger transitory variation” (Introduction, p. 242). The consumption/GNP ratio is special because “it is stable over long time periods (consumption and GNP are cointegrated), while consumption is nearly a random walk. As a result, if GNP is more than its customary ratio to consumption, GNP must be forecast to decline until the ratio is reestablished” – in effect, “consumption defines the ’trend’ in GNP.”

Table I presents a VAR of log real GNP and log nondurable-plus-services consumption growth on their own lags and the lagged log consumption/GNP ratio, using quarterly U.S. data from 1947:1-1989:3. The consumption/GNP ratio enters the GNP-growth equation with a t-statistic of 3.45, “verifying the hunch that the ratio helps to forecast GNP,” while it enters the consumption-growth equation only weakly (Section II.A, pp. 243-244). The variance decomposition in Table I shows the “permanent” consumption shock accounts for 97 percent of the variance of consumption growth but only 30 percent of the variance of GNP growth, while the “temporary” GNP shock – orthogonal to consumption – accounts for 70 percent of the variance of GNP growth and 85 percent of the variance of one-step-ahead GNP forecast errors (footnote 5 reports these fractions rise to 80 and 89 percent using private GNP).

In response to a consumption shock, “consumption is almost a random walk: its impulse response function is almost flat,” while “GNP has a hump-shaped response to the consumption shock,” which Cochrane notes Fama [1993] interprets “as the lagged response of investment to a wealth shock” (Section II.A, p. 246). In response to a GNP shock – “a shock to GNP that does not contemporaneously shock consumption” – “this shock has a small impact on consumption at any horizon, but the response of GNP to this shock is almost completely transitory.” Cochrane stresses this transitory component is not just statistically present but “economically important,” since the variance-decomposition calculation “does not include the transitory variation in GNP seen in the hump-shaped response to the consumption shock” – so the true transitory share is understated by the headline 70 percent figure.

A univariate autoregression of GNP growth on its own lags shows “a good deal of persistence: in response to a unit shock, GNP climbs to about 1.6 after a year, and then declines to only about 1.4” – the familiar postwar-persistence finding of authors like Campbell and Mankiw [1987] (Section II.B, p. 246). Cochrane explains the divergence with three reasons: the consumption/GNP ratio forecasts long-term GNP growth better than lagged GNP growth; the bivariate system isolates two different shocks (one permanent, one transitory) that “a single univariate shock mixes”; and cointegration means consumption and GNP share the same long-run behavior, so since “consumption is nearly a random walk, its long-run properties are almost the same” as GNP’s long-run orthogonalized properties (pp. 247-248).

Following Beveridge and Nelson [1981], Cochrane defines the GNP trend as “the level GNP will reach after all transitory dynamics work themselves out. Equivalently, the trend in GNP is GNP plus all expected future GNP growth,” formally z_t = lim_{k to infinity} E_t(y_{t+k} - k*mu) (Section III, p. 250). Because consumption growth is poorly forecastable, “if consumption were a pure random walk, the Beveridge-Nelson trend would be exactly consumption less the mean log GNP/consumption ratio,” and the two turn out to be “almost the same” empirically – so “consumption provides a good measure of the trend in GNP, since it measures consumers’ expectations of long-run GNP.” Cochrane proposes this as an alternative to “potential GNP” defined via the unemployment rate, or to Hodrick-Prescott filtering: “what would GNP be if the consumption/GNP ratio was at its historical mean.”

Table II presents a VAR of log dividends and log price (cumulated returns) on the value-weighted CRSP NYSE portfolio, using annual data (1927-1988, to avoid the seasonal in dividends), analogous in structure to Table I with dividends in place of consumption and prices in place of GNP (Section IV.A, pp. 252-253). “The dividend/price ratio forecasts returns much more strongly than it forecasts dividend growth, so prices rather than dividends adjust to bring the ratio back to its mean.” The variance decomposition shows the “permanent” dividend shock accounts for 99 percent of the variance of dividend growth but only 43 percent of price-growth variance, while the “temporary” price shock accounts for 57 percent of the variance of returns and 55 percent of one-step-ahead return forecast-error variance – Cochrane calls this “economically as well as statistically significant.”

“In response to a dividend shock, prices and dividends move immediately to their long-run values. On the other hand, a price shock with no movement in dividends has a completely transitory effect on prices and no effect on dividends,” with the transitory price movement unwinding over “a half-life of about five years,” longer than the “half-life of about one-two years” found for the analogous transitory GNP movement (Section IV.A, p. 255). As with the univariate/bivariate GNP contrast, Cochrane notes that univariate impulse responses for stock prices alone show “little evidence for univariate mean reversion no matter how estimated”; the transitory component only appears once the bivariate, dividend-orthogonalized shock is isolated – consistent with, but methodologically distinct from, long-horizon-regression or variance-ratio evidence of return predictability (Fama and French 1988a; Poterba and Summers 1988).

If dividend growth and discount rates (expected returns) are stationary, the present-value relation implies price/dividend ratios are stationary; and “if managers smooth dividends by setting dividends equal to the discounted value of earnings,” dividends follow a random walk just as consumption does under the permanent-income hypothesis, jointly implying that a price shock with constant dividends must be transitory (Section IV.B, p. 256). Under this model, “an increase in dividends signals an increase in long-term earnings, as perceived by managers… [so] the earnings shock gives rise to simultaneous, permanent shocks to prices and dividends, just like the ‘dividend’ shock in the VAR,” while “a decrease in expected returns (risk premiums, not risk-free rates)” raises prices with no dividend change and reverts over time, “just like the ‘price’ shock in the VAR.”

“Comparing the price/dividend and consumption/GNP VARs, one might think that prices should take the place of consumption, since prices are a forecast of future dividends as consumption is a forecast of future income,” which would hold if expected returns were constant, since then “price/dividend ratios would forecast long-term dividend growth and not returns, and prices would be a random walk” (Section IV.B, p. 257). “However, expected returns are not constant, and aggregate long-run dividends happen to be nearly unpredictable. Hence, price, like GNP, is the series with the interesting temporary component; dividends, like consumption, is the near-random walk that defines the ’trend’; and the PIH analogy is that dividends equal ‘permanent earnings,’ not that prices equal ‘permanent dividends.’” This closing correction is the paper’s key conceptual payoff: the formal parallel between the two systems is exact, but which variable plays which economic role is an empirical, not definitional, question – and the data assign prices the GNP-like (transitory-rich) role, not the consumption-like (permanent, trend-defining) role a surface reading of present-value theory might suggest.