Lawrence H. Summers | Macro Paper Warehouse

Assessing Dynamic Efficiency: Theory and Evidence

This paper asks whether actual capitalist economies have overaccumulated capital relative to the Golden Rule — the condition Diamond (1965) showed can leave an economy “dynamically inefficient,” so that a Pareto improvement exists by consuming down the capital stock. The authors generalize Phelps’ (1961) Golden Rule criterion to a stochastic economy with a very general production technology, and show that dynamic efficiency can be assessed simply by comparing the cash flow investors receive from the corporate/capital sector (profit net of investment, the “dividend”) with zero: if that net cash flow is always positive, the economy is dynamically efficient; if it is always negative, the economy is inefficient. Applied to United States national accounts data (1929-1985 in this draft) and to several other OECD economies (1960-1984), the criterion is satisfied “by a wide margin in all years” — capital income has exceeded gross investment by more than 15 percent of GNP every year since 1929 — so the authors conclude these economies are dynamically efficient. The paper then explains, using a simple infinite-horizon “fruit tree” asset-pricing example, why this finding is fully consistent with the empirical puzzle that safe real interest rates are often far below measured growth rates or even negative: capital-price risk can permanently depress the safe rate below the growth rate in an economy that is nonetheless dynamically efficient, so comparisons of the safe interest rate to the growth rate — unlike the cash-flow test — are not a valid way to diagnose overaccumulation.

Does the Stock Market Rationally Reflect Fundamental Values?

Summers argues that the standard statistical tests used to support the Efficient Markets Hypothesis – tests for serial correlation in excess returns, and for predictable excess returns conditional on an estimated mispricing – have very low statistical power against a specific, economically interesting alternative: that market valuations differ from the rational present value of fundamentals by a large, slowly-decaying (but not exploding) multiplicative error that behaves like “fads.” In a numerical example calibrated to match the observed variance of monthly U.S. stock returns, a valuation error with a standard deviation of about 30 percent of price, and a half-life of around three years, generates a theoretical first-order autocorrelation in excess returns of only about -0.008 – smaller than the roughly 0.04 standard error one would get from fifty years of monthly data, so this large, persistent mispricing would be statistically undetectable; achieving a 50 percent chance of rejecting market efficiency in this example would require just over 5,000 years of data. Because “the same problems of identification which plague financial economists also plague would-be speculators,” the paper argues the inability of statistical tests to detect such errors also implies that speculative arbitrage is unlikely to eliminate them, so that failures to reject market efficiency should not be read as evidence that market prices are, in fact, rational reflections of fundamental value – a distinction Summers says matters most for macroeconomic theories, such as Tobin’s q theory of investment, that treat asset prices as if they faithfully reveal the present value of future cash flows.

Noise Trader Risk in Financial Markets

This paper builds a simple overlapping-generations model of an asset market with two types of traders – “noise traders,” who hold erroneous, randomly-varying beliefs about an asset’s expected return, and rational “sophisticated investors” who trade against them – to formalize why arbitrage does not fully correct noise traders’ mispricing even though there is no fundamental (dividend) risk at all. Because next period’s noise traders’ beliefs are themselves unpredictable, today’s arbitrageur who bets against the current mispricing bears a risk – “noise trader risk” – that noise traders might become even more extreme before he can liquidate; this risk limits how aggressively sophisticated investors will bet against them, so prices can diverge significantly from fundamental values, and the paper shows that noise traders can earn a higher expected return than sophisticated investors precisely by bearing more of the price risk that their own unpredictable trading creates. The model does not imply that noise traders profit merely for bearing genuine economic risk – “for the economy as a whole, there is no risk to be borne” – and the condition for noise traders to out-earn sophisticated investors (on average bullish, but not too bullish) is narrow, since relative returns are pulled up by a “hold more” effect and a “create space” effect but pulled down by a “price pressure” effect and a “buy high, sell low” effect that dominates at high bullishness. The authors argue the model offers a unified, qualitative account of several asset-pricing anomalies: excess volatility and mean reversion in stock and bond returns, the persistent, fluctuating discount of closed-end fund prices below net asset value, and – more speculatively – the Mehra-Prescott equity premium puzzle, since noise trader risk pushes the risky asset’s average price below fundamental value independently of its covariance with aggregate consumption.

Some Skeptical Observations on Real Business Cycle Theory

This 1986 Federal Reserve Bank of Minneapolis Quarterly Review piece, responding directly to Edward Prescott’s companion article “Theory Ahead of Business Cycle Measurement” in the same issue, argues that real business cycle (RBC) models of the type Prescott surveys “have nothing to do with the business cycle phenomena observed in the United States or other capitalist economies.” Summers raises four objections: the model’s key parameters (the time discount rate implying a 4 percent real interest rate, and the one-third household time-share devoted to market work) are not, in his reading of the same micro evidence Prescott cites, well tied down; there is no independent evidence for the technology shocks the model treats as the sole driving force, and postwar productivity declines are better explained by labor hoarding than by technological regress; the model is “price-free” in that it never confronts data on real wages, interest rates, or asset returns with its predictions, which Summers says have fared poorly elsewhere; and the model entirely omits breakdowns of the exchange mechanism — such as credit-market disruptions — which Summers argues are central to the largest historical fluctuations, including the Great Depression. He closes by cautioning against a “lengthy professional detour into the analysis of stochastic Robinson Crusoes” and suggesting credit-crunch accounts of postwar recessions as a more promising direction. The piece is explicitly framed as a skeptical, polemical assessment rather than a formal rebuttal, and Prescott’s direct reply appears in the same Quarterly Review issue immediately following it.