Journal of Monetary Economics 17 (1986) 349-362. North-Holland RULING OUT DIVERGENT SPECULATIVE BUBBLES* Maurice OBSTFELD Columbia University, New York, NY 10027, USA Kenneth ROGOFF Universi~ of Wisconsin, Madison, WI 53706, USA The growth in the empirical literature on testing for divergenr (in mean) speculative bubbles indicates that existing theoretical arguments for ruling out such price paths are not sufficiently compelling. Here we strengthen the case for ruling out explosive or implosive bubbles a priori by filling in two gaps. First, we demonstrate why divergent stochastic bubbles arising from purely extrinsic uncertainty [as in Blanchard (1979)] cannot be equilibria in a monetary optimizing model. Second, we show why existing arguments for ruling out implosive price bubbles are insufficient in some cases, and we provide stronger arguments. 1. Introduction This paper is concerned with ruling out divergent (explosive or implosive) asset price bubbles. We refer to a bubble as divergent if the asset price series exhibits a higher order of non-stationarity than any of the underlying funda- mentals. [Diba and Grossman (1984) provide this characterization.] Among all the various types of bubbles identified by theorists, divergent bubbles are in some sense a narrow and restrictive class.’ However, such bubbles are very important in the empirical literature, mainly because divergent bubbles have clearly identifiable characteristics2 Non-divergent bubbles, on the other hand, *We are indebted to Guillermo Calvo and Roque B. Femandez for showing us the counter- example that stimulated the analysis of section 3. We also benefited from the comments of an anonymous referee. Obstfeld acknowledges with thanks financial support from the National Science Foundation and the Alfred P. Sloan Foundation. ‘See, for example Azariadis (1981), Cass and Shell (1983), Diamond and Dybvig (1983), Farmer and Woodford (1984). and Waldo (1985). Tirole (1985) provides an example of an equilibrium in which the price level falls at the rate of interest even though the money supply is constant. We would not characterize his example as a divergent bubble [i the sense of Diba and Grossman (1984)], because the deflation is caused by population growth (which is also a fundamental). ZEconometricians have tested for asset price bubbles across a broad range of markets and historical episodes, including the gold market, the stock market, the foreign exchange market, and the domestic currency market during episodes of hyperinflation. See, for example, Blanchard and Watson (1982), Calvo (1978). Diba and Grossman (1984). Flood and Garber (1980), Meese (1986), West (1984a. b), and Woo (1984). Some of these studies investigate non-explosive as well as explosive bubbles. 0304-3923/86/$3.5001986, Rlsevier Science Publishers B.V. (North-Holland)