Are the Liquidity and Collateral Roles of Asset Bubbles Different?

Abstract

Several recent papers introduce different mechanisms to explain why asset bubbles are observed in periods of larger growth. These papers share common assumptions, heterogeneity among traders and credit market imperfection, but differ in the role of the bubble, used to provide liquidities or as collateral in a borrowing constraint. In this paper, we introduce heterogeneous traders by considering an overlapping generations model with households living three periods. Young households cannot invest in capital, while adults have access to investment and face a borrowing constraint. Introducing bubbles in a quite general way, encompassing the different roles they have in the existing literature, we show that the bubble may enhance growth when the borrowing constraint is binding. More significantly, our results do not depend on the-liquidity or collateralrole attributed to the bubble. We finally extend our analysis to a stochastic bubble, which may burst with a positive probability. Because credit and bubble are no more perfectly substitutable assets, the liquidity and collateral roles of the bubble are not equivalent. Growth is larger when bubbles play the liquidity role, because the burst of a bubble used for liquidity is less damaging to agents who invest in capital.

Entrepreneurship, Growth and Productivity With Bubbles

“…Third, if i t+1 > 0 and i t+1 = 0 then (41) and (42) imply that i 2;t+1 = 0 and (38) and (39) imply that i 1;t = i 2;t+1 R t+1 and i 2;t+1 = i 3;t+2 R t+2 : This case characterizes the savers that do not invest in productive capital and are not credit constrained. From the last two equations, we obtain that c i 2;t+1 = ( = ) c i 1;t R t+1 and c i 3;t+2 = ( = ) c i 2;t+1 R t+2 : Combining these two equations with the budget constraints (5)-(7), we obtain (12), (13) in the main text and the optimal consumptions are given by:…”

“…We next obtain the market clearing condition for …nancial assets. To this end, we …rst use (3), (12) and (13) to deduce that the aggregate value of the …nancial assets owned by young and adult savers is:…”

“…An equilibrium of this economy is a path of R t ; z t ; t ; t ; t 1 t=1 that, given R 1 and z 1 ; solves the two market clearing conditions (24) and (31), satis…es (21), (23) and (29), and along which the value of the bubble is non-negative, t 0: 13 In the following section, we show that this equilibrium can converge to two di¤erent steady states: a bubbly steady state with t > 0 and a bubbleless one with t = 0:…”