Asset bubbles and borrowing constraints

Bubbles and Crowding-in of Capital via a Savings Glut

“…In this case, the borrowing constraint will be binding at the bubbly steady state (i.e., x ∈ X B provided it exists), but also at the bubbleless steady state. In this case, a necessary and sufficient condition for x to exist is R 0 B (s) < 1, which is precisely the existence condition in Kunieda (2008). Note that unlike the previous case, the existence of a bubbly steady state is compatible with underaccumulation of capital at the bubbleless steady state (i.e., f ′ (k 0 ) > 1).…”

“…Perfect competition in the credit and capital markets implies that the return R t+1 adjusts until either the constraint (8) or (10) binds in equilibrium. Thus, given k t+1 determined by (4) we obtain…”

“…To obtain explicit results and closed-form solutions, the remainder of this paper assumes a Cobb-Douglas production technology f (k) := k θ , 0 < θ < Kunieda 2008). As in these models, a bubble return less than unity is necessary to ensure existence of a bubbly steady state in the same savings regime (if a bubbleless steady state in the respective regime fails to exist, one should interpret the condition as a shadow return).…”

“…As in these models, a bubble return less than unity is necessary to ensure existence of a bubbly steady state in the same savings regime (if a bubbleless steady state in the respective regime fails to exist, one should interpret the condition as a shadow return). While these conditions are also sufficient in Tirole (1985) in the absence and in Kunieda (2008) in the presence of financial frictions, more is required here to ensure consistency with the savings behavior of semi-entrepreneurs. Section 5 offers a detailed discussion of these conditions.…”

“…Note that unlike the previous case, the existence of a bubbly steady state is compatible with underaccumulation of capital at the bubbleless steady state (i.e., f ′ (k 0 ) > 1). One may view our model as a special case of Kunieda (2008) in this second case. As in his model, crowding-in is excluded.…”