Liquidity, Macroprudential Regulation, and Optimal Policy Roberto Chang Rutgers March 2013 R. Chang (Rutgers) Liquidity and Policy March 2013 1 / 22
Liquidity Management and Policy So far we have emphasized models in which …nancial frictions a¤ect aggregate outcomes R. Chang (Rutgers) Liquidity and Policy March 2013 2 / 22
Liquidity Management and Policy So far we have emphasized models in which …nancial frictions a¤ect aggregate outcomes And asset prices can determine the severity of …nancial frictions R. Chang (Rutgers) Liquidity and Policy March 2013 2 / 22
Liquidity Management and Policy So far we have emphasized models in which …nancial frictions a¤ect aggregate outcomes And asset prices can determine the severity of …nancial frictions The valuation of net worth becomes an important determinant of policy R. Chang (Rutgers) Liquidity and Policy March 2013 2 / 22
Holmstrom-Tirole, and others: investors presumably predict that they may be subject to liquidity constraints in the future R. Chang (Rutgers) Liquidity and Policy March 2013 3 / 22
Holmstrom-Tirole, and others: investors presumably predict that they may be subject to liquidity constraints in the future As a response, they choose how much liquidity to hold today vis a vis tomorrow R. Chang (Rutgers) Liquidity and Policy March 2013 3 / 22
Holmstrom-Tirole, and others: investors presumably predict that they may be subject to liquidity constraints in the future As a response, they choose how much liquidity to hold today vis a vis tomorrow Typically, this leads to a crucial tradeo¤ between investment and liquidity R. Chang (Rutgers) Liquidity and Policy March 2013 3 / 22
The Pecuniary Externality Problem Lorenzoni: If collateral constraints depend on asset prices, then individual liquidity choices do not lead to a socially correct decision R. Chang (Rutgers) Liquidity and Policy March 2013 4 / 22
The Pecuniary Externality Problem Lorenzoni: If collateral constraints depend on asset prices, then individual liquidity choices do not lead to a socially correct decision This is because each individual ignores the impact of his decision on asset prices and, therefore, on other agents’ collateral constraints R. Chang (Rutgers) Liquidity and Policy March 2013 4 / 22
The Pecuniary Externality Problem Lorenzoni: If collateral constraints depend on asset prices, then individual liquidity choices do not lead to a socially correct decision This is because each individual ignores the impact of his decision on asset prices and, therefore, on other agents’ collateral constraints This implies that there may be a welfare improving role for policy R. Chang (Rutgers) Liquidity and Policy March 2013 4 / 22
Macroprudential Policy Or Mopping After the Crash? Some have advocated ex ante restrictions on borrowing and lending R. Chang (Rutgers) Liquidity and Policy March 2013 5 / 22
Macroprudential Policy Or Mopping After the Crash? Some have advocated ex ante restrictions on borrowing and lending Others to enact corrective policies only if collateral constraints become binding R. Chang (Rutgers) Liquidity and Policy March 2013 5 / 22
Macroprudential Policy Or Mopping After the Crash? Some have advocated ex ante restrictions on borrowing and lending Others to enact corrective policies only if collateral constraints become binding Jeanne-Korinek (2012) gives a nice model to express these ideas R. Chang (Rutgers) Liquidity and Policy March 2013 5 / 22
Jeanne-Korinek t = 0 , 1 , 2 Entrepreneurs and workers R. Chang (Rutgers) Liquidity and Policy March 2013 6 / 22
Workers Linear utility: Ec w 0 + c w 1 + c w 2 � ω ( l 1 + l 2 ) This pins the real wage at ω , and the interest rate at zero. R. Chang (Rutgers) Liquidity and Policy March 2013 7 / 22
Entrepreneurs Linear utility too: E ( c 0 + c 1 + c 2 ) Access to production function y t = ( A t k t ) α l 1 � α t Let κ A t k t = pro…t function A 1 is stochastic (the only source of uncertainty in the model) A 2 depends on investment x at t = 1 : A 2 = A ( x ) R. Chang (Rutgers) Liquidity and Policy March 2013 8 / 22
Budget Constraints Workers are endowed with goods in period 0 ( y 0 ) Then budget constraints are given by Period Entrepreneurs Workers c w t = 0 c 0 + I ( k ) = d 0 k 0 + b 0 = y 0 c w t = 1 xk + c 1 + d 0 k = κ A 1 k + d 1 k 1 + b 1 = ω l 1 + b 0 c w t = 2 c 2 + d 1 k = κ A 2 k 2 = ω l 2 + b 1 R. Chang (Rutgers) Liquidity and Policy March 2013 9 / 22
Collateral Constraint If an entrepreneur walks away, his capital is seized and sold at some price p t = κ ˜ A t (where the tilde denotes the average value of A t ) Hence debt contracts will satisfy: d t � φ min p t + 1 t R. Chang (Rutgers) Liquidity and Policy March 2013 10 / 22
First Best (No Collateral Constraints) Assume there are no collateral constraints R. Chang (Rutgers) Liquidity and Policy March 2013 11 / 22
First Best (No Collateral Constraints) Assume there are no collateral constraints Easy to show that U w = y 0 R. Chang (Rutgers) Liquidity and Policy March 2013 11 / 22
First Best (No Collateral Constraints) Assume there are no collateral constraints Easy to show that U w = y 0 So the …rst best allocation maximizes the welfare of entrepreneurs: E [ κ A 1 + κ A ( x ) � x ] k � I ( k ) R. Chang (Rutgers) Liquidity and Policy March 2013 11 / 22
First Best (No Collateral Constraints) Assume there are no collateral constraints Easy to show that U w = y 0 So the …rst best allocation maximizes the welfare of entrepreneurs: E [ κ A 1 + κ A ( x ) � x ] k � I ( k ) FOCs are κ A 0 ( x ) = 1 I 0 ( k ) = E [ κ ( A 1 + A 2 ) � x ] R. Chang (Rutgers) Liquidity and Policy March 2013 11 / 22
Laissez Faire Equilibrium In period 2, the liquidation price of capital is p 2 = κ A 2 = κ A ( x ) R. Chang (Rutgers) Liquidity and Policy March 2013 12 / 22
Laissez Faire Equilibrium In period 2, the liquidation price of capital is p 2 = κ A 2 = κ A ( x ) Hence the collateral constraint faced by each entrepreneur in period t = 1 is d i 1 � φ p 2 = κφ A ( x ) R. Chang (Rutgers) Liquidity and Policy March 2013 12 / 22
Laissez Faire Equilibrium In period 2, the liquidation price of capital is p 2 = κ A 2 = κ A ( x ) Hence the collateral constraint faced by each entrepreneur in period t = 1 is d i 1 � φ p 2 = κφ A ( x ) Combining with budget constraint, this implies x i + d i 0 � κ [ A 1 + φ A ( x )] R. Chang (Rutgers) Liquidity and Policy March 2013 12 / 22
Laissez Faire Equilibrium In period 2, the liquidation price of capital is p 2 = κ A 2 = κ A ( x ) Hence the collateral constraint faced by each entrepreneur in period t = 1 is d i 1 � φ p 2 = κφ A ( x ) Combining with budget constraint, this implies x i + d i 0 � κ [ A 1 + φ A ( x )] In a symmetric equilibrium, x i = x . Assume κφ A 0 ( x ) < 1 to avoid multiple equilibria. R. Chang (Rutgers) Liquidity and Policy March 2013 12 / 22
Laissez Faire Equilibrium In period 2, the liquidation price of capital is p 2 = κ A 2 = κ A ( x ) Hence the collateral constraint faced by each entrepreneur in period t = 1 is d i 1 � φ p 2 = κφ A ( x ) Combining with budget constraint, this implies x i + d i 0 � κ [ A 1 + φ A ( x )] In a symmetric equilibrium, x i = x . Assume κφ A 0 ( x ) < 1 to avoid multiple equilibria. Then, if constraint binds, note the ampli…cation e¤ect: κ dx = 1 � φκ A 0 ( x ) dA 1 R. Chang (Rutgers) Liquidity and Policy March 2013 12 / 22
Easy to see that c 0 = c 1 = 0 , so 0 = d ( k i ) = I ( k i ) d i k i Assume collateral constraint does not bind at t = 0 Then the entrepreneur chooses k i to maximize the expectation of � κ A 1 + κ A ( x i ) � x i � k i � I ( k i ) + λ i � � κ A 1 + φκ A 2 � x i � d ( k i ) k i max x i Note that the FOC for x i is κ A 0 ( x i ) = 1 + λ ´ ı Main result: If E ( λ LF ) > 0 then k LF < k FB This says that if the collateral constraint is expected to bind, then the productivity enhancing expenditure x is expected to be below its …rst best level, which reduces the incentive to invest. R. Chang (Rutgers) Liquidity and Policy March 2013 13 / 22
Externalities Consider the problem of a planner that chooses k and x to maximize the expectation of max [ κ A 1 + κ A ( x ) � x ] k � I ( k ) + λ [ κ A 1 + φκ A ( x ) � x � d ( k )] k x This di¤ers from the problem of the representative entrepreneur in that the planner knows p 2 = κ A 2 = κ A ( x ) The FOC for x is λ = κ A 0 ( x ) � 1 ˜ 1 � φκ A 0 ( x ) This says that the value of x to the planner is higher than in laissez faire: an increase in x increases p 2 , which relaxes the collateral constraint R. Chang (Rutgers) Liquidity and Policy March 2013 14 / 22
Macroprudential Regulation KJ ask: what if the planner discourages investment in period 0 with a lump sum tax? Answer : Proposition 2: k MP < k LF ( < k FB ) : the planner chooses lower investment in period 1 0 Intuition: R. Chang (Rutgers) Liquidity and Policy March 2013 15 / 22
Recommend
More recommend
