Financial Frictions and Leverage in Macroeconomics, Lecture notes of Economic Analysis

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Lecture 2 Credit Cycles and Information Frictions

Shengxing Zhang LSE October 3, 2017

Capital structure of an agent (firm, bank, household)

I (^) Leverage ratio: Value of debt Value of equity I (^) What is the determinant of leverage? I (^) What is the implication of leverage on macroeconomics?

Potential impact of financial frictions on aggregate economy

Amplification. The initial driving force of movements in economic activities are nonfinancial factors such as drops in productivity or monetary policy shocks. However, as investment and employment fall, the credit ability of borrowers deteriorates more than the financing need after the drop in economic activity. This could happen, for instance, if the fall in investment generates a fall in the market value of assets used as collateral. The presence of financial frictions will then generate a larger decline in investment and employment compared to the decline we would observe in absence of financial frictions. Therefore, financial frictions amplify the macroeconomic impact of the exogenous changes.

Potential impact of financial frictions on aggregate economy

Financial shocks. The initial disruption arises in the financial sector of the economy. There are no initial changes in the nonfinancial sector. Because of the disruption in financial markets, fewer funds can be channeled from lenders to borrowers. As a result of the credit tightening, borrowers cut on spending and hiring, and this generates a recession.

Subprime mortgage and 2008 financial crisis

Financial Frictions and an Amplification Mechanism

Endowment, Preference and Technology

I (^) The economy lasts two periods I (^) Two types of agents: farmer and gatherer I (^) Farmers I (^) endowed with k 0 F units of land I (^) values consumption at period 2: U(cF 1 , c 2 F ) = c 2 F I (^) production of period 2 good using kF^ units of land: AkF I (^) Gatherer can produce consumption goods at constant unit cost in period 1 I (^) endowed with K k 0 F units of land I (^) preference: U(c 1 G , c 2 G , h) = cG 1 + c 2 G I (^) production function using k units of land: G (kG^ ), with G 0 (kG^ ) > 0, G 00 (kG^ ) < 0, G 0 ( 0 ) = A. I (^) Land: in fixed supply, K ; the value of land at period 2: p 2.

Planner’s solution

max c 2 F ,c 1 G ,c 2 G ,h,kF^ ,kG cF 2 + c 1 G + c 2 G subject to c 2 F = AkF^ + p 2 kF c 1 G + c 2 G = G (kG^ ) + p 2 kG K kG^ + kF kG^ , kF^ 0. Simplified problem: max kF^ ,kG^ 0 ,kF^ +kG^ =K (A + p 2 )kF^ + G (kG^ ) + p 2 kG Solution: A = G 0 (kG^ ) ) kF^ = K , kG^ = 0.

Model – market structure

I (^) two markets at period 1: I (^) market for one period bond: R I (^) land market: p 1

Gatherer’s problem

maxkG (^) ,bG (^) ,cG 1 ,c 2 G c 1 G + c 2 G s.t. c 1 G bG R

• p 1 kG^ = p 1

K k 0 F

c 2 G = G (kG^ ) + p 2 kG^ bG^ , bG^  ✓p 2 kG^. Substitute c 1 G , c 2 G by the budget constraints in period one and two, and then write down the Lagrangian. L = bG R

• p 1 (K kG^ ) + G (kG^ ) + p 2 kG^ bG^ + G^ (✓p 2 kG^ bG^ ) @L @bG^

R

1 G^ = 0

@L

@kG^ = p 1 + G 0 (kG^ ) + p 2 + G^ ✓p 2 = 0

Equilibrium definition

A competitive equilibrium is allocations c 1 G , c 2 G , c 2 F , h, kG^ , kF^ and prices R, p 1 such that I (^) Given prices, allocations solve the problem of gatherers and famers. I (^) The markets for land and bond clear.

Equilibrium characterization

I (^) Market clearing for the bond market: bG^ + bF^ = 0. If 1 < bG^ < 0 and bB^ > 0, R = 1, G^ = 0. I (^) Market clearing for the land market. p 1 = G 0 (kG^ ) + p 2 + G^ ✓p 2 = G 0 (kG^ ) + p 2. Assume that A is large enough so that the borrowing constraint of the farmer is binding kF^ and bF^ satisfies: p 1 kF | {z } land purchase = p 1 k 0 F | {z } down payment

• bF^ /R | {z } borrowing bF^ = ✓p 2 kF kF^ = p 1 k 0 F p 1 ✓p 2 /R

Amplification mechanism in a dynamic economy

Limited commitment due to moral hazard