Regional President Speech

Connecting Asset and Labor Markets in a Heterogeneous Agent Model Narayana Kocherlakota FRB-Minneapolis

Disclaimer The views expressed in this talk are my own. • They may not be shared by others in the Federal Reserve System ... • Especially my colleagues on the Federal Open Market Committee. •

Acknowledgements I thank participants in a FRB-Minneapolis bag lunch for comments.

Changes in Asset Markets There have been changes in asset markets since 2007. • — Borrowing constraints have tightened. — Increase in perceived macroeconomic risk. — Decline in supply of "risk-free" assets. Combined effect: increase in net asset demand. • These changes seem likely to reverse only slowly. •

Treasury Real Yield Curve Rates Percent 5 4 3 2 10-year 5-year 1 0 -1 -2 Source: U.S. Department of the Treasury

Changes in Employment Employment/population in US fell sharply from late 2007 to late 2009. • This change has been highly persistent: • Employment/population has risen little since late 2009. •

Employment-Population Ratio Index: December 2007 = 100 102 101 100 99 98 97 96 95 94 93 92 Source: Bureau of Labor Statistics

Employment-Population Ratio, Men 25-54 Index: December 2007 = 100 102 101 100 99 98 97 96 95 94 93 92 Source: Bureau of Labor Statistics

Connecting the Two Changes: The Model In this talk, I link these two persistent changes. • I use a heterogeneous agent model with: • — inelastic labor supply (recent micro-evidence on extensive margin) — incomplete insurance markets (Bewley-Huggett) — flexible or rigid nominal wage growth

Connecting the Two Changes: The Shock I posit a permanent exogenous increase in net asset demand. • — Many possible sources of this shock - I use tighter borrowing constraints The impact of this shock depends on the flexibility of wages. •

Connecting the Two Changes: The Results If wages are flexible: The shock has no impact on employment. If nominal wage growth is fixed (can’t rise): The shock causes employment to fall unless monetary policy is eased enough.

Intuition for Flexible Case Key equilibrating mechanism: • — Excess labor supply pushes up nominal wage growth. In turn, anticipated inflation rises. • People buy more goods today and firms demand more workers ... • Until labor markets clear. •

Intuition for Rigid Case Suppose nominal wage growth can’t rise. • Then anticipated inflation can’t rise. • If the nominal interest rate is not lowered enough, then ... • The real interest rate doesn’t fall enough. • Product demand remains too low, and employment is too low. •

Outline 1. Model 2. Equilibrium 3. Comparative Statics 4. Conclusions

MODEL

Preferences: Consumption Unit measure of agents. • Each agent maximizes expected value of: • ∞  1  ( ) 0    1     0 −  0 00 − =1 X where  is consumption in period . 

Preferences: Labor At each date, each agent wants to work ( = 1) or not ( = 0) • The binary state  is a Markov chain with transition matrix Φ  • The autocorrelation of  is non-negative. • No aggregate shocks (evolution is iid across agents). •

Involuntary Non-Employment Conditional on  = 1, an agent’s labor  is equal to: • — 1 with probability (1 ) − —  ( small but positive) with probability  Conditional on  = 0 an agent’s labor  = 0 • The variable  is endogenous, while Φ is exogenous. • I refer to  as labor market slack. •

Technology There are a large number of competitive firms. • Firms produce  units of consumption with  units of labor. •

Trading At each date, agents trade a one-period risk-free nominal bond. • Bonds are available in zero net supply. • Nominal interest rate is set by monetary policy. • Agents face a real borrowing limit  . ∗ •

Budget Set   +  (1 + )   +    +1    ≤    +1 +1 ∗ ≥ −

EQUILIBRIUM

Budget Equivalence Agents have budget sets defined by: •   +  (1 + )   +    +1    ≤    +1 ∗ +1 ≥ − Define (and assume time invariance of): • ( )  − ≡ 1 +    +1   − ≡      ≡  

Divide original budget set through by  and define  =   .     • We get equivalent (Bewley-Huggett) budget sets: •  +1  +  +     1 +  ≤   +1 ∗ ≥ −

Bewley-Huggett Demand Functions Suppose agent has budget set: •  +  (1 + )  +   +1   ≤   +1 ∗ ≥ − Labor  follows the Markov chain determined by:  • — Φ (exogenous transition of willingness to work) —  (endogenous labor market slack)

 Let  (;    ) be (long-run) average bondholdings. ∗ •  Result:  is weakly decreasing in the borrowing limit   ∗ •  Result:  is increasing in the real interest rate  •  Assumption:  is decreasing in labor market slack  •

Stationary Equilibrium Wage inflation  , price inflation  and slack  satisfy:  •  =  (firm optimality)      ( − ;    ) = 0 (asset mkt clears) ∗ 1 +  Need a third equilibrium condition somewhere! •

Flexible Wage Equilibrium Flex-wage equilibrium conditions: •  =  (firm optimality)      ( − ;    ) = 0 (asset mkt clears) ∗ 1 +   = 0 (no slack) Nominal wage growth adjusts so that there is no labor market slack. •

Equilibrating Mechanism Suppose the labor market is out of equilibrium (  0) • Households bid down current wages (relative to future wages). • Counterintuitive (?): labor market slack pushes up wage growth. •

Product competition: higher wage growth means more inflation. • People demand more consumption and firms demand more labor. • Process continues until  = 0 •

Rigid Wage Equilibrium Rigid wage eq’m: wage inflation is exogenous ( ).  • Rigid wage equilibrium conditions: •  =  (firm optimality)      ( − ;    ) = 0 (asset mkt clears) ∗ 1 +   =  (rigid wage growth)   The real interest rate is exogenous. • Asset market clears via changes in labor market slack. •

Equilibrating Mechanism Suppose the asset market is out of equilibrium: •      ( − ;    )  0 ∗ 1 +   Too much asset demand implies that there’s too little product demand • Given that low product demand, firms scale back labor demand ( rises). • With less labor income, asset demand falls until market clears. •

COMPARATIVE STATICS

Experiments How does eq’m output depend on borrowing constraint  ? ∗ • How does eq’m output depend on monetary policy ? • The answer depends on eq’m notion (flex or rigid). •

Flexible Wage Equilibrium In equilibrium, for any  or   slack  equals 0 ∗ • The borrowing limit and monetary policy don’t affect aggregate quantities. •

But they do affect equilibrium outcomes. • Suppose the borrowing constraint is tighter (   ) ... ∗∗ ∗ • Or monetary policy is tighter (   ) ∗∗ ∗ • Both of these changes push up on asset demand. •

To clear asset market, the real interest rate must fall. • That’s accomplished via an increase in nominal wage growth: •  =    =  ∗∗ ∗∗ ∗ ∗ .

Rigid Wage Equilibrium Wages grow at exogenous rate    • Competition among firms implies that inflation  =    • The real interest rate adjusts through changes in monetary policy () •

Suppose the borrowing constraint tightens (   ) ... ∗∗ ∗ • OR monetary policy tightens (   ) ... ∗∗ ∗ • These changes push up on asset demand. •

The real interest rate can’t adjust because  and  are fixed.  • To clear asset market, labor market slack must rise: •    ∗∗ ∗ The rise in slack pushes down on income and so on asset demand. •

Conclusions Suppose borrowing limit ( ) shrinks. ∗ • This fall in the borrowing limit increases net asset demand. • How does this increase in asset demand affect labor markets? •

Impact on labor markets depends on wage adjustment. • Flexible wages: no effect on output or employment. • Rigid wages: output and employment fall. • — This decline can be offset with easier monetary policy.

CONCLUSIONS

Changes Since 2007 A number of changes in asset markets since 2007. • Asset demand has risen: • — increased uncertainty — lower potential growth estimates — tighter borrowing constraints

Outside supply of risk-free assets has fallen. • — Sovereign debt is riskier. — US land values are lower - and land is riskier. — Partial offset: increase in sovereign debt. Overall: Net asset demand has risen. •

Implications of a Heterogeneous Agent Model I used a standard incomplete financial markets model. • After an increase in net asset demand, asset markets clear via: • — a fall in the real interest rate — OR a fall in economic activity

Suppose nominal wage growth is fixed, so it can’t rise. • Then the real interest rate depends only on  (monetary policy). • If  is kept too high (ZLB?), then the real interest rate won’t fall enough. • And the asset demand shock results in a fall in economic activity. •

Modern Models, Old Implications The analysis is based on a standard workhorse "modern macro" model. • It delivers neoclassical conclusions if wages are flexible. • It delivers Keynesian conclusions if ... • Nominal wage growth fails to rise enough to eliminate excess labor supply. •

Future Research The question is: • How do nominal wages respond to excess labor suppy? We need a lot more work on this question. • Useful approaches: micro-evidence and surveys. •