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Bubbles and Unemployment March 25, 2011 Narayana Kocherlakota Federal Reserve Bank of Minneapolis Disclaimer • Usual disclaimer: I am not speaking for others in the Federal Reserve or on the Federal Open Market Committee. • But I’ll make an even stronger disclaimer: I’m exploring a new theoretical model ... • And so the results do not necessarily reflect my thinking about policy. Lots of Exciting Research on Great Recession • But relatively little concerns the behavior of unemployment. — Nice exception: Farmer (2011) • I will describe a (SIMPLE!) model that connects: — a bubble collapse — insufficiently accommodative monetary policy — elevated unemployment Basic Modeling Approach • Take a rational bubble model (in this case, OG). • “Glue” a Diamond-Mortensen-Pissarides (DMP) model onto it. • One key element: Ignore DMP job creation margin. — jobs are created as needed to satisfy demand Basic Structure of Equilibria • Continuum of bubbly equilibria — the size of the bubble varies across equilibria — zero real interest rate in all equilibria • Continuum of non-bubbly equilibria — indexed by the real interest rate ≤ 0 — no bubble in any of them Result 1 • Take any bubbly equilibrium. • There exists a non-bubbly equilibrium with same labor market outcomes. — it has a negative real interest rate • Interpretation: Bubble collapses don’t affect labor market if real interest rate falls enough. Result 2 • Take any non-bubbly equilibrium with a negative real interest rate. • The non-bubbly equilibrium with a zero real interest rate has: — higher unemployment — more slack in the labor market • Interpretation: If monetary policy is not sufficiently accommodative after a bubble collapse, the economy will have high unemployment. Similar Ideas to ... • Hall (2011) and Krugman (1998) — ZLB disrupts adjustment of real interest rate — creates labor market disequilibrium • Farmer (2011) — continuum of steady-state unemployment rates indexed by beliefs Outline 1. Sketch of the DMP Model 2. Some Empirics 3. DMP - Meet OG 4. Structure of Equilibria 5. Results 6. Decline in Matching Efficiency 7. Conclusions 1. Sketch of the DMP Model • Firms create jobs at exogenous cost k. • Get matched with qualified worker with probability f (θ). — θ = v/u is endogenous • (Nash) bargain over wages. Exogenous Parameters • A is worker output in job • z is unemployed worker output • β is worker bargaining power • s is separation rate • φ is matching efficiency Endogenous Parameters • u is unemployment rate • v is vacancy rate • θ ≡ v/u is market tightness Steady-State in DMP Model k = (1 − β)(A − z) βθ s u = s + φf (θ) (approx. job creation) (Beveridge curve) 2. Some Empirics • Job creation wedge has grown in past three years: (1 − β)(A − z) −k βθ • θ has fallen by 65% from December 2007 to December 2010. — BLS data on unemployment and job openings • The matching efficiency parameter has also fallen ... • s(1 − u) φ= uf (θ) • φ has fallen between 32% and 44% over the past three years — as elasticity of f ranges between 0.5 and 0.3 3. DMP - Meet OG • Consider a standard OG model, with 2-period lived households. • Households have apple endowments (ey , eo). • They have utility functions U (cy ) + U (co + h) over banana consumption. — h is a small positive parameter — U has non-decreasing relative risk aversion A Bubbly Asset • Initial old each have one unit of intrinsically useless asset (land). • Assume: ey > eo + h. • This creates possibility of bubbly equilibria (usual OG). DMP Part of the Model • Distinct equal population of infinitely lived workers. — Matched workers/firms create A bananas. — Unmatched workers create z bananas, z < A. • Worker and firm owners have linear utility over apples • They can’t participate in asset markets. Two Novel Features of Model • Firms create jobs as needed to satisfy banana demand. — no job creation condition in equilibrium. • Central bank picks real interest rate. 4. Structure of Equilibria • Define bubbly equilibria • Define non-bubbly equilibria • Apples (household endowment) are numeraire. Bubbly Equilibria y B ,u • Given a land price P L, (cbub, cobub, Pbub bub, θ bub) is a bubbly equilibrium iff: y U 0(cbub) = U 0(cobub + h) y B c y − PL = e Pbub bub B co = eo + P Pbub L bub y ububz + (1 − ubub)A = cbub + cobub ubub = s s + φf (θbub) Properties • The bubbly equilibria are indexed by P L; r∗ = 0 in all equilibria • Given a specification for P L: B Pbub = ey − eo − 2P L h (ey + eo)h [ububz + (1 − ubub)A] = (ey − eo − 2P L) • Big bubbles imply low banana prices, high agg. demand, and low unemployment. • They also imply small wedges in job creation first-order condition because k (A − z)(1 − β) − βθbub Pbub is small. Non-Bubbly Equilibria y B , u , θ ) is a non-bubbly equi• Given an interest rate r∗, (cnb, conb, Pnb nb nb librium iff: y U 0(cnb) = (1 + r∗)U 0(conb + h) y B c = ey Pnb nb B co = eo Pnb nb y unbz + (1 − unb)A = cnb + conb unb = s s + φf (θnb) 4. Results Result 1 • Suppose (cy∗, co∗, P B∗, u∗, θ∗) is a bubbly equilibrium given P L. • Then: There exists (cy0, co0, r∗) such that: • (cy0, co0, P B∗, u∗, θ∗) is a non-bubbly equilibrium given r∗. • Pick (cy0, co0, r∗) so that: cy0 = ey y∗ + co∗) (c ey + eo co0 = eo y∗ + co∗) (c ey + eo (1 + r∗) = U 0(cy0) U 0(co0 + h) • Simple intuition: Divide the aggregate bananas so that young don’t save. Interpretation • Note: r∗ < 0. • Given appropriate monetary policy, a bubble collapse has no impact on labor market outcomes. • Bubble collapse does mean that households are worse off (lower r∗). Result 2 • Suppose (cy0, co0, P B∗, u∗, θ∗) is a non-bubbly equilibrium given r∗ < 0. • Suppose (cy00, co00, P B00, u00, θ00) is a non-bubbly equilibrium given r0 = 0. • Then: u00 > u∗ and θ00 < θ∗ Mechanics B satisfies Euler equation: • Equilibrium banana price Pnb ey eo 0 ∗ 0 U ( B ) = (1 + r )U ( B + h) Pnb Pnb • Comparative statics: B) d(1/Pnb = dr B (1 + r ∗) Pnb B eo/Pnb B B y o −CRRA(e /Pnb) + CRRA(e /Pnb + h)( o B ) e /P +h nb < 0 • Denominator is negative because U has non-decreasing RRA. B rises, and so u • As r∗ rises, Pnb nb rises. Intuition • Think of there being three goods - apples, bananas, and banana bonds. • Young households demand banana bonds that pay off when they are old. — that drives up the price of banana bonds in terms of apples • But - with the fixed real interest rate - the price of bananas has to go up. • Conclusion: all households demand fewer bananas. Interpretation • Bubble collapse implies no effect on unemployment if r∗ is lowered enough. • BUT: ZLB + sticky inflation expectations imply lower bound on r∗. • If r∗ doesn’t fall enough, then we get an increase in unemployment. Increase in Labor Market Wedge B rises, and θ falls. • As r∗ rises, u rises, Pnb • Hence, the firm’s job creation wedge: (1 − β)(A − z) k − B βθnb Pnb rises. • As noted: over past three years, wedge has increased by 65% in US data. 6. Decline in Matching Efficiency • We have seen that US labor market matching efficiency has declined since 2007. • What’s the impact of such a decline in the model, assuming: — r∗ is fixed — no bubbles No Effect on Unemployment Rate y B ) satisfy: • Given r∗, (cnb, conb, Pnb y U 0(cnb) = (1 + r∗)U 0(conb + h) ey y cnb = B Pnb eo o cnb = B Pnb • Then, unb is pinned down by aggregate demand: y unbz + (1 − unb)A = cnb + conb • Decline in φ has no effect on the unemployment rate. Increased Job Openings Rate • With fixed unb, fall in φ implies that θnb rises: s unb = s + φf (θnb) • Hence, with fixed r∗, fall in φ results generates vertical upward shift in Beveridge curve. • Intuition: need more job openings to replace separations. 7. Conclusions • Kocherlakota (2011) considers a wide class of rational bubble models. • That paper describes how a bubble collapse can generate a fall in labor supply. — Loss of wealth leads to increase in labor supply. — Fall in real interest rate leads to decrease in labor supply. — Aggregate effect is ambiguous but can be negative. • In this paper: unemployment rate is wholly determined by demand. — labor supply is irrelevant • Bubble collapse generates a fall in demand ... • and unemployment rises if ZLB prevents accommodative monetary policy. • It would be useful to extend results to a wider class of rational bubble models.