Aggregate Demand, Idle Time, and Unemployment Pascal Michaillat (LSE) & Emmanuel Saez (Berkeley) September 2014 1 / 44
Motivation 11% Unemployment rate 9% 7% 5% 3% 1974 1984 1994 2004 2014 2 / 44
Motivation Unemployment rate 11% 9% 7% 5% Technology? Aggregate demand? Mismatch? Low job search? Low participation? 3% 1974 1984 1994 2004 2014 2 / 44
Motivation Unemployment rate 11% Technology? Mismatch? 9% Aggregate demand? Low job search? Low participation? 7% Transfers? Monetary policy? 5% Unemployment insurance? Payroll tax? Nothing? 3% 1974 1984 1994 2004 2014 2 / 44
The available models 1. matching model of the labor market tractable but no aggregate demand 2.? 3. New Keynesian DSGE model many shocks but greater complexity 3 / 44
The general disequilibrium model? vast literature after Barro & Grossman [1971] recent revival after Great Recession Mankiw & Weinzierl [2011] Caballero & Farhi [2014] captures important intuitions but difficult to analyze 4 / 44
This model equilibrium version of the Barro-Grossman model, with matching frictions on product + labor markets: graphical representation of GE and welfare frictional + classical + Keynesian unemployment 5 / 44
Basic model (no labor market) 6 / 44
Setup static model measure 1 of identical households production takes place within households households cannot consume own production households trade production on frictional market 7 / 44
Matching function and tightness k units of produced good v visits 8 / 44
Matching function and tightness capacity k sales CRS matching function h(k,v) purchases visits v 8 / 44
Matching function and tightness capacity k tightness: x = v / k sales = = output: y = h(k,v) purchases = = visits v 8 / 44
Low product market tightness 9 / 44
High product market tightness 10 / 44
Matching cost: ρ goods per visit [ ] output = 1 + τ(x ) consumption + proof: y }{{} output = c }{{} consumption [ y 1 ρ ] = c q(x) ρ y = 1 + c q(x) ρ y + ρ v = c + ρ }{{} q(x) trading [ ] 1 + τ(x ) c + 11 / 44
Tightness and aggregate supply product market tightness x capacity: k quantity of produced good 12 / 44
Tightness and aggregate supply capacity k product market tightness x output: y = f(x) k quantity of produced good 12 / 44
Tightness and aggregate supply output y capacity k product market tightness x consumption: quantity of produced good 12 / 44
Tightness and aggregate supply aggregate supply c output y capacity k product market tightness x consumption trading cost idle time quantity of produced good 12 / 44
Nonproduced good valued by consumers in fixed supply traded on a perfectly competitive market examples: real money, land, gold, fixed capital as in Barro & Grossman [1971], Hart [1982], and Blanchard & Kiyotaki [1987] 13 / 44
Households take price p and tightness x as given choose c, m to maximize utility χ 1 + χ c ε 1 1 ε + 1 + χ m ε 1 ε }{{}}{{} produced good nonproduced good subject to budget constraint ε ε 1 m }{{} numeraire +p (1 + τ(x)) c }{{} produced good = µ }{{} endowment + f (x) p k }{{} labor income 14 / 44
Optimal consumption decision first-order condition 1 (1 + τ(x)) p }{{} 1 + χ m 1 χ ε = 1 + χ c 1 ε product price }{{}}{{} MU of nonproduced good MU of produced good aggregate demand (as m = µ): c d (x,p) = χ ε µ (1 + τ(x)) ε p ε 15 / 44
Tightness and aggregate demand product market tightness x c d (x, p) = µ (1 + (x)) p consumption c 16 / 44
Definition of equilibrium equilibrium is (x,p) such that supply = demand: c s (x) = c d (x,p) 1 equation, 2 variables: indeterminacy need a price mechanism to select equilibrium fixed price efficient price 17 / 44
Comparative statics with fixed price and efficient price 18 / 44
Increase in AD with fixed price AS output y capacity k product market tightness x AD equilibrium quantity 19 / 44
Increase in AD with fixed price AS output y capacity k product market tightness x AD quantity 19 / 44
Increase in AS with fixed price AS output y capacity k product market tightness x AD quantity 20 / 44
Comparative statics with fixed price effect on: output tightness increase in: y x aggregate demand + + aggregate supply + 21 / 44
Definition of efficient price AS price is too high product market tightness x x* AD slack equilibrium c* consumption c 22 / 44
Definition of efficient price AS price is too low product market tightness x x* AD tight equilibrium c* consumption c 22 / 44
Definition of efficient price AS price is efficient product market tightness x x* AD efficient equilibrium c* consumption c 22 / 44
Comparative statics with efficient price effect on: output tightness increase in: y x aggregate demand 0 0 aggregate supply + 0 23 / 44
Complete model 24 / 44
Labor market and unemployment labor supply n employment l labor force h labor market tightness θ producers recruiters unemployment number of workers 25 / 44
Firms employ producers and recruiters and sell production take real wage w and tightnesses x and θ as given choose number of producers n to maximize profits f (x) }{{} selling probability a }{{ n α } production [1 + ˆτ(θ)] w n }{{} wage of producers + recruiters 26 / 44
Optimal employment decision first-order condition: f (x) }{{} selling probability α } a {{ n α 1 } = [1 + ˆτ(θ)] }{{} MPL matching wedge labor demand: demand for producers n d (θ,x,w) = [ f (x) a α ] 1 1 α (1 + ˆτ(θ)) w w }{{} real wage 27 / 44
Partial equilibrium on labor market labor supply employment l labor force h labor market tightness θ partial equilibrium labor demand number of workers 28 / 44
General equilibrium (x,θ,p,w) supply = demand on product and labor markets c s (x,θ) = c d (x,p) n s (θ) = n d (θ,x,w) 2 equations, 4 variables: indeterminacy need price and wage mechanisms 29 / 44
Keynesian, classical, and frictional unemployment equilibrium employment: ( f (x) a α l = w ) 1 ( 1 α 1 1 + ˆτ(θ) frictional unemployment from ˆτ(θ) > 0 classical unemployment from w > a α ) α 1 α Keynesian unemployment from f (x) < 1 30 / 44
Comparative statics with fixed prices product effect on: labor output tightness tightness employment increase in: y x θ l aggregate demand + + + + technology + + + labor supply + + mismatch + + 31 / 44
Comparative statics with fixed prices product effect on: labor output tightness tightness employment increase in: y x θ l aggregate demand + + + + technology + + + labor supply + + mismatch + + 31 / 44
Comparative statics with efficient prices product effect on: labor output tightness tightness employment increase in: y x θ l aggregate demand 0 0 0 0 technology + 0 0 0 labor supply + 0 0 + mismatch 0 0 32 / 44
Rigid or flexible prices? 33 / 44
Construct proxy for product market tightness from capacity utilization measure in Survey of Plant Capacity: 85% 80% 75% 70% 65% 60% 55% 1974 1979 1984 1989 1994 1999 2004 2009 2013 34 / 44
Fluctuations in product market tightness: rigid price 0.08 Log deviation from HP trend 0.04 0 0.04 0.08 0.12 0.16 1974 1979 1984 1989 1994 1999 2004 2009 2013 35 / 44
Fluctuations in labor market tightness: rigid real wage 0.6 Log deviation from HP trend 0.4 0.2 0 0.2 0.4 0.6 0.8 1974 1979 1984 1989 1994 1999 2004 2009 2013 36 / 44
Effect of labor supply and demand shocks labor supply shocks: negative correlation between employment and labor market tightness labor demand shocks: positive correlation between employment and labor market tightness 37 / 44
Evidence of labor demand shocks 0.8 0.6 0.4 0.2 0 0.2 0.4 Labor market tightness (left scale) 0.04 0.03 0.02 0.01 0 0.01 0.02 0.6 0.03 Employment (right scale) 0.8 1974 1979 1984 1989 1994 1999 2004 2009 2013 0.04 38 / 44
Cross-correlogram: labor market tightness and employment 1 0.8 0.6 0.4 0.2 0 0.2 4 3 2 1 0 1 2 3 4 Lags (quarters) 39 / 44
Labor demand shocks: AD or technology shocks? 40 / 44
Effect of AD and technology shocks AD shocks: positive correlation between output and product market tightness technology shocks: negative correlation between output and product market tightness 41 / 44
Evidence of AD shocks 0.09 0.06 0.03 0 0.03 0.06 0.09 0.12 Output (right scale) Product market tightness (left scale) 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 0.15 1974 1979 1984 1989 1994 1999 2004 2009 2013 0.1 42 / 44
Cross-correlogram: product market tightness and output 0.6 0.5 0.4 0.3 0.2 0.1 0 0.1 0.2 4 3 2 1 0 1 2 3 4 Lags (quarters) 43 / 44
Conclusion tractable model of unemployment fluctuations empirical series to measure tightness product market tightness labor market tightness origins of unemployment fluctuations 1. importance of price and wage rigidity (not flexibility) 2. importance of labor demand shocks (not labor supply) 3. importance of AD shocks (not technology) 44 / 44