Unemployment and Productivity in the Long Run: the Role of Macroeconomic Volatility Pierpaolo Benigno, Luca Ricci, Paolo Surico October 2010 Pierpaolo Benigno, Luca Ricci, Paolo Surico () October 2010 1 / 35
Unemployment and its low frequency component 11 11 9 9 7 7 5 5 Unemployment Unemployment trend: time-varying VAR Unemployment trend: 5 year rolling windows 3 3 1965 1965 1970 1970 1975 1975 1980 1980 1985 1985 1990 1990 1995 1995 2000 2000 2005 2005 Pierpaolo Benigno, Luca Ricci, Paolo Surico () October 2010 2 / 35
Unemployment trend and productivity growth trend 5 year rolling windows VAR estimates 4 2.6 Unemployment T rend 7 Productivity Growth T rend 9 2.4 3 Productivity Growth Trend (%) Unemployment Trend (%) Productivity Growth Trend (%) Unemployment Trend (%) 2.2 6 6 2 2 1 1.8 5 3 Unem ployment T rend Productivity Growth T rend 0 1.6 1965 1965 1970 1970 1975 1975 1980 1980 1985 1985 1990 1990 1995 1995 2000 2000 2005 2005 2010 2010 1965 1965 1970 1970 1975 1975 1980 1980 1985 1985 1990 1990 1995 1995 2000 2000 2005 2005 2010 2010 Pierpaolo Benigno, Luca Ricci, Paolo Surico () October 2010 3 / 35
Unemployment trend and productivity growth trend OLS ESTIMATES u t = 0 . 10 ˜ ( 0 . 002 ) � 2 . 24 ( 0 . 088 ) � ˜ g t + ˆ ε t with R 2 = 0.77. Empirical works : Bruno and Sachs (1985), Phelps (1994), Blanchard and Wolfers (2000), Staiger, Stock, and Watson (2001), Pissarides and Vallanti. Theoretical works : on labor demand: Mortensen and Pissarides (1998), Pissarides (2000), Pissarides and Vallanti (2007). on labor supply: Ball and Mankiw (2002), Ball and Mo¢tt (2002). Pierpaolo Benigno, Luca Ricci, Paolo Surico () October 2010 4 / 35
But... In the 80s, productivity growth cannot explain a large portion of the fall in long-run unemployment. (The Great Moderation) In the early 90s, a ‡at productivity growth cannot explain the fall in long-run unemployment. Since the early 2000s, an increase in productivity growth comes with a puzzling rise in long-run unemployment. Pierpaolo Benigno, Luca Ricci, Paolo Surico () October 2010 5 / 35
Unemployment trend and productivity growth volatility VAR estimates 5 year rolling windows Unemployment T rend Unemployment T rend 7 0.06 Productivity Growth Variance Productivity Growth Variance 9 0.04 ) e 0.04 % c ) e n % c ( a n d ( i a n r d a i e n r V a r 6 e T r V h T t t h n w 6 t e t n w o e m r o G m r y G o y y t o y l p i v 0.02 t l p i m i v t c m i e t u c n e d u U o n d r U o P r P 5 0 3 0.02 1965 1965 1970 1970 1975 1975 1980 1980 1985 1985 1990 1990 1995 1995 2000 2000 2005 2005 2010 2010 1965 1965 1970 1970 1975 1975 1980 1980 1985 1985 1990 1990 1995 1995 2000 2000 2005 2005 2010 2010 Pierpaolo Benigno, Luca Ricci, Paolo Surico () October 2010 6 / 35
Unemployment trend, productivity trend and volatility V A R es tim ates V A R es tim ates 2.6 U nemp loy ment Trend U nemp loy ment Trend 7 7 Produ c tiv ity G row th Tren d Produc tiv ity G row th Varianc e 2.4 0.04 Productivity Growth Trend (%) Productivity Growth Variance Unemployment Trend (%) Unemployment Trend (%) 2.2 6 6 2 1.8 5 5 1.6 0.02 19 6 5 19 7 0 19 7 5 19 8 0 19 8 5 19 9 0 19 9 5 20 0 0 20 0 5 20 1 0 19 6 5 19 7 0 19 7 5 19 8 0 19 8 5 19 9 0 19 9 5 20 0 0 20 0 5 20 1 0 19 6 5 19 7 0 19 7 5 19 8 0 19 8 5 19 9 0 19 9 5 20 0 0 20 0 5 20 1 0 19 6 5 19 7 0 19 7 5 19 8 0 19 8 5 19 9 0 19 9 5 20 0 0 20 0 5 20 1 0 Pierpaolo Benigno, Luca Ricci, Paolo Surico () October 2010 7 / 35
Unemployment trend and productivity growth volatility OLS ESTIMATES σ 2 u t = 0 . 08 ( 0 . 001 ) � 1 . 68 ( 0 . 047 ) � ˜ g t + 50 . 89 ( 1 . 974 ) � ˜ t + ˆ ˜ ε t where R 2 =0.95! Back of the envelope calculations show that during the 80s a fall in the volatility of productivity contributed to more than 50% of the fall in long-run unemployment, while since 2000 the rise in the volatility contributed to more than 70% of the rise in long-run unemployment. No literature on this relationship! Pierpaolo Benigno, Luca Ricci, Paolo Surico () October 2010 8 / 35
Our explanation for joint role of productivity and volatility Real wage rigidities naturally imply a negative long-run relationship between unemployment and productivity growth Asymmetric real wage rigidities strongly reinforce this relationship at low trends of productivity growth and can also account for the role of its volatility Intuition Real Pro…ts = Y � W P L = AL α � W P L When the productivity trend is low and real wage W / P is stickier downward than upward, recessions are much worse and expansions are not better. When the trend in A is ‡at and W / P is stickier downward than upward, then higher volatility of A leads to lower L on average. Pierpaolo Benigno, Luca Ricci, Paolo Surico () October 2010 9 / 35
The model The economy is subject to an aggregate productivity shock A t , whose logarithmic a t is distributed as a Brownian motion da t = gdt + σ dB t where B t denotes a standard Brownian motion with zero drift and unit variance. Household j has preferences over time given by " Z ∞ ! # t � l 1 + η ( j ) e � ρ ( t � t 0 ) ln C j t E t 0 dt 1 + η t 0 ρ > 0 is the rate of time preference. Standard intertemporal budget constraint and optimality conditions apply. Pierpaolo Benigno, Luca Ricci, Paolo Surico () October 2010 10 / 35
Firms Technology for the production of all goods y t ( i ) = A t L t ( i ) α , for a parameter α with 0 < α < 1. Prices are ‡exible and set in a monopolistic-competitive goods market. Optimality conditions implies W t L t ( i ) W t L t p t ( i ) = P t = µ p = µ p Y t Y t where µ p � θ p / [( θ p � 1 ) α ] > 1 denotes the mark-up. The demand for labor of type j is given by � W t ( j ) � � θ w l d t ( j ) = L t W t Pierpaolo Benigno, Luca Ricci, Paolo Surico () October 2010 11 / 35
Labor supply Given labor demand, wage setters set real wages to maximize present discounted value of the marginal utility of wage income minus the disutility of working. Equivalent formulation of the labor-supply problem is the maximization of the following objective � Z ∞ � e � ρ ( t � t 0 ) π ( w t ( j ) , w t , A t ) dt E t 0 t 0 by choosing real wages f w t ( j ) g ∞ t = t 0 , where π ( w t ( j ) , w t , A t ) � ! 1 + η � w t ( j ) � 1 � θ w 1 � α � w t ( j ) � � ( 1 + η ) θ w � A t � 1 + η 1 1 1 1 � α � µ p w t 1 + η µ p w t w t Pierpaolo Benigno, Luca Ricci, Paolo Surico () October 2010 12 / 35
Flexible wages Static problem. Optimality condition: π w j ( w t ( j ) , w t , A t ) = 0 Labor is constant 1 L f = ( µ p µ w ) � 1 + η Real wages are proportional to the aggregate productivity shock t = 1 ( L f ) α � 1 A α w f t µ p Pierpaolo Benigno, Luca Ricci, Paolo Surico () October 2010 13 / 35
Unemployment As in Galí (2010), unemployment is de…ned as the di¤erence between the “notional”amount of labor that workers would be willing to supply in a competitive and frictionless market at the current real wage and the amount of labor currently employed. u t = ln L s t � ln L t Notional labor supply de…ned as the amount of labor that equates the marginal rate of substitution between labor and (current) consumption at the current real wage t ) η C t = W t ( L s P t Unemployement and output gap are related through u t = u f � 1 + η x t η where x t is the output gap and u f is the ‡exible-price-wage unemployment rate. Pierpaolo Benigno, Luca Ricci, Paolo Surico () October 2010 14 / 35
Sticky real wages Wage setters take into account the costs of changing real wages V ( w t ( j ) , w t , A t ) = � Z ∞ � e � ρ ( t � t 0 ) [ π ( w t ( j ) , w t , A t ) � h ( π R , t ( j ))] dt π R , t ( j ) E t 0 max t 0 Assume linex function for adjustment costs h ( π R , t ( j )) = e χλπ R , t ( j ) � χλπ R , t ( j ) � 1 λ 2 for some parameters χ , λ , where real wage changes are π R , t ( j ) dt � dw t ( j ) / w t ( j ) . χ is a measure of the costs of adjustment; λ measures the asymmetries in the cost function. Pierpaolo Benigno, Luca Ricci, Paolo Surico () October 2010 15 / 35
When λ ! 0, standard symmetric quadratic cost function h ( π R , t ( j )) = χ 2 ( π R , t ( j )) 2 , 2 When λ < 0 it is more costly to adjust real wages downward than upward and viceversa when λ > 0. When λ ! � ∞ real wages are in‡exible downward and fully ‡exible upward Pierpaolo Benigno, Luca Ricci, Paolo Surico () October 2010 16 / 35
Optimality condition requires h π ( π R , t ( j )) = V w j w t ( j ) , Marginal costs of changing real wages follow a stochastic di¤erential equations of the form "� L t # � 1 + η ρ h π ( π R , t ) dt = θ w � 1 � 1 dt + E t dh π ( π R , t ) L f µ p Under a quadratic cost function can be simpli…ed to "� L t # � 1 + η ρπ R , t dt = k � 1 dt + E t d π R , t L f Pierpaolo Benigno, Luca Ricci, Paolo Surico () October 2010 17 / 35
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