Involuntary (‘Unlucky’) y ( y ) Unemployment and the Business C Cycle l Lawrence Christiano, Mathias Trabandt (ECB) and d Karl Walentin (Riksbank)

Background • There is a class of models that has received a lot of attention in central banks. • People have used the models to place p p structure on discussions about monetary policy. – Recent: Curdia ‐ Woodford, Gertler ‐ Kiyotaki. • In recent years, there has been a push to introduce labor market variables like unemployment.

What We Do: • We investigate a particular approach to W i ti t ti l h t modeling unemployment. – Hopenhayn and Nicolini (1997), Shavell and Weiss ( ) (1979) • We explore the implications for monetary l h i li i f DSGE models. – Simple NK model without capital. • Okun’s law, natural rate of unemployment. – Standard empirical NK model (e.g., ACEL, CEE, SW) • Estimate the model. • Does well reproducing response of unemployment and D ll d i f l d labor force to three identified shocks.

Unemployment • To be ‘unemployed’ in US data, must To be unemployed in US data, must – be ‘willing and able’ to work. – recently, made efforts to find a job. • Our presumption: a person has lower utility when unemployed than when employed. – consumption drops typically about 10 percent upon the loss of a job (Gruber, 1997, Chetty and Looney, 2006) – Some indicators of happiness (suicide, subjective sense of well being) deteriorate when the unemployment rate rises (Brenner, 1979; Ruhm, 2000; Schimmack et al, 2008) • Current monetary DSGE models with ‘unemployment’: – Utility jumps when you lose your job. – Finding a job requires no effort – Finding a job requires no effort. – US Census Bureau employee dropped into current monetary DSGE models would find zero unemployment .

What we do: • Explore the simplest possible model of p p p unemployment, which satisfies two key features of unemployment. • To be unemployed: – Must have made recent efforts to find a job Must have made recent efforts to find a job. • To find a job, household must make an effort, e , which increases the probability, p(e) , of finding a job. – Unemployed worse off than employed. • assume household search effort, e , is not publicly observable observable. • full insurance against household labor market outcomes is not possible. ot poss b e – under perfect consumption insurance, no one would make an effort to find a job.

Outline Outline • Insert our model of unemployment into – Simple Clarida ‐ Gali ‐ Gertler (CGG) NK model Simple Clarida Gali Gertler (CGG) NK model. – CEE model: evaluate model’s ability to match US macroeconomic data including unemployment macroeconomic data, including unemployment and labor force

CGG Model • Goods Production: Goods Production: f 1 Y i , t 1 f di Y t , 1 ≤ f . , f i , t 0 0 • Monopolists produce intermediate goods – Technology: Y i , t A t h i , t – Calvo sticky prices: P P i , t − 1 with prob. p b ith P i , t with prob. 1 − p chosen optimally – Enter competitive markets to hire labor.

CGG Model: Monetary Policy • Taylor rule: ̂ t R R ̂ t − 1 1 − R r ̂ t r y x ̂ t t R • Here: ̂ t x output gap (percent deviation of output – – from efficient level) – • Efficient equilibrium: – Monopoly power and inflation distortions p y p extinguished.

Households Households • This is where the new stuff is This is where the new stuff is……..

Typical Household During Period Typical Household During Period l Draw privately observed, idiosyncratic shock, , 0,1 0,1 from Uniform, , that determines utility cost from Uniform, , that determines utility cost Household that stays out Household that stays out of work: of labor market does not F t 1 L l L . work and has utility out of labor force log c t log c t l l After observing , decide whether to join After observing decide whether to join the labor force or stay out. t+1 t Household that joins labor force tries to find a job by choosing effort, e , and receiving ex ante utility ex post utility in case household finds a job ex post utility in case of unemployment w − F − t 1 L l L − 1 u − 1 p e t log c t 2 e t 1 − p e t log c t 2 e t 2 2 p e t ae t

Household Insurance • They need it: • They need it: – Idiosyncratic work aversion. – Job ‐ finding effort e may or may not produce a job Job finding effort, e , may or may not produce a job. • Assume households gather into large families like Assume households gather into large families, like in Merz and Andolfatto – With complete information: • Households with low work aversion told to make big effort to find work. • All households given same consumption. All households given same consumption. • Not feasible with private information. – With private information Wi h i i f i • To give households incentive to look for work, must make them better off in case they find work.

Optimal Insurance • Relation of family to household: standard principal/agent relationship. principal/agent relationship. – family receives wage from working households – family observes current period employment status of household. • For family with given C, h : w , c t nw c t – allocates consumption: w / c t nw c t – must be big enough to provide incentives. b bi h id i i / – must satisfy family resource constraint: w 1 − h t c t nw C t . h t c t

Family Indirect Utility Function • Utility: u C t , h t , t log C t − z h t , t u C t , h t , t log C t z h t , t • Where z h t , t log h t e F t 1 L f h t , t L − 1 1 a 2 t t 2 1 L L L 2 f h t , t 2 L 1 − t L f h t , t L 1 . 2 L 1 L 1 L − f h f h 2 L 1 • Clarida ‐ Gali ‐ Gertler utility function: • Clarida ‐ Gali ‐ Gertler utility function: h 1 L u C h log C u C t , h t , t log C t − t h t

Family Problem Family Problem C t h t B t 1 E 0 ∑ t log C t − z h t , t max C t , h t , B t 1 t 0 – Subject to: P t C t B t 1 ≤ B t R t − 1 W t h t Transfers and profits t . • Family takes market wage rate as given and F il t k k t t i d tunes incentives so that marginal cost of extra work equals marginal benefit: k l i l b fit W t C z h C t z h h t , t t P t .

Observational Equivalence Result q • Because of the simplicity of the assumptions, the model is observationally equivalent to h d l i b i ll i l standard NK model, when represented in terms of output, interest rate, inflation: f i i fl i 1 1 1 − p 1 − p ̂ t E t ̂ t 1 ̂ t 1 z x p ̂ ̂ ∗ ∗ . ̂ ̂ E ̂ x t E t x t 1 − R R t − t 1 − R t R ̂ ̂ ̂ ̂ t r y x ̂ ̂ t t , R t R R t − 1 1 − R r

Observational Equivalence Result q z function: disutility of labor for family • Because of the simplicity of the assumptions, the model is observationally equivalent to h d l i b i ll i l z ≡ z hh h ‘curvature of disutility of labor’: z h standard NK model, when represented in terms of output, interest rate, inflation: f i i fl i 1 1 1 − p 1 − p ̂ t E t ̂ t 1 ̂ t 1 z x p ̂ ̂ ∗ ∗ . ̂ ̂ E ̂ x t E t x t 1 − R t − t 1 − R t R R ̂ ̂ ̂ ̂ t r y x ̂ ̂ t t , R t R R t − 1 1 − R r

Unemployment Gap • Can express everything in terms of unemployment gap: unemployment gap: 1 2 m L 1 − u g − okun x okun a 2 L 2 2 ̂ t . u t 2 m L 0. 1 − u a 2 L efficient level of unemployment actual rate of unemployment g ∗ − u t u t u t Non ‐ accelerating rate of inflation level of unemployment, NAIRU

Properties of the Model Properties of the Model • Calibrated model first Calibrated model first….

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