Involuntary (Unlucky) Unemployment and the Business Cycle. Lawrence Christiano Mathias Trabandt Karl Walentin

Transcription

1 Involuntary (Unlucky) Unemployment and the Business Cycle Lawrence Christiano Mathias Trabandt Karl Walentin

2 Background New Keynesian (NK) models receive lots of attention ti in central lbanks. People use these models to place structure on discussions about monetary policy. Recent: Curdia Woodford, Gertler Kiyotaki. In recent years, push to introduce labor market variables like unemployment.

3 Why Unemployment? Viewed by some as a direct observation on the efficiency with which resources are used (output gap). With a theory of unemployment, can investigate this in a structured way. Becauseof imperfect labor market insurance, unemployment viewed as an indicator of welfare cost of business cycles. Can assess general presumption that Lucas cost of business cycles conclusion not robust to assumption of imperfect labor market insurance.

4 What We Do: Investigate a particular approach to modeling unemployment. Hopenhayn Nicolini (1997), Shavell Weiss (1979). Explore the implications for monetary equilibrium (DSGE) models. Simple NK model without capital (CGG) Standard empirical NK model (e.g., CEE, ACEL, SW) Estimate the model. Does well reproducing response of unemployment and labor force to three identified shocks.

5 Unemployment To be unemployed in US data, must be willing and able to work. recently, made concrete efforts to find a job. Our presumption: a person has lower utility when unemployed thanwhenemployed employed. Some indicators of utility (health, suicide, subjective sense of well being, kids well being) deteriorate when people experience unemployment Brenner (1979), Ruhm (2000), Oreopoulos, et al (2008), Schimmack et al (2008), Sullivan and von Wachter (2009) Current monetary DSGE models dlwith unemployment : Unemployed are the lucky ones. Finding a job requires no effort. US Census Bureau employee dropped dinto current monetary DSGE models would find zero unemployment.

6 Miracle to Malaise: What s next for Japan, Cox and Koo, Economic letter, Dallas Fed, Jan

7 Unemployment To be unemployed in US data, must be willing and able to work. recently, made concrete efforts to find a job. Our presumption: a person has lower utility when unemployed thanwhenemployed employed. Some indicators of utility (health, suicide, subjective sense of well being, kids well being) deteriorate when people experience unemployment Brenner (1979), Ruhm (2000), Oreopoulos, et al (2008), Schimmack et al (2008), Sullivan and von Wachter (2009) Current monetary DSGE models dlwith unemployment : Unemployed are the lucky ones. Finding a job requires no effort. US Census Bureau employee dropped dinto current monetary DSGE models would find zero unemployment.

8 What we do: We explore a simple prototype model of unemployment, which has two key features. Probability, p(e), of securing a job is increasing in effort, e. Essential component of empirical measure of unemployment Unemployed worse off than employed. assume household search effort, e, is not publicly observable. full insurance against household labor market outcomes is not possible. under perfect consumption insurance, no one would make an effort to secure a job.

9 Outline Simple Clarida Gali Gertler (CGG) NK model Information in unemployment on the output gap. Welfare cost of business cycles. CEE model Evaluate model s ability to match US macroeconomic data, including unemployment and labor force No loss on standard macro variables. Do fine on unemployment rate and labor force.

10 Clarida Gali Gertler Model Goods Production: Y t 0 1 Yi,t 1 f di f,1 f. Monopolists produce intermediate goods Technology: Y i,t A t h i,t Calvo sticky prices: P i,t P i,t 1 chosen optimally with prob. p with prob. 1 p Enter competitive markets to hire labor. Policy: R t R R t 1 1 R r t r y x t t

11 Households This is where the new stuff is...

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

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

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

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

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

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

18 Household Insurance They need it: Idiosyncratic work aversion. Job finding effort, e, may or may not produce a job. 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. Not feasible with private information. With private information: To give households incentive to look for work, must make them better off in case they find work. Trade off between incentives and insurance.

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

20 Family Indirect Utility Function Utility: 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 a2 t 2 1 L L 2 2 L 1 Clarida Gali Gertler utility function: f h t, t 2 L 1 t L f h t, t L 1. 1 u C t,h t, t log C t t h t 1 L

21 Family Indirect Utility Function Utility: 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 a2 t 2 1 L L 2 2 L 1 Clarida Gali Gertler utility function: f h t, t 2 L 1 t L f h t, t L 1. 1 u C t,h t, t log C t t h t 1 L

22 Family Indirect Utility Function Utility: 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 a2 t 2 1 L L 2 2 L 1 Clarida Gali Gertler utility function: f h t, t 2 L 1 t L f h t, t L 1. 1 u C t,h t, t log C t t h t 1 L

23 Family Problem Subject to: max E 0 C t,h t,b t 1 t 0 t log C t z h t, t 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 tunes incentives so that marginal cost of extra work equals marginal benefit: C t z h h t, t W t P t.

24 Family Problem Subject to: max E 0 C t,h t,b t 1 t 0 t log C t z h t, t 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 tunes incentives so that marginal cost of extra work equals marginal benefit: C t z h h t, t W t P t.

25 Reduced Form Properties Model is observationally equivalent to standard NK model, when represented in terms of output, interest rate, inflation: t E t t 1 1 p 1 p p 1 z x t E R R x t E t x t 1 R t t 1 R t. R t R R t 1 1 R r t r y x t t,

26 Reduced Form Properties Model is observationally equivalent to standard NK model, when represented in terms of output, interest rate, inflation: t E t t 1 1 p 1 p p 1 z x t x t E t x t 1 R t t 1 R t. R t R R t 1 1 R r t r y x t t,

27 Reduced Form Properties z function: disutility of labor for family Model is observationally equivalent to standard NK model, when represented in terms of output, interest curvature rate, inflation: of disutility of labor : z z hhh z h t E t t 1 1 p 1 p p 1 z x t x t E t x t 1 R t t 1 R t. R t R R t 1 1 R r t r y x t t,

28 Unemployment Gap Can express everything in terms of unemployment gap: 2 u g t okun x t. okun a2 2 L m L 1 u 1 u a 2 2 L m L 0. u t g actual unemployment ut natural rate of unemployment ut

29 Unemployment Gap Can express everything in terms of unemployment gap: 2 u g t okun x t. okun a2 2 L m L 1 u 1 u a 2 2 L m L 0. u t g actual rate of unemployment ut efficient level of unemployment ut

30 Unemployment Gap Can express everything in terms of unemployment gap: 2 u g t okun x t. okun a2 2 L m L 1 u 1 u a 2 2 L m L 0. u t g actual rate of unemployment ut efficient level of unemployment ut Non accelerating rate of inflation level of unemployment, NAIRU

31 Properties of the Model Calibrated model first...

32 Calibration of the Model Tbl Table 1: StructuralP Parameters of SmallMdlHldFi Model Held Fixed Across Numerical lexperiments Parameter Value Description Discount factor g A Technology growth p 0.75 Price stickiness f 1.2 Price markup R 0.8 Taylor rule: interest smoothing r 1.5 Taylor rule: inflation r y 0.2 Taylor rule: output gap g 0.2 Government consumption share on GDP Diffusion speed of technology into government consumption To g parameterize 0.8 preference AR(1) government and search consumption function, set: g i A labor force 0.8 participation AR(1) technology rate: m= employment 0.8 rate: AR(1) disutility h=0.63 of labor unemployment rate: u=0.056 g a Standard deviation government consumption shock

33 Replacement ratio Properties c nw c w 0.18 Very low! In model with habit persistence in preferences, replacement ratio = Cost of business cycles (in % of consumption) Limited Information Model Full Information Model Technology Shock Only 0.52% 0.57% Government Spending Shock Only 0.11% 0.13% Monetary Policy Shock Only

34 Replacement ratio Properties c nw c w 0.18 Very low! In model with habit persistence in preferences, replacement ratio = Cost of business cycles (in % of consumption) Limited Information Model Full Information Model Technology Shock Only 0.52% 0.57% Government Spending Shock Only 0.11% 0.13% Monetary Policy Shock Only

35 Replacement ratio Properties c nw c w 0.18 Very low! In model with habit persistence in preferences, replacement ratio = Cost of business cycles (in % of consumption) Limited Information Model Full Information Model Technology Shock Only 0.52% 0.57% Government Spending Shock Only 0.11% 0.13% Monetary Policy Shock Only Ongoing: analysis in simple RBC model

36 Replacement ratio Properties c nw c w 0.18 Very low! In model with habit persistence in preferences, replacement ratio = Cost of business cycles (in % of consumption) Limited Information Model Full Information Model Technology Shock Only 0.52% 0.57% Government Spending Shock Only 0.11% 0.13% Monetary Policy Shock Only

37 Using Unemployment to Estimate the Output Gap CTW, Handbook chapter Estimated Simple CGG model: 2 observables: real GDP per capita growth, unemployment rate 4 shocks: technology, labor supply, Phillips curve, monetary policy Calibrate economic parameters Estimate parameters of exogenous processes using: i) Bayesian moment matching estimation and ii) Bayesian full information estimation

38 Using Unemployment to Estimate the Output Gap What is the information content tof the unemployment rate for the output gap? Experiment: Examine impact of including unemployment on estimate of the output gap for the US economy.

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42 Put our theory of unemployment into a medium sized i ddsge Model dl Habit persistence in preferences. Variable capital utilization. Investment adjustment costs. Wage setting frictions as in Erceg Henderson Levin. Impulse response matching by Bayesian methods: prices reoptimized i on average every quarters. wages reoptimized on average every 4 quarters.

43 Finding Estimate VAR impulse responses of macro variables ibl to two technology shocks and monetary policy shock (following Fisher and ACEL). Results: Performance on standard macro variables same as CEE and ACEL. Performance on unemployment and the labor force is fine.

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45 Micro Implications of Model Model: consumption premium higher in booms. Have time series evidence on cross household variance, V, of log consumption. Heathcote, Perri and Violante (2010) show V goes down in three of past 5 recessions. V t 1 h t h t log w 2. c t w c t nw Model: search intensity lower in recessions Consistent with evidence on discouraged workers

46 Conclusion Integrated a model of involuntary (unlucky) unemployment into monetary DSGE model. Results: Obtained a theory of Okun s gap, NAIRU. Able to match responses of unemployment and labor force to macro shocks. Ri Raises several further empirical ii questions. Why introduce unemployment? A policy variable of direct interest. Useful for estimating output gap (CTW, handbook chapter ). By bringing in more data, get a better read on unobserved shocks and may improve forecasts.