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Stock return comovement when investors are distracted: more, and more homogeneous

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Michael Ehrmann, European Central Bank
David-Jan Jansen, De Nederlandsche Bank
May 2018

Published in: Economy & Finance
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Stock return comovement when investors are distracted: more, and more homogeneous

  1. 1. Learning on the job and the cost of business cycles Karl Walentin and Andreas Westermark Sveriges Riksbank Eesti Pank, April 2018 Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 1 / 61
  2. 2. Cost of business cycles Long standing question in macroeconomics: How large are the welfare costs of business cycles? Costs of aggregate consumption ‡uctuations are small I Lucas (1987) Costs of countercyclical idiosyncratic consumption risk might be larger I Imrohoro¼glu (1989) and many others E¤ects of cycles on the average level of output I Seminal idea in DeLong and Summers (BPEA, 1989) I Hassan and Mertens (AER, 2017) - risk premium from misperceptions I Duprez, Nakamura and Steinsson (2017) - downward nominal wage rigidity I Den Haan and Sedlacek (QE, 2014) - ine¢ cient separations I Jung and Kuester (JEDC, 2011) - non-linearity of matching function Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 2 / 61
  3. 3. Our research question How large is the employment, output and welfare cost of business cycles? Speci…cally, we document and quantify a new channel whereby business cycles reduce the average level of employment and output due to two aspects in the labor market Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 3 / 61
  4. 4. Our research question How large is the employment, output and welfare cost of business cycles? Speci…cally, we document and quantify a new channel whereby business cycles reduce the average level of employment and output due to two aspects in the labor market: 1 Negative Beveridge correlation, i.e. correlation (vacancies,unemployment) < 0 ) employment is reduced by aggregate volatility 2 Learning on-the-job (LotJ) implies that the human capital distribution is increasing in the employment rate I General human capital stemming from learning on-the-job: Pissarides (1992) and Ljungqvist and Sargent (1998) Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 4 / 61
  5. 5. Beveridge correlation + matching function In a search model the number of new jobs m is a non-linear function of vacancies (v) and unemployment (u) Using a standard Cobb-Douglas matching function: mt = ftut = vt ut 1 ω ut The employment ‡ow equation then implies that aggregate volatility reduces the number of new jobs: Em ¯m δ δ + ¯f (1 ω) ¯f ¯v cov (v, u) ¯f ¯u var (u) + (Ef ¯f ) Eu δ denotes the exogenous separation rate and ω is the matching function elasticity Take-away: The number of new jobs decrease with aggregate volatility if the Beveridge correlation is negative and (Ef ¯f ) 0 Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 5 / 61
  6. 6. Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 6 / 61
  7. 7. Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 7 / 61
  8. 8. Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 8 / 61
  9. 9. Goal of exercise - what we do Set up search and matching model with learning on-the-job and skill loss when unemployed to capture the main mechanism Provide credible quanti…cation by capturing the main determinants of the size of output cost of business cycles Use the model to quantify the cost of business cycles of this mechanism Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 9 / 61
  10. 10. Preview of main result and its determinants Our results indicate sizeable negative e¤ects of aggregate volatility on employment, output and welfare. Welfare costs of our mechanism = 0.52-1.49% of steady state welfare If account for transition dynamics: 0.20-1.09% of steady state welfare Size of the e¤ects of business cycles is mainly determined by: 1 The sensitivity of the human capital distribution to changes in employment, and 2 The sensitivity of job creation to changes in the human capital distribution. Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 10 / 61
  11. 11. Related literature, in terms of modelling (technical) Modelling heterogenous workers and …rms, and wage bargaining framework: I Lise and Robin (AER, 2017) I Cahuc, Postel-Vinay and Robin (ECMA, 2006) Earnings loss size and persistence - models to …t the facts in Davis and von Wachter (BPEA, 2011 ) I Burdett, Carrillo-Tudela and Coles (2015) I Jarosch (2015) I Jung and Kuhn (JEEA, 2016) I Krolikowski (AEJ-Macro, 2015) I Huckfeldt (2016) - only one of these papers with aggregate shocks Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 11 / 61
  12. 12. Model overview Workers: Random search, both on and o¤ the job Firms face standard matching function and linear vacancy posting costs LotJ: Worker heterogeneity in terms of human capital, x I Markov process πxe (πxu) F x increases if employed, decreases if unemployed One-worker …rms Job (match) heterogeneity in productivity, y I Drawn after posting vacancy y v g (y) Utility is linear in consumption Surplus sharing with job ladder (Cahuc, Postel-Vinay and Robin, 2006) Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 12 / 61
  13. 13. Key assumptions Job heterogeneity in productivity + On-the-job search On the job search: takes the e¤ect of employed workers on job creation into account Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 13 / 61
  14. 14. Key assumptions Job heterogeneity in productivity + On-the-job search On the job search: takes the e¤ect of employed workers on job creation into account ) Job (productivity) ladder - lower average productivity of …rst match after unemployment than average existing match Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 14 / 61
  15. 15. Key assumptions Job heterogeneity in productivity + On-the-job search On the job search: takes the e¤ect of employed workers on job creation into account ) Job (productivity) ladder - lower average productivity of …rst match after unemployment than average existing match Wage ladder steeper than productivity ladder, as no negotiation capital at …rst job after unemployment Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 15 / 61
  16. 16. Timing within a period 1 Shocks are realized: I Idiosyncratic human capital, x I Aggregate productivity, z I A fraction ν of workers retire/exit 2 Exogenous and endogenous separations of matches 3 Firms post vacancies and workers search 4 New matches are formed, wages are set and production takes place Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 16 / 61
  17. 17. Distribution of matches - law of motion Shock realization and separations yields distribution of matches hs (x, y) Matching step yields: h (x, y) = hs (x, y) +mass hired from unemployment mass lost to more productive matches +mass poached from less productive matches Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 17 / 61
  18. 18. Value of unemployment and total value of a match The value of unemployment B (x, z, Γ) = b + 1 ν 1 + r ∑ x02X ∑ z02Z [ ∑ y02Y f z0 , Γ0 g y0 B x0 , z0 , Γ0 + β max P x0 , y0 , z0 , Γ0 B x0 , z0 , Γ0 , 0 + 1 f z0 , Γ0 B x0 , z0 , Γ0 ] πxu x, x0 π z, z0 , β is worker bargaining power, ν is probability of exiting and r is the discount rate Γ is the endogenous state Total value of a match, P ( ) , where p ( ) = xyz: P (x, y, z, Γ) = p (x, y, z) + future terms Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 18 / 61
  19. 19. Centrality of total surplus of a match, S Surplus S = P B Employer gets a share of the surplus when bargaining ) S determines the level of vacancy postings and which matches are formed E¢ cient separations ) S determines endogenous separations (Note: Wages are not allocative) Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 19 / 61
  20. 20. Worker value - connection to wage Worker value W () W () = w + 1 ν 1 + r (future terms) Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 20 / 61
  21. 21. Worker wage setting Following Cahuc, Postel-Vinay and Robin (2006) Case 1: Workers hired out of unemployment: Wage w0 set so that worker value W satis…es: W w0 , x, y, z, Γ = B (x, z, Γ) + βS (x, y, z, Γ) . Case 2: Employed workers meeting another …rm, ˜y: If S (x, ˜y, z) > S (x, y, z) the worker switches to the new match and w0 is set so that: W w0 , x, ˜y, z, Γ = P (x, y, z, Γ) + β [S (x, ˜y, z, Γ) S (x, y, z, Γ)] . else, stays with old match and w is set so that: W w0 , x, y, z, Γ = max fP (x, ˜y, z, Γ) + β [S (x, y, z, Γ) S (x, ˜y, z, Γ)] , W (w, .)g Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 21 / 61
  22. 22. Worker wage setting (part II) Case 3: Employed workers not meeting another …rm Value restricted by bargaining set: B (x, z, Γ) + βS (x, y, z, Γ) 6 W (w, x, y, z, Γ) 6 P (x, y, z, Γ) If outside this set ) set to closest boundary of set by changing w If none of these cases, then the wage, w, is …xed Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 22 / 61
  23. 23. The resulting worker value function Γ denotes endogenous aggregate states W (w, x, y, z; Γ) = w + 1 ν 1 + r ∑ x0 ∑ z0 πxe x, x0 π z, z0 2 4 s0 unemployment value + (1 s0) (1 s1f (z0, Γ0)) non-poach value +s1f (z0, Γ0) poach value 3 5 where s0 : separation all values are functions of x0 , y0 , z0 and Γ0 job …nding rate: f z0 , Γ0 = αθ z0 , Γ0 1 ω Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 23 / 61
  24. 24. Tightness Total search e¤ort, L ∑ x2X us (x) + s1 ∑ x2X ∑ y2Y hs (x, y) us (x) denotes distribution of unemployed workers and hs (x, y) denotes distribution of matches Cobb-Douglas meeting function, M = αLωV1 ω Optimality condition for vacancy posting: c0 (v) = qJ q : Probability of a …rm (vacancy) meeting a worker J : Expected value of a new match to an employer ) Aggregate labor market tightness (using symmetry, V = v): θ (z, Γ) V L = αJ (z, Γ) c0 1 ω Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 24 / 61
  25. 25. Expected value of a new match to an employer J = 1 L ∑ x2X ∑ y2Y us (x, z) max f(1 β) S (x, y, z, Γ) , 0g g (y) + s1 L ∑ x2X ∑ y2Y ∑ ˜y2Y hs (x, ˜y, z) max f(1 β) (S (x, y, z, Γ) S (x, ˜y, z, Γ)) , 0g g (y) Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 25 / 61
  26. 26. Solution algorithm (part I of II) Solving for B and P requires use of value function iteration ) Need to put state variables on a grid State includes endogenous aggregate distributions hs (x, y) and us (x) for the next period I These distributions matter only through next period labor market tightness, θ0 I θ itself fully determined by L and J I L proportional to m1 = ∑x us (x) I J adds two moments representing its two terms:m2, m3 I Aggregate endogenous state Γ captured by 3 moments I To compute next period values of these moments we assume a linear relationship to today’s moments: m0 m = Hm m1, m2, m3, z0 Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 26 / 61
  27. 27. Solution algorithm (part II of II) Obtain θ0 by: I Simulating allocations including θ and mi and then running regressions I Predict the 3 moments fmi g using 1-period lag of fmi gi=1,2,3, z and regression coe¢ cients I Compute implied θ0 = Θ (m0 1, m0 2, m0 3; z) (R2 > 0.995) )The large-dimensional distributions can be replaced by mi , State vector becomes 0 B @ w, x, y | {z } idiosyncratic ; z, m1, m2, m3 | {z } aggregate 1 C A Using the functions Hm and Θ we can compute values B and P I ...and then the entire allocation Solve for wages w residually, given the expected future values for the worker: w = W (.) future value Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 27 / 61
  28. 28. Calibration approach 1 Well established parameter values set outside model 2 Following 7 parameter values set by matching 7 moments of the model I Matching function productivity I Relative search intensity of employed I Human capital dynamics I Unemployment payo¤ I Distribution of initial match-speci…c productivity g I Volatility of (exogenous) TFP I Worker bargaining power Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 28 / 61
  29. 29. Parameters set outside model Monthly frequency Explanation Value Source ω Matching function elasticity 0.5 Pissarides (2009) δ Exogenous match sep. rate 0.030 JOLTS & Fujita-Ramey c0 Vacancy posting cost 0.06375 Fujita-Ramey ν Retirement rate 1/(40 12) 40 year work life ρ TFP shock persistence 0.960 Hagedorn-Manovskii r Interest rate 1.051/12 1 Annual r = 5% Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 29 / 61
  30. 30. Moments matched Moment Target value (data) Model value U2E transition rate, mean 0.340 0.357 J2J transition rate, mean 0.0320 0.0290 Unemployment, std.dev. 0.107 0.0973 GDP, std.dev. 0.0136 0.0136 Wage disp: Mean-min ratio 1.50 1.70 Wage elasticity wrt productivity 0.449 0.445 Return to experience 0.0548 0.0518 Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 30 / 61
  31. 31. Unusual moments matched - detailed de…nitions 1 Wage dispersion: Mean-min ratio (50th percentile/10th percentile) 2 Return to experience: Buchinsky et al. (2010) I The wage increase in the 3rd year for workers who works at least three years for the same employer Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 31 / 61
  32. 32. Parameters set through moment matching Parameter Explanation Main identifying moment α Matching function productivity U2E transition rate, mean s1 Search intensity of employed J2J transition rate, mean xup Human capital gain, probability Return to experience b Unemployment payo¤ Unemployment, std.dev. β Bargaining strength of workers Wage elasticity wrt prod. σy Match-speci…c productivity disp Wage disp: Mean-min ratio 100σz TFP shock std.dev. GDP, std.dev. Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 32 / 61
  33. 33. Parameters set through moment matching Parameter Explanation Value α Matching function productivity 0.686 s1 Search intensity of employed 0.426 xup Human capital gain, probability 0.0427 b Unemployment payo¤ 0.374 β Bargaining strength of workers 0.848 σy Match-speci…c productivity disp 0.259 100σz TFP shock std.dev. 0.698 Unemployment payo¤/output in best possible match=0.60 Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 33 / 61
  34. 34. Human capital dynamics The estimated human capital parameters imply, on average: 1.41% loss of human capital per month of unemployment 0.207% gain of human capital per month of employment I Our estimate for employed workers is in between Huckfeldt (2016) and Jarosch (2015), I Our estimate for unemployed workers is about as large as in these papers. Note: only learning on-the-job subset of total human capital - excludes formal schooling Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 34 / 61
  35. 35. Welfare measure Linear utility in consumption )aggregate welfare=aggregate consumption Two ways of interpreting unemployment payo¤ b 1 Pecuniary transfer: C=GDP-vacancy costs 2 Home production (util of leisure): C=GDP-vacancy costs+b u Presumably, the truth is an intermediate case: b consists of both home production and transfers I We report upper and lower bounds for the welfare cost Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 35 / 61
  36. 36. Gains from eliminating business cycles We solve our model with and without aggregate shocks to compute the cost of business cycles Gains of eliminating bc (%) Welfare, b transfer 1.49 Welfare, b home prod 0.52 GDP 1.45 Employment 1.34 Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 36 / 61
  37. 37. Importance of human capital dynamics Baseline No human capital dynamics Welfare, b transfer 1.49 0.26 Welfare, b home prod 0.52 0.02 GDP 1.45 0.25 Employment 1.34 0.34 Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 37 / 61
  38. 38. E¤ects from human capital on job creation Job creation determined by J (z, Γ) = ∑ x2X ∑ y2Y 1 L us (x, z) max f(1 β) S (x, y, z, Γ) , 0g g (y) + ∑ x2X ∑ y2Y ∑ ˜y2Y s1 L hs (x, ˜y, z) max f(1 β) (S (x, y, z, Γ) S (x, ˜y, z, Γ)) , 0g g (y) . L is total search e¤ort of workers us and hs are the distributions over unemployed and employed workers First term recruitment from unemployment - E (x u ( )) Second term recruitment from other …rms - E (x h ( )) Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 38 / 61
  39. 39. E¤ect of eliminating business cycles on human capital distribution: E¤ects of eliminating bc (%) E (x u ( )) 4.36 E (x h ( )) 0.18 Elasticity of J wrt E (x u ( )) is dJ dE (x u ( )) E (x u ( )) J = 1.27 Elasticity of J wrt E (x h ( )) is dJ dE (x h ( )) E (x h ( )) J = 0.39 =) E¤ects through the unemployed dominate Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 39 / 61
  40. 40. Robustness of gains from eliminating business cycles Model version Welfare, b transfer (home pr) GDP Empl Baseline 1.49 (0.52) 1.45 1.34 Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 40 / 61
  41. 41. Robustness of gains from eliminating business cycles Model version Welfare, b transfer (home pr) GDP Empl Baseline 1.49 (0.52) 1.45 1.34 Wide human cap range 1.94 (0.94) 1.89 1.43 Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 41 / 61
  42. 42. Robustness of gains from eliminating business cycles Model version Welfare, b transfer (home pr) GDP Empl Baseline 1.49 (0.52) 1.45 1.34 Wide human cap range 1.94 (0.94) 1.89 1.43 β = 0.50 1.78 (0.56) 1.83 1.42 Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 42 / 61
  43. 43. Welfare gains, accounting for transition Welfare, b home prod Welfare, b transfer Steady state 0.52 1.49 Transition 0.20 1.09 Two reasons for gains being lower when accounting for transition: 1 Discounting of future - half-time of GDP transition is 4.5 years 2 Cost of reaching higher employment - extra vacancy posting needed Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 43 / 61
  44. 44. Indicative empirical evidence of our mechanism 1 Hairault et al. (2010) …nd signi…cant positive e¤ects of TFP volatility on average unemployment. 2 Ramey and Ramey (AER, 1995) and Luo et al. (2016) …nd signi…cant negative relationship between volatility of output and the growth rate of output Direct (non-earnings based) evidence of general human capital loss is scarce. One exception: Edin and Gustavsson (2008) - Intellectual ability loss from unemployment I Being out-of-work for a year implies losing skills equivalent to 0.7 years of schooling. Evidence of high local unemployment a¤ecting future "employability" Yagan (2017) Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 44 / 61
  45. 45. Summary Described and quanti…ed new mechanism that makes business cycles costly in terms of average level of output and consumption I Learning on-the-job makes ampli…es business cycle cost substantially Welfare cost of business cycles from new mechanism is large: I 0.52-1.49% di¤erence between steady states I 0.20-1.09% including transition dynamics Policy implication: Stabilizing unemployment raises the average level of output I Rationalizes an unemployment stabilization mandate for policy makers (e.g. central banks) Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 45 / 61
  46. 46. Future research Can apply model to other questions regarding cyclical employment, wages or earnings I Hysteresis I Speci…c follow-up project: Quantify how much potential output has fallen due to Great Recession, due to lower employment 2009-2012 F Lower aggregate human capital F Higher mismatch / lower match-speci…c productivity (fell down the job ladder) Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 46 / 61
  47. 47. Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 47 / 61
  48. 48. If you prefer hiring costs... The mechanism yielding a negative impact of aggregate volatility on employment still stands: Eu ¯u 1 δ + ¯f f(cov (f , u)) + (Ef ¯f ) Eug Under the condition: corr (f , u) < 0 Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 48 / 61
  49. 49. Key assumptions to get main result - discussion 1 Negative Beveridge correlation, i.e corr (vacancies,unemployment) < 0 and a matching function, or corr (f , u) < 0 I Additional mechanisms with similar implications exist: Convexity of vacancy posting costs, capital adjustment costs, other convex costs Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 49 / 61
  50. 50. Simplifying assumptions made No physical capital I can be relaxed Utility linear in consumption I harder to relax Only one aggregate shock, “exogenous TFP”- catch all Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 50 / 61
  51. 51. Full expression for match value P P (x, y, z, Γ) = p (x, y, z) + 1 ν 1 + r ∑ x02X ∑ z02Z [(1 (1 δ) po P>B ) Bs f ∑ ˜y02Y s1f z0 , Γ0 P x0 , y, z0 , Γ0 + β max P x0 , ˜y0 , z0 , Γ0 P + 1 s1f z0 , Γ0 P x0 , y, z0 , Γ0 g]πxe x, x0 π z, z0 where ˜y0 denotes the match quality of the poaching …rm and the indicator for non-separation is: po P B = 1 Ps x0 , y, z0 , Γ0 Bs x0 , z0 , Γ0 . Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 51 / 61
  52. 52. Wage distribution - law of motion Non-trivial task to keep track of wage distribution, hw (w, x, y, z; Γ) Γ denotes aggregate endogenous state vector From previous period have hw (w, xold , yold , zold ; Γold ) 1 Shock realization and separations yields hw + (w, x, y, z; Γ) 2 Matching and wage setting step monstrous: hw (w, x, y, z; Γ) = hw + (w, x, y, z; Γ) +mass hired from unemployment mass lost to more productive matches +mass poached from less productive matches mass lost (+won) due to wage changes within match Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 52 / 61
  53. 53. Mechanic illustration of why business cycles are costly (in terms of earnings losses) Comparing a non-stochastic world to a two-state world Expansion Recession Non-stoch # Displaced workers 1 3 2 Earnings loss/worker 1 year 2 years 1.5 years Aggregate earning losses 1 year 6 years 3 years Avg aggregate 3.5 years > 3 years Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 53 / 61
  54. 54. Mechanic illustration (cont’d) Aggregate earnings loss=earnings loss per worker*number workers displaced Both factors are increasing in unemployment rate If neither factor too concave in unemployment rate: Aggregate earnings loss a convex function of unemployment rate ) Business cycles are costly in terms of earnings loss E¤ect is on the level of aggregate output I Not about idiosyncratic risk and how that is shared (Krebs, 2007, AER) Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 54 / 61
  55. 55. What causes earnings loss? Components 1 The obvious one: Unemployment implies no earnings I Cyclical variation in unemployment duration matters 2 Lower wage at next job I Loss of match quality (y): immediate I Loss of negotiation capital (the promised value W ): immediate F Unemployment implies starting negotiation from scratch (from B) I Loss of human capital (x): gradual over unemployment spell 3 Higher probability of additional job separations as... I Recently displaced workers have lower human capital and worse match-quality Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 55 / 61
  56. 56. The e¤ect on the x-distribution of changing employment (e) A one period change in e and u yield the following number of net increases in x: #∆x = xup∆e xdn∆u Note u = 1 e, yielding #∆x = xup∆e xdn∆ (1 e) #∆x = (xup + xdn) ∆e For a permanent decrease in e the x-distribution (h(x) + u(x)) will keep on shifting downwards until: (xup + xdn) ∆e =increase in number of hits of the lower bound+ decrease in number of hits of the upper bound I Note the vicious circle on the way: as x-distribution falls, e keeps on falling further I No closed form way (in particular not independent of the x-grid) of quantifying the total change in the x-distribution from aWalentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 56 / 61
  57. 57. Comparison to Jung and Kuester (2011, JEDC) As an extension Jung and Kuester consider impact of LotJ on the cost of business cycles They get very small e¤ects from LotJ ( 0.06% of welfare and GDP) compared to us This is due to several factors: 1 Their wage bargaining assumption minimizes the e¤ect of cycles on employment compared to standard bargaining, as can be seen from the larger e¤ects in Hagedorn and Manovski 2 Their human capital loss happens both at separation and gradually during unemployment ) human capital distribution less sensitive to changes in employment 3 Their human capital scales match output and unemployment bene…t equally. This minimizes the e¤ect on job creation from a decrease in the human capital distribution 4 Absence of endogenous (cyclical) separations in their modelWalentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 57 / 61
  58. 58. Human capital dynamics - interaction with match-speci…c productivity Ljungqvist and Sargent/Jung and Kuester uses di¤erent assumption of human capital loss Some part of x lost at separation I Seems suitable in their model without match-speci…c productivity I Less suitable for our model Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 58 / 61
  59. 59. Numerical details We use Tauchen and Hussey’s (1991) discretization of AR(1) processes with optimal weights from Flodén (2008). I This algorithm has been shown by Flodén (2008) to be accurate for processes with high persistence. The number of gridpoints for x, y and z are 10, 8 and 5 respectively. The wage grid contains 15 points and the mi grid 2 points I Linear interpolation over the moments, mi . For the grid for human capital, x, we follow Ljungqvist and Sargent (1998, 2008) in setting the ratio between the maximum and minimum value of x to 2. Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 59 / 61
  60. 60. Labor market ‡ows - separations and shock realizations (subperiods 1-2) Distribution (density) of matches: hs (x, y, z) = ∑ x 1 ∑ y 1 (1 ν) (1 δ) 1 fS (x, y, z) 0g πxe (x 1, x) πy (y 1, y) h (x 1, y 1, z 1) Distribution of unemployed develops analogously: us (x, z) = ν1 fx = xg + (1 ν) [∑ x 1 πxu (x 1, x) u (x 1, z 1) + ∑ x 1 ∑ y 1 (1 fS (x, y, z) < 0g + δ1 fS (x, y, z) 0g) πxe (x 1, x) πy (y 1, y) h (x 1, y 1, z 1)]. Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 60 / 61
  61. 61. Labor market ‡ows - new matches Distribution of matches after new matches are formed: h (x, y, z) = hs (x, y, z) +s0 M L u+ (x, z) 1 fS (x, y, z) 0g f (y) | {z } mass hired from unemployment +s1 M L ∑ ˜y hs (x, ˜y, z) 1 fS (x, y, z) > S (x, ˜y, z)g g (y) | {z } mass poached from less productive matches s1 M L hs (x, y, z) ∑ ˜y 1 fS (x, ˜y, z) > S (x, y, z)g g (˜y) | {z } mass lost to more productive matches Walentin and Westermark () LotJ and the cost of business cycles Eesti Pank, April 2018 61 / 61

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