What drives matching efficiency in the labor market?

What drives matching e¢ ciency in the labor market?Regis Barnichon (CREI) Andrew Figura (Board Fed) October 2011 9th Trobada Barcelona GSE

Matching e¢ ciency of the labor market I Important determinant of the functioning of the labor market ! the ability of the labor market to match unemployed workers to jobs. I Characteristics of job searchers, in the nature of new jobs, in the location of job creation and job destruction, and in the search behavior of the unemployed will all a¤ect matching e¢ ciency.

The aggregate matching function mt = m0t Utσ Vt1 σ I Relates the ‡ow of new hires to the stocks of vacancies and unemployment I Convenient device that “partially captures a complex reality [...] with workers looking for the right job and …rms looking for the right worker” (Blanchard and Diamond, 1989). I Analogous to production function Yt = At Ktα L1 t α

Matching e¢ ciency mt = m0t Utσ Vt1 σ I In matching function apparatus, matching e¢ ciency m0 , akin to a Solow residual I Lots of work on determinants of the Solow residual or TFP in the context of the production function I Little work on the behavior and on determinants of matching e¢ ciency.

Matching e¢ ciencyThe Solow residual of the matching function I With CRS Cobb-Douglas matching function, ‡ow of new matches given by mt = m0t Utσ Vt1 σ I mt Workers job …nding rate given by jft = Ut I Regress Vt ln jft = (1 σ) ln θ t + ln m0 + εt , with θ t = Ut I ln m0t = ln m0 + εt

Matching e¢ ciencyThe Solow residual of the matching function (4 qtrs MA)

Matching e¢ ciencyThe Solow residual of the matching function I No trend I Cyclical, lags the business cycle; declines in aftermaths of recessions and increases in later stages of expansions or during recessions I Large decline with 2008-2009 recession adding 1 3 ppt to U 4 (and preventing it from declining)

This paper This paper: Composition and Dispersion I a framework to analyze movements in m0t I studies the determinants of m0t ‡uctuations over 1976-2010

Overview 1. A framework to study matching e¢ ciency: composition and dispersion 2. Matching e¢ ciency since 1976 2.1 using micro CPS data 1976-2010 2.2 building a new dataset with highly disaggregated data on U and V over 2006-2010 ! necessary to capture dispersion in labor market conditions

Empirical Framework

Empirical frameworkMain idea I Aggregate job …nding probability JFt is an average over heterogenous workers j in heterogenous labor markets i Uij ,t JFt = ∑ Ut JFij ,t . i ,j

Empirical frameworkModeling individual job …nding probabilities The job …nding probability of individual of type j in labor market segment i (geographic location, industry group or occupation group) JFij ,t I Individual type j de…ned by vector Xjt of K characteristics n o k xjt

Empirical frameworkModeling individual job …nding probabilities The job …nding probability of individual of type j in labor market segment i (geographic location, industry group or occupation group) JFij ,t I Individual type j de…ned by vector Xjt of K characteristics n o k xjt I Labor market segment i characterized by labor market v tightness θ it = uit , and average matching e¢ ciency mi it

Empirical frameworkModeling individual job …nding probabilities The job …nding probability of individual of type j in labor market segment i (geographic location, industry group or occupation group) JFij ,t I Individual type j de…ned by vector Xjt of K characteristics n o k xjt I Labor market segment i characterized by labor market v tightness θ it = uit , and average matching e¢ ciency mi it I JFij ,t = JF (Xjt , mi , θ it , θ t )

Empirical frameworkA decomposition of the determinants of average JF Uij ,t JFt = ∑ Ut JF (Xjt , mi , θ it , θ t ) i ,j ¯ Second-order Taylor expansion θ it θ t and (Xjt , mi ) (X , m0 ) θ it JFt = JF t (θ t ) + ∑ JFtU ,k + JFtm MMt + ηt k θt

The determinants of average JF θ it JFt JF t (θ t ) + ∑ JFtU ,k + JFtm MMt | {z } k θt 1 1. First term: JF t (θ t ) = JFij ,t (X , θ t , θ t ) = m0 θ 1 ¯ t σ Average job …nding rate absent heterogeneity ) What an aggregate matching function would perfectly capture

The determinants of average JFComposition e¤ect θ it JFt JF t (θ t ) + ∑ JFtU ,k + JFtm MMt θt |k {z } 2a 2a. E¤ect of composition Uj ,t ∂JF JFtU ,k = ∑ Ut ∂xjt k k xjt xk ¯ j ¯ θ t ,X If share of a group (e.g. job losers) with low JFij increases in recessions, then average JF will decline

The determinants of average JFComposition e¤ect θ it JFt JF t (θ t ) + ∑ JFtU ,k + JFtm MMt k |{z} θt 2b 2b. E¤ect of composition Ui ,t ∂JF JFtm = ∑ Ut ∂mi ¯ (mi mo ) i θ t ,X If more unemployed concentrated in segment with higher matching e¢ ciency, average JF increases

The determinants of average JFDispersion e¤ect θ it JFt JF t (θ t ) + ∑ JFtU ,k + JFtm MMt k θt | {z } 3 3. E¤ect of dispersion θ it θ it MMt = MM0 (θ t ) Var θt θt If JF (Xjt , mi , θ it , θ t ) concave in θ it , MM0 (θ t ) > 0 =) Dispersion in labor market tightness across segments will negatively a¤ect average JF

E¤ect of dispersion on JF I Two labor market segments: P1 with θ 1 and P2 with θ 2 6= θ 1 I Job …nding rate lower than if P1 =P2 =Paverage UE (1- σ) λ =m θ 0 P 2 P 0 P average P 1 θ Dispersion ) Lower average JF

Postulating a functional form for JF(ij) Logistic functional form (1 σ)ω (1 σ)(1 ω ) JFij ,t 1 e m i θ it θt ln = βXjt + ln (1 σ)ω (1 σ)(1 ω) + η ij ,t with ω 2 [0,1] 1 JFij ,t e m i θ it θt

Postulating a functional form for JF(ij) Logistic functional form (1 σ)ω (1 σ)(1 ω ) JFij ,t 1 e m i θ it θt ln = βXjt + ln (1 σ)ω (1 σ)(1 ω) + η ij ,t 1 JFij ,t e m i θ it θt I Absent heterogeneity, reduces to 1 σ JFijt = 1 e m0 θt or jfijt = m0 θ 1 t σ

Postulating a functional form for JF(ij) Logistic functional form I With only labor market tightness heterogeneity, reduces to (1 σ)ω (1 σ)(1 ω ) jfijt = m0 θ it θt

Postulating a functional form for JF(ij) Logistic functional form I With only labor market tightness heterogeneity, reduces to (1 σ)ω (1 σ)(1 ω ) jfijt = m0 θ it θt I ω 2 [0, 1] captures impermeability of the local labor market - If ω = 1, labor market segments impossible to cross, no impact of agg θ t on jfijt (usual assumption in literature with heterogeneity) - If ω = 0 there are no barriers between labor markets, a worker’ job …nding rate only depends on the aggregate θ t . s

A decomposition of aggregate matching e¢ ciency Some algebra gives ! ln m0t ET ln m0t = h (σ, θ t ) ∑ JFtU ,k + JFtm ∆mmt + ζ t . k with θ it mmt = g (σ, ω )Var θt

A decomposition of aggregate matching e¢ ciency ln m0t ET ln m0t composition dispersion

The determinants of matching e¢ ciency 1. CPS micro data 1976-2010 2. New dataset on labor market dispersion 2006-2010+

Estimation I Matched CPS micro data 1976-2010 (1.2 million obs)

Estimation I Matched CPS micro data 1976-2010 (1.2 million obs) I Individual characteristics Xjt : - age, sex, (education, race) - reason for unemployment: quit, temp. or perm. layo¤, LF entrant - U duration & U duration interacted with avg U duration

The e¤ect of duration on JFDuration dependence is weaker in recessions =) Heterogeneity hypothesis, no hysteresis (depreciation of human capital)

Estimation I Matched CPS micro data 1976-2010 (1.2 million obs) I Individual characteristics Xjt : - age, sex, (education, race) - reason for unemployment: quit, temp. or perm. layo¤, LF entrant - U duration & U duration interacted with avg U duration I Labor market segment state/industry and θ it proxied by θt unemployment rate in state/industry uit ut

E¤ect of extended UI on search intensity I Can test the e¤ect of extended U insurance (UI) on m0t (through search intensity)

E¤ect of extended UI on search intensity I Can test the e¤ect of extended U insurance (UI) on m0t (through search intensity) I Add a dummy for period where extended UI is in e¤ect Identi…cation: (Kuang and Valletta, 2010) - Job losers eligible for UI bene…ts - Job leavers and new labor force entrants not eligible

E¤ect of composition on JF Reas on for Unemploy ment Demographic s 0.015 0.015 0.01 0.01 Changes in JF probability Changes in JF probability 0.005 0.005 0 0 -0.005 -0.005 -0.01 -0.01 -0.015 -0.015 -0.02 -0.02 -0.025 -0.025 1976 1980 1984 1988 1992 1996 2000 2004 2008 1976 1980 1984 1988 1992 1996 2000 2004 2008 Duration Searc h Effort and EEB 0.015 0.015 0.01 0.01 Changes in JF probability Changes in JF probability 0.005 0.005 0 0 -0.005 -0.005 -0.01 -0.01 -0.015 -0.015 -0.02 -0.02 -0.025 -0.025 1976 1980 1984 1988 1992 1996 2000 2004 2008 1976 1980 1984 1988 1992 1996 2000 2004 2008 Indus try c ompos ition Dis pers ion 0.015 0.015 0.01 0.01 Changes in JF probability Changes in JF probability 0.005 0.005 0 0 -0.005 -0.005 -0.01 -0.01 -0.015 -0.015 -0.02 -0.02 -0.025 -0.025 1976 1980 1984 1988 1992 1996 2000 2004 2008 1976 1980 1984 1988 1992 1996 2000 2004 2008

E¤ect of composition on JF I 2 key factors: I Fraction of permanent layo¤s (vs. temporary layo¤s and quits) I Fraction of long-term unemployed I Both of these characteristics are persistent in the U pool

Composition and matching e¢ ciency (4-qters MA) Recall:

Composition and matching e¢ ciency (4-qters MA) Using richer framework: Decom position of changes in m atching efficiency 0.1 0 Log points of jf -0.1 -0.2 Aggregate matching efficiency Composition -0.3 1976 1980 1984 1988 1992 1996 2000 2004 2008 0.1 Log points of jf 0 -0.1 Residual -0.2 1976 1980 1984 1988 1992 1996 2000 2004 2008

Composition and matching e¢ ciency I Composition explains most of ‡uctuations in m0t until 2006 I Fit particularly good after CPS redesign in 94 I mot lags the cycle because fraction of long-term U and job losers are inertial I 60% of decline in m0t unexplained after 2006

A closer look at dispersion over 2006-2010 I Very di¢ cult to measure the e¤ect of dispersion: V Need highly disaggregated data on θ i = Uii ) But limited data on Vi before 2000

A closer look at dispersion over 2006-2010 I Very di¢ cult to measure the e¤ect of dispersion: V Need highly disaggregated data on θ i = Uii ) But limited data on Vi before 2000 I Even after 2000, JOLTS provides Vit for only 10 industries and impossible to get Vit by industry and location

A closer look at dispersion over 2006-2010 I Very di¢ cult to measure the e¤ect of dispersion: V Need highly disaggregated data on θ i = Uii ) But limited data on Vi before 2000 I Even after 2000, JOLTS provides Vit for only 10 industries and impossible to get Vit by industry and location I We build a new dataset on θ it with unique level of disaggregation over 2006-2010

A closer look at dispersion over 2006-2010 I Very di¢ cult to measure the e¤ect of dispersion: V Need highly disaggregated data on θ i = Uii ) But limited data on Vi before 2000 I Even after 2000, JOLTS provides Vit for only 10 industries and impossible to get Vit by industry and location I We build a new dataset on θ it with unique level of disaggregation over 2006-2010 I V We observe θ it = Uit over 564 labor markets de…ned by it occupation (6) and location (94)

A new dataset with V data by geography and occupation Since November 2006, the Conference Board has published I Number help-wanted online ads by state and occupation I Number of ads by metropolitan statistical areas (MSA) and occupation

A new dataset with V data by geography and occupation I Ideal units have segments of equal sizes

A new dataset with V data by geography and occupation I Ideal units have segments of equal sizes I Focusing on states may be problematic because some states very large (largest unit is CA with 17% of US U) ! diminishes the likely e¤ect of dispersion

A new dataset with V data by geography and occupation I Ideal units have segments of equal sizes I Focusing on states may be problematic because some states very large (largest unit is CA with 17% of US U) ! diminishes the likely e¤ect of dispersion I By combining MSAs and States, we can get a signi…cantly less uneven distribution

A new dataset with V data by geography and occupation I Ideal units have segments of equal sizes I Focusing on states may be problematic because some states very large (largest unit is CA with 17% of US U) ! diminishes the likely e¤ect of dispersion I By combining MSAs and States, we can get a signi…cantly less uneven distribution I With 94 geo. units, largest unit (NYC) represents only 5% of US U)

A new dataset with V data by geography and occupation I Ideal units have segments of equal sizes I Focusing on states may be problematic because some states very large (largest unit is CA with 17% of US U) ! diminishes the likely e¤ect of dispersion I By combining MSAs and States, we can get a signi…cantly less uneven distribution I With 94 geo. units, largest unit (NYC) represents only 5% of US U) I By splitting further across 6 occupation groups, largest unit (NYC/sales) represents only 1.5% of US U

Measurement issue I Vi across segments may not be comparable because of di¤erent levels of informal hiring e.g., a lot of hiring in construction occurs without formal posting of a vacancy

Measurement issue I Vi across segments may not be comparable because of di¤erent levels of informal hiring e.g., a lot of hiring in construction occurs without formal posting of a vacancy I Matching function e¢ ciency mi may di¤er across segments

Measurement issue I Vi across segments may not be comparable because of di¤erent levels of informal hiring e.g., a lot of hiring in construction occurs without formal posting of a vacancy I Matching function e¢ ciency mi may di¤er across segments I Treat informal hiring as a measurement error in vacancy posting

Composition and matching e¢ ciency (4-qters MA) Recall: Decom position of changes in m atching efficiency 0.1 0 Log points of jf -0.1 -0.2 Aggregate matching efficiency Composition -0.3 1976 1980 1984 1988 1992 1996 2000 2004 2008 0.1 Log points of jf 0 -0.1 Residual -0.2 1976 1980 1984 1988 1992 1996 2000 2004 2008

Dispersion over 2006-2010 and matching e¢ ciency ) The increase in dispersion coincides with decline in match e¢ ciency!

Geographic dispersion by occupation

Dispersion over 2006-2010 and matching e¢ ciency θ it ∆mmt g (ω, σ)∆Var θt Quantitatively, dispersion accounts for 40% of decline in composition-adjusted matching e¢ ciency

Dispersion at a higher level of disaggregation I 564 labor market segments may still be too low to capture magnitude of increase in dispersion ∆Var θ it θt

Dispersion at a higher level of disaggregation I 564 labor market segments may still be too low to capture magnitude of increase in dispersion ∆Var θ it θt I Denote θ i labor market tightness over elementary labor market unit

Dispersion at a higher level of disaggregation I 564 labor market segments may still be too low to capture magnitude of increase in dispersion ∆Var θ it θt I Denote θ i labor market tightness over elementary labor market unit I We only observe segment j with n units ¯ ) measure only θ j , the average of θ i over many units

Dispersion at a higher level of disaggregation I 564 labor market segments may still be too low to capture magnitude of increase in dispersion ∆Var θ it θt I Denote θ i labor market tightness over elementary labor market unit I We only observe segment j with n units ¯ ) measure only θ j , the average of θ i over many units I A simple model shows that true dispersion θi ¯ θj Var = f (n)Varn θ θ with f (.)>1, f 0 (.)>0 and f concave.

Dispersion at a higher level of disaggregation I Empirically, can use UK data to estimate the scaling law f (n ) I UK public employment o¢ ce collects vacancies at low levels to very high levels (20,000 segments) I Estimate power law f (n ) = na , a < 1

Dispersion at a higher level of disaggregation I Construct an estimator of true Var θi θ θi ¯ θj d Var n f (n )Varn θ θ

Dispersion at a higher level of disaggregation I Construct an estimator of true Var θi θ θi ¯ θj d Var n f (n )Varn θ θ I Assuming 81 occupations and 232 geographic units in US, we get that f (n ) 6 ! With ω=0.3, increase in dispersion explains ∆mmt 0.17 log points, i.e. all decline in match e¢ ciency

Conclusion I In the US, matching e¢ ciency displays no trend, but is cyclical I Composition of U pool is responsible for cyclicality until 2006. I Fraction of job losers I Fraction of long-term U (mainly, unobserved characteristics) I Since 2006, large increase in dispersion that reduced matching e¢ ciency to record lows ! misallocation/mismatch

Future work I Just like TFP, study matching e¢ ciency across countries

UK Declining trend in matching e¢ ciency .5 Agg matching efficiency UK (log points) .4 .3 .2 .1 .0 -.1 -.2 -.3 1970 1975 1980 1985 1990 1995 2000 2005

Comparison with previous measures of mismatch In the literature, various measures to quantify the e¤ect of misallocation on the unemployment rate 1/2 I ∑ Ui U Vi V (Jackman and Roper 1987, Franz 1991, Brunello 1991), ∑ Ui Vi U V i i 2 (Bean and Pissarides, 1991) , and others ∑ Ei E U i /E i U /E V i /E i V /E (Layard, Nickell i and Jackman, 1991) I Unemployment rate dispersion measures ∑ ui2 or ∑ ui 2 u (e.g., i i Jackman, Layard and Savouri (1991), Attanasio and Padoa Schioppa (1991)) , I Some measures weighted, some not ) Absent a unifying framework, no consensus on the most appropriate measure I The measure we propose can be directly related to aggregate matching e¢ ciency and thus to the equilibrium unemployment rate

What drives matching efficiency in the labor market?

by Barcelona Graduate School of Economics (GSE)

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