Slow to Hire, Quick to Fire: Employment Dynamics with Asymmetric Responses to News Cosmin Ilut
Matthias Kehrig
Martin Schneider
Duke & NBER
UT & Mannheim
Stanford & NBER
September 2014
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Motivation Cyclical changes in employment growth distributions I I
aggregate: conditional volatility; “macro volatility” firm level: cross-sectional dispersion; “micro volatility”
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US employment growth 0.06
0.24
Ind. Employment Growth Cross−Sect. Inter−Quartile Range 0.03
0.22
0
0.2
−0.03
0.18
−0.06
0.16
−0.09
0.14
−0.12
1975
1980
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1990
1995
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0.12
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Motivation Cyclical changes in employment growth distributions I I
aggregate: conditional volatility; “macro volatility” firm level: cross-sectional dispersion; “micro volatility”
What is the link? I
Correlated shocks? Cross-section (‘micro’) vs aggregate (‘macro’)
This paper: Concave responses to idiosyncratic signals Empirical contribution: Hiring policy of firms is strongly concave I Quantitative contribution: Mechanism can explain 75% of volatility changes and all of observed asymmetry (negative skewness) I consistent with new empirical fact: negative skewness ⇒ generate simultaneous and endogenous changes in volatility and dispersion from symmetric and homoskedastic shocks I I
Background
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Asymmetric responses can explain micro & macro volatility Consider simple setup with two model ingredients 1
Firms choose labor given dispersed signals about profits I
2
e.g. signals about TFP, demand
Firms respond more to bad signals than to good signals Examples: I I
Adjustment costs – hiring more costly than firing Information processing – with ambiguous signal quality, firms optimally respond as if bad signals more precise
Consequences: micro volatility: employment dispersion high in bad times macro volatility: conditional volatility high in bad times employment dispersion across firms negatively skewed: average contracting firm further from the mean than average expanding firm aggr. employment growth asymmetric: sharp recessions, meek booms BUT: Is hiring really a concave function of shocks? Does it matter? Ilut/Kehrig/Schneider (Duke/UT/Stanford)
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Data Annual Survey of Manufactures (ASM/CMF) I I I
annual data 1972-2011 55k establishments per year; 2.2m total data on all inputs and output of an establishment: sales, inventories, employees, hours, capital; also: investment expenditures, industry, ...
Plant Capacity Utilisation Survey (PCU) I I
subset of ASM; 5k establishments per year; 200k total additional information on utilisation and hiring constraints
NBER Manufacturing Database I
6-digit NAICS industry deflators for sales, material and energy inputs
BLS price data I
deflators for equipment and structure investment
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Estimating the hiring response to TFP shocks Estimate establishment-level Solow residual I
TFP
detrended Solow residual with aggregate and idiosyncratic innovations i Zti = ρZt−1 + uat + uit
I
data: innovations not skewed over time or cross-section
Interested in shape of hiring response to TFP signals: ∆et = f (sit ) I
firm receives signals sit on TFP innovations sit = uat + vta + uit + vti
I
Gua , Gui , Gva , Gvi are time-invariant and symmetric distributions! recover conditional expectation g(uat + uit ) = E f (sit )|uat + uit inference about f (sit ) not affected by var(uit |uat )
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5
12
4
8
3
4
2
0
z: 0.18 n: 0.7
z: 0 n: 0 z: −0.18 n: −1.8
1
0 −0.5
−4
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
Employment Growth: non−parametric estimate (in %)
Density of TFP innovations
Non-parametric evidence: Hiring response is concave
−8
TFP Innovation Ilut/Kehrig/Schneider (Duke/UT/Stanford)
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Asymmetric responses can explain micro & macro volatility
Bad aggregate shock: I I I
more firms get negative signals & respond strongly... on average → strong decrease in aggregate employment to idiosyncratic signals → increase in cross-sectional dispersion
Good aggregate shock: I I I
more firms get positive signals & respond weakly... on average → weak increase in aggregate employment to idiosyncratic signals → decrease in cross-sectional dispersion
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employment growth
Asymmetric responses can explain micro & macro volatility
signal about profitability
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employment growth
Bad aggregate shock
signal about profitability
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employment growth
Bad vs Good aggregate shock
signal about profitability
More Ilut/Kehrig/Schneider (Duke/UT/Stanford)
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Countercyclical micro & macro volatilities For any two aggregate shock realizations a < a0 , 1
higher measures of cross-sectional dispersion at a: I
conditional volatility: var (∆e|a) > var (∆e|a0 )
I
¯: range between any two quantiles x and x −1 0 x|a) − G−1 x|a0 ) − G−1 G−1 ∆e (¯ ∆e (x|a) > G∆e (¯ ∆e (x|a )
2
higher sensitivity of aggregate action wrt aggregate shock at a: d d E [∆e|˜ a] > E [∆e|˜ a] d˜ a d˜ a a ˜=a a ˜=a0
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Illustrative time series 0.5
0.3 Aggregate TFP Aggregate Hiring Cross−sectional IQR
0.4 0.3
0.1 0
0.2
−0.1
Cross−sectional IQR
Aggregate Hiring
0.2
−0.2 −0.3 −0.4 −0.5
Higher aggregate volatility 0
2
4
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Aggregate US employment volatility is countercyclical Lower aggregate volatiltiy 0.04 0.02 0 −0.02 −0.04 −0.06 −0.08 −0.1
Higher aggregate volatility
−0.12 1975
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Micro & macro skewness should be negative Skewness of random variable x: h i E (x − E [x])3 γ (x) =
3
var (x) 2
Concave response induces negative skewness 1
Cross section: for any a, conditional skewness of employment growth lower than that of signals: γ (∆e|a) < γ (s|a)
2
Time series: unconditional skewness of aggregate employment lower than that of common signal: γ (E [∆e|a]) < γ (a)
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employment growth
Concave response leads to negative skewness
signal about profitability
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Employment across US firms is negatively skewed 0
0
−0.002
−0.2
−0.004
−0.4
−0.006
−0.6
−0.008
−0.8
−1
−0.01
−0.012
−0.014
3rd moment Skewness 1975
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−1.4
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Illustrative time series 0.5
0.3 Aggregate TFP Aggregate Hiring Cross−sectional IQR
0.4 0.3
0.1 0
0.2
−0.1
Cross−sectional IQR
Aggregate Hiring
0.2
−0.2
Negative skew
−0.3 −0.4 −0.5
0
2
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Employment growth is negatively skewed
Cross-sectional skewness across establishments for a given year I
data: average Skewnesst = −0.4; negative every year and acyclical
Time-series skewness of individual establishment I
data: average Skewnessi = −0.38; employment weighted = −0.55
Time-series skewness of aggregate employment growth I
data: = −0.91; employment weighted: = −0.83
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Concave hiring response to TFP shocks
Relate industry skewness to industry concavity index: φg ≡ 1 − I I I
[g 0 (0)]2 var(u) var [g(u)]
share of variance in g(u) explained by linear term φg ≈ 0.46 industry comparison: higher φg should imply more negatively skewed employment distribution
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More asymmetric industries are more negatively skewed XS Skewness(Empl.) − XS Skewness(TFP Innov.)
0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −1 −1.2 −1.4 −1.6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Asymmetry Ilut/Kehrig/Schneider (Duke/UT/Stanford)
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Quantitative analysis Given estimated hiring rule how much dispersion and skewness can our setup generate? Simulate TFP shocks for a cross section of 50k firms and 40 years; use estimated hiring rule to compute fitted employment response how do simulated moments compare to actual ones? Moment Data Simulation A. Cross sectional moments IQRrec −1 28% 22% IQRboom γ(x) -0.48 -1.17 E[x|x<0] -1.47 -1.73 E[x|x≥0] B. Time series moments Firm-level skewness -0.55 -1.12
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Conclusion Objective: endogenous joint changes in distributions I I I
volatility and skewness in aggregate and firm-level employment growth from symmetric and homoskedastic shocks model of concave decision rules
Key mechanism I I
firms receive dispersed signals firms optimally respond more to bad than to good signals
The concave response generates: I I I
countercyclical aggregate volatility and cross-section dispersion negative skewness in the time-series and cross-section model’s key properties consistent with micro and macro data and quantitatively relevant
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Literature 1
Exogenous uncertainty shocks I
I
2
‘macro’ stochastic volatility: Stock and Watson (2003), Justiniano and Primiceri (2008), Gourio (2010), Fernandez-Villaverde and Rubio-Ramirez (2011), Basu and Bundick (2011), Bloom et al. (2012) ‘micro’ stochastic volatility: Bloom (2009), Arellano et al. (2010), Gilchrist et al. (2010), Chugh (2012), Bloom et al. (2012), Schaal (2012), Bachmann and Bayer (2013), Christiano et al. (2014)
Endogenous uncertainty I
I
I
I
3
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aggregate volatility clustering in actions: non linearity in decision rules Gourio (2013), Bianchi and Mendoza aggregate volatility clustering in beliefs: non linearity in learning Orlik and Veldkamp (2013), Fajgelbaum et al. (2013) asymmetric business cycle: Chakley and Lee (1998), van Nieuwerburgh and Veldkamp (2006), Ferraro (2013) cross-sectional dispersion in actions: Bachmann and Moscarini (2011), Tian (2012), D’Erasmo et al. (2014)
Empirical cross-sectional variation I
Eisfeldt&Rampini (2006), Kehrig (2013), Bachmann&Bayer (2014), Slow to Hire, Quick to Fire September 2014 25 / 30 Bloom (2012)
Ilut/Kehrig/Schneider (Duke/UT/Stanford)
Countercyclical micro & macro volatilities For any two aggregate shock realizations a < a0 , 1
higher measures of cross-sectional dispersion at a: I
conditional volatility: var (∆e|a) > var (∆e|a0 )
I
¯: range between any two quantiles x and x −1 0 G−1 x|a) − G−1 x|a0 ) − G−1 ∆e (¯ ∆e (x|a) > G∆e (¯ ∆e (x|a )
2
higher sensitivity of aggregate action wrt aggregate shock at a: d d E [∆e|˜ a] > E [∆e|˜ a] d˜ a d˜ a a ˜=a a ˜=a0
Back to 2nd moment Ilut/Kehrig/Schneider (Duke/UT/Stanford)
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Illustrative time series 0.5
0.3 Aggregate TFP Aggregate Hiring Cross−sectional IQR
0.4 0.3
0.1 0
0.2
−0.1
Cross−sectional IQR
Aggregate Hiring
0.2
−0.2 −0.3 −0.4 −0.5
0
2
4
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A model candidate for asymmetry: information processing Continuum of firms I I
beginning of period: get signal about TFP & choose employment end of period: TFP realized
Firm i’s log productivity and signal: zti = uat + uit −
1 2 σa + σu2 2
Ambiguous signals (set of beliefs about variance of noise) sit = zti + σε,t εit ;
σε,t ∈ [σ ε , σ ε ]
Firm maximizes worst case expected profit i α max min E σε exp zti Lt − wLit Lit [σ ε ,σ ε ]
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Stronger response to bad vs good signals Define relative precision γt =
var(zti ) 2 var(zti ) + σε,t
Firm problem simplifies to max min exp γt sit Lit
[σ ε ,σ ε ]
Lit
α
− wLit
Hiring decision: asymmetric, based on ‘worst case’ precision 1 hα i 1−α γ if sit < 0 i ∗ i ∗ Lt = exp γt st ; γt = γ if sit ≥ 0 w Worst case precision: high for bad news, low for good news.
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Estimating technology shocks 1
Constructing Solow residuals from Cobb-Douglas production function (in logs) yijt = srijt + βjk kijt + βjl lijt + βje eijt + βjm mijt I I
i establishment, j industry, t time P Pi∈j,t Wage billijt 1 l P βj = T t revenues i∈j,t
2
ijt
Constructing measure of TFP innovations I I I I
srijt = gj t + Aj + αij + Zijt gj : average long-run productivity growth of industry j αij : firm-specific fixed effect Zijt : stochastic technology; assumed to follow AR(1) Zijt = ρj Zijt−1 + uijt
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