The Ins and Outs of Unemployment: A
Conditional Analysis
Fabio Canova, ICREA-UPF, AMeN and CEPR
Claudio Michelacci, CEMFI and CEPR
David Lopez Salido, Federal Reserve Board and CEPR
December 2008
Motivation
- Conventional wisdom: recessions (high unemployment) begin with layoffs
and persist because unemployed can’t find jobs.
- Hall (2005) and Shimer (2007): job finding rate fluctuates; job separation
rate acyclical.
- Problems:
i) What drives fluctuations in finding rates?
ii) What is the direction of causality? Could movements in separation rates
drive fluctuations in finding rates?
iii) Do conclusions hold true for important business cycle shocks?
Contribution
- Analyze the dynamics of unemployment in technology induced recessions
(consider investment-neutral and investment-specific shocks).
- Look both the intensive margin (hours per employee) and the extensive
margin (number of employed workers) of the labor market.
- Characterize unemployment dynamics in terms of the job separation and
the job finding rates.
Results 1
- Investment-neutral technology shocks increase unemployment in the short
run and affect labor market variables along the extensive margin.
- Investment-specific technology shocks expand aggregate hours (both
hours per worker increase and unemployment falls), but the intensive margin more important.
- Impact response of unemployment is almost entirely due to a jump in the
separation rate. Dynamics due to movements in the finding rate.
- Neutral shocks important sources of cyclical fluctuations in unemployment. They explain the recession of the late 80’s and the subsequent
(jobless) recovery of the early 90’s.
Results 2
Results challenge sticky price explanation of technology shock/hours relationship (Galı́ (1999)).
- When technology improves and monetary policy is not accommodating
enough, demand is sluggish to respond and firms take advantage of technology improvements to economize on labor input.
- Naturally applies to the intensive margin - displacing workers is more
costly than changing prices.
- Extensive margin plays a key role for neutral shocks. Fall in hours is
related to the reallocation of workers across jobs. Consistent with the
Schumpeterian creative destruction (see model in Canova, et. al. (2007)).
The empirical model
- Basic specification: X = ( ∆q, ∆yn, h, u, s, f )0.
- q and GDP scaled by output deflator.
- Identification of shocks: long run restrictions as in Fisher (2006) or
Michelacci and Lopez Salido (2007).
- Use a VAR with 8 lags, a constant and a decay restriction.
- f and s: both approximate/exact flow rates as in Shimer (2005).
Problem: low frequency movements
- There is a bias in full sample results because of low frequency comovements
- Taking subsamples is inefficient and probably biased - LR restrictions
used on a small sample problematic.
- Subsample dynamics roughly unchanged; VAR constant is affected. Break
the constant at 1973:2 and 1997:1.
Neutral Shock
Investment Specific Shock
55:I-00:IV (continuous), 55:I-73:I (dotted), 73:II-97:I (dash-dotted)
0.24
Relative Price of Investment
Finding Rate
1.4
55:I-00:IV (continuous), 55:I-73:I (dotted), 73:II-97:I (dash-dotted)
-0.25
Relative Price of Investment
0.0
-0.50
0
0.08
-1.4
-0.75
-1
0.00
-2.8
-1.00
-2
-0.08
-4.2
-1.25
5
10
15
20
25
Labor Productivity
0.90
5
1
0.54
0
0.36
-1
0.18
15
20
25
Separation Rate
2
0.72
10
10
15
20
25
Unemployment
5.4
10
15
20
25
Labor Productivity
-0.0
0.0
-0.1
-0.5
-0.2
-1.0
10
15
20
25
Hours per Employee
10
15
20
25
Unemployment
1.2
0.00
0.0
-0.6
-0.24
-1.2
5
20
25
10
20
25
15
20
25
15
20
25
15
Hours per Employee
0.48
0.6
-0.16
15
-2.0
5
-0.08
10
Separation Rate
-1.5
-0.4
5
5
0.5
-0.3
0.08
3.6
-3
5
0.1
-2
5
Finding Rate
1
0.16
0.32
1.8
0.16
0.0
-1.8
-0.32
5
10
15
20
25
Hours
0.2
10
15
20
25
Output
1.00
-0.16
5
10
15
20
25
Hours
0.6
0.75
-0.0
0.00
-1.8
5
5
10
Output
0.54
0.36
0.4
0.50
0.18
-0.2
0.2
0.25
-0.4
0.00
0.0
0.00
-0.6
-0.25
5
10
15
20
25
-0.18
-0.2
5
Neutral shock
10
15
20
25
-0.36
5
10
15
20
25
5
10
Investment specific shock
Evidence
- (Positive) Neutral shock increases unemployment; hours fall. Change in
hours-per-employee small and insignificant.
- Unemployment increases on impact due to the rise in the separation rate
and of the fall in the job finding rate. The separation rate returns quickly
to normal; the job finding rate takes up to fifteen quarters to recover.
- Output takes about 5 quarters to significantly respond but then gradually
increases until it reaches its new higher long-run value.
- Positive investment specific shock increases output and hours per capita;
unemployment fall (insignificant).
- The fall of unemployment on impact is due to a drop in the separation
rate. This effect is partly compensated by a fall in the job finding rate.
- The increase in hours is due to the sharp and persistent increase in the
number of hours-per-employee.
- Labor market adjustments to neutral technology shocks along the extensive margin; those in response to an investment specific technology
shock along the intensive margin.
Neutral Shock
0.20
Relative Price of Investment
Investment Specific Shock
Finding Rate
-0.0
-0.32
Relative Price of Investment
-1.6
Finding Rate
1.8
-0.48
0.15
0.9
-0.64
0.10
0.0
-0.80
-3.2
0.05
-0.9
-0.96
0.00
-4.8
5
10
15
20
25
Labor Productivity
0.90
-1.12
5
15
20
25
Separation Rate
2.0
0.72
10
-1.8
5
10
15
20
25
Labor Productivity
0.08
5
0.0
1.5
0.00
-0.5
1.0
-0.08
-1.0
0.5
-0.16
-1.5
0.0
-0.24
10
15
20
25
20
25
20
25
20
25
Separation Rate
0.54
0.36
0.18
-0.5
5
10
15
20
25
Unemployment
4.8
10
15
20
25
Hours per Employee
0.09
-2.5
5
10
15
20
25
Unemployment
0.8
-0.00
3.2
-2.0
-0.32
5
5
10
15
Hours per Employee
0.6
-0.0
0.4
-0.09
-0.8
-0.18
1.6
0.2
-1.6
-0.27
0.0
-0.36
5
10
15
20
25
Hours
0.2
-2.4
5
10
15
20
25
Output
1.00
0.0
5
10
15
20
25
Hours
0.75
5
10
15
Output
0.70
0.75
-0.0
0.50
0.50
0.35
0.25
0.00
-0.2
0.25
-0.4
0.00
-0.6
-0.25
5
10
15
20
25
0.00
5
Neutral shock
10
15
20
25
-0.35
5
10
15
20
25
5
10
15
Investment specific shock
Approximate rates.
Neutral Shock
Relative Price of Investment
0.100
Investment Specific Shock
Finding Rate
0.0
-0.4
0.075
-1.4
0.050
0.025
-2.8
0.000
-0.025
-4.2
5
10
15
20
25
Labor Productivity
0.9
Relative Price of Investment
1.0
-0.8
0.5
-1.0
0.0
-1.2
-0.5
-1.4
5
10
15
20
25
Separation Rate
3.6
Finding Rate
1.5
-0.6
-1.0
5
10
15
20
25
Labor Productivity
0.00
5
10
15
20
25
20
25
15
20
25
15
20
25
Separation Rate
0
0.8
0.7
0.6
2.4
-0.12
-1
1.2
-0.24
-2
0.5
0.4
0.0
5
10
15
20
25
Unemployment
5
-0.36
5
10
15
20
0.00
-3
25
Hours per Employee
5
10
15
20
25
Unemployment
0.0
5
10
15
Hours per Employee
0.48
4
3
2
-0.12
-0.7
0.32
-0.24
-1.4
0.16
-0.36
-2.1
1
0
5
10
15
20
25
Hours
0.00
5
10
15
20
25
Output
1.00
0.00
5
10
15
20
25
Hours
0.6
10
Output
0.48
0.75
-0.16
5
0.32
0.4
0.50
0.16
-0.32
0.25
-0.48
0.00
0.2
0.00
-0.64
-0.16
-0.25
5
10
15
20
25
0.0
5
10
15
20
25
-0.32
5
10
15
20
25
5
10
(a) Neutral technology shock
(b) Investment specific technology shock
Exact rates (dotted lines) and approximated rates (solid lines).
Comparison exact/approximate rates
- The sign/shape of responses are similar.
- For neutral shocks: with exact rates, dynamics of the separation rate
more accentuated.
- For investment shocks with exact rates, the separation rate falls more on
impact. The fall in the unemployment rate is more pronounced (extensive
margin more important).
Difference with Hall (2005) and Shimer (2007)
- Analysis is conditional on technology shocks, rather than unconditional.
- Measures the ins and outs of unemployment on impact and over the
adjustment path, rather that at generic business cycle frequencies.
- Permits feedbacks in response to technology shocks.
Fujita and Ramey (2006) and Yashiv (2007) look unconditionally to the
same data as Hall and Shimer, but results differ.
How important is the separation rate?
- Stock of unemployment evolves as:
u̇t = S(lt − ut ) − F ut
(1)
lt =labor force and ut = unemployment, S and F are the separation and
finding rates in levels. The unemployment rate converges to the following
fictional rate:
S
exp(s)
ũ =
≡
.
S+F
exp(s) + exp(f )
- Shimer (2007): ũ close to actual unemployment rate.
- Can calculate the contribution of f and s to the cyclical fluctuations in
ũ and evaluate how accurately ũ approximates u in technology induced
recessions (misses movements in and out of the labor force).
Contribution of Separation rate
Contribution of Separation rate
u (continuous), u-fictional (dotted), Separation only (dash-dotted)
u (continuous), u-fictional (dotted), Separation only (dash-dotted)
Neutral Shock
2.7
Neutral Shock
2.7
1.8
1.8
0.9
0.9
0.0
0.0
-0.9
-0.9
5
10
15
20
25
Investment Specific Shock
-0.16
5
-0.25
-0.48
-0.50
-0.64
-0.75
-0.80
-1.00
-0.96
15
20
25
20
25
Investment Specific Shock
0.00
-0.32
10
-1.25
5
10
15
20
25
5
10
15
Approximated rates
Exact rates
True unemployment rate: solid line; ũ:dotted line. Dash-dotted is ũ|f fixed
- Impact effect of ũ after a neutral shock explained by s, especially with
exact rates (90 per cent). Contribution falls to 40 per cent after one
quarter and to 20 per cent one year after the shock.
- Impact response of actual and fictional unemployment different: flow in
and out of the labor force important.
- Following an investment specific shock, unemployment falls little on impact with approximate rates(the fall in s and the fall in f compensate each
other) and a lot with exact rates (mainly due to the fall in s).
- Impact response of actual and fictional unemployment similar: others
labor market flows small.
The contribution of technology shocks
Variable
Neutral
Horizon (quarters)
1
8 16 32
A. Approximated rates
Output
1
6 30 55
Hours
8
9
8
7
Hours per Worker
5
5
4
4
Unemployment
23 21 21 21
Finding Rate
17 17 17 17
Separation Rate
10 8
7
6
B. Exact rates
Output
8
4 17 37
Hours
22 19 18 16
Hours per Worker
14 12 11 10
Unemployment
34 30 29 27
Finding Rate
1 25 24 24
Separation Rate
34 34 30 26
Investment specific
Horizon (quarters)
1
8 16 32
3
14
17
3
0
5
5
16
23
3
1
8
5
21
29
6
2
12
4
22
29
6
2
14
14
24
35
3
0
0
8
15
27
1
1
1
6
14
28
1
2
1
6
14
28
1
3
1
- Neutral shocks explain a substantial proportion of the volatility of unemployment (20 per cent with approximate rates), little of hours (5 percent).
- Investment specific shocks account for a substantial proportion of the
volatility of hours (20 per cent of hours per capita, 30 per cent of hours
per worker) and little of unemployment (less than 10 per cent).
- With exact rates the numbers are larger.
Data and Technology component
Unemployment
Hours
32
5.0
16
2.5
0
0.0
-16
-2.5
-32
-5.0
1974
1978
1982
1986
1990
1994
1998
Finding
24
1974
1978
1982
1986
1990
1994
1998
1990
1994
1998
Separation
32
12
16
0
0
-12
-24
-16
1974
1978
1982
1986
1990
1994
1998
1974
1978
1982
1986
Original solid; component due to technology dotted
All filtered with HP(1600). Grey areas are NBER recessions.
- Technology shocks drive cyclical fluctuations in labor market variables
(more for unemployment than for hours).
- They account for several important business cycle episodes, including the
recession of the late 80’s and the subsequent remarkably slow labor market
recovery of the early 90’s.
Original solid, component due to technology shocks dotted
Exact rates. All HP(1600) filtered. The vertical lines comprise the NBER recession.
- Recession of late 1980 generated a jobless recovery (see Bernanke (2003)).
- Downturn in employment severe; peak in unemployment lags by two years
the trough in output - different from previous episodes.
- The technology component of the data tracks quite closely the evolution
of the raw data.
- Mainly due to neutral shocks that naturally induce jobless recoveries: following the initial rise in job separation and unemployment, output increases
to its new higher long run value, while unemployment remains above trend
because of the low job finding rate, which induces a remarkably slow recovery in the labor market.
Robustness
Results robust to
- omitted variables/omitted shocks.
- VAR lag length.
- Alternative treatment of low frequency components.
- Medium, sign or long-run identifying restrictions.
- Choice of Price deflators for q and GDP.
- Alternative data sets (Elsby, et. al (2007)).
Conclusions
- Neutral/investment specific shocks produce different labor market responses. VAR with just one technology shock is not enough.
- Distinction extensive vs. intensive margin important to understand propagation of technology shocks.
- Unemployment rate moved both by separation and finding rate - roughly
as conventional wisdom would suggest. On impact separation rate crucial.
- Neutral shocks important sources of cyclical fluctuations in unemployment. They explain the recession of the late 80’s and the subsequent
(jobless) recovery of the early 90’s.