The Impact of Uncertainty Shocks:
Firm-Level Estimation and a 9/11 Simulation
Nick Bloom
Stanford and Centre for Economic Performance
March 2006
Monthly US stock market volatility
Cambodia, Franklin
Kent State National
JFK
assassinated
Cuban
missile
crisis
Monetary
turning point
OPEC I
Afghanistan
OPEC II
9/11
Enron
Russia
Gulf
& LTCM
War II
Asian
Gulf War I Crisis
0
30
10
20
40
(%)
deviation
standard
Annualized
50
Black Monday*
1960
1965
1970
1975
Actual Volatility
1980
1985
Year
1990
1995
2000
2005
Implied Volatility
Note: CBOE VXO index of % implied volatility, on a hypothetical at the money S&P100 option 30 days to expiry, from 1986 to 2004. Pre 1986 the VXO index is
unavailable, so actual monthly returns volatilities calculated as the monthly standard-deviation of the daily S&P500 index normalized to the same mean and
variance as the VXO index when they overlap (1986-2004). Actual and implied volatility correlated at 0.874. The market was closed for 4 days after 9/11, with
implied volatility levels for these 4 days interpolated using the European VX1 index, generating an average volatility of 58.2 for 9/11 until 9/14 inclusive.
* For scaling purposes the monthly VOX was capped at 50 affecting the Black Monday month. Un-capped value for the Black Monday month is 58.2.
Monthly stock market levels
September 114
JFK
assassinated
Vietnam
Cuban
missile
crisis
Russian
& LTCM
Default
Cambodia,
Kent State
Asian
Crisis
Monetary cycle
turning point
OPEC I, ArabIsraeli War
Franklin National
financial crisis
WorldCom
& Enron
Black Monday3
Gulf
War II
Gulf War I
Afghanistan
0
50
OPEC II
1960
1965
1970
1975
1980
1985
Year
1990
1995
2000
2005
Note: S&P500 monthly index from 1986 to 1962. Real de-trended by deflating by monthly “All urban consumers” price index, converting to logs, removing the
time trend, and converting back into levels. The coefficient (s.e.) on years is 0.070 (0.002), implying a real average trend growth rate of 7.0% over the period.
The FOMC discussed uncertainty a lot after 9/11
Frequency of word “uncertain” in FOMC minutes
9/11
0.6%
0.5%
0.4%
0.3%
0.2%
0.1%
Ja
n
Fe
b
Ma
r
Ap
r
Ma
y
Ju
n
Ju
l
Au
g
Se
p
Oc
t
No
v
De
c
Ja
n
Fe
b
Ma
r
Ap
r
Ma
y
Ju
n
Ju
l
Au
g
0.0%
2001
2002
Source: [count of “uncertain”/count all words] in minutes posted on http://www.federalreserve.gov/fomc/previouscalendars.htm#2001
The FOMC also believed uncertainty mattered
“The events of September 11 produced a marked increase in uncertainty
….depressing investment by fostering an increasingly widespread waitand-see attitude about undertaking new investment expenditures”
FOMC minutes, October 2nd 2001
“The heightened degree of uncertainty and risk aversion following the
terrorist attack seemed to be having a pronounced effect on business
and household spending”
FOMC minutes, November 6 2001
“Because the attack significantly heightened uncertainty it appears that
some households and some business would enter a wait-and-see
mode….They are putting capital spending plans on hold”
FOMC member Michael Moskow, November 27th
and even the Brits believed this mattered too
“A general increase in uncertainty could lead to a greater reluctance to
make commitments……Labour hiring and discretionary spending are
likely to de deferred for a while, to allow time for the situation to clarify”
Bank of England minutes, October 17th 2001
Motivation
•
Major shocks have 1st and 2nd moments effects
•
Policymakers believe both matter – is this right?
– Lots of work on 1st moment shocks
– Much less work on 2nd moment shocks
•
Closest work probably Bernanke (1983, QJE)
– Predicts wave like effect of uncertainty flucatuations
• I confirm, quantify & extend this work
Summary of the paper
Stage 1: Build and estimate structural model of the firm
• Standard model augmented with
– time varying uncertainty
– mix of labor and capital adjustment costs
• Estimate on firm data by Simulated Method of Moments
Stage 2: Simulate 2nd moment shock
• Generates rapid drop & rebound in
– Hiring, investment & productivity growth
• Confirm robustness to GE, risk-aversion, and AC estimates
Stage 3: Compare to one example – 9/11
• Fits 9/11 data pretty well in magnitude and duration
– Especially with additional 1st moment shock
• Consistent with FOMC (and other central bank) comments
Model
Estimation
Results
Shock Simulations
Base my model as much as possible on literature
Investment
• Firm: Guiso and Parigi (1999), Abel
and Eberly (1999) and Bloom, Bond
and Van Reenen (2005), Chirinko
(1993)
• Macro/Industry: Bertola and
Caballero (1994) and Caballero and
Engel (1999)
• Plant: Doms & Dunn (1993),
Caballero, Engel & Haltiwanger
(1995), Cooper, Haltiwanger &
Power (1999)
Labour
• Caballero, Engel & Haltiwanger
(1997), Hamermesh (1989), Davis &
Haltiwanger (1992)
Labour and Investment
• Shapiro (1986), Hall (2004),
Merz and Yashiv (2004)
Simulation estimation
• Cooper and Ejarque (2001),
Cooper and Haltiwanger (2003),
and Cooper, Haltiwanger and
Willis (2004)
Real Options & Adjustment costs
• Abel and Eberly (1994), Abel and
Eberly (1996), Caballero &
Leahy (1996), and Eberly & Van
Mieghem (1997)
• MacDonald and Siegel (1986),
Pindyck (1988) and Dixit (1989)
Firm Model outline
Net Revenue Function, R
Model has 3 main
components
Labor & capital “adjustment costs”, C
Stochastic processes, E[ ]
Firms problem = max E[ Σt(Rt–Ct) / (1+r)t ]
Revenue function (1)
Cobb-Douglas Production


Q  AK ( L  H )
A is productivity, K is capital
L is # workers, H is hours, α+β≤1
Constant-Elasticity Demand
P  BQ
B is the demand shifter
1/ e
Gross Revenue
PQ  Y
1 a b
K (L  H )
a
b
Y is “demand conditions”, where
Y1-a-b=A(1-1/e)B
a=α(1-1/e), b=β(1-1/e)
Revenue function (2)
Firms can freely adjust hours but pay an over/under time premium

wages( H )  w1  (1  w2 H )
W1 and w2 chosen so hourly wage rate is lowest at a 40 hour week
Net Revenue = Gross Revenue - Wages

R(Y , K , L, H )  PQ  w1  (1  w2 H )  L
“Adjustment costs”
“Adjustment Cost”
Factor
Concept
Partial Irreversibility (PI)
Labor
Capital
hiring/firing cost per person
cost per unit capital resold
Quadratic (QD)
Labor
Capital
“rapid” hiring/firing more costly
“rapid” investment more costly
Fixed (FC)
Labor
Capital
lump sum hire/fire cost
lump sum investment cost
C (Y , K , L, H )  PI QD  FC
Stochastic processes (1)
“Demand conditions” evolve as a Random Walk
• Hall (1987), Evans (1987), Dunne et al. (1989) for larger/older firms
Yi ,t  Yi ,t 1  (1  μ  σ i ,t X i ,t ) X i ,t ~N( 0,1 )
1st MOMENT SHOCK
Stochastic processes (2)
Uncertainty is comprised of a firm and macro component
σ
2
i ,t
2F
i ,t
 σ σ
2M
t
Firm level uncertainty is auto-regressive
• Poterba and Summers (1986)
σ
2F
i ,t
σ
2F
i ,t 1
 ρ (σ
F
σ
2* F
σ
2F
i ,t 1
)  σ  Zi,t Zi ,t ~N( 0,1 )
F
σ
Macro level uncertainty has jumps
• From initial graph
σ
2M
t
σ
2M
t 1
 ρ (σ
M
σ
2*M
σ
2M
t 1
)  σ  St St ~{0,1}
M
σ
2nd MOMENT SHOCK
The optimisation problem is tough
Value function
V (Y , L, K ,  F ,  M , p K )  max R(Y , L, K , H )  C (Y , L, K , H , I , E , p K )
I ,E ,H

1
F
M
K

E V (Y  dY , ( L  E )(1   L ), ( K  I )(1   K ),  ,  , p )
1 r

Note: I is gross investment, E is gross hiring/firing and H is hours
Simplify by solving out 2 state and 1 control variables
– Micro and macro uncertainty similar half-life (≈ 2 months), so
assume σσM= σσF, and define σ2=σ2 F+σ2 M
– Homogenous degree 1 in (Y,K,L) so normalize by K
– Hours are flexible so pre-optimize out
Simplified value function
~
~
Q( y, l ,  , p )  max R ( y, l )  C ( y, l , i, e, p K )
K
i ,e
(1   K )(1  i )

E Q( y  dy, (l  e)(1   L ),  , p K )
1 r


Solving the model
• Analytical methods for broad characterisation:
– Unique value function exists
– Value function is strictly increasing and continuous in (Y,K,L)
– Optimal hiring, investment & hours choices are a.e. unique
• Numerical methods for precise values for any parameter set
“Demand Conditions”/Capital: Ln(Y/K)
Example hiring/firing and investment thresholds
Invest
Fire
Inaction
Hire
“Real options”
type effects
Disinvest
“Demand Conditions”/Labor: Ln(Y/L)
“Demand Conditions”/Capital: Ln(Y/K)
High and low uncertainty thresholds
Larger “Real
options” at higher
uncertainty
Low uncertainty
High uncertainty
“Demand Conditions”/Labor: Ln(Y/L)
Taking the model to real data
• Model predicts many “lumps and bumps” in investment and hiring
• See this in truly micro data – i.e. GMC bus engine replacement
– But (partially) hidden in plant and firm data by cross-sectional
and temporal aggregation
• Address this by building cross-sectional and temporal aggregation
into the simulation to consistently estimate on real data
Including cross-sectional aggregation
• Assume firms owns large number of units (plants or markets)
• Units demand process combines firm and unit shock
Yt  Yt  Yt
U
F
where YtF is a firm-level process as earlier
Yt  Y  (1    i,tUt )
U
U
t 1
U
Ut ~N( 0,1 )
ΦU relative unit
uncertainty
• Simplifying to solve following broad approach of Bertola & Caballero
(1994), Caballero & Engel (1999), and Abel & Eberly (1999)
– Assume unit-level optimization (managers optimize own “P&L”)
– Links across units in same firm all due to common shocks
Including temporal aggregation
• Shocks and decisions typically at higher frequency than annually
• Limited survey evidence suggests monthly frequency most typical
• Model at monthly underlying frequency and aggregate up to yearly
Model
Estimation
Results
Shock Simulations
Estimation overview
• Need to estimate all 20 parameters in the model
– 8 Revenue Function parameters
• production, elasticity, wage-functions, discount, depreciation and quit rates
– 6 “Adjustment Cost” parameters
• labor and capital quadratic, partial irreversibility and fixed costs
– 6 Stochastic Process parameters
• “demand conditions”, uncertainty and capital price process
• No closed form so use Simulated Method of Moments (SMM)
– In principle could estimate every parameter
– But computational power restricts SMM parameter space
• So estimate 6 adjustment cost parameters & pre-determine
the rest from the data and literature
Pre-determined parameters
Parameter:
Value:
Source:
α (capital coefficient)
1/3
Prod function estimation
β (labor coefficient)
2/3
Prod function estimation
δK (capital depreciation)
10%
Depreciation estimates
δL (labor quit rate)
10%
Matched to capital
w1 (wage parameter)
1/3
10 employees per unit
w2 (wage parameter)
7e-06
40 hour working week
γ (wage parameter)
2.5
Overtime share 27%
μ (demand drift)
5%
Compustat average growth
ε (demand elasticity)
-3
50% mark-up
pk* (capital price process) 1
Normalized to unity
ρpk (capital price process) 0.12
NBER 4-digit industry data
σpk (capital price process) 0.27
NBER 4-digit industry data
σ* (uncertainty process)
0.29
Firm level share returns vol
Fσ (uncertainty process)
0.16
Firm level share returns vol
ρσ (uncertainty process)
0.42
Firm level share returns vol
Simulated Method of Moments estimation
• SMM minimizes distance between actual & simulated moments
A
S
A
S
ˆ
  min [   ()]' W [   ()]

actual
data
moments
simulated
moments
weight
matrix
• Efficient W is inverse of variance-covariance of (ΨA - ΨS (Θ))
• Lee & Ingram (1989) show under the null W= (Ω(1+1/κ))-1
– Ω is VCV of ΨA, bootstrap estimated
– κ simulated/actual data size, I use κ=10
Data is firm-level from Compustat
• 10 year panel 1991 to 2000 to “out of sample” simulate 9/11
• Large continuing manufacturing firms (>500 employees, mean 4,500)
– Focus on most aggregated firms
– Minimize entry and exit
• Final sample 579 firms with 5790 observations
Note: This methodogly enables use of public firm data, avoiding the
need to access the LRD and allowing match to firm financial data etc.
Model
Estimation
Results
Shock Simulations
TABLE 2
Actual SMM Estimate
“Adjustment
cost”
estimates
Labor
estimation
moments
Capital
estimation
moments
Labor hire/fire costs (PI)
4.9 weeks wages
Labor fixed costs (FC)
2.4 weeks revenue
Labor quadratic costs (QD)
0
Capital resale cost (PI)
42.1% price capital
Capital fixed costs (FC)
0.3 weeks revenue
Capital quadratic costs (QC)
4.74 of K*(I/K)2
Std (ΔL/L)
0.197
0.234
Skew (ΔL/L)
0.213
0.437
Corr (ΔL/L)t, (ΔL/L)t-2
0.111
0.106
Corr (ΔL/L)t, (I/K)t-2
0.102
0.152
Corr (ΔL/L)t, (ΔS/S)t-2
0.137
0.174
Std (I/K)
0.141
0.146
Skew (I/K)
1.404
1.031
Corr (I/K)t, (ΔL/L)t-2
0.139
0.207
Corr (I/K)t, (I/K)t-2
0.305
0.318
Corr (I/K)t, (ΔS/S)t-2
0.210
0.325
Closer match
between left
and right
columns of
moments
means a
better fit
Results for estimations on restricted models
Capital “adjustment costs” only
• Fit is only moderately worse
• Both capital & labor moments reasonable
• So capital ACs and (σt,pK) dynamics approximate labor ACs
Labor “adjustment costs” only
• Labor moments fit is fine
• Capital moments fit is bad (too volatile & low dynamics)
• So OK for approximating labor data
Quadratic “adjustment costs” only
• Poor overall fit (too little skew and too much dynamics)
• But industry and aggregate data little/no skew and more dynamics
• OK for approximately more aggregated data
Robustness - measurement error (ME)
• Labor growth data contains substantial ME from
– Combination full time, part-time and seasonal workers
– Rounding of figures
– First differencing to get ΔL/L
• Need to correct in simulations to avoid bias
• I estimate ME using a wage equation and find 11%
– Hall (1989) estimates comparing IV & OLS & finds 8%
• Then build 11% ME into main SMM estimators
– Also robustness test without any ME and find larger FCL
Robustness – volatility measurement
• Volatility process calibrated by share returns volatility
– But could be concerns over excess volatility due to “noise”
• Jung & Shiller (2002) suggest excess volatility more macro problem
• Vuolteenaho (2002) finds “cash flow” drives 5/6 of S&P500 relative
returns
• Use 5/6 relative S&P500 returns variance and results robust
– Find slightly higher adjustment costs
Model
Estimation
Results
Shock Simulations
Simulating 2nd moment uncertainty shocks
Structurally simulate shocks hard because big and unprecedented
To recap combined micro and macro uncertainty process is as follows
σ σ
2
i ,t
2
i ,t 1
2*
 ρσ(σ  σ
2
i ,t 1
)  σ  Zi ,t  σ  St
F
σ
M
σ
where σ2*=σ2F*+σ2M* and ρσ=ρσM=ρσF
St ~{0,1}
Macro uncertainty shock
Simulation of macro shock sets St=1 for one period
• σMσ = σ* so shock doubles average σ2i,t
• Calibrated from doubling macro share volatility after large shocks
Auto-regressive σt approximated by Markov-chain
Tauchen & Hussey (1991) to define 5-point space and transition matrix
- Normal times (St=0) calibrated from firm share returns volatility
σ=8%
σ=17%
σ=25%
σ=38%
σ=76%
σ=8%
0.645
0.249
0.084
0.020
0.002
σ=17%
0.249
0.361
0.255
0.115
0.020
σ=25%
0.084
0.255
0.321
0.255
0.084
σ=38%
0.020
0.255
0.255
0.361
0.249
σ=76%
0.002
0.020
0.084
0.249
0.645
- Shock period (St=1) calibrated to double uncertainty
σ=8%
σ=17%
σ=25%
σ=38%
σ=76%
σ=8%
0.001
0.008
0.033
0.132
0.825
σ=17%
0.000
0.000
0.000
0.007
0.993
σ=25%
0.000
0.000
0.000
0.001
0.999
σ=38%
0.000
0.000
0.000
0.000
1.000
σ=76%
0.000
0.000
0.000
0.000
1.000
Simulation uncertainty macro “impulse”
Average Uncertainty (σi,t)
uncertainty shock
Run model monthly
with 100,000 firms for 5
years to get steady
state then hit with
uncertainty shock
Month
Simulation percentiles of firm uncertainty
uncertainty shock
Uncertainty (σt)
90th Percentile
uncertainty shock
shifts distribution
of σit upwards
75th Percentile
50th Percentile
25th Percentile
Month
10th Percentile
Actual percentiles of firm volatility after 9/11
100
9/11
Actual Compustat firm level data
Real 9/11 shock
did actually shift
distribution of
returns volatility
upwards
50
90th Percentile
75th Percentile
0
50th Percentile
25th Percentile
10th Percentile
2001.5
Monthly data
2002
Year
Calculated from CRSP daily share returns volatility within each month of balanced panel of 1,052 firms in CRSP-Compustat matched sample with over 500
employees and full daily trading data from 1990 to 2003. 9/11 month volatility taken from the first trading day after the attack until the end of the month (the 9
trading days from 9/17/2001 until 9/28/2001).
sd10
sd25
Aggregate net hiring rate (%)
Net hiring rate
uncertainty shock
Month
Percentiles of firm net hiring rates (%)
Net hiring rate
99th Percentile
95th Percentile
5th Percentile
1st Percentile
Month
Macro gross investment rate (%)
Investment rate
uncertainty shock
Month
Firm percentiles of gross investment rates (%)
Investment rate
99th Percentile
95th Percentile
5th Percentile
1st Percentile
Month
Productivity growth rate (%)
Productivity growth
uncertainty shock
Total
Between
Within
Cross
Productivity & hiring,
period of shock
Gross hiring rate
Gross hiring rate
Productivity & hiring,
period before shock
Month
Productivity (logs)
Productivity (logs)
GDP loss from 2nd moment shock
Estimate rough magnitude of GDP loss, noting
• Only from temporary 2nd moment shock (no 1st moment effects)
• Ignores GE (will discuss shortly) so only look at first few months
GDP loss from an uncertainty shock (% of annual value)
First 2 months
First 4 months
First 6 months
Input Factors
0.30
0.74
1.16
TFP (reallocation)
0.07
0.11
0.14
Total
0.37
0.85
1.30
Reasonable size – uncertainty effects wipes out growth for ½ half year
Investment rate
After a 1st moment shock
expect standard U-shape
downturn, bottoming out
after about 6-12 months
Hiring rate
After a 2nd moment shock
everything drops – just
like a 1st moment shock
- but then bounces back
within 1 month
Prod. growth
Highlights importance identifying 1st & 2nd moment
components of shocks
To distinguish try using:
(i) volatility indicators;
(ii) plant spread;
to help distinguish
Month
Robustness – Risk aversion
• Earlier results assumed risk-neutrality
• But can model discount rate (r) as a function of uncertainty
• Re-simulate with an “ad-hoc” risk aversion correction
– Calibrated so that increases average (r) by 2.5%
Investment rate
uncertainty shock
risk-neutral
risk-averse
Month
Robustness – Adjustment costs estimation
• Need some non-convex costs - nothing with convex ACs only
• Robust to type non-convex ACs (Dixit (1993) and Abel & Eberly
(1996) show thresholds infinite derivate AC at AC≈0 )
PI=10%, all other AC=0
Aggregate Hiring
Hiring Distribution
Productivity
Hiring Distribution
Productivity
FC=1%, all other AC=0
Aggregate Hiring
Robustness - General Equilibrium effects
• Could build in GE using approximation for the cross-sectional
distribution of firms
– But need another program loop, so much slower - thus choice
between: (i) estimating ACs, or (ii) doing GE
– Estimate ACs as more sensitive to this and do GE later
• Less sensitive to GE for two reasons
– Uncertainty shocks very rapid and big, but wages and prices
“sticky” at monthly frequency and interest rates bounded at zero
• Uncertainty shock adds 6% to 10% to hurdle rates, but after
9/11 interest rates fell by only 1.75%
– Drop and rebound optimal with GE anyway as correct factor
allocation unclear, expensive to change so a pause is good
Robustness – Combined 1st and 2nd moment shock
• Earlier results 2nd moment shock only ~ thought experiment
• But shocks typically have 1st and 2nd moment component
Investment rate
• Re-simulate assuming
– 2nd moment shock (doubles uncertainty as before)
– 1st moment shock (-5% ≈ 1 years growth)
2nd moment shock
1st & 2nd moment shock
Month
How does the simulation fit against actual data?
Look at 9/11 because
• Large 2nd moment shock with relatively small 1st moment effect
– So “cleaner” test of the model
• Recent, so can match up data for
– Central Bank minutes (FOMC from 1996, BOE from 1997)
– Consensus forecasts (from 1998)
9/11 did generate a rapid drop and rebound
Quarterly Net Hiring (total private, thousands) 1
9/11
0
Forecast of 23rd
August 20013
Lowest quarterly value since 1980
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Year
Quarterly Investment (% contribution to real GDP growth) 2
forecast
dempq
dempq1
0
5
Forecast of 23rd
August 20013
-5
Lowest quarterly value since 1982
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Year
1
BLS Current Employment Statistics survey,
Total private employees (1000s), seasonally adjusted, quarterly net change, from series CES0500000001
forecast
z
BEA National Income and Product Accounts,
Contributions
to % change
in real Gross Domestic
Product, seasonally adjusted at annual rates, from Table 1.1.2
Gross
private
domestic
investment
3 Federal Reserve Bank of Philadelphia “Survey of Professional Forecasters” average of 33 economic forecasters, www.phil.frb.org/file/spf/survq301.html
2
9/11 did generate a rapid drop and rebound
Quarterly Net Hiring (total private, thousands) 1
9/11
Forecast of 23rd
August 20013
Forecast of 14th
November 2001
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Year
Quarterly Investment (% contribution to real GDP growth) 2
forecast1
Forecast of 23rd
August 20013
0
5
forecast
dempq
-5
Forecast of 14th
November 2001
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Year
1
BLS Current Employment Statistics
survey, Total private employees (1000s), seasonally adjusted, quarterly net change, from series
CES0500000001
forecast
forecast1
BEA National Income and ProductGross
Accounts, Contributions
% change in realinvestment
Gross Domestic Product, seasonally adjusted at annual rates, from Table 1.1.2
private to
domestic
3 Federal Reserve Bank of Philadelphia “Survey of Professional Forecasters” average of 33 economic forecasters, www.phil.frb.org/file/spf/survq301.html
2
THE POLICY VERDICT
Looks like the FOMC did the right thing after 9/11
• Pumped in liquidity to reduce uncertainty
• Did not cut interest rates much
– Cut Federal Funds Rates by 1.75%, but this was already falling
(2-year market rates fell be less than 1%)
Congress on the other hand was not so perfect…
• “A key uncertainty in the outlook for investment spending was the
outcome of the ongoing Congressional debate relating to tax
incentives for investment in equipment and software. Both the
passage and the specific contents of such legislation remained in
question”
FOMC Minutes, November 6th 2001
A QUICK HISTORICAL DIGRESSION
(not really part of the paper)
The Great Depression was notable for very high volatility
60
90
The Great
Depression
0
30
9/11
1880
1890
1900
1910
1920
Year
1930
1940
1950
1960
Note: Volatility of the daily returns index from “Indexes of United States Stock Prices from 1802 to 1987” by Schwert (1990). Contains daily stock returns to the
Dow Jones composite portfolio from 1885 to 1927, and to the Standard and Poor’s composite portfolio from 1928 to 1962. Figures plots monthly returns
volatilities calculated as the monthly standard-deviation of the daily index, with a mean and variance normalisation for comparability following exactly the same
procedure as for the actual volatility data from 1962 to 1985 in figure 1.
Did uncertainty play a role in the Great Depression?
• Romer (1990) suggests uncertainty played a role in the initial 19291930 slump, which was propagated by the 1931 banking collapse
“during the last few weeks almost everyone held his plans in
abeyance and waited for the horizon to clear”, Moody’s 12/16/1929
• In the model a GD sized persistent increase in uncertainty would
also generate persistently slower productivity growth
• TFP “inexplicably” fell by 18% from 1929-33 (Ohanian, 2001)
• Output “oddly” not shifted to low-cost firms (Bresnahan &
Raff, 1991)
GNP growth in the Great Depression
Fall in
Rise in
volatility volatility
Banking
panics
Source: Romer (1992, JEH)
END OF DIGRESSION
Conclusions
• Uncertainty spikes after major economic & political shocks
• Estimation and simulation predicts rapid drop & rebound
– For 9/11 appears to roughly match actual data
• This time profile looks different from a levels shock
• Suggests policy makers try to distinguish levels & uncertainty effects
– Financial volatility (VXO) and compression of firm activity
Current extension in progress
Build GE model by approximating cross-sectional distribution. Should
help with a number of business-cycle issues, in particular:
• Lack of negative TFP shocks - 2nd moment shocks mimic these
(especially after detrending)
• Drop on impact for TFP shocks - 1st moment shocks raise uncertainty
when the shock first hits (dynamic inference)
• Instability of VARs without 2nd moment controls
Also model link between volatility and growth – less reallocation (which
drives about ½ to ¾ of TFP growth) at higher uncertainty
Approximating cross-sectional distributions
Number of ways to approximate cross sectional distributions, i.e.
– Moments (Krussell and Smith)
– Characteristics functions (Caballero and Engel)
I use bins exploiting the fact agents know distribution is bounded, i.e:
Actual distribution
Bin approximation
Capital/Demand (K/Y)
BACK-UP
“Adjustment costs” (2)
• 1 period time to build
• Exogenous quit rate δLand depreciation rate δK
• Relative capital price is AR(1) stochastic
p  p  ρ p K (p  p )  σ p K U t
K
t
K
t 1
K*
K
t 1
U t ~N( 0,1 )
Impact of a levels shock looks different
1st moment shock (3%)
Hiring
1st moment shock (3%)
Investment
Month
Month
Total
Between
Within
Cross
99th percentile
95th percentile
Hiring
percentiles
Productivity
5st percentile
1st percentile
Month
Month
Robustness- general equilibrium effects (2)
• Thomas (2002) and Veracierto (2002) suggest GE important
– In particular they find under GE
dM t
d(
)
dYt
0
dNC
Mt is a BC variable like labor, or capital
Yt is aggregate productivity/demand
NC is some non-convex cost
– But I look at
dM t
d t
σt is uncertainty
• So correctly highlight importance of GE, but on a different issue
Also need to deal with aggregation
Structures Equipment Vehicles
Total
Firms
5.9
0.1
n.a.
0.1
Establishments
46.8
3.2
21.2
1.8
Single plants
53.0
4.3
23.6
2.4
Small single plants 57.6
5.6
24.4
3.2
Aggregation across lines of capital
standard deviation/mean of growth rates (US firm data)
Quarterly
Yearly
Sales
6.78
2.97
Investment
1.18
0.84
Aggregation across time
Aggregation across units
% annual zero investment episodes (UK Firm and Plant data)
8
Interest rates
Federal
Funds rate
2-year rate (T-Bill)
2
4
6
9/11
2000
2001
2002
2003
2004
2005
Year
3-year T-Bills
ir
Fiscal position ≈ flat 2001-02 excluding personal tax cuts
% GDP
01 Q1
01 Q2 01 Q3
01 Q4
02 Q1
02 Q2 02 Q3 02 Q4
Budget surplus
1.1
0.5
-1.8
-1.3
-3.3
-3.7
-3.7
-4.3
…exc. personal tax
-11.8
-12.5
-12.7
-13.4
-13.6
-13.7
-13.6
-13.9
Source: Federal Reserve Board Statistical Release - http://www.federalreserve.gov/releases/H15/data.htm
Employment quits, layoffs and
9/11
Month
Source: Hall (2005a)
“Adjustment costs” (1)
Active literature with range of approaches, e.g.
Labor or capital
Labor and Capital
Convex1
Traditional Euler and Tobin’s Q Shapiro (1986); Hall (2004),
models
Merz and Yashiv (2003)
Convex1 and
Non-Convex2
Abel & Eberly (1999); Cooper
& Haltiwanger (2003); Cooper,
Haltiwanger and Willis (2004)
I look at convex & non-convex
adjustment costs for both labor
and capital
1
Convex typically quadratic adjustment costs
2 Non-convex typically fixed cost or partial irreversibility