The Impact of Uncertainty Shocks: Firm-Level Estimation and a 9/11 Simulation Nick Bloom Stanford and Centre for Economic Performance March 2006

1
The Impact of Uncertainty ShocksFirm-Level
Estimation and a 9/11 SimulationNick
BloomStanford and Centre for Economic
PerformanceMarch 2006
2
Monthly US stock market volatility
Black Monday
9/11
Russia LTCM
Enron
Franklin National
Cambodia,Kent State
Gulf War II
Monetary turning point
JFK assassinated
Asian Crisis
OPEC I
Afghanistan
Cuban missile crisis
Gulf War I
OPEC II
Annualized standard deviation ()
Actual Volatility
Implied Volatility
Note CBOE VXO index of implied volatility, on
a hypothetical at the money SP100 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 SP500 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.
3
Monthly stock market levels
September 114
Russian LTCMDefault
JFK assassinated
Vietnam
Asian Crisis
Cuban missile crisis
Cambodia, Kent State
Monetary cycle turning point
WorldCom Enron
OPEC I, Arab-Israeli War
Black Monday3
Gulf War II
Gulf War I
Franklin National financial crisis
Afghanistan
OPEC II
Note SP500 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.
4
The FOMC discussed uncertainty a lot after 9/11
Frequency of word uncertain in FOMC minutes
9/11
2001
2002
Source count of uncertain/count all words in
minutes posted on http//www.federalreserve.gov/fo
mc/previouscalendars.htm2001
5
The FOMC also believed uncertainty mattered
The events of September 11 produced a marked
increase in uncertainty .depressing investment
by fostering an increasingly widespread
wait-and-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 spendingFOMC 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
holdFOMC member Michael Moskow, November 27th
6
and even the Brits believed this mattered too
A general increase in uncertainty could lead to
a greater reluctance to make commitmentsLabour
hiring and discretionary spending are likely to
de deferred for a while, to allow time for the
situation to clarifyBank of England minutes,
October 17th 2001

7

• 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

8
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

9
Model
Estimation
Results
Shock Simulations
10
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)

11
Firm Model outline
Net Revenue Function, R
Model has 3 main components
Labor capital adjustment costs, C
Stochastic processes, E
Firms problem max E St(RtCt) / (1r)t
12
Revenue function (1)

• Cobb-Douglas Production
• A is productivity, K is capital
• L is workers, H is hours, aß1
• Constant-Elasticity Demand
• B is the demand shifter
• Gross Revenue
• Y is demand conditions, where
• Y1-a-bA(1-1/e)B aa(1-1/e),
  bß(1-1/e)

13
Revenue function (2)

• Firms can freely adjust hours but pay an
  over/under time premium
• W1 and w2 chosen so hourly wage rate is lowest at
  a 40 hour week

Net Revenue Gross Revenue - Wages
14
Adjustment costs
Concept
Adjustment Cost Factor

• hiring/firing cost per person
• cost per unit capital resold
• rapid hiring/firing more costly
• rapid investment more costly
• lump sum hire/fire cost
• lump sum investment cost

Partial Irreversibility (PI) Labor Capital Qu
adratic (QD) Labor Capital Fixed
Labor Capital
Partial Irreversibility (PI) Labor Capital Qu
adratic (QD) Labor Capital Fixed (FC)
Labor Capital
15
Stochastic processes (1)

• Demand conditions evolve as a Random Walk
• Hall (1987), Evans (1987), Dunne et al. (1989)
  for larger/older firms

1st MOMENT SHOCK
16
Stochastic processes (2)
Uncertainty is comprised of a firm and macro
component

• Firm level uncertainty is auto-regressive
• Poterba and Summers (1986)

• Macro level uncertainty has jumps
• From initial graph

2nd MOMENT SHOCK
17
The optimisation problem is tough
Value function
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 ssM ssF, and define s2s2
  Fs2 M
• Homogenous degree 1 in (Y,K,L) so normalize by K
• Hours are flexible so pre-optimize out

Simplified value function
18
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

19
Example hiring/firing and investment thresholds
Invest
Demand Conditions/Capital Ln(Y/K)
Hire
Inaction
Fire
Real options type effects
Disinvest
Demand Conditions/Labor Ln(Y/L)
20
High and low uncertainty thresholds
Larger Real options at higher uncertainty
Low uncertainty
Demand Conditions/Capital Ln(Y/K)
High uncertainty
Demand Conditions/Labor Ln(Y/L)
21
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

22
Including cross-sectional aggregation

• Assume firms owns large number of units (plants
  or markets)
• Units demand process combines firm and unit shock
• where YtF is a firm-level process as
  earlier
• FU 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 PL)
• Links across units in same firm all due to common
  shocks

23
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

24
Model
Estimation
Results
Shock Simulations
25
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

26
Pre-determined parameters
Parameter Value Source
a (capital coefficient) 1/3 Prod function estimation
ß (labor coefficient) 2/3 Prod function estimation
dK (capital depreciation) 10 Depreciation estimates
dL (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
? (wage parameter) 2.5 Overtime share 27
µ (demand drift) 5 Compustat average growth
e (demand elasticity) -3 50 mark-up
pk (capital price process) 1 Normalized to unity
?pk (capital price process) 0.12 NBER 4-digit industry data
spk (capital price process) 0.27 NBER 4-digit industry data
s (uncertainty process) 0.29 Firm level share returns vol
Fs (uncertainty process) 0.16 Firm level share returns vol
?s (uncertainty process) 0.42 Firm level share returns vol
27
Simulated Method of Moments estimation

• SMM minimizes distance between actual simulated
  moments
• Efficient W is inverse of variance-covariance of
  (?A - ?S (T))
• Lee Ingram (1989) show under the null W
  (O(11/?))-1
• O is VCV of ?A, bootstrap estimated
• ? simulated/actual data size, I use ?10

actual data moments
simulated moments
weight matrix
28
Data is firm-level from Compustat

• 10 year panel 1991 to 2000 to out of sample
  simulate 9/11
• Large continuing manufacturing firms (gt500
  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.

29
Model
Estimation
Results
Shock Simulations
30
TABLE 2
Actual SMM Estimate
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 (?L/L) 0.197 0.234
Skew (?L/L) 0.213 0.437
Corr (?L/L)t, (?L/L)t-2 0.111 0.106
Corr (?L/L)t, (I/K)t-2 0.102 0.152
Corr (?L/L)t, (?S/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, (?L/L)t-2 0.139 0.207
Corr (I/K)t, (I/K)t-2 0.305 0.318
Corr (I/K)t, (?S/S)t-2 0.210 0.325
Adjustment cost estimates
Labor estimation moments
Closer match between left and right columns of
moments means a better fit
Capital estimationmoments
31
Results for estimations on restricted models

• Capital adjustment costs only
• Fit is only moderately worse
• Both capital labor moments reasonable
• So capital ACs and (st,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

32
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 ?L/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

33
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 SP500 relative returns
• Use 5/6 relative SP500 returns variance and
  results robust
• Find slightly higher adjustment costs

34
Model
Estimation
Results
Shock Simulations
35
Simulating 2nd moment uncertainty shocks
Structurally simulate shocks hard because big and
unprecedented
To recap combined micro and macro uncertainty
process is as follows
where s2s2Fs2M and ?s?sM?sF
Macro uncertainty shock
Simulation of macro shock sets St1 for one period

• sMs s so shock doubles average s2i,t
• Calibrated from doubling macro share volatility
  after large shocks

36
Auto-regressive st approximated by Markov-chain
Tauchen Hussey (1991) to define 5-point space
and transition matrix
- Normal times (St0) calibrated from firm share
returns volatility
s8 s17 s25 s38 s76
s8 0.645 0.249 0.084 0.020 0.002
s17 0.249 0.361 0.255 0.115 0.020
s25 0.084 0.255 0.321 0.255 0.084
s38 0.020 0.255 0.255 0.361 0.249
s76 0.002 0.020 0.084 0.249 0.645
- Shock period (St1) calibrated to double
uncertainty
s8 s17 s25 s38 s76
s8 0.001 0.008 0.033 0.132 0.825
s17 0.000 0.000 0.000 0.007 0.993
s25 0.000 0.000 0.000 0.001 0.999
s38 0.000 0.000 0.000 0.000 1.000
s76 0.000 0.000 0.000 0.000 1.000
37
Simulation uncertainty macro impulse
uncertainty shock
Run model monthly with 100,000 firms for 5 years
to get steady state then hit with uncertainty
shock
Average Uncertainty (si,t)
Month
38
Simulation percentiles of firm uncertainty
uncertainty shock
90th Percentile
uncertainty shock shifts distribution of sit
upwards
Uncertainty (st)
75th Percentile
50th Percentile
25th Percentile
10th Percentile
Month
39
Actual percentiles of firm volatility after 9/11
9/11
Actual Compustat firm level data
Real 9/11 shock did actually shift distribution
of returns volatility upwards
90th Percentile
75th Percentile
50th Percentile
25th Percentile
10th Percentile
Monthly data
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).
40
Aggregate net hiring rate ()
uncertainty shock
Net hiring rate
Month
Percentiles of firm net hiring rates ()
99th Percentile
Net hiring rate
95th Percentile
5th Percentile
1st Percentile
Month
41
Macro gross investment rate ()
uncertainty shock
Investment rate
Month
Firm percentiles of gross investment rates ()
99th Percentile
Investment rate
95th Percentile
5th Percentile
1st Percentile
Month
42
Productivity growth rate ()
uncertainty shock
Total
Between
Productivity growth
Within
Cross
Month
Productivity hiring,period before shock
Productivity hiring,period of shock
Gross hiring rate
Gross hiring rate
Productivity (logs)
Productivity (logs)
43
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
44
Highlights importance identifying 1st 2nd
moment components of shocks
Investment rate
After a 1st moment shock expect standard U-shape
downturn, bottoming out after about 6-12
monthsAfter a 2nd moment shock everything drops
just like a 1st moment shock- but then bounces
back within 1 monthTo distinguish try
using(i) volatility indicators (ii) plant
spreadto help distinguish
Hiring rate
Prod. growth
Month
45
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

uncertainty shock
risk-neutral
Investment rate
risk-averse
Month
46
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 AC0 )

PI10, all other AC0
Aggregate Hiring
Hiring Distribution
Productivity
FC1, all other AC0
Aggregate Hiring
Hiring Distribution
Productivity
47
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

48
Robustness Combined 1st and 2nd moment shock

• Earlier results 2nd moment shock only thought
  experiment
• But shocks typically have 1st and 2nd moment
  component
• Re-simulate assuming
• 2nd moment shock (doubles uncertainty as before)
• 1st moment shock (-5 1 years growth)

2nd moment shock
Investment rate
1st 2nd moment shock
Month
49
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)

50
9/11 did generate a rapid drop and rebound
Quarterly Net Hiring (total private, thousands) 1
9/11
Forecast of 23rd August 20013
Lowest quarterly value since 1980
Quarterly Investment ( contribution to real GDP
growth) 2
Forecast of 23rd August 20013
Lowest quarterly value since 1982
1 BLS Current Employment Statistics survey, Total
private employees (1000s), seasonally adjusted,
quarterly net change, from series CES0500000001 2
BEA National Income and Product Accounts,
Contributions to change in real Gross Domestic
Product, seasonally adjusted at annual rates,
from Table 1.1.2 3 Federal Reserve Bank of
Philadelphia Survey of Professional Forecasters
average of 33 economic forecasters,
www.phil.frb.org/file/spf/survq301.html
51
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
Quarterly Investment ( contribution to real GDP
growth) 2
Forecast of 23rd August 20013
Forecast of 14th November 2001
1 BLS Current Employment Statistics survey, Total
private employees (1000s), seasonally adjusted,
quarterly net change, from series CES0500000001 2
BEA National Income and Product Accounts,
Contributions to change in real Gross Domestic
Product, seasonally adjusted at annual rates,
from Table 1.1.2 3 Federal Reserve Bank of
Philadelphia Survey of Professional Forecasters
average of 33 economic forecasters,
www.phil.frb.org/file/spf/survq301.html
52
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 questionFOMC Minutes,
  November 6th 2001

53
A QUICK HISTORICAL DIGRESSION (not really part of
the paper)
54
The Great Depression was notable for very high
volatility
The Great Depression
9/11
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 Poors
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.
55
Did uncertainty play a role in the Great
Depression?

• Romer (1990) suggests uncertainty played a role
  in the initial 1929-1930 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, Moodys 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)

56
GNP growth in the Great Depression
Fall in volatility
Rise in volatility
Banking panics
Source Romer (1992, JEH)
57
END OF DIGRESSION
58
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

59
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

60
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)
61
BACK-UP
62
Adjustment costs (2)

• 1 period time to build
• Exogenous quit rate dLand depreciation rate dK
• Relative capital price is AR(1) stochastic

63
Impact of a levels shock looks different
1st moment shock (3)
1st moment shock (3)
Hiring
Investment
Month
Month
Total
Between
99th percentile
Within
Cross
95th percentile
Productivity
Hiring percentiles
5st percentile
1st percentile
Month
Month
64
Robustness- general equilibrium effects (2)

• Thomas (2002) and Veracierto (2002) suggest GE
  important
• In particular they find under GE Mt
  is a BC variable like labor, or capital Yt is
  aggregate productivity/demand NC is some
  non-convex cost
• But I look at
• st is uncertainty
• So correctly highlight importance of GE, but on a
  different issue

65
Also need to deal with aggregation

• annual zero investment episodes (UK Firm and
  Plant data)

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 units
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
66
Interest rates
9/11
Federal Funds rate
2-year rate (T-Bill)
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/H
15/data.htm
67
Employment quits, layoffs and
9/11
Month
Source Hall (2005a)
68
Adjustment costs (1)

• Active literature with range of approaches, e.g.
• I look at convex non-convex adjustment costs
  for both labor and capital

Labor or capital Labor and Capital
Convex1 Traditional Euler and Tobins Q models Shapiro (1986) Hall (2004), Merz and Yashiv (2003)
Convex1 and Non-Convex2 Abel Eberly (1999) Cooper Haltiwanger (2003) Cooper, Haltiwanger and Willis (2004)
1 Convex typically quadratic adjustment costs 2
Non-convex typically fixed cost or partial
irreversibility