The Impact of Uncertainty Shocks:Firm-Level Estimation and a 9/11 Simulation

Nick Bloom (Stanford & NBER)

April 2007

010

20

30

40

50

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005Year

Monthly US stock market 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.

OPEC II

Monetary turning point

Black Monday*

Gulf War I

Asian Crisis

Russia & LTCM

9/11Enron

Gulf War II

Implied VolatilityActual Volatility

Afghanistan

JFK assassinated

Cuban missile

crisis

Cambodia,Kent State

OPEC I

Franklin National

An

nu

aliz

ed s

tan

dar

d d

evia

tio

n (

%)

Vietnam build-up

Stock market volatility appears to proxy uncertainty

• Political uncertainty correlated with stock market volatility(Mei & Guo 2002, Voth 2002, Wolfers and Zitewitz, 2006)

• Professional forecaster spread over GDP growth correlated 0.437 with stock market volatility (bi-annual, Livingstone)

• Cross-sectional industry TFP growth spread correlated 0.429 with stock market volatility (annual, NBER)

• Common factor of exchange rate, oil price and interest rate volatility correlated 0.423 with stock market vol. (monthly)

Monthly stock market levels

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.

050

100

150

Real

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005Year

OPEC II

Monetary cycle turning point

Black Monday3

Gulf War I

Asian Crisis

Russian & LTCMDefault

September 114

WorldCom & Enron

Gulf War II

Afghanistan

JFK assassinated

Cuban missile

crisis

Cambodia, Kent State

Vietnam build up

OPEC I, Arab-Israeli War

Franklin National financial crisis

2001 2002

9/11

Frequency of word “uncertain” in FOMC minutes

The FOMC discussed uncertainty a lot after 9/11

Source: [count of “uncertain”/count all words] in minutes posted on http://www.federalreserve.gov/fomc/previouscalendars.htm#2001

“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 FOMC also believed uncertainty mattered

“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

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 & estimate this work

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 stylized 2nd moment shock (micro to macro)• Generates rapid drop & rebound in

– Hiring, investment & productivity growth• Confirm robustness to GE, risk-aversion, and AC estimates

Stage 3: Compare to empirical evidence, and show reasonable fit• VAR results show volatility shocks cause a rapid drop and

rebound in output (and employment)• 9/11 event study shows drop & rebound against expectations,

plus a drop and rebound in cross-sectional investment activity

Summary of the paper

Time out…

Two things that I tried to do:• Start with some kind of big picture, and also use a graph

• Provide a summary of where I am going and what the results will be

This risks are this is quite long – sometimes this can take while to talk through. If lots of early questions come up take some of them but also be discplined and simply move on

Estimation

Model

Results

Shock Simulations

Firm Model outline

Model has 3 main components

Net revenue function, R

Labor & capital “adjustment costs”, C

Stochastic processes, E[ ]

Firms problem = max E[ Σt(Rt–Ct) / (1+r)t ]

Time out…

I put the previous slide in just to settle people down – it is obvious to most people (hence need to be fast) but useful as a guide.

Revenue function (1)

Cobb-Douglas Production

A is productivity, K is capital

L is # workers, H is hours, α+β≤1

Constant-Elasticity Demand

B is the demand shifter

Gross Revenue

Y is “demand conditions”, where

Y1-a-b=A(1-1/e)Ba=α(1-1/e), b=β(1-1/e)

)( HLAKQ

eBQP /1

baba HLKYPQ )(1

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

)1()( 21HwwHwages

LHwwPQHLKYR )1(),,,( 21

Net Revenue = Gross Revenue - Wages

“Adjustment costs” (1)

Active literature with range of approaches, e.g.

Look at convex & non-convex adjustment costs for both labor and capital

Labor or capital Labor and Capital

Convex1 Traditional Euler and Tobin’s 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 costs2 Non-convex typically fixed cost or partial irreversibility

Time out…

The prior slide is controversial in some places (there is a lot of work in this area and not everyone agrees). So in advance of any important presentation:

1) Workout who will be your audience. Spend time looking at each persons page on the web-site – for a typical seminar this takes me about 3 or 4 hours (and I will already know some of the people as well)

2) Use this to make sure your presentation is correctly styled

“Adjustment costs” (2)

• 1 period (month) time to build

• Exogenous labor attrition rate δLand capital depreciation rate δK

• Relative capital price is AR(1) stochastic

tp

Kt

K

p

Kt

Kt Uσ)p(pρpp KK 1

*1 ),~N(U t 10

Stochastic processes – the “first moment”

“Demand conditions” combines a macro and a firm random walk

)1(1Mtt

Mt

Mt WσμYY ),~N(W M

t 10

1st MOMENT SHOCK

The macro process is common to all firms

Fti

Mtti YYY ,,

The firm process is idiosyncratic

)1( ,1,,Ftit

FFti

Fti WσYY ),~N(W F

ti 10,

Assumes firm and macro uncertainty move together - consistent with the data for large shocks (i.e. Campbell et al. 2001)

Stochastic processes – the “second moment”

2nd MOMENT SHOCK

tσZtσtt SσZσ)σ(σρσσ 1*

1

}10{ ,~St

Uncertainty is AR(1) process with infrequent jumps

• σσ=σ* so shocks roughly double average σ2t (note σZ is much smaller)

• Prob(St=1) is 1/60, so one shock expected every 5 years

)1,0(~NZ t

Time out…

Be animated when explaining your work

Also be enthusiastic – if you are not no-one else will be!

Never self criticise your work – for example say (“this is very boring, only a nerd would do this” etc..)

The optimisation problem is tough

Simplify by solving out 1 state and 1 control variable– Homogenous degree 1 in (Y,K,L) so normalize by K– Hours are flexible so pre-optimize out

Value function

),),1)((),1)((,(1

1

),,,,,,(),,,(max),,,,(,,

KKL

K

HEI

K

pIKELdYYVEr

pEIHKLYCHKLYRpKLYV

Simplified value function

),),1)((,(1

)1)(1(

),,,,(~

),(~

max),,,(,

KL

K

K

ei

K

peldyyQEr

i

peilyClyRplyQ

Note: I is gross investment, E is gross hiring/firing and H is hours

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”/Labor: Ln(Y/L)

“Dem

and

Co

nd

itio

ns”

/Cap

ital

: L

n(Y

/K)

Example hiring/firing and investment thresholds

InactionFire

Invest

Disinvest

Hire

“Real options” type effects

High and low uncertainty thresholds

Low uncertainty

High uncertainty

Larger “real options” at higher uncertainty

“Demand Conditions”/Labor: Ln(Y/L)

“Dem

and

Co

nd

itio

ns”

/Cap

ital

: L

n(Y

/K)

Time out…

Figures work well – these graphs are always much nicer to present then the theory and help get the message across

Be creative in preparing your presentation and try to think how you can graphically display any complex results

Taking the model to real micro 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 (lines, plants or markets)

• Units demand process combines macro, firm and unit shock

where YF and YM are the firm and macro processes as before

ΦU is 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

UFM YYYY

),~N(UUYY tttUU

tUt 10 )1(1

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

Estimation

Model

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 (currently) estimate 6 adjustment cost parameters & pre-determine the rest from the data and literature

Simulated Method of Moments estimation

• SMM minimizes distance between actual & simulated moments

• 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

)]([)]'([minˆ

SASA W

actual data

moments

simulated moments

weight matrix

Pre-determined parametersParameter: 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

σσ (uncertainty process) 0.29 Macro shock doubles σt

ρσ (uncertainty process) 0.42 1.5 month shock half-life

θF (uncertainty process) 1.13 Firm/macro returns vol

θU (uncertainty process) 0.34 Local unit/firm employment vol

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, but relies on representativeness of public data

see (Davis, Haltiwanger, Jarmin and Miranda, 2006)

Time out…

Sad but true – for the job-market you need a little bit of algebra. Not loads, but a couple of slides somewhere with greek letters and curly deltas…

If this really is inappropriate put it in the appendix – at least people flicking through your paper will see this

Estimation

Model

Results

Shock Simulations

Actual SMM EstimateLabor 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

Labor estimationmoments

Capital estimationmoments

“Adjustment cost” estimates

Closer match between left and right columns of moments means a better fit

TABLE 2

Results for estimations on restricted models

Capital “adjustment costs” only

• Fit is only moderately worse

• Both capital & labor moments reasonable

• So capital ACs and 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

• So OK for approximating 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%

• So I 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

Time out…

The last two slides I have typically do not present – I skip them having thought in advance they are less important

Estimation

Model

Results

Shock Simulations

Simulating 2nd moment uncertainty shocks

To recap the uncertainty process is as follows

Simulation of macro shock sets St=1 for one period (and Zt≡0)

• σσ = σ*, so shocks doubles average σ2

t (from initial graph)

• Prob(St=1) is 1/60, so shocks every 5 years (from initial graph)

Run the thought experiment of just a second moment shock

– Will add 1st moment shocks, but leave out initially for clarity

tσZtσtt SσZσ)σ(σρσσ 1*

1

}10{ ,~St)1,0(~NZ t

Simulation uncertainty macro “impulse”

Month

Un

cert

ain

ty (

σt)

uncertainty shock

Run model monthly with 100,000 firms for 5 years to get steady state then hit with uncertainty shock

Net

hir

ing

rat

e

Percentiles of firm net hiring rates (%)

Aggregate net hiring rate (%)

Month

uncertainty shock

99th Percentile

Month

95th Percentile

5th Percentile

1st Percentile

Net

hir

ing

rat

e

Inve

stm

en

t ra

te

Firm percentiles of gross investment rates (%)

Macro gross investment rate (%)

Month

uncertainty shock

Inve

stm

en

t ra

te

99th Percentile

Month

95th Percentile

5th Percentile

1st Percentile

Productivity & hiring,period after shock

Pro

du

ctiv

ity

gro

wth

Month

uncertainty shock

Productivity (logs)

Productivity growth rate (%)

Productivity (logs)

Productivity & hiring,period before shock

Gro

ss h

irin

g r

ate

Gro

ss h

irin

g r

ate

Total

Between

Within

Cross

GDP loss from uncertainty shock

Estimate very 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

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

Rough GDP loss from an uncertainty shock (% of annual value)

Reasonable size – uncertainty effects wipes out growth for ½ half year

Highlights importance identifying 1st & 2nd moment components of shocks

Pro

d.

gro

wth

Month

Inve

stm

ent

rate

After a 1st moment shock expect standard U-shape downturn, bottoming out after about 6-18 months

After a 2nd moment shock everything drops – just like a 1st moment shock- but then bounces back within 1 month

To distinguish try using:(i) volatility indicators; (ii) plant spread;to help distinguish

Hir

ing

rat

e

Robustness – Risk aversion

Month

In

vest

men

t ra

te

• Earlier results assumed firms risk-neutrality

• Re-simulate with an “ad-hoc” risk correction where rt = a + bσt

– Calibrated so that increases average (r) by 2.5%

uncertainty shock

risk-averse

risk-neutral

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

FC=1%, all other AC=0

Aggregate Hiring Hiring Distribution Productivity

Aggregate Hiring Hiring Distribution Productivity

Robustness - General Equilibrium effects• Could run GE approximating the cross-sectional distribution of firms

– But need another program loop, so much slower – so choice:(i) estimating ACs, or (ii) doing GE

– Estimate ACs as probably 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 & rebound probably optimal with GE anyway as correct factor allocation unclear, expensive to change so pause is good

• Sim (2007) estimates simple GE version and finds impact temporary uncertainty shocks reduced by ½ by GE, but still large.

Month

In

vest

men

t ra

te

• 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)

1st & 2nd moment shock

2nd moment shock

Robustness – Combined 1st and 2nd moment shock

How does the simulation fit against actual data?

• Estimate VAR on monthly data 1962-2006

• Look at 9/11 as an event study

Estimate an orthogonal VAR

Shock-measure:

• Baseline: (1/0) measure for 16 shocks on figure, dated max month

• Robustness: Actual value, first month, & oil/war/terror shocks only

Variables & ordering:

• Baseline: log(industrial production), log(employment), inflation, hours, interest rates, volatility and log(stock-market levels)

• Robustness: use smaller data sets and different orderings

Detrending:

• Baseline: HP filter with smoothing parameter of 144,000

• Robustness: More smoothing (1440) and linear detrending (∞)

-1-.

50

.51

0 6 12 18 24 30 36year

-2-1

01

0 6 12 18 24 30 36year

VAR baseline impact of an uncertainty shock%

im

pac

t

Notes: VAR Cholesky orthogonalized impulse response functions estimated on monthly data from July 1963 to July 2005 using 12 lags. Dotted lines in top and bottom figures are one standard error bands around the response to a volatility shock indicator, coded as a 1 for the 15 labelled shocks in Figure 1, and 0 otherwise. Variables (in order) are log industrial production, log employment, hours, inflation, federal funds rate, log stock market levels and the volatility shock indicator. All data detrended using a Hodrick-Prescott filter with smoothing parameter of 14400

Months after the shock

Response to 1% shock to the Federal Funds Rate

% i

mp

act

Months after the shock

Response to 20% shock to volatility

Response to 1% shock to the Federal Funds Rate

Response to 20% shock to volatility

Industrial Production

Employment

010

20

30

40

50

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005Year

Categorizing exogenous volatility shocks

OPEC II

Monetary turning point

Black Monday*

Gulf War I

Asian Crisis

Russia & LTCM

9/11Enron

Gulf War II

Implied VolatilityActual Volatility

Afghanistan

JFK assassinated

Cuban missile

crisis

Cambodia,Kent State

OPEC I

Franklin National

An

nu

aliz

ed s

tan

dar

d d

evia

tio

n (

%)

Vietnam build up

Shocks classification: “Oil” “Terror” “War” “Economic”

Arguably exogenous

-1.5

-1-.

50

.51

0 6 12 18 24 30 36year

-3

-2

-1

01

0 6 12 18 24 30 36year

VAR robustness to different shock definitions

Trivariate (industrial production, log employment and volatlity)

Bivariate (industrial production and volatility)

Months after the shock

Months after the shock

% p

rod

uct

ion

im

pac

t

Trivariate in reverse order (volatlity, log employment and industrial production)

Notes: VAR Cholesky orthogonalized impulse response functions estimated on monthly data from July 1963 to July 2005 using 12 lags. All data detrended using a Hodrick-Prescott filter with smoothing parameter of 14400. In top panel variables (in order) are log industrial production, log employment, hours, inflation, federal funds rate, log stock market levels and the volatility indicator. The volatility indicator used is different for each plot as follows: “actual volatility” is the de-trended series itself, “shocks scaled by actual volatility” uses the 16 shocks but scales these by their actual de-trended level, “shocks dated by first month” uses the 16 events with the timing defined by their first month, and “terror, war and oil shocks only” uses a 1/0 indicator for just the 10 shocks defined as terror, war or oil related. In the bottom panel the standard volatility indicator is used (a 1/0 for each of the 16 shocks in Figure 1 timed by the peak volatility month) but the variable sets and ordering var as noted.

Terror, War & Oil shocks

Actual volatility series

Shocks dated first month

Shocks scaled by volatility

% p

rod

uct

ion

im

pac

t

How does the simulation fit against actual data?

• Estimate VAR on monthly data 1962-2006

• Look at 9/11 as an event study

-1000-500

0500

1000

forecast/dem

pq1/dem

pq

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004Year

forecast dempq1

dempq

-5

-2.5

02.5

5

forecast/z/G

ross priv

ate dom

estic

in

vestm

ent

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004Year

forecast z

Gross private domestic investment

Quarterly Investment (% contribution to real GDP growth) 2

9/11 did generate a rapid drop and reboundQuarterly Net Hiring (total private, thousands) 1

9/11

1 BLS Current Employment Statistics survey, Total private employees (1000s), seasonally adjusted, quarterly net change, from series CES05000000012 BEA National Income and Product Accounts, Contributions to % change in real Gross Domestic Product, seasonally adjusted at annual rates, from Table 1.1.23 Federal Reserve Bank of Philadelphia “Survey of Professional Forecasters” average of 33 economic forecasters, www.phil.frb.org/file/spf/survq301.html

Lowest quarterly value since 1980

Lowest quarterly value since 1982

Forecast of 23rd August 20013

Forecast of 23rd August 20013

1 Compustat quarterly investment rates (%). Numerator equals plant, property and equipment purchases less resales, plus net change in inventories; denominator equals total stock of net fixed assets plus inventories averaged over the current and prior quarter. Balanced panel of all 375 publicly quoted manufacturing firms with at least $20m average sales and complete quarterly data from 1990 to 2005. The standard deviation (SD) of quarterly investment has been normalized at the quarterly level based on the pre-2001 SD of investment.

9/11Cross sectional standard deviation of investment rates1

Investment rate histogram,2001 Q3 (before 9/11)

…and investment rates appeared to compress

Investment rate histogram,2002 Q1 (after 9/11)

68

10

12

14

1990 1995 2000 2005Year

9/11

01

02

03

04

05

06

0

Pe

rcen

t

-100 -50 0 50 100ninv

01

02

03

04

05

06

0

Pe

rcen

t

-100 -50 0 50 100ninv

A QUICK HISTORICAL DIGRESSION(not really part of the paper)

030

60

90

1880 1890 1900 1910 1920 1930 1940 1950 1960Year

9/11

The Great Depression was notable for very high volatility

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.

The Great Depression

Recession of 1937

Oil & coal strike

Banking panic

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”, 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)

END OF DIGRESSION

Time out…

Doing this is risky, but probably OK for this paper. I put this up as people really engaged with the bigger picture and historical context. Again graphs….

Conclusions

• Uncertainty spikes after major economic & political shocks

• Estimation and simulation predicts rapid drop & rebound– For VAR 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

• Working on parameter estimations in current paper, and into GE with Nir Jaimovich

Current extension in progress

Build GE model by approximating cross-sectional distribution. Shouldhelp 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

BACK-UP

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 (2006), 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), Davis & Haltiwanger (1999),

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)

-5

-2.5

02.5

5

forecast/forecast1/G

ross priv

ate dom

estic

in

vestm

ent

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004Year

forecast forecast1Gross private domestic investment

-1000-500

0500

1000

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004Year

forecast forecast1dempqQuarterly Investment (% contribution to real GDP growth) 2

Forecasters also roughly predicted drop & reboundQuarterly Net Hiring (total private, thousands) 1

9/11

1 BLS Current Employment Statistics survey, Total private employees (1000s), seasonally adjusted, quarterly net change, from series CES05000000012 BEA National Income and Product Accounts, Contributions to % change in real Gross Domestic Product, seasonally adjusted at annual rates, from Table 1.1.23 Federal Reserve Bank of Philadelphia “Survey of Professional Forecasters” average of 33 economic forecasters, www.phil.frb.org/file/spf/survq301.html

Forecast of 23rd August 20013

Forecast of 23rd August 20013

Forecast of 14th November 2001

Forecast of 14th November 2001

Partial Irreversibility (PI) LaborCapital

Quadratic (QD) LaborCapital

Fixed Labor

Capital

“Adjustment costs” (1)

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

Concept

FCQDPI ),,,( HLKYC

“Adjustment Cost” Factor

Partial Irreversibility (PI) LaborCapital

Quadratic (QD) LaborCapital

Fixed (FC) Labor

Capital

Source: Romer (1992, JEH)

Rise in volatility

Fall in volatility

Banking panics

GNP growth in the Great Depression

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:

Capital/Demand (K/Y)

Actual distribution

Bin approximation

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

THE POLICY VERDICT

Firm level volatility after 9/110

5010

0

2001.5 2002Year

sd10 sd25sd50 sd75sd90

90th Percentile

75th Percentile

50th Percentile

10th Percentile25th Percentile

9/11

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).

Real 9/11 shock did actually shift distribution of returns volatility upwards

Monthly data

Actual Compustat firm level data

Auto-regressive σt approximated by Markov-chain

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

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% 0.001 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

- Shock period (St=1) calibrated to double uncertainty

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

σt is uncertainty

• So correctly highlight importance of GE, but on a different issue

t

t

d

dM

0

)(

dNC

dY

dMd

t

t

Also need to deal with aggregation

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

Quarterly Yearly

Sales 6.78 2.97

Investment 1.18 0.84

standard deviation/mean of growth rates (US firm 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

Ag

greg

ation

across u

nits

Aggregation across time

Aggregation across lines of capital

24

68

2000 2001 2002 2003 2004 2005Year

3-year T-Bills ir

Source: Federal Reserve Board Statistical Release - http://www.federalreserve.gov/releases/H15/data.htm

2-year rate (T-Bill)

Federal Funds rate

9/11

Interest rates

% 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

Fiscal position ≈ flat 2001-02 excluding personal tax cuts