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The Impact of Uncertainty Shocks: Firm-Level Estimation and a 9/11 Simulation Nick Bloom (Stanford & NBER) April 2007PowerPoint Presentation

The Impact of Uncertainty Shocks: Firm-Level Estimation and a 9/11 Simulation Nick Bloom (Stanford & NBER) April 2007

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### The Impact of Uncertainty Shocks:Firm-Level Estimation and a 9/11 SimulationNick Bloom (Stanford & NBER)April 2007

Monthly US stock market volatility

Black Monday*

9/11

Enron

Russia & LTCM

Franklin National

Cambodia,Kent State

Gulf War II

Monetary turning point

JFK assassinated

OPEC I

Asian Crisis

Afghanistan

Cuban missile crisis

Gulf War I

OPEC II

Vietnam build-up

Annualized standard deviation (%)

Actual Volatility

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.

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

September 114

JFK assassinated

Russian & LTCMDefault

Vietnam build up

Cuban missile crisis

Asian 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: 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

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 wait-and-see attitude about undertaking new investment expenditures”FOMC minutes, October 2nd 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

- Major shocks have 1stand 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

- Predicts wave like effect of uncertainty flucatuations

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

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

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 ]

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

Yis “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

W1 and w2 chosen so hourly wage rate is lowest at a 40 hour week

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

1 Convex typically quadratic adjustment costs

2 Non-convex typically fixed cost or partial irreversibility

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:

- 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)
- 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

Stochastic processes – the “first moment”

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

The macro process is common to all firms

1st MOMENT SHOCK

The firm process is idiosyncratic

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”

Uncertainty is AR(1) process with infrequent jumps

2nd MOMENT SHOCK

- 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

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

Value function

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

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

Simplified value function

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

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)

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)

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

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 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

- 8 Revenue Function parameters
- 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 distancebetween 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

actual data moments

simulated moments

weight matrix

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)

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

“Adjustment cost” estimates

Labor estimation

moments

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

Capital estimationmoments

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

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

Simulating 2nd moment uncertainty shocks

Run the thought experimentof just a second moment shock

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

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 σ2t (from initial graph)
- Prob(St=1) is 1/60, so shocks every 5 years (from initial graph)

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

Uncertainty (σt)

Month

uncertainty shock

Net hiring rate

Month

Percentiles of firm net hiring rates (%)

99th Percentile

Net hiring rate

95th Percentile

5th Percentile

1st Percentile

Month

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

uncertainty shock

Total

Between

Productivity growth

Within

Cross

Month

Productivity & hiring,period before shock

Productivity & hiring,period after shock

Gross hiring rate

Gross hiring rate

Productivity (logs)

Productivity (logs)

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

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

Investment rate

After a 1st moment shock expect standard U-shape downturn, bottoming out after about 6-18 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 spread;to help distinguish

Hiring rate

Prod. growth

Month

- 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-neutral

Investment rate

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

FC=1%, all other AC=0

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

- Uncertainty shocks very rapid and big, but wages and prices “sticky” at monthly frequency and interest rates bounded at zero
- Sim (2007) estimates simple GE version and finds impact temporary uncertainty shocks reduced by ½ by GE, but still large.

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

How does the simulation fit against actual data?

- Estimate VAR on monthly data 1962-2006
- Look at 9/11 as an event study

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 (∞)

VAR baseline impact of an uncertainty shock

Industrial Production

Response to 1% shock to the Federal Funds Rate

% impact

Response to 20% shock to volatility

Months after the shock

Employment

Response to 1% shock to the Federal Funds Rate

% impact

Response to 20% shock to volatility

Months after the shock

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

Categorizing exogenous volatility shocks

Shocks classification:

“Oil”

“Terror”

“War”

“Economic”

Arguably exogenous

Black Monday*

9/11

Enron

Russia & LTCM

Franklin National

Cambodia,Kent State

Gulf War II

Monetary turning point

JFK assassinated

OPEC I

Asian Crisis

Afghanistan

Cuban missile crisis

Gulf War I

OPEC II

Vietnam build up

Annualized standard deviation (%)

Actual Volatility

Implied Volatility

VAR robustness to different shock definitions

Actual volatility series

Shocks scaled by volatility

% production impact

Shocks dated first month

Terror, War & Oil shocks

Months after the shock

Bivariate (industrial production and volatility)

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

% production impact

Trivariate (industrial production, log employment and volatlity)

Months after the shock

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.

How does the simulation fit against actual data?

- Estimate VAR on monthly data 1962-2006
- Look at 9/11 as an event study

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

1BLS Current Employment Statistics survey, Total private employees (1000s), seasonally adjusted, quarterly net change, from series CES0500000001

2BEA National Income and Product Accounts, Contributions to % change in real Gross Domestic Product, seasonally adjusted at annual rates, from Table 1.1.2

3Federal Reserve Bank of Philadelphia “Survey of Professional Forecasters” average of 33 economic forecasters, www.phil.frb.org/file/spf/survq301.html

…and investment rates appeared to compress

Cross sectional standard deviation of investment rates1

9/11

9/11

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

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

1Compustat 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.

(not really part of the paper)

The Great Depression was notable for very high volatility

The Great Depression

Recession of 1937

Banking panic

Oil & coal strike

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 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 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)

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….

- 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

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

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)

Forecasters also roughly predicted drop & 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

1BLS Current Employment Statistics survey, Total private employees (1000s), seasonally adjusted, quarterly net change, from series CES0500000001

2BEA National Income and Product Accounts, Contributions to % change in real Gross Domestic Product, seasonally adjusted at annual rates, from Table 1.1.2

3Federal Reserve Bank of Philadelphia “Survey of Professional Forecasters” average of 33 economic forecasters, www.phil.frb.org/file/spf/survq301.html

“Adjustment costs” (1)

“Adjustment Cost” Factor

Concept

Partial Irreversibility (PI) Labor Capital

Quadratic (QD) Labor Capital

Fixed Labor

Capital

Partial Irreversibility (PI) Labor Capital

Quadratic (QD) Labor Capital

Fixed (FC) Labor

Capital

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

GNP growth in the Great Depression

Fall in volatility

Rise in volatility

Banking panics

Source: Romer (1992, JEH)

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)

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

Firm level 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).

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

- 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 capitalYt is aggregate productivity/demandNC is some non-convex cost
- But I look at
σt is uncertainty

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

Also need to deal with aggregation

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

Aggregation across units

Aggregation across lines of capital

standard deviation/mean of growth rates (US firm data)

Aggregation across time

9/11

Federal Funds rate

2-year rate (T-Bill)

Fiscal position ≈ flat 2001-02 excluding personal tax cuts

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

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