The Impact of Uncertainty Shocks Nick Bloom Stanford

The Impact of Uncertainty Shocks Nick Bloom (Stanford & NBER) October 2008

Monthly US stock market volatility Annualized standard deviation (%) Black Monday* Cambodia, Franklin Kent State National Monetary JFK turning point assassinated OPEC I Afghanistan Cuban missile OPEC II crisis Vietnam build-up Actual Volatility Credit crunch* 9/11 Russia Enron & LTCM Gulf War II Asian Crisis Gulf War I Implied Volatility Note: CBOE VXO index of % implied volatility, on a hypothetical at the money S&P 100 option 30 days to expiry, from 1986 to 2007. Pre 1986 the VXO index is unavailable, so actual monthly returns volatilities calculated as the monthly standard-deviation of the daily S&P 500 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 VX 1 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. Un-capped values for the Black Monday peak are 58. 2 and for the Credit Crunch peak are 64. 4

Stock market volatility appears to proxy uncertainty • Correlated with many other uncertainty proxies, for example with the cross-sectional spread of: • Quarterly firm-level earnings-growth (corr = 0. 536) • Monthly firm-level stock-returns (corr = 0. 534) • Annual industry-level TFP growth (corr = 0. 582) • Bi-annual GDP forecasts (corr = 0. 618) • Robust to including trend and period dummies (Table 1)

Stock market volatility is also quite distinct from stock market levels (shown log-detrended below) Detrended stock market levels correlated with monthly volatility at -0. 340 Russia & LTCM JFK assassinated Cuban Vietnam missile build-up crisis Cambodia, Kent State Asian Crisis 9/11 Enron Gulf War II OPEC I Franklin National Credit crunch Black Monday Afghanistan Monetary turning point OPEC II Gulf War I Note: S&P 500 index from 1962 to 2008. Log de-trended by converting to logs, removing the time trend, and converting back into levels. The coefficient (s. e. ) on days is 0. 0019 (0. 000038), implying a nominal average trend growth rate of 7. 4% over the period.

But do these uncertainty shocks matter empirically? Want to look at the average impact of an uncertainty shock Estimate a monthly orthogonal VAR: • log(S&P 500 level), uncertainty shocks, FFR, log(wages), log(CPI), hours, log(employment), log(industrial production) uncertainty shocks defined by a (1/0) indicator for the 16 shocks

Annualized standard deviation (%) Bars denote the 16 uncertainty shocks in the VAR Actual Volatility Implied Volatility Shocks selected as those 2 SD above the HP filtered trend. VAR run on data until 2007 (so credit crunch not covered)

VAR estimate of the impact of an uncertainty shock % impact Industrial Production Response to an uncertainty shock Response to 1% shock to the Federal Funds Rate Months after the shock % impact Employment Response to an uncertainty shock Response to 1% shock to the Federal Funds Rate Months after the shock Note: results robust to different variable inclusion, ordering & detrending (see appendix figures A 1 to A 3 ). Dotted lines are +/- one standard-error bands

Policy makers also appeared to talk a lot more about uncertainty after one recent shock – 9/11 Frequency of word “uncertain” in FOMC minutes 9/11 2002 Source: [count of “uncertain”/count all words] in minutes posted on http: //www. federalreserve. gov/fomc/previouscalendars. htm#2001

And they appeared to believe 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 2 nd 2001 *Federal Open Market Committee

Policymakers also worried about uncertainty from the credit crunch “Several [survey] participants reported that uncertainty about the economic outlook was leading firms to defer spending projects until prospects for economic activity became clearer” FOMC minutes, 2008

Motivation • Major shocks have 1 st and 2 nd moments effects • VAR (and policymaker) evidence suggest both matter – Lots of work on 1 st moment shocks – Less work on 2 nd moment shocks • Paper will try to model 2 nd moment (uncertainty) shocks – Closest work is probably Bernanke (1983)

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 Stage 2: • Estimate on firm data by Simulated Method of Moments Stage 3: Simulate stylized 2 nd moment shock (micro to macro) • Generates rapid drop & rebound in – Hiring, investment & productivity growth • Investigate robustness to a range of issues

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 (2007), Ramey and Shapiro (2001), 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) Real Options & Adjustment costs • Abel and Eberly (1994), Abel and Eberly (1996), Caballero & Leahy (1996), and Eberly & Van Mieghem (1997), Bloom (2003) • Mac. Donald and Siegel (1986), Pindyck (1988) and Dixit (1989) Time varying uncertainty • Bernanke (1983), Hassler (1996), Fernandez-Villaverde and Rubio. Ramirez (2006) Simulation estimation • Cooper and Ejarque (2001), Cooper and Haltiwanger (2003), and Cooper, Haltiwanger & Willis (2004)

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 ~ 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 A is “business conditions” ~ where A 1 -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 W 1 and w 2 chosen so hourly wage rate is lowest at a 40 hour week Net Revenue = Gross Revenue - Wages

Allow for three types of adjustment costs (1) Quadratic: C(I, K) = αKK(I/K)2 C(E, L) = αLL(E/L)2 where I=Gross investment, αK≥ 0 where E=Gross hiring/firing, αL≥ 0 ‘Partial irreversibility’: C(I, K) = b. I[I>0] + s. I[I<0] where b≥s≥ 0 C(E, L) = h. E[E>0] - f. E[E<0] where h≥ 0, f≥ 0 Fixed costs: C(I, K) = FCKPQ[I≠ 0] C(E, L) = FCLPQ[E≠ 0] where FCK≥ 0 where FCL≥ 0

“Adjustment costs” (2) • Assume 1 period (month) time to build • Exogenous labor attrition rate δL and capital depreciation rate δK • Baseline δL=δK=10% (annualized value) • Robustness with δK=10% and δL=20%

Stochastic processes – the “first moment” “Business conditions” combines a macro and a firm random walk The macro process is common to all firms The firm process is idiosyncratic Assumes firm & macro uncertainty move together (consistent with results on the 3 rd slide and Table 1)

Stochastic processes – the “second moment” Uncertainty modelled for simplicity as a two state Markov chain σH = 2×σL so high uncertainty twice the ‘baseline’ low value (from Figure 1) With the following monthly transition matrix σL σH σL 35/36 1/36 σH 0. 29 0. 71 Defined so on average (from Figure 1): • σH occurs once every 3 years • σH has a 2 month half-life

The optimisation problem Value function Note: I is gross investment, E is gross hiring/firing and H is hours Simplify by solving out 1 state and 1 control variable – Homogenous degree 1 in (A, K, L) so normalize by K – Hours are flexible so pre-optimize out Simplified value function

Solving the model • Analytical methods for broad characterisation: – Unique value function exists – Value function is strictly increasing and continuous in (A, K, L) – Optimal hiring, investment & hours choices are a. e. unique • Numerical methods for precise values for any parameter set

“Business Conditions”/Capital: Ln(A/K) Example hiring/firing and investment thresholds Invest Fire Inaction Hire Disinvest “Business Conditions”/Labor: Ln(A/L)

“Business Conditions”/Capital: Ln(A/K) High and low uncertainty thresholds Larger “Real option” values at higher uncertainty (≈7. 5% rise in hurdle rate) Low uncertainty High uncertainty “Business Conditions”/Labor: Ln(A/L)

Distribution of units between the thresholds 6 Hiring region Distribution of units (dashed red line) Hiring/Firing rate (solid black line) Distribution of units 8 4 2 Firing region Inaction region “Business Conditions”/Labor: Ln(A/L) Note: Plotted for low uncertainty, high drift and the most common capital/labor (K/L) ratio. 0

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 AF and AM are the firm and macro processes as before • Simplifying assumptions following approach of Bertola & Caballero (1994), Caballero & Engel (1999), and Abel & Eberly (2002) – 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 23 parameters in the model – 9 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 – 8 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 10 key parameters & predefine the rest remaining 13 from the data and literature

Simulated Method of Moments estimation • SMM minimizes distance between actual & simulated moments 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=25

The 13 pre-determined parameters Parameter: Value: Source: α (capital coefficient) 1/3 Capital share in output e (demand elasticity) 4 33% mark-up (also try 20% mark-up) w 1 (wage parameter) 0. 8 Hourly wage minimized at 40 hour week w 2 (wage parameter) 2. 4 e-9 Arbitrary scaling parameter σH (uncertainty shock size) 2 Doubles baseline (also try 1. 5 and 3) πσL, H 1/36 Shock every 3 -years πσH, H 0. 71 Shocks 2 -month half-life (also try 1 & 6) (μH+μL)/2 0. 02 Average annual real growth rate of sales is 2% (gap between μH-μL is estimated) πμL, H πμH, L Firm-growth matrix assumed symmetric (πμL, H is estimated) δK (capital depreciation) 0. 1 10% annualized capital depreciation δL (labor quit rate) 0. 1 For numerical speed (also try δL=0. 2) r (long-run discount rate) 6. 5% Long run US average (King & Rebelo, 1999) N (units per firm) 250 Chosen for complete aggregation (also try N=25 and N=1)

Data is firm-level from Compustat • 20 year panel 1981 to 2000 • Large firms (>500 employees, mean 4, 500) – Focus on most aggregated firms – Minimize entry and exit • Final sample 2548 firms with 22, 950 observations

Model Estimation Results Shock Simulations

Estimation results (table 3) • Top half shows the parameter estimates • Bottom half shows sales, investment and hiring moments Too much for 1 page so focus on adjustment cost only in main specification

Large capital resale loss & moderate fixed costs. No quadratic investment costs. Moderate person hiring/firing costs & large fixed costs. No quadratic hiring costs. Adjustment cost estimates identified by: • skewed investment rates (no disinvestment) • moderate investment dynamics (some auto-correlation) • weak employment dynamics and wide cross-sectional spread

Results for estimations on restricted models Capital “adjustment costs” only • Fit is moderately worse • Seems best approximation if using just one factor Labor “adjustment costs” only • Labor moments fit are fine, Capital moments fit is bad • 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 No temporal or cross-sectional aggregation • Estimate much lower fixed costs and higher quadratic costs

Robustness • Table 4 runs some robustness checks of the different predetermined parameter estimates • Makes some difference, but broad findings and simulations appear reasonably robust

Model Estimation Results Shock Simulations

Simulating 2 nd moment uncertainty shocks Run the initial thought experiment of just a second moment shock – Will add 1 st moment shocks, but leave out initially for clarity Simulate an economy with 1000 units – Allow the model to run for 10 years – Set σt=σH in month 1 of year 11 Repeat this 25, 000 times and take the mean (to average over firstmoment macro shocks)

Uncertainty (σt) Average σt (normalized to 1 on pre- shock date) The second moment shock in the simulation Month (normalized to 0 for month of shock)

Uncertainty (σt) conditions) Aggregate At (business (normalized to 1 on shock date) The simulation has no first moment shock Actual De-trended Month (normalized to 0 for month of shock)

Aggregate Lt (de-trended & normalized to 1 on pre_shock date) Aggregate labor drops, rebounds and overshoots Month (normalized to 0 for month of shock)

Aggregate Lt (de-trended & normalized to 1 on pre_shock date) Splitting out the uncertainty and volatility effects ‘Volatility effect’ only Baseline (both effects) ‘Uncertainty effect’ only Month (normalized to 0 for month of shock)

Distribution of units [slide copied from earlier] 6 Hiring region Distribution of units (dashed red line) Hiring/Firing rate (solid black line) Distribution of units 8 4 2 Firing region Inaction region “Business Conditions”/Labor: Ln(A/L) Notes: The hiring response and unit-level density for low uncertainty (σL), high-drift (μH) and the most common capital/labor (K/L) ratio. 0

Average Kt (de-trended & normalized to 1 on pre-shock date) Aggregate capital drops, rebounds and overshoots Month (normalized to 0 for month of shock)

Aggregate TFP growth also slows and rebounds Definition: TFPt = ∑Li, t. Ai, t / ∑Li, t TFP growth (%) (TFPt+1 -TFPt)/TFPt Total Reallocation Within Month after the shock Hiring/Firing rate Month before the shock Log(Ai, t/Li, t)

So de-trended TFP levels drop, rebound & overshoot Solow TFPt (de-trended & normalized to 1 on pre-shock date) Solow TFPt = Aggregate Output/Factor Share Weighted Inputs Month (normalized to 0 for month of shock)

Average Output (de-trended & normalized to 1 on pre-shock date) Output also drops and rebounds Matches up well to the VAR estimates for industrial production: • Six-month U-shaped drop in activity • Lowest point about 2% below trend • Longer-run overshoots Interestingly, looks like 1 st moment shock Month (normalized to 0 for month of shock)

Robustness - General Equilibrium effects • Could run GE approximating the cross-sectional distribution of firms (i. e. Kahn and Thomas, 2003) – But need another program loop, so much slower – so choice: (i) estimating ACs (in PE), or (ii) doing GE (with calibrated ACs) – Estimated ACs first and do full GE later (in work with Max Floetotto and Nir Jaimovich) • But, can get a first indication of the likely short-run impact of GE by feeding in prices after uncertainty shocks estimated using VAR

VAR estimated impact of an uncertainty shock on prices Federal Funds rate (% points change) % impact CPI (% change) Wages (% change) Months after the shock Approximate this in the simulation by assuming that when σt=σH – Interest rates 1. 1% lower – Prices of capital and output 0. 5% lower – Wages 0. 3% lower Firms expect this since incorporated into the model Certainly not exact! Simply guidance on possible GE effect

‘Pseudo GE’ effects have little very short-run impact Average Outputt (de-trended & normalized to 1 on pre-shock date) GE impact initially small due to ‘cautionary’ effect of uncertainty • Thresholds move out with high σt, so not responsive • As σt falls back down GE effects have more bite Also suggests limited very short-run response to policy stimulus after shocks Pseudo GE Partial Equilibrium Month (normalized to 0 for month of shock)

Finish with some other robustness experiments • Combined 1 st and 2 nd moment shocks • Different predetermined parameters • Different assumptions on adjustment costs • Different sizes of uncertainty shocks • Different durations of uncertainty shocks

Average Outputt (de-trended & normalized to 1 on pre-shock date) Adding first moment shocks Second moment shock only First and second moment shock First moment shock only Month (normalized to 0 for month of shock)

Average Outputt (de-trended & normalized to 1 on pre-shock date) Different predetermined parameters N=1 N=25 20% markup 20% labor attrition Month (normalized to 0 for month of shock)

Average Outputt (de-trended & normalized to 1 on pre-shock date) Different types of adjustment costs Fixed costs only Partial irreversibilities only Quadratic only Month (normalized to 0 for month of shock)

Average Outputt (de-trended & normalized to 1 on pre-shock date) Different sizes of uncertainty shocks Larger (σH=3×σL) Baseline (σH=2×σL) Smaller (σH=1. 5×σL) Month (normalized to 0 for month of shock)

Average Outputt (de-trended & normalized to 1 on pre-shock date) Different durations of uncertainty shocks Shorter lived (1 month half -life) Baseline (2 month half-life) Longer live (6 month half-life) Month (normalized to 0 for month of shock)

A FINAL HISTORICAL DIGRESSION (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 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)

END OF DIGRESSION

Conclusions • Uncertainty appears to spike after major economic & political shocks • VAR estimation suggest these cause a rapid drop and rebound in output and employment • Estimation and simulation predicts a similar rapid drop & rebound Next steps • Building a GE model with 1 st and 2 nd moment shocks, non-convex adjustment costs & many plants (with Jaimovich and Floetotto) – Motivation that all uncertainty proxies rise strongly in recessions – So possible that counter-cyclical uncertainty can address the “where are the negative shocks? ” critique of real-business cycles

BACK-UP

THE 9/11 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 predicted to fall by about 1. 3% pre-9/11 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 6 th 2001

Robustness- general equilibrium effects • 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

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)

VAR robustness of industrial production plots % impact Shock definitions Shocks dated by first month Actual volatility series Terror, War and Oil shocks only Shocks scaled by actual volatility Months after the shock Variables & ordering Trivariate (shocks, employment & production) % impact Reverse trivariate (production, employment & shocks) Bivariate (shocks and production) Months after the shock

VAR robustness of industrial production plots % impact Detrending Monthly HP (HP=129, 600) Linear (HP=∞) Baseline (no detrending) High frequency (HP=1296) Months after the shock % impact Oil, credit spread and yield curve Baseline plus Moody Aaa and Baa rates Baseline plus oil prices Months after the shock

And they appeared to believe 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 2 nd 2001 As with the recent sub-prime shock “Financial market conditions have deteriorated, and tighter credit conditions and increased uncertainty have the potential to restrain economic growth going forward. ” FOMC statement, August 17 th 2007

Credit Crunch: A Plot of Daily Stock Market Volatility Credit Crunch Implied Volatility on the S&P 100 (%) Updated October 27 th Russian & LTCM Default Gulf War I 9/11 World. Com & Enron Gulf War II Asian Crisis Year