Can stimulating demand

drive costs down?

World War II as a natural experiment

Francois Lafond (Oxford)Diana Greenwald (US National Gallery of Art)

J. Doyne Farmer (Oxford)

Solar photovoltaic panels experience curve

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●

●

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●

(Cumulative) MWp of PV modules

PV

mod

ule

pric

e in

201

6 $/

Wp

0.5

1

2

5

10

20

50

1 102 104

1976

2016

Solar photovoltaic panels experience curve

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MWp of PV modules

PV

mod

ule

pric

e in

201

6 $/

Wp

0.5

1

2

5

10

20

50

1 102 104

annualproduction

cumulativeproduction

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●●

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●

1980 1990 2000 2010

1

100

10000

MW

p

annualproduction

cumulativeproduction

Summary

• Does a product become cheaper if we increaseproduction experience?

• Usually, there are issues:

• Endogeneity: lower cost will increase demand• Multicollinearity: log production, log experience and

“time” have very similar time series patterns

• During WWII:

• Demand for military products was driven bybattlefield needs

• Production went up and down

• Conclusion

• There is a causal effect of experience on costs• Experience growth and “time” are responsible

for about half of cost decrease each

Literature

• Learning-by-doing and experience curves.Alchian (1963), Arrow (1962), Thompson (2001, 2007,2012), Argote & Epple (1990), Levitt et al. (2013)

• Climate change models e.g. WITCH or POLES, seealso Nordhaus (2014) and Witajewski-Baltvilks et al.(2015)

• WWII as a natural experiment for governmentspending, e.g. Ramey (2009), Barro & Redlick(2011), Nakamura & Steinsson (2014)

• Innovation policy, endogenous growth,technology forecasting and operations research,etc.

Endogeneity (Nordhaus 2014)

Unit cost c as a function of experience Z and an exogenous trend

ct = c0Z−bt e−at.

Production equals demand. Price equals unit cost.Constant elasticity demand with an exogenous demand growth

Qt = Dt = D0c−εt edt.

Taking log and first differences gives the system:

∆ log c = −a− b∆ logZ,

∆ logQ = −ε∆ log c+ d.

Production grows exponentially, which implies

∆ logQ ≈ ∆ logZ.

Solution of the system becomes

∆ log c =−a− bd1− bε

,

∆ logZ = ∆ logQ =aε+ d

1− bε.

Endogeneity (Nordhaus, 2014)

Experience curve studies consider c = c0Zβ , that is

β =∆ log c

∆ logZ=−a− bdaε+ d

6= −b.

β can be interpreted as the effect of experience only when there is noexogenous time trend: if a = 0 then β = −b.

But in the case of exogenous demand (ε = 0), still growingexponentially at rate d:

∆ log c = −a− bd∆ logZ ≈ ∆ logQ = d,

or∆ log c = −a− b∆ logZ

Collinearity

log c = k + αt+ β logZ V S log c = k + β logZ

Productivity (notcosts)

34 industrygroups,

US, 1947 (or1959)-2007

Source:Nordhaus(2014)

Exogenous demand:The “Arsenal of Democracy”

I want to make it clear that it is the purpose of the nationto build now with all possible speed every machine, everyarsenal, every factory that we need to manufacture ourdefense material, fireside chat on December 29, 1940

U. S. MUNITIONS OUTPUT

osCO

©ooCOzo- 2

In Standard Munitions Dollars

FALL OFFRANCE

1940

INVASIONOFPHILIPPINES

INVASIONOF <IS-0F LEYTE>, NORMANDY//

INVASIONOF ITALY

INVASIONOFNORTHAFRICA£-we

GUADALCANAL

CD-

BATTLE OF THE BULGE

<^V-EDAY

CO

oCOzo

2 -

1941 1942 1943 1944 1945 1946

1940, and today could hurl 4,500 tons of steel at an enemyin 15 seconds. Annual and cumulative production of a

large number of individual munitions items are shownin the tables on pages 105 through no.

DEVELOPMENT OF CONTROLSThe beginnings of the War Production Board control

system antedated the War Production Board itself. Ishall leave for the detailed history of WPB, now in preparation, the story of how the Board grew out of SPAB,OPM, NDAC, and even more remote ancestry, how thelegal foundation for its authority was established, andhow it struggled to perfect a workable organization toadminister its controls.

The basic philosophy under which the control sys

tem was set up was a simple one. We were determined

to impose any controls within our authority whichwould contribute significantly to speeding victory. Wewere equally determined not to impose any restrictions

or any burden of paper work on business unless we were

confident that it would hasten the winning of the war.

And we have consistently followed a policy of modifyingor dropping controls promptly if they proved unworkable or outlived their usefulness.

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ARSENAL OF DEMOCRACY

Hitler invades Poland

1939

Adapted from Wartime Production Achievement, War production Board, 1945

A well-known example: Willow Run

WWII Solar panels

5 50 500 5000

number of planes

man

hour

s pe

r po

und

of a

irfra

me

0.2

0.5

1

2

5

10

20 ●

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monthlyproduction

cumulativeproduction

Willow Run plant, Detroit

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MWp of PV modules

PV

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e in

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6 $/

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0.5

1

2

5

10

20

50

1 102 104

annualproduction

cumulativeproduction

Demand was exogenous

“A war cannot be run like an industry; thecriterion is not low costs but victory.” (Smith1959)

War Production Board’s criteria for the placement ofcontracts

• 1940: 12 criteria including speed of delivery, qualityand price.

• March 1942: 3 ordered criteria:• Speed of delivery,• Conserving of superior facilities for the most difficult

items of production,• Placement of contracts with firms needing the least

amounts of additional machinery and equipment

• No other major change to the criteria until the defeatof Germany.

Data: Three datasets

Dataset Sources N Timespan

Cost data Aggregation

LaborProduc-tivity

SourceBook, Searle(1945),and Fordarchives

152 01/1940to11/1945,T ∈(2, 64)

Manhoursper unit

Plant orproduct

OMPUS-USMH

USMH andOMPUS

523 08/1942to08/1945,T = 2

“Early”and “Late”“StandardDollarWeight” perunit

Product

ContractPrices

Crawford &Cook (1952)

10 01/1942to08/1945,T = 44

Index of con-tract prices

War (sub)depart-ments

Dataset 1: Labor productivity

1 100 10000

1

10

100

1000

10000

experience

man

hour

s pe

r un

it

SearleFordSource Book

• Searle (1945): 5Ships

• Ford: 23 products(mostly motorvehicle)

• Source Book:(Alchian 1963):124 plants

Dataset 2: USMH-OMPUS

1e+00 1e+03 1e+06 1e+09

1e−

011e

+01

1e+

031e

+05

experience

unit

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Air ForceShipsOrdnanceQuartermasterChemicalSignalEngineersTransportation

• Total unit costs atan “Early” and“Late” date, at theproduct level, fromUnited StatesMunitionHandbook

• Matched with theOfficial MunitionsProduction of theUnited States

Dataset 3: Contract Prices

1e+02 1e+03 1e+04 1e+05

60

70

80

90

100

110

120

experience (million dollars)

cont

ract

pric

e in

dex

(Oct

. 42

= 1

00)

Chemical

Engineers

Medical

Ordnance

Quartermaster

Signal

Transport

AAF

ASF

Total

slope = −1/3

• Index of the pricesof contracts

• Index ofproduction volume

• about half of thetotal value of Warprocurement

• Total=Air Force(AAF)+ ServiceForces (ASF)

• ASF= Medi-cal+Chemical+. . .

Prior experienceExperience = Cumulative Production. Zt =

∑tτ=−∞Qτ

Prior experience as a proportion of total war experience

Zi,t︸︷︷︸Experience

=(

ζi︸︷︷︸Product-specific factor

T∑τ=1

Qi,τ︸ ︷︷ ︸Total War expe.︸ ︷︷ ︸

Initial Experience

)+

t∑τ=1

Qi,τ︸ ︷︷ ︸War experience

Main categ. Subcateg. ζ N War Dep.Aircraft Fighter 0.21 12 Air ForceShips Mine Craft 0.81 1 ShipsOrdnance Army Rocket Launchers 0.40 6 OrdnanceOrdnance Combat Vehicles (Tanks) 0.01 6 OrdnanceOrdnance Light Trucks 1.99 3 OrdnanceComm. Army (Radar) 0.0003 4 SignalOther Misc. Equipment and

Supplies0.50 28 Quartermaster

ζi determined at the level of the OMPUS table of contents (81 items)using historical data and guesstimates.

From a standard micro setup

Cobb-Douglas production function

Qt = AtKθkt L

θlt , At = Zbt e

at,

Optimal labor demand per unit of production

logL∗tQt≡ log lt = BL − (a/s)t− (b/s) logZt + (1/s− 1) log Qt,

where s = θk + θl represents economies of scale.Total cost function at optimum

logCtQt≡ log ct = BC − (a/s)t− (b/s) logZt + (1/s− 1) log Qt,

In first differences

∆ log c = ∆ log l = −(a/s)− (b/s) logZt + (1/s− 1) log Qt.

With s = 1∆ log c = ∆ log l = −a− b logZt

Results: Labour Productivity

∆ log lit = αi + βi∆ logZit + ηit.

●●

●●

●

−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2

−1.5

−1.0

−0.5

0.0

0.5

βi^(αi = 0)

β i^(α

i≠0)

●●

●●

●

●

Source bookFordSearle (1945)

Ford M−20

Results: Labour Productivity

Fixed effects

log lit = κi + αt+ β logZit + γ logQit + ηit.

First-differences

∆ log lit = α+ β∆ logZit + γ∆ logQit + εit.

Fixed Effects First DifferencesExperience -0.326∗∗∗ -0.304∗∗∗ -0.276∗∗∗ -0.253∗∗∗ -0.217∗∗∗ -0.203∗∗∗

(0.017) (0.020) (0.024) (0.020) (0.022) (0.025)

Time -0.004 -0.006 -0.022∗∗∗ -0.024∗∗∗

(0.003) (0.003) (0.004) (0.005)

Production -0.036∗ -0.010(0.015) (0.007)

N 3034 3034 2981 2830 2830 2740R2 0.75 0.75 0.75 0.13 0.13

Results: OMPUS-USMH

Fixed effects

log cit = κi + αt+ β logZit + γ logQit + ηit.

Equivalently for the point estimates: Heterogenous Differences(T = 2)

log cit1i − log cit0i = α(t1i − t0i) + β(logZit1i − logZit0i)

+ γ(logQit1i − logQit0i) + ηit.

Fixed-Effects/Heterog. Differences Growth rates cross sectionExperience -0.098∗∗∗ -0.055∗∗ -0.058∗∗ -0.086∗∗ -0.079 -0.098

(0.015) (0.017) (0.019) (0.031) (0.040) (0.052)

Time -0.004∗∗∗ -0.005∗∗∗ -0.002 -0.002(0.001) (0.001) (0.003) (0.003)

Production 0.008 0.024(0.009) (0.044)

N 1046 1046 964 523 523 482R2 0.13 0.17 0.19 0.06 0.09

∆ log cit = αi + βi∆ logZit + ηit.

●

●

●

●

●

●

●

●

● ●

−0.4 −0.2 0.0 0.2

−0.5

0.0

0.5

βi^(αi = 0)

β i^(α

i≠0)

Chemical

Engineers

Medical

Ordnance

Quartermaster

Signal

Transport

AAF

ASFTotal

Figure: Estimated coefficient of the first difference regression ofthe log of contract prices on the log of experience, including orexcluding an exogenous time trend. The lines shows plus orminus 2 HAC standard errors.

Results: Contract Prices

Fixed effects

log cit = κi + αt+ β logZit + γ logQit + ηit.

First-differences

∆ log cit = α+ β∆ logZit + γ∆ logQit + εit.

Fixed Effects First DifferencesExperience -0.205∗∗ -0.155∗ -0.170∗∗ -0.188∗∗∗ -0.107 -0.120∗

(0.036) (0.052) (0.045) (0.023) (0.046) (0.042)

Time -0.002 -0.003 -0.004 -0.004(0.003) (0.002) (0.003) (0.003)

Production 0.040∗ 0.006∗

(0.016) (0.002)N 308 308 308 301 301 301R2 0.77 0.78 0.81 0.05 0.06

Exogenous trend vs Experience

E[∆ log c] = α + βE[∆ logZ]

Growth rates Coefficients Share exo.c Z Q β α α/∆ log c

Labor Productivity -6.6 20.1 4.4 -21.7 -2.2 33.3OMPUS-USMH -0.8 7.4 5.2 -5.5 -0.4 60.4Contract Prices -0.8 3.5 3.0 -10.7 -0.4 53.1

All values are multiplied by 100.Growth rates are average monthly log growth rates.(Based on Fixed Effects instead of First Differences forUSMH-OMPUS)

Conclusion

Does stimulating demand drive costs down?

• Setting

• Cost ∼ Experience almost like Price ∼ Demand• WWII: Exogenous demand also breaks the

collinearity between production, experience and time

• Data

• Three datasets, each with its own challenges• Need to exploit cross sectional variation

• Results

• Effect of experience on cost remains• Exogenous factors are also important

• Limitations

• Omitted variables• Aggregation• External validity

Appendix - Robustness Checks

Generally, the results

• hold well for Labour Productivity

• hold less well for Contract Prices

• It is hard to go further with USMHPanel time series models

• Two way fixed effects

• Lag of Experience

• Dynamic Panels

Heterogeneous coefficients

• Fixed effects in first differences

• Heterogenous coefficients models (Swamy, Pesaran-Smith)

Controls and Instruments

• Control Prices

• Instruments

• External Learning

Data cleaning

• Changes in initial experience (ζi → fζi)

Time Fixed Effects

log cit = κi + θt + β log(Zit) + ηit

Labor Productivity USMH ContractsExperience -0.300∗∗∗ -0.059∗∗ -0.173∗

(0.018) (0.020) (0.059)Observations 3034 1046 308R2 0.789 0.250 0.806

return

Lagged Experience

Replace Zit with Zit−1.

Table: Panel regression results for Experience lagged 1 period

Labor Productivity USMH ContractsFE FD FE FE FD

Experience(t-1) -0.236∗∗∗ -0.109∗∗∗ -0.033∗∗ -0.154∗ -0.122∗

(0.019) (0.020) (0.013) (0.052) (0.047)

Time -0.008∗∗ -0.036∗∗∗ -0.005∗∗∗ -0.002 -0.004(0.003) (0.004) (0.001) (0.003) (0.003)

N 2912 2719 1046 308 301R2 0.717 0.046 0.159 0.788 0.060

return

Dynamic Panel Models

log cit = κi + a log ci,t−1 + β log(Zit) + ηit

Two-step Arellano-Bond dynamic panel models for labourproductivity and contracts

Labour Productivity Contractsall lags all lags 20 lags all lags all lags 5 lags

t-1 0.744∗∗∗ 0.639∗∗ 0.707∗∗ 0.579 -0.277 0.562(0.211) (0.235) (0.251) (2.202) (43.418) (1.189)

t-2 0.104 -0.066(0.267) (35.459)

Experience -0.026 -0.022 -0.031 -0.071 0.031 -0.497(0.100) (0.164) (0.178) (4.638) (10.103) (3.648)

Time -0.003 -0.003 -0.004 -0.002 -0.016 0.012(0.010) (0.015) (0.024) (0.115) (0.479) (0.091)

Observations 2660 2504 2660 294 287 294Number of instruments 1585 1563 1048 276 275 203p(AR1) 0.00 0.07 0.00 0.93 0.98 0.93p(AR2) 0.48 0.99 0.49 0.97 0.97 0.91Experience, long-run -0.101 -0.087 -0.106 -0.169 0.023 -1.136

return

Robustness: Time-Trend Heterogeneity

∆ log cit = αi + β∆ log(Zit) + ηit

Table: Fixed effects on the first differences

Labor Productivity ContractsExperience -0.210∗∗∗ 0.003

(0.020) (0.082)Observations 2830 301R2 0.105 0.000

return

Experience coefficient heterogeneity

Model: Heterogenous slopes models (Swamy’s random coeffficientsmodel and Pesaran and Smith’s mean group estimator):

Table: Heterogenous coefficients models (Swamy and Meangroup)

Labor Productivity ContractsSwamy MG Swamy MG

Experience -0.272∗∗ -0.362∗∗∗ -0.032 -0.030(0.087) (0.082) (0.058) (0.044)

Constant -0.013 -0.015 -0.007∗ -0.008∗

(0.016) (0.015) (0.004) (0.003)Observations 2817 2817 301 301

return

Initial Experience: Labour Productivity

0.01 0.05 0.20 1.00 5.00

−0.6

−0.5

−0.4

−0.3

−0.2

f

β

0.01 0.05 0.20 1.00 5.00

−0.045

−0.040

−0.035

−0.030

−0.025

−0.020

f

α

0.01 0.05 0.20 1.00 5.00

0.3

0.4

0.5

0.6

0.7

f

α µ

return

Initial Experience: USMH

0.01 0.05 0.20 1.00 5.00

−0.055

−0.050

−0.045

−0.040

−0.035

f

β

0.01 0.05 0.20 1.00 5.00

−0.0050

−0.0045

−0.0040

−0.0035

−0.0030

−0.0025

f

α

0.01 0.05 0.20 1.00 5.00

0.4

0.5

0.6

0.7

0.8

f

α µ

return

Initial Experience: Contract Prices

0.01 0.05 0.20 1.00 5.00

−0.15

−0.10

−0.05

0.00

f

β

0.01 0.05 0.20 1.00 5.00

−0.009

−0.008

−0.007

−0.006

−0.005

f

α

0.01 0.05 0.20 1.00 5.00

0.6

0.7

0.8

0.9

1.0

1.1

f

α µ

return

Robustness: Control for Prices

Adding Producer Price Index as control, interacted or not.(Note: Prices were controlled during the War)

Labor Productivity USMH ContractsExperience -0.219∗∗∗ -0.222∗∗∗ -0.061∗∗∗ -0.050∗∗ -0.111∗ -0.105

(0.022) (0.022) (0.017) (0.018) (0.044) (0.056)

Time -0.024∗∗∗ -0.023∗∗∗ 0.003 0.001 -0.005 -0.005(0.004) (0.004) (0.003) (0.004) (0.003) (0.004)

PPI 0.899 -3.901∗ 0.280∗

(0.593) (1.752) (0.095)PPI Interacted No Indiv. No War Dep. No Indiv.N 2830 2830 1046 1046 301 301R2 0.235 0.279 0.174 0.186 0.342 0.353

return

Instruments

Endogeneity concerns

• Product substitution: no, operation at max. capacity

• c = TC/Q: Q on both sides

Possible instruments

• Demand side, e.g. battles: not relevant (max. capacity reached)

• Supply-side, e.g. Bartik-like on raw materials: Yes, but noproduct-level data

• Past experience

Labor productivity ContractsExperience -0.209∗∗∗ -0.219∗∗∗ -0.125∗∗∗ -0.126∗∗∗

(0.021) (0.018) (0.033) (0.029)

Time -0.021∗∗∗ -0.021∗∗∗ -0.003 -0.004∗∗

(0.005) (0.004) (0.002) (0.001)

Production -0.025 -0.006(0.014) (0.083)

N 2578 2719 301 301R2 within 0.70 0.70 0.77 0.77

return

External Learning

Total War effort: Total real military spendings byGovernment.

Labor Productivity USMH ContractsExperience -0.218∗∗∗ -0.218∗∗∗ -0.051∗∗ -0.058∗∗ -0.107 -0.118∗

(0.022) (0.022) (0.017) (0.018) (0.045) (0.047)

Time -0.021∗∗∗ -0.021∗∗∗ -0.001 -0.005∗∗∗ -0.004 -0.007(0.004) (0.004) (0.002) (0.001) (0.003) (0.003)

War Effort 0.012 0.049∗ -0.000(0.010) (0.020) (0.008)

Cumul. War Effort 0.023 -0.035 0.129(0.015) (0.043) (0.066)

N 2830 2830 1046 1046 301 301R2 0.126 0.126 0.174 0.167 0.047 0.049

return

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