Structural Econometrics in Industrial
Organization: DemandMarc Rysman
Boston UniversityFebruary 13, 2009

What is a structural model?

Definition 1
A structural model estimates the parameters in a theoreticalmodel.

Definition 2
A structural model estimates the parameters in the objection
function of agents.
Consider a theoretical model with 2 equilibria, where equ. 1 isselected with prob. θ. Estimating θ is structural under Def. 1 but
not Def. 2.

Why estimate a structural model

I Construct counterfactuals
I Provides a disciplined method for handling complex

situations
I But usually requires many assumptions
I and can be numerically demanding.

Why do we estimate demand?

I Learn price elasticities
I Learn elasticities to other product characteristics
I Learn value of new goods
Iconstruct price indices

Why estimate with aggregate data?

I Disaggregate data

Observe actual prices, outside options
Account for interaction of household and productcharacteristics explicitly
I Panel data allows for rich models of learning, stockpiling,switching, etc.
II

I Aggregate dataIIOften all that is available
Necessary for accurate market share data, which isimportant for oligopoly analysis

Standard Approach
Or at least, standard at one time

Let indirect utility over J products be:ln(V ) =JX
j=1

βj ln(Pj ) +JJ X
Xβjk
j=1 k =12ln(Pj ) ln(Pk )Roy’s Identity: ∂ ln(V )/∂ ln(Pj ) = Xj ⇒Xj = βj + βjj ln(Pj ) +JX
1k 6=j2

βjk ln(Pk )I Read elasticities right off of regression

Problems

1. Problems with many products
IJ × J + 1 parameters

2. Doesn’t handle entry and exit wellI

What does it mean to drop a product?
p = ∞? p =choke value?

3. Doesn’t look like a discrete choice model

Discrete Choice Model
Can solve all 3I Think of goods as a collection of characteristics.
IWe can project lots of goods onto a space of only a fewchars.

I Model: Utility to i from product j is:uij = uj + ij
I Consumer picks j s.t. uij ≥ uik ∀kI uj is a function of observable variables. In disaggregate

data, it could vary by i.

Logit model
I Assume ij ∼ Extreme ValueI CDF for Extreme Value distribution with mean α andvariance π 2 µ2 /6 is:F () = e−e− −αµ +γ()

where γ is euler’s constant.
I Has bell shape with fat tails
I Logit magic: probability that i picks j:euj /µPj = P u /µkkeI Proof: Chapter 2, Anderson, De Palma and ThisseWelfareMore logit magic!
I Indirect utility to i is V + 0 where:iJX
V = µ ln euj /µ j=1and 0i is distributed EV with variance parameter µI Note similarity to CES utility function:Ve =J Xµ(eu1 )1/µ + (eu1 )1/µ + . . .

j=1I Entry and exit handled naturally.

Application to aggregate data

I Let utility to consumer i from product j be:

uij = xj β − αpj + ξj +ij{z}|δj

I Assume our population contains a continuum ofconsumers with ij ∼ EV.
I Market shares:

sj =exp(δj )PJ
1 + k =1 exp(δj )Berry (RAND, 1994)

sj =exp(δj )PJ
1 + k =1 exp(δj )
⇒s0 =

11+PJ

k =1 exp(δj )sj= δjs0⇒ ln(sj ) − ln(s0 ) = xj β − αpj + ξj
I Estimate via OLS, linear IV
I Note that there is a general principal at work – inverting

market shares to get mean utilities.

What’s not to like about Logit?

Relative market shares do not depend on characteristics orpresence of other goods

Independence of Irrelevant Alternatives (IIA)
sjeuj= uske k∂sj= −sj sk βp∂pk

Random Coefficient model

uij = xj βi − αi pj + ξj + ij

uij = xj β − αpj + ξj +|{z}δjI Dimensionality of xj is L.
I νi ∼ N(0, 1).

LX

σl xjl νil +ij

l=1|{zµ(xj ,σ,νi )}Market shares
exp δj + µ(xj , σ, νi )sij =P
1 = Jk =1 exp (δk + µ(xk , σ, νi ))Z
−→ sj = sij δ , µi f (νi )dνi
With logit:
I sj had a closed form solution as function of
I AND the function could be inverted.

−→δSolutions

1. Numerically integrate:
II

Draw ns values of νiCompute:nssj =exp (δj + µ(xj , σ, νi ))1 XPJnsexp (δk + µ(xk , σ, νi ))1+k =1i=1

2. Invert via a fixed point equation:→−
δj0 = δj + ln(sj ) − ln(ŝj ( δ , σ))| {z } |{z}datamodel

Full Algorithm

1. Draw a set of νi
2. Pick parameters β, α, σ→−
3. Guess δ→−
4. Compute δ 0 = δ + ln(sj ) − ln(ŝj ( δ , σ))→ −−→
5. If d( δ 0 , δ ) > cutoff, go to 3.
6. Compute ξj = δj − xj β + αpj
7. Compute m = z 0 ξ and obj = m0 wm
8. Find β,α,σ that minimizes obj, go to 2.

Instruments

I Cost shifters don’t provide enough variation acrossproducts.
I but remember: P = MC + Mark − up
I Use instruments that shift the mark-up.
I Measures of competition in product space.
I Requires assumption that characteristics are exogenous –Controversial!

Supply Side
I Older research used accounting data to measure cost but

the modern view is that accounting data is unreliable.
I Instead, we estimate marginal cost.
I We can use the demand system and an assumption about

equilibrium play (i.e. Bertrand Nash) to compute marginal
revenue and assume it is equal to marginal cost.
I Firm f that sells all products j ∈ Ff solves:max

pj ,j∈Ff⇒ sj +

X→−(pj − mcj )Msj ( p )j∈FfXk ∈Ff(pk − mck )

∂sk=0
∂pj

Estimate marginal cost
I In matrix notation:−→→ −→−s + ∆( p − mc) = 0→−→−−→
p + ∆−1 s = mc→−→−= wγ + ωln p + ∆−1 sI Now moments are:m = z 0ξ

z 0ω

I Some papers add moment from dissagregate data sets at

this stage, for instance, the average income conditional onpurchase (Petrin, JPE, 2002).

Application: Berry, Levinsohn, Pakes (AER, 1999)

I What is the impact of Japanese voluntary export

restraints?
I Japanese auto manufacturers obtained increasing markets

shares in the US throughout the 1970’s.
I US firms ask for protection and Reagan “asked” Japan toinstitute “voluntary export restraints."

Sales and402VER limits
TABLE 1-U.S.

Year

THEAMERICANECONOMICREVAUTOMOBILE IMPORTS FROM JAPANInternationalTrade
Commission data

VER limit

U.S. imports fromJapanincluding
Puerto Rico
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990

1,833,313
1,831,198
1,851,694
2,031,250
2,605,407
2,518,707
2,377,383
2,115,304
2,015,920
1,911,828

Difference(Imports-VER)

1,832,500a
1,832,500
1,832,500
2,016,000b

2,506,000C
2,506,000
2,506,000
2,506,000
2,506,000
2,506,000

813-1,302
19,194
15,25099,407
12,707-128,617-390,696-490,080-594,172

Sources: The ITC figures are for "VER years" which ran
from April 1 to March 31. The ITC data are from the Mayinvent
1981,
likely,up theoption
shouldple, ifable t
might
Unitedyear, Nmodelmand
1982 Vshippeprocedyear w(ii) The stHedonic regression

VOL.89 NO. 3

EXPORTRESTRAINTSON AUTOMOBILESBERRYET AL.: VOLUNTARYTABLE 4-A FIRST PASS AT EXAMINING THE EFFECT OF
THE VER ON AUTOMOBILE PRICESAN ORDINARY LEAST-SQUAREs HEDONIC REGRESSION[DEPENDENT VARIABLE IS LN(PRICE)]

Variable

Parameter
estimater

Standard
efror

Constantln(HP/Weight)ln(Space)ln(MP$)
Air
TrendJapanEuro
jtrendetrendln(e-rate)
Lag[ln(e-rate)]ln(e-rate)*Japanln(e-rate)*Euro
VER80
VER81
VER82
VER83
VER84
VER85
VER86
VER87
VER88
VER89
VER90
DOM80
DOM81
DOM82
DOM83
DOM84
DOM85
DOM86
DOM87
DOM88
DOM89
DOM90

2.248
0.593
1.038
-0.312
0.479
0.021
2.358
2.357
-0.006-0.018-0.272
0.258
0.295
0.374
-0.199-0.155-0.156-0.099-0.148-0.149-0.120-0.122-0.191-0.257-0.280-0.056
0.018
0.112
0.130
0.109
0.076
0.216
0.171
0.164
0.111
0.063

0.044
0.027
0.056
0.035
0.015
0.0042.945
0.436
0.018
0.005
0.091
0.089
0.300
0.070
0.078
0.083
0.114
0.121
0.135
0.151
0.115
0.118
0.129
0.137
0.150
0.037
0.039
0.041
0.043
0.048
0.050
0.057
0.060
0.065
0.069
0.073

Note: The regression had 2,217 observationsand an R2 of415

allows for characteristics not included in thespecification (our unobserved characteristics).
On the cost side, we include a constant aswell as the following vehicle attributes:ln(HP/Weight), ln(Size), and Air. We include region
dummies for Europe and Japan, as well as
trendsfor the United States, Europe,and Japan.
Finally, we also include the log of the exchange
rate of the exportingcountry (lagged one year)
and the log of the wage rate in the producingcountry. We experimentedwith the contemporaneous exchange rate and found its effect wasalways about zero and imprecisely estimated.
We include VER dummies for each year
since 1981, the year the policy was implemented.These dummyvariablesare set to one if
the VER applies to that automobilemodel. Ourbase case assumesJapanesemodels producedin
the United Statesdid not count againstthe VER,
while captive importsdid. Note thatthis implies
that Japanese wages and the yen to dollar exchangerate aredeterminantsof costs for captive
imports while U.S. wages are determinantsof
costs for the Japanese models produced in theUnited States.
The estimates for our base case and theirstandarderrorsare given in Table 5. We begin
with a discussion of the demand-sideparameters. When interpretingthese parameters,it isimportantto keep in mind that demand for aparticularcar is driven by the maximum, andnot by the mean, of the utilities heterogeneous
consumers place on that car. Hence, there aretwo ways to explain why cars with, say, highHP/Weightare popular.Either a high mean forthe distributionof tastes for HP/Weight or alarge varianceof tastes will have a tendency toincrease the share of consumers who buy carsModelI Treat VER as a type of cost, constraining firms to set

MR > MC.
⇒ sj +X(pk − mck − λt VERt )

k ∈Ff

∂sk=0
∂pj

I Intuition: Do J firms set prices at a point where MR isrelatively higher than US firms?

Main results
THEAMERICANECONOMICREVIEW

416

TABLE 5-ESTIMATED PARAMETERS OF THE DEMAND AND
PRICING EQUATIONS: BASE CASE SPECIFICATION

1971-1990 DATA, 2,217 OBSERVATIONS

Variable

Parameter Standarderror
estimate

Demand-sideparameters
Constant
HP/Weight
Size
Air
MP$-5.901
2.946
3.430
0.934
0.202

0.712
0.486
0.342
0.199
0.084

Standarddeviations
Constant(rn's)
HP/Weight
Size
Air
MP$

1.112
0.167
1.392
0.377
0.416

1.171
4.652
0.707
0.886
0.132

44.7944.541

Constantln(HP/Weight)ln(Size)
Air
TrendJapan
Japan*trend
Euro
Euro*trendlag[ln(e-rate)]ln(wage)

0.035
0.6041.291
0.484
0.018
3.255
-0.0363.205-0.032
0.026
0.356

0.310
0.063
0.106
0.043
0.004
0.667
0.008
0.525
0.006
0.024
0.079

VER81
VER82
VER83
VER84
VER85
VER86
VER87
VER88
VER89
VER90

-0.085-0.022
0.001
0.403
0.361
0.675
1.558
1.490
1.277
1.063

0.187
0.228
0.248
0.245
0.303
0.307
0.353
0.379
0.458
0.469

Means (,'s)

Term on price (a)(-P/Y)
Cost-side parameters

VER dummies

Japanese and European marginal costs aretrending slightly downwards.The elasticity ofmarginalcost with respect to wages is just overJUNE 1999

rates just do not seem to matter much.
This finding contrasts to other estimates of
exchange-ratepass-through(see Feenstraet. al.,1993), but our estimates are based on moredisaggregated data and on a more detailed
model of the industry.
There are several ways to interpretthe magnitude of the utility and cost parameters.One
way which is easy to understandand captures
the informationon both the utility and cost sidesof the model is to examine price-marginalcost
markups.These markupsdependon the demandelasticities implied by the O3'sand a's as well as
the marginal cost function parameters(all ofwhich have been jointly estimated).A representative sample of these markupsfor a handfulof1990 models representingthe quality spectrum
is presented in Table 6.20 These estimates appear quite reasonable and are generally in linewith other studies. The standarderrors of themarkupsare presented in column 4 and imply
that the markupsare quite precisely estimated.
(A discussion of how the standarderrors arecomputed is given below in "Implications,"
subsection C.)
The coefficients on the VER dummies address the following question:Suppose the VER
was instead implemented as a specific tax onJapanese automobiles, and no other aspect ofthe model changed.What is the level of that tax
that would generateequilibriumprices equal tothose we observe when we have the VERs? Acoefficient (or tax) of zero would imply that theVER did not raise the prices of Japanesecars,
while larger values correspondto a larger implicit tax. These coefficients are given in thebottom panel of Table 5.
In 1981, 1982,and 1983,thepointestimatesare
aboutzerowith a standarderrorbetween$187 and$248. Intheseyears,thepointestimatesimplythat
the VER had almost no effect on prices, and wecannotrejectthatthe effect was nil. In 1984 and1985, the pointestimatesof the implicittax rise to$403 and $361 respectively,but these estimateshave standarderrorsof $243 and$303. Again,wecannotrejectthe hypothesisthatthe VER did notraiseJapaneseprices,althoughit shouldbe notedSimulations

I VER causes J prices to climb substantially, US prices only

a bit.
I

Price sensitive consumers are the ones that switch.

I VER causes J profits to go up.
IVER implements the collusive outcome

I CS down 13 mil, profits up 10mil, total loss 3 milII

But standard error is 7.5mil.
Should use a tariff?