NBER WORKING PAPER SERIESEARLY 20TH CENTURY AMERICAN EXCEPTIONALISM:
PRODUCTION, TRADE AND DIFFUSION OF THE AUTOMOBILE
Dong Cheng
Mario J. Crucini
Hyunseung Oh
Hakan Yilmazkuday
Working Paper 26121
http://www.nber.org/papers/w26121

NATIONAL BUREAU OF ECONOMIC RESEARCH
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July 2019

The authors wish to thank Bettina Aten, Diego Comin, Alan Heston, Zhu Wang and Alex
Chernoff for constructive discussions, and participants at the International ComparisonsConference 2016, Midwest Macro Fall Meetings 2016, ISIR Session at the ASSA Meetings 2017,
Midwest Macro Spring Meetings 2017, Canadian Economic Association Annual Conference
2017, Midwest Macro Fall Meetings 2017, QED Frontiers of Macroeconomics Workshop 2018,
Midwest Macroeconomics Meetings (Fall 2018 and Spring 2019), and numerous seminars forhelpful comments and advises. Any remaining errors are the joint responsibility of the authors.
The views expressed herein are those of the authors and do not necessarily reflect the views of the
National Bureau of Economic Research.
NBER working papers are circulated for discussion and comment purposes. They have not been
peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies
official NBER publications.
© 2019 by Dong Cheng, Mario J. Crucini, Hyunseung Oh, and Hakan Yilmazkuday. All rights
reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit
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Early 20th Century American Exceptionalism: Production, Trade and Diffusion of the Automobile
Dong Cheng, Mario J. Crucini, Hyunseung Oh, and Hakan Yilmazkuday
NBER Working Paper No. 26121
July 2019
JEL No. F1,L62,N60,N70,O33
ABSTRACTThe beginning of the twentieth century provides a unique opportunity to explore the interaction of
rapid technological progress and trade barriers in shaping the worldwide diffusion of a new, highly
traded good: the automobile. We scrape historical data on the quantity and value of passenger
vehicles exported from the United States to other destination countries, annually from 1913 to1940. We model the rise of US automobile from global obscurity toward a level dependent upon
the extent of long-run pass-through of US prices into destination markets and destination GDP per
capita. The results based on a diffusion model with CES preferences and non-unitary income
elasticity shows that 62% of the gap in diffusion levels between the U.S. and the rest of the worldis due to price frictions such as markups, tariffs, and trade costs, while the remaining 38% is due toincome effects.
Dong Cheng
Lippman Hall 221
807 Union Street
Schenectady, NY 12308
chengd@union.edu
Mario J. Crucini
Department of Economics
Vanderbilt University
Box 1819 Station B Nashville,
TN 37235-1819 and NBER
mario.j.crucini@vanderbilt.edu

Hyunseung Oh
Department of Economics
Vanderbilt University
VU Station B, Box #351819
Nashville, TN 37235
hyunseung.oh@vanderbilt.edu
Hakan Yilmazkuday
Department of Economics
Florida International University
Miami, FL 33199
skuday@gmail.com

1. Introduction
This paper tells the coming-of-age-story of the automobile. Our narrative begins in 1913, one
year prior to Henry Ford’s introduction of full assembly-line production of the Model T chassis.
This process innovation has been credited with reducing labor input requirements for chassis
production from 12.5 to 1.5 (hours), a factor of more than 8 (Baldwin et al. (1987)). Shortly
thereafter, the average US domestic sales price of the automobile plummeted from $ 1,227 in
1913 to $ 659 in 1917 (in 1940 USD).1
Figure 1 presents a more complete history of the average US domestic sales price andexport unit values from 1913 to 1940. The distinctive convex shape of the time-path of therelative price of the automobile is characteristic of new product diffusion. The relative pricedeclines very rapidly in the first decade and stablizes by the mid-1920s.

The path of therelative price over time and across countries will be the key driver of product diffusion in ourmodel. Notice also that the average markup of export prices over domestic sales is about 20%
at the start of the sample and falls to zero by the mid-1920s. As we shall show later in thepaper, there is considerable cross-country variation around this average.
Based on theories of new product diffusion, one would expect automobile registrations per
capita to rise quickly from a zero base toward a saturation point as the relative price settles
into its long-run stationary position (which is about $550 in real 1940 dollars in the case of
the automobile).

Figure 2 presents time series on automobile registrations for the UnitedStates and an aggregate of 23 other nations, for which we also have macroeconomic data.2 As
the relative price of automobiles falls, aggregate adoption levels rise and when relative prices
stop falling, adoption rates tend to stabilize. Once the stock reaches its long-run steady state,neoclassical theory predicts that the stock of automobiles would be mainly driven by businesscycle shocks.
This diffusion story is largely born out by the evidence: a rapidly rising stock of automobiles from a low base toward a steady-state in the late 1920s, followed by a large negative
business cycle shock, the Great Depression. The striking feature of Figure 2 is that the US
automobile stock per capita is consistently 10 times higher than in the rest of the world: itreaches a peak of 200 automobiles per 1,000 population compared to less than 20 in the restof the world. The apparent voracious appetite for automobiles in the US has been noted in
the historical literature, but as far as we know, there has been no systematic documentation ofinternational diffusion patterns over time, nor an explanation for the quantitative differences
1
By US sales price, we mean the total value of domestic automobile sales divided by the quantity sold domestically. Automobile industry census of manufacturing data in 1929, 1931, 1933 and 1935 allow benchmark
comparisons of the these prices to average prices of automobiles at the factory gate. All are within 9% of theannual sales price data from the US statistical abstract.
2

The 23 countries in Figure 1 are: Argentina, Australia, Brazil, Canada, Chile, Colombia, Denmark, France,
Greece, Italy, Japan, Mexico, New Zealand, Norway, Peru, Philippines, Portugal, Spain, Sweden, Switzerland, theUnited Kingdom, Uruguay, and Venezuela.

1across countries. Our goal is to fill this gap.
This is much more challenging than first meets the eye. Even when one abstracts frominternational preference differences and restricts the functional form of preferences in eachcountry to the homothetic, constant elasticity form, the low adoption level abroad can be fully
accounted for by a loci of trade friction and elasticity pairs.
For example, using a traditional trade cost friction of 15%, the 10-fold difference between
the US and foreign (aggregate) automobile adoption can be fully accounted for with an Armington elasticity of 16. Our first result is to provide a comprehensive accounting of interwar
frictions equaling 79% (ad-valorem-equivalent) and a corresponding trade elasticity estimate
of about 5. By carefully measuring the full menu of interwar frictions, we demonstrate how
upward biases in the trade elasticity arise when trade frictions are under-estimated.
Our second result deconstructs the cross-country mean international price friction into its
individual parts. The benchmark estimation uses three cross-sections, 1928, 1929 and 1930
and includes four frictions: an export markup at the dock, an automobile import tariff, a traditional trade cost and a Penn Effect. Together these four frictions combine to an aggregate,ad-valorem relative price friction of 79%, when averaged across countries. The largest component is the Penn Effect accounting for 38% of the total friction, with the remaining threefrictions (export markups, tariffs and trade costs) accounting for about 20% each.
Our third result relates to the differences in the international price frictions across the
23 nations in our panel. The cross-sectional variance is substantial, at 28%. The Penn effectaccounts for almost the entire cross-sectional variance across destination markets. On theother hand, the tariff and export markups tend to cancel out. This negative covariance could be
due to US producers setting relatively low prices into high tariff markets; it is also consistent
with an endogenous national tariff-setting response to import penetration, or a combination ofboth.

2. Related Literature
Our work contributes to both the product diffusion literature and the voluminous empirical
work that estimates the Armington trade elasticity.
Economists have measured product diffusion in two ways. One measure takes flow purchases of the good (or accumulated stocks in the case of durables) and normalizes the quantity
purchased by an aggregate scale variable with the aim of finding a demand saturation point
for the ratio of the two. The automobile is a good case in point. Because very few households
will find it optimal to exceed one passenger vehicle per driving-age household member, a natural scale variable for the automobile is the one we use, population. Going back far enough intime, the level of adoption is zero and it rises toward a stationary quantity per capita. As with2

most product diffusions, there is a period of acceleration, followed by deceleration, in the rateof change in the adoption level. The inflection point in between is when the diffusion curve
switches from convex to concave. The technical appendix reports estimates of these reducedform diffusion curves for each country in our cross-section, including the US.
An alternative measure of diffusion is intended to document how new products or technologies replace old ones. The simplest such measure takes a simple count of a new and an old
vintage (or vintages) and divides each count by the total count, across all vintages currently inuse. This approach has the desirable feature that it measures the market share of each vintage. However, the measure is misleading if not carefully constructed, because new products
are different from old ones and some attempt must be made to convert them into a comparable
flow of consumption services (or production services in the case of intermediate inputs).
A surprising feature of the existing diffusion literature is how often just two vintages of
products are sufficient to characterize the relevant product space. In part, this may reflect
researchers selection of products or technologies that are differentiated enough to be economically interesting.3 One prominent historical example is the replacement of the steam engine
with the diesel engine in the powering of US locomotives. This process started in about 1935
and was not completed until the early 1960’s.4 A more recent example is rapid access memory(RAM) which also has consisted of at most two vintages at any point in time. In sharp contrast
to locomotive engines, the product cycles of RAM capacities are completed in only a few years(see, Jovanovic and MacDonald (1994)). It is worth noting that the economic impact of themove from steam to diesel is demonstrably more amenable to economic measurement than theadvance of RAM in personal computers. Part of the reason is that energy can be measured ona uniform scale (e.g., joules) and, using the laws of physics, a conversion based on mass, speed
and friction is possible. While the total economy-wide stock of RAM is quantifiable, measuring
the end economic uses to which this RAM is obviously a daunting task.
In the context of the passenger vehicle, similar modeling challenges present themselves.
Perhaps the most complete product chronology for automobiles is the volume by Baldwin etal. (1987); they summarize makes and models of automobiles spanning a century (1885 to
1987).

The authors devote at least a few paragraphs to each the top 1,000 models out ofapproximately 4,000 that business historians have unearthed.

In the interest of empiricaland theoretical tractability, our focus is on the substitution margin between automobiles andan aggregate of all other goods. This approach matches up more concretely with the Armington
assumption with automobiles being the US good and other goods being of foreign origin.
Following this traditional Armington-trade approach creates a point of contact with a voluminous literature that estimates trade elasticities. The recent literature has narrowed the3

For example, by focusing on electric appliances that replace mechanical ones, rather than roller blades replacing roller skates.
4Here, “started” and “completed” means dominance of one of the two technologies in powering locomotives.

3

range of plausible values from a low of about 3 (the lower bound reported in Simonovska andWaugh (2014)) to a high of about 13 (the upper bound of estimates in Romalis (2007)). Estimates can be difficult to compare across the literature due to the different set of goods, levelsof aggregation, time periods and estimation methods employed. Helpful in this regard is Anderson, Larch and Yotov (2015), who use a single panel (82 countries from 1990 to 2011 fromthe 8.0 version of the PWT); they report elasticity estimates spanning almost the complete
range found in our survey of the literature: 4 to 11. All of our elasticity estimates fall within
this range. However, the estimates are shown to fall toward the lower end of this range as we
successively add observed trade frictions of different types.
Our work is also related to Comin et al. (2018) who study the role of technological progress
and non-homothetic demand on international structural transformation from agriculture to
manufacturers and services. They attribute a large role to income changes in structural transformation and a small role to relative price changes. Our findings show that the accounting
was quite different during the interwar period, which featured a historic international tariffwar.

3. The Model
This section develops a theoretical diffusion curve for the automobile as the solution to a consumer optimization problem. Consumers choose an optimal mix of the stock of automobiles
and a composite of other goods in their aggregate consumption bundle in each year.
From this optimization problem, it is possible to derive a diffusion curve for the stock ofautomobiles. Using the diffusion curve for the US as the reference country (and the source ofimports by foreign destinations), the US and foreign diffusion curve can be combined to backout a theoretical wedge that reconciles foreign automobile registration levels relative to the US
as a function of the US domestic relative price of the automobile and foreign relative income(when preferences are not homothetic). The preference parameters governing this decision
are: a substitution elasticity, an income elasticity of automobiles relative to other goods, and ataste bias. Only the latter is allowed to be country-specific. The theoretical wedge is thus therelative price difference faced by foreign consumers relative to US consumers that completely
accounts for the different levels of diffusion observed in the data. In the empirical section,
this theoretical wedge is deconstructed into an export markup at the border, a tariff on US
automobile imports, a trade cost, a Penn Effect, and a residual.

3.1. The Consumers Problem
Consumers have preferences over passenger vehicles (which were refer to as automobiles hereafter) and a composite of all other goods. The appendix provides the detailed derivation of these4

optimal choices, subject to a period-by-period budget constraint. The maintained assumption
is that the intra-period Euler equations holds at each date for each country.
Following an extensive literature at the intersection of macroeconomics and trade, we allow for both homothetic and non-homothetic CES preferences. We follow Comin et al. (2018) interms of the functional form of the non-homotheticity. Specifically, the aggregate consumption
index for county j, C j,t , is implicitly defined via the constraint,
²

σ−1

1

²

1

σ−1

O σ
(Ω j C j,tA ) σ (A j,t ) σ + ((1 − Ω j )C j,t) (O j,t ) σ = 1.

(1)

The parameter, Ω j > 0 is a taste parameter. When the CES aggregator is used in trade theory, it is referred to as the Armington aggregator to denote aggregation is taken across goods
identified by their country of origin. In the two-good model referenced here we have: the US
automobile, A j,t , and a foreign bundle of all other traded goods, O j,t . The taste parameter Ω j
is commonly used to generate home bias in consumption to reconcile the theory with observed
trade shares. As is well-known, for every choice of the home bias parameter, there is an advalorem-equivalent trade cost the delivers the same degree of home bias in consumption, with
its value determined by the elasticity of substitution. Our approach is to attribute the so-called
home bias to observable trade frictions, while calibrating the preference share parameter, Ωsuch that it reproduces the observed interwar US automobile expenditure share. Finally, ² A(²O ) is the income elasticity of demand for automobiles (other goods). When these two elasticities are equal to σ − 1, the preferences collapse to the standard CES, unitary income elasticity
formulation.
Using the CES demand functions that arise from these preference structures, a few linesof algebra are necessary to derive a theoretical diffusion curve, which expresses the demand
for automobiles, A j,t as a function of the sum of automobile demand and the real consumption
index of all other goods. Formally, we have
ω j,t =A j,t
A j,t + O j,t

=

1

(2)

A σ
1 + θ i (RP j,t)AA
where, RP j,t≡ P j,t/P O
and θ i ≡ (1−Ω i )/Ω i . The corresponding diffusion curve for non-homotheticj,t

CES preferences is:ω j,t =A j,t
A j,t + O j,t=1²O −² AA σ
1 + θ i (C j,t)(RP j,t
)

.

5

.

(3)

3.2. The Theoretical Wedge
In what follows it is convenient to utilize the concept of a theoretical wedge, denoted as 1 + τ∗j,t .
By theoretical wedge, we literally mean the ad-valorem-equivalent wedge between the US
domestic relative price and the foreign relative price that is necessary to exactly account for
the relative adoption rates of the automobile at home and abroad, given the agents preferences
and relative incomes.
A
To fix notation, the relative price of the automobile in country j, is RP j,t, with j = u,denoting the comparable relative price in the US domestic market. The theoretical wedge isdefined as:
AA
RP j,t= (1 + τ∗j,t )RP u,t.

and, given the home and foreign diffusion equations derived earlier, a few lines of algebra showthat the theoretical wedge must satisfy the following equation for the homothetic CES case:

1 + τ∗j,t =

³
´¡
´
¢
· 1 + θ i (RP A )σ ωu,t − 1 ¸ σ1
u,t

ω j,t

(4)

A σ
θ i (RP u,t)

and the corresponding theoretical wedge for the non-homothetic CES case is:

1 + τ∗j,t =

³
´
´¡
¢
· 1 + θ i (RP A )σ (C u,t )(²O −² A ) ωu,t − 1 ¸ σ1
ω j,t

u,t

A σ
θ i (RP u,t) (C j,t )(²O −² A ).

(5)

Notice that if we observe the same diffusion in the US and country j, ωu,t = ω j,t , this implies
an absence of trade frictions, τ∗j,t = 0, for homothetic preference case. When preferences are
non-homothetic, we also require aggregate consumption to be equal, C u,t = C j,t .
The empirical challenge is to estimate the trade-friction and elasticity pair that best fits
the equilibrium quantities observed in each country. Figure 3 provides a straightforward
illustration. It shows two demand curves intersecting at the US source price and the stockof automobiles in the US. This point is set to match the US adoption of about 200 passenger
vehicles per 1,000 population at a relative price of $500 (in constant 1940 USD). The othertwo points reconcile the US and foreign choices (20) with two measures of the trade friction
and two different elasticities. One measure of the trade friction is the one typically used ingravity estimation, the physical trade cost, which we set to 15%, based on the seminal workof Hummels (2001). The second measure is the total of all empirical frictions in our interwar
data, including the markups, tariffs, trade costs and the Penn Effect, which is about 79%.
The figure illustrates the fact that underestimation of the friction leads to an overestimation of the trade elasticity. In the case of the automobile, the elasticity is biased upward from
5.4 to 34.1, when only the gravity trade friction is included.

6

4. The Data
The lion’s share of data used in this study is a newly constructed historical panel of US automobile exports to worldwide destinations. These data were collected from annual reports filedby the Director of the Bureau of Foreign and Domestic Commerce to the Secretary of Commerce. These reports are published as an annual serial volume called the Foreign Commerceand Navigation of the United States (FCNUS). The data pulled from these reports are: the dollar value of exports and number of passenger vehicle exported to each destination country asreported in Table No. 3, Exports of Domestic Merchandise From the United States, by Articles
and Countries, During the Calendar Year. The resulting unbalanced panel spans 81 nations
from 1913 to 1940. Due to the empirical demands of our project most of the analysis focuses ona balanced panel of 23 countries for which macroeconomic and tariff data are also available.
The export quantity data is combined with foreign production data and a stock-flow model
to estimate the stock of passenger vehicles in each destination market. These constructs arecompared to international passenger vehicle registration data come from the Cross-country
Historical Adoption of Technology (CHAT) database compiled by Comin and Hobijn (2009).5
Because the CHAT registration data are available for only a handful of countries during thetime span of our study, the role of the CHAT is limited to cross-validation of our estimates ofautomobile stocks, when both measures are available.
Export prices are not recorded in the FCNUS, we compute them by dividing the value ofexports to a particular destination by the number of units exported to that destination. In the
trade literature, these average prices are called ‘export unit values,’ which is the phrase we use
throughout this paper. Aside from the level of detail they provide about the international pricedistribution of automobiles, important for our purposes is that they are not index numbers,
since our goal is to relate absolute price level differences to differences in the physical quantity
purchased.
As our focus is on the role of relative prices in determining foreign automobile adoption
compared to that of the US, it is crucial to understand the valuation method in these export
data. As stated on page v. of FCNUS (1928): “Articles of domestic production when exported
shall be valued at their actual cost or the values which they may truly bear at the time ofexportation in the ports of the United States from which they are exported. In contrast, foreignexports which are goods not changed in condition and previously imported are recorded whenexported in terms of their import value.” Thus our export unit values are free-on-board prices.
Our approach follows the recent macroeconomics and trade literature in which Euler equations are used with a set of observable variables to back-out the composite wedge that makes
5

CHAT is an unbalanced panel dataset with information on the adoption of over 100 technologies in more than150 countries since 1800. The data is available for downloading at: http://www.nber.org/data/chat.

7

the Euler equation hold exactly over time (and here across nations).6 The goal, then, is an empirical deconstruction of a panel of 23 nation-specific theoretical wedges over the period 1913
to 1940 into a set of observable trade frictions (or proxies for them). The frictions include: 1)
markups at the dock, 2) tariffs, 3) trade costs (freight and insurance), and 4) retail distribution
costs at the destination, the Penn effect. Due to the novelty of these data, sources and methods are discussed in considerable detail in this section. Readers interested in the elasticity
estimation may skip to section 5 (the Results) without loss of continuity.

4.1. International Stocks of Automobiles
The first data requirement of the theory is an estimate of each nation’s stock of automobiles,
as this is what appears in the representative agent’s utility function. There exist very few
national estimates of the stocks of automobiles for the interwar period, our aim is to fill thisvoid.
As with the construction of any capital stock, there are two methods of estimation. One
entails taking a census of the outstanding stock (analogous to a population census), the alternative accumulates the flow of new purchases (investment), depreciates the pre-existing stockby a fixed proportion and sets an initial condition for the stock. Given data availability, we will
rely almost exclusively on the latter method. For countries and time periods where registration data and our constructed stocks overlap, they will be compared to one another as a formof empirical cross-validation.
There are advantages and disadvantages of each estimation approach. The use of registration data is arguably the most direct method as it is the closest to a full census count of
automobiles in use. And yet, the potential for significant estimation bias is real. The available registration data does not record the year the automobile was produced. This leads toan upwardly biased estimate of the effective units of transportation services embodied in thestock, because there is no account made of depreciation. Consider a newly purchased vehicle,
it receives the same weight in the registration data as a vehicle that is five years old. At adepreciation rate of 0.2, the five-year old vehicle should receive a weight of 0.4. This problem
is exacerbated in the context of a newly diffusing durable good, such as the automobile, because the average age is rising fast in the initial period of the diffusion before settling into a
steady-state.
Registration data may conversely lead to downward biased estimates of true automobile
stocks because of lags in the introduction of registration requirements or lax enforcement of existing ones. In the US, automobile production starts in the late 1800’s, but many US states do
not introduce registration as a legal requirement until the 1930s. The timing of product entry
and registration was close in California, the first state to introduce registration requirements.
6

This wedge accounting method was first introduced into the business cycle literature by Chari et al. (2007).

8

It did so in 1901.

While less is known about the timing of the introduction of registration

requirements and their enforcement in other nations, we would expect less uniformity acrossnations, than across US states.
Flow data, in the form of automobile sales, are available for only a handful of nations,most of whom are also producers of automobiles. In order to achieve something close to aninternational census of the stock of automobiles by country, some creativity is called for. This
is where the US export quantity data gains currency, provided the following three assumptions
hold to a reasonable approximation.
Assumption 1: Initial condition. When registration data is lacking, the initial condition
for the stock of automobiles in country j, A j,1912 is set to zero in 1912 (the year before
the first year of our study).

With the exception of the United States and a handfulof advanced countries that produce automobiles, this seems to be a reasonable initialcondition. Moreover, the fact that we are studying diffusion of a new product works in ourfavor because the impact of the estimation error of the initial stock literally ‘depreciates’
away.
Assumption 2: Domestic production. When no domestic production data is found, it is set
to zero.

For most nations of the world (there are over 80 destination markets in thefull panel), this is literally true. Even in the case of the advanced industrialized countries, with a few exceptions, foreign production levels paled in comparison to the UnitedStates.

In 1928, world production is estimated to be 5,273,941 of which the UnitedStates produced 4,359,759 vehicles (82.6%), compared to 242,382 in the next largest single producer, Canada (4.6%).7 The largest producing nations in Europe (U.K, France,
Germany and Italy) account for an additional 629,400 (11.9%) of world production. Nineother European nations produced the remaining 1%. The dominance of the US industry
in production is truly staggering.
Assumption 3: Non-US exports and re-exports. For the US export flow to a destination
to add to the stock of automobiles consumed in that destination, it is required that the
automobiles not be re-exported to a third country and also that non-US producers are
not substantial sources of imports. We have no information on the extent of re-exports.
Table 1 presents data for the four largest exporters of automobiles worldwide, the UnitedStates, Canada, the United Kingdom and France. Consistent with our assumptions, theUS is by far the dominant source even among these industrialized countries.
Turning to the details, estimation of the automobile stock in country j, year t, A j,t , using
the stock-flow method is given by the following equation:
A j,t = (1 − δ)A j,t−1 + X j,t + Y j,t
7

Note that foreign subsidiaries of US companies operated in Canada and these are included in the Canadianproduction numbers. Thus these numbers slightly understate US production dominance.

9where X j,t represents the additions to the stock via exports to destination j from the US, Y j,t
is production in the destination, and δ is the depreciation rate (set to 0.2). The reader should
keep in mind, there is no domestic production in most international destinations (i.e., Y j,t = 0
for most j).
Figure 4 presents estimates of the stock of automobiles per 1,000 population for Canada,
the UK, France and Italy. The first observation to make is that while the volume of automobile production by these countries was dramatically lower than that of the United States, it
was sufficient to supply most of domestic demand. This fact is evident in the enormous gulf
between the black dashed lines and the red dashed lines, which represents the contribution ofdomestic production to the evolution of the stock. The reader is cautioned to the fact that welack production data before 1922. Comparing the registration-based estimate to the stock-flow
estimate, the correspondence is close for the U.K. and Italy, but not so for Canada and particularly, France. The tendency for overestimation of stocks using registration data in three of thefour cases is consistent with the lack of depreciation of the stocks when the registration data
is used.
The Philippine Islands is more typical of the international cross-section in the sense that
US automobiles were the only, or by far the dominant, source of supply. Figure 5 plots the registration and the US export-based estimates of the stock using export flows. The registration
data, again, consistently overstates the adoption of the automobile.

4.2. US Prices and International frictions
Our goal is to provide a comprehensive accounting of interwar trade frictions, as they pertain
to the automobile. Toward this end, consider the following identity that relates the observed
US relative price of the automobile (RP uA ) to the conjectured destination relative price (RP jA )of the automobile in destination market j:
RP jA = (

P jA
P uA

)(1 + s j )(1 + t j )(S j PuPj)RP uA = (1 + τ̂ j )RP uA .

The retail price difference between the US and destination country j is attributed uniquely tofour trade-related frictions. As they appear in the equation, they are:
1. A markup of the export prices over the domestic price, (P jA /P uA ). This markup is a standard feature of trade models that feature imperfect competition. In these settings, theproducer has the ability to segment markets and engage in third-degree price discrimination (pricing-to-market).
2. A trade cost, s j , associated with the gravity model of trade. Typically this margin is
estimated by regressing bilateral trade data on distance (a proxy for the cost) and othercontrols.
10

3. An official barrier to trade, the ad-valorem-equivalent tariff imposed by country j onimports of US automobile, t j .
4. A macroeconomic friction, the aggregate real exchange rate (i.e., the long-run deviationfrom PPP). This is referred to as the Penn Effect in what follows.

4.3. Discussion of the Individual Frictions
This subsection discusses each of the individual frictions that make up the total estimateddeviation of destination prices from the US price as well as the sources and methods used toconstruct them.

4.3.1. Markups
The traditional definition of a markup in international trade is the free-on-board price to aparticular destination market relative to the domestic price.
Toward this end, the export unit values in USD terms are defined as the US dollar valueAof exports of passenger vehicles to country j (V j,t) divided by the number of passenger vehicles
A
exported to that destination, (X j,t
):
A
P j,t
=

A
V j,t
A
X j,t

.

To compare the entire cross-sectional distribution of these markups to US relative prices ofautomobiles, we divide them by the US CPI index. Figure 6 plots the median and first andthird quartile of these relative prices from 1913 to 1940.
The international relative price distribution has three notable features: 1) a convex shape,with relative prices starting high, dropping rapidly and stabilizing in the last two-thirds of thesample, consistent with the earlier value-weighted version (Figure 1); 2) a non-trivial amountof dispersion in the cross-section as evident in the width of the interquartile range; and 3) the
median and cross-sectional variance are unstable during World War I.

4.3.2. Tariffs
The US commercial policy narrative begins with campaign promises of increased tariffs by
Herbert Hoover in 1928 (the business cycle peak). Originally envisioned as measures to help
agriculture after the post World War I decline in the relative price of agricultural goods, thetariff revisions quickly extended to virtually all sectors of the economy (Irwin and Kroszner(1996)). Most of the available tariff history relies on the ratio of customs duties to dutiable
imports as a proxy for protectionism.

Aside from the obvious problem of substitution bias,

there is no reason to expect the duty on automobiles to be close to this aggregate measure.
11

The most comprehensive analysis of microeconomic tariff distortions in the United States is
Bond et al. (2013), which covers more than 5,000 tariff-lines. The mean ad-valorem-equivalenttariff rose from 32% to 46% after the passage of Hawley-Smoot in June 1930. The tariff levels
ranged from 0% to over 200%. Specific to automobiles, US import duties on automobiles wereactually cut from 25% to 10% (though import duties on automobile parts remained constant at
25%).
In the 1920s, many countries had much higher duties on automobiles than did the UnitedStates and raised them, partly in retaliation to higher US duties on their exports to the UnitedStates. We have two cross-sections of automobile tariffs spanning 23 countries. The medianad-valorem-equivalent tariff rate across these countries increased from 17% to 34%, from 1920
to 1921. Averaging across the two years, the cross-country average tariff was 25%. Table 2reports country level ad-valorem-equivalent tariff rates for all 23 countries in 1920, 1921 andthe average of these two years. The calibration results below use the average tariff across 1920
and 1921, the cross-sections for which we also have GDP data.

4.3.3. Trade Costs
One of the most robust empirical relationships in the trade literature is the fact the bilateral
trade between nations is declining in the distance between them. This ‘gravity’ model of tradealso has found that the volume of trade between two nations is roughly proportional to the
product of their aggregate output.
Following the empirical trade-gravity model, we regress the logarithm of the ratio ω j,t /ωu,t(the inverse of the ratio of our Euler equation) on a constant and the logarithm of distance(between capital cities):z j,t = ln ω j,t − ln ωu,t = 0.52 − 0.44 ln(d j ) + ² j,t .
(0.73)(0.08)

The coefficient on distance is −0.44, is remarkably close to the average reported in the meta
analysis of the gravity literature (Disdier and Head (2008)).
As is well-known from the theoretical gravity literature, the reduced form coefficient on
distance is the product of a substitution elasticity and the slope coefficient linking distance totrade costs (typically: ln(1 + τ) = β ln(d j )). In principle, it is possible to disentangle these two
margins, by substituting the predicted values of the gravity equation for quantities into theEuler equation with the US domestic relative price set to unity, to generate a cross-sectionof implied trade cost frictions. As if often the case with this method of indirect inference,
the absolute size of the friction is implausibly large: over 50% ad-valorem-equivalent for aplausible trade elasticity. Rather than rely on this dubious estimate, we use direct estimatesof automobile freight costs Hummels (2001). While his work uses contemporary data, the advalorem-equivalent levels are more plausible, in the neighborhood of 15%.

12

4.3.4. The Penn Effect
The Penn Effect is the robust positive correlation between aggregate price levels and income
level across countries. To understand its role in studying the demand for the automobile,
suppose the LOP held exactly for automobiles. Since prices are, in general, higher in richcountries, the automobile would be relatively inexpensive in high income countries. In practice,
how much less expensive they will be depends on the difference between the share of retail
distribution costs for the automobile relative to the other goods in the consumption basket.
While it is difficult to determine these values for the interwar period, contemporary estimatesof the distribution share for the aggregate consumption basket are about 0.55, while thosefor the automobile are about 0.25. Therefore, the relative Penn Effect is 0.25-0.55=-0.30. Put
differently, an automobile that satisfies the Law-of-One-Price across destination based upon
the price at the destination port will be 3% less expensive in relative terms across countries
that have a 10% real income differential. Due to possible structural changes as the retailsector grows in economic importance latter in US history, we include a sensitivity analysis for
the Penn effect.

5. Results
The section reports the results of estimating substitution and income elasticities. We also
conduct variance decompositions of the theoretical wedge into its observable empirical trade
frictions: trade costs, tariffs, export markups and the Penn Effect.
From this point forward, we suppress the time subscripts and mention the time dimension
only when it is used in the estimation.

5.1. Elasticity Estimation
We begin by noting variables that are pre-set, including normalizations. The automobile shareof aggregate consumption expenditure is set to Ω A, j = 0.03 based on the extensive study ofdurable goods during the interwar period by Onley (1985). The US CPI is used to proxy for the
O 8
price index of the non-automobile basket, P u,t. The relative price of the automobile in the US,A
RP u,t, is set to 1 in 1921. Finally, real PPP-adjusted income in each country is normalized to

the level of real PPP-adjusted income in the US in 1921. In words, US real income is 1 in 1921
and other country’s income is measured relative to this base.
The elasticity of substitution and differential income elasticity (for the non-homothetic
preference case) are estimated by minimizing the distance between the theoretical wedge and8

Because of the small expenditure share of automobiles, replacing the CPI index with a constructed nonautomobile price index yields the same quantitative results.

13the total measured empirical friction:1(1 + τ∗j,t ) = 

σ
e
A σ ω
((1 + (RP u,t) )( ωeu,t ) − 1)j,tA σ(RP u,t
)

 =(

A
P j,t

S j,t P u,t

P u,t

P j,t

)(1 + s j )(1 + t j )(A)(1 + ² j ) .

(6)

At this point, the reader may wish to refer back to the empirical section to understandthe composition structure of the aggregate empirical friction. Notice that there are two timevarying components and two time-invariant components. The time varying empirical frictions
are the export unit values relative to US domestic prices and the aggregate real exchange rate.
The time-invariant empirical frictions are the traditional trade cost and the foreign tariff on
US automobile imports.

5.2. Cross-sectional versus Time Series Variation
One key advantage of our panel constructs is that the price and quantity data are not index
numbers. As such, there is meaningful variation both in the cross-sectional dimension andthe time series dimension. To fully understand the sources of microeconomic variation in ourpanel, we follow the variance decomposition method employed by Crucini and Telmer (2019).
var(ln(1 + τ∗j,t )) = var j [E t (ln(1 + τ∗j,t ))] + E j [var t (ln(1 + τ∗j,t ))]
V

= C+T

In words: the total variance of the logarithm of the theoretical wedge in the panel (V ) may be
decomposed into the cross-sectional variance (across nations) of the conditional mean (the time
averaged wedges), denoted by C, and the mean (average across countries) of the conditionalvariance (time series variance by country) relative to these long-run means, denoted by T.
We begin with the variance decomposition of the quantity ratios, since the variance of thetheoretical wedges will depend upon the elasticity of substitution. The first row of Table 3
reports this two-way analysis of variance for the diffusion ratios (foreign relative to the US).
The total variation in relative automobile diffusion per capita is substantial at 8.55%. Of thistotal, 7.18% is cross-sectional variation – variation in the time-averaged levels of diffusion. The
remaining 4.64% is time series variation around these long-run, county-specific, time averages.
The lower panel repeats the exercise for the theoretical wedges using calibrations of theelasticity of substitution of 6 and 9. The theoretical Euler equation predicts that as the elasticity of substitution declines, the variation of the relative price for a given observed variationin relative quantities, must rise. This is manifest in the increase in the total variance of thetheoretical wedge from 14.2% to 21.1% as the elasticity of substitution is lowered from 9 to
6. Notice that while the absolute level of the variance rises, its composition remains highly
skewed in favor of the cross-sectional component. The ratio of cross-sectional to total vari14

ance is about three-quarters in both cases. Note, also, that this ratio is similar to that of thequantity ratios reported in the upper part of the table.

5.3. Elasticity Estimates
Table 4 reports a comprehensive set of non-linear least squares estimation results. The computation method we follow is the Levenberg-Marquardt nonlinear least squares algorithm that
iterates parameters of interest to minimize the sum of squared deviations.
There are 32 estimated substitution elasticities. The columns labelled time averaged referto estimation results where the data have been averaged over the sample periods noted. The
columns labelled pooled cross-section use the full panel data, again for the sample periods
noted. Notice that the elasticity estimates are virtually identical across these cases. Thisfinding is entirely consistent with the variance decomposition method of the previous section.
Recall that 75% of the variation in the relative diffusion level is cross-sectional, not time series.
An implication of this is that the elasticity estimates are not much affected by averaging away
the latter source of variation. A more subtle implication of this is that the results are also
insensitivity to the sample period of estimation. This can be seen by comparing estimatesacross rows in a particular column and panel. For example, the substitution elasticity when
all observed frictions are included is 5.385, for the 1928-1930 period and 5.621, for the 19131940 period.
Given that most of the transitional diffusion dynamics have been worked off by the 19281930 period, these are the results we consider most reliable given our use of a static Euler
equation. But, for the purpose of substitution elasticity comparisons, it really does not mattermuch. What matters a great deal, is the measurement of the empirical frictions.
The panels are organized so that results with the full set of trade frictions appear in Panel
A and the single, export markup friction, results appear in Panel D. In between, the Penn
Effect is set to an intermediate level (i.e., less strongly correlated with destination income thanin the benchmark) or eliminated entirely. As predicted by the theory with CES homothetic
preferences, the substitution elasticity increases monotonically as the empirical frictions are
removed, one-by-one. Put differently, the substitution elasticity is biased upward to the extent
the empirical frictions are underestimated (or ignored). These biases are substantial. Consider
the time-averaged case using the 1929-1930 sample. The elasticity of substitution is 5.385 withall three frictions, it rising to 9.142 when the Penn Effect is removed and further to 20.4 when
all frictions except the export markups are excluded. The non-homothetic case tells a similarstory. Without the Penn Effect, the elasticity of substitution is 7.3 and it rises to 17.2 when the
only trade friction is the export markup friction.
Notice that the Penn Effect also has consequences for the estimated differential income
elasticity across automobiles and other goods. Recall, the Penn Effect works to make prices

15

relatively low in high income destinations (high real exchange rate or price level countries).
Consequently, the Penn Effect works in the same direction as the differential income elasticity
for automobiles. As the Penn effect is weakened, or eliminated, the estimated income differential effect strengthens.
The bottom line of the estimation results is that the elasticity of substitution is in therange of 5 to 9, with our preferred estimates closer to the bottom of this range. Preferred,
being either the homothetic case with a full set of frictions, or the non-homothetic case withat least the trade cost and tariff frictions included. These elasticities are in the range of thosefound in the contemporary literature. However, the size and composition of the trade frictions
may be quite different. To explore these issues, we turn to a decomposition of the theoreticalwedge into individual empirical frictions.

6. Variance Decomposition of Wedges into Frictions
In what follows, our focus is on the time averaged data for 1928-1930; effectively cross-sectionalvariance at about the time countries had reached a stationary, pre-Depression adoption level.

6.1. Variance Decomposition of the Trade Frictions
Table 5 reports two benchmark cases, the case will all four empirical frictions (each enumerated in a separate column) and a case that excludes the Penn Effect. The first section of eachpanel is the cross-country average friction, so a single value. The average foreign friction is
0.79 in the data, when we include all four components of the frictions, effectively a 79% advalorem-equivalent friction. The implied theoretical wedge necessary to match the quantity
data is 73%, so our cumulative empirical friction is 6% higher than needed to account forthe mean difference of adoption between the average foreign country and the US. The second
row normalizes all columns by the theoretical wedge, indicating the empirical friction is 8.1%
higher than the theoretical friction implied by the quantity data.
The third row normalizes each empirical trade friction to their sum, to give a sense of theirrelative contribution. The largest individual component is the Penn Effect, which accounts foralmost 40% of the total. The remaining three empirical frictions, the export markup, tariff andtrade cost each contribute about 20%.
Panel B omits the Penn Effect. In this case the aggregate empirical friction is only 49%
since the Penn Effect was 30% in Panel A. Keep in mind that the estimated elasticity increases
to compensate, from 5.385, in Panel A, to 9.142, in Panel B. The upshot is that the theoreticalwedge and empirical frictions are still comparable in magnitude, but both are smaller in absolute value. The contributions of the export markup, tariff and trade cost rise in proportion,
but – of course – remain the same relative order of magnitude to one another as was the case16

with all four trade frictions included. Now, these three trade frictions each contribute in theneighborhood of one-third to the total variance.
The lower two panels explore the variance of the theoretical and empirical frictions acrosscountries. These variance decompositions are computed using the covariance method:var j (ln(1 + τ∗j )) =X

cov j (ln(1 + τ∗j ), ln(1 + τ i j )) .

i

where τ∗j is the theoretical wedge in country j and t i j is the ad-valorem-equivalent friction oftype i in country j.
Like the mean, the variance of the theoretical wedge across countries is higher whenthe elasticity of substitution is lower, 0.262 in Panel C compared to 0.154 in Panel D. The
model with all empirical frictions accounts for 53.5% of the cross-sectional variation in thetheoretical wedges (and, by implication, quantities). However, when the Penn Effect is omitted
that fraction drops to just 2%.
The dramatic decline in the ability of the model to account for cross-country differencesin the theoretical wedge when the Penn effect is omitted, reflects two features of the empiricalfrictions.
First, the trade cost is set to a common value across countries. While this is a calibration
decision, recall the distance between each nation and the US is about equal with the exceptionof a few bilateral pairs. So, the fact of the matter is that distance is not going to account forthe cross-sectional variance of the theoretical wedge even though it contributes significantly to
explaining the mean theoretical wedge.
Second, the tariff is negatively correlated with the aggregate theoretical wedge. This
likely reflects the joint endogeneity of export unit values and tariff setting. As the price of US
automobiles falls and this gets reflected in export unit values, countries may be raising theirtariffs to offset the pass-through of automobile prices into their respective domestic markets.
Alternatively, Ford may be charging lower markups into destination markets with higher tariffs to establish a market presence in those destinations. The upshot is that these two margins
tend to cancel out in the cross-section, leaving the Penn Effect to capture the lion’s share of thecross-sectional variation.
We do not report analogous decompositions of wedges for the case of non-homothetic preferences because the numbers are very similar. Instead, we turn to decompositions of the diffusion levels themselves, in terms of the predicted contribution of prices (substitution effects)
and income (income effects).

17

6.2. Variance Decomposition of Relative Automobile Adoption Rates
Table 6 investigates the model’s implications for variation in the relative diffusion rates under
non-homothetic CES preferences using the same frictions and data as used in Table 5.
Beginning with the mean, the average ratio of foreign to US diffusion per capita is 0.055.
Recall, that this means US consumers have about 18 (1/0.055) registered passenger vehicles
per 1,000 population for every 1 vehicle registered per 1,000 population in foreign countries.
The substitution (or price) effect accounts for 62% of this difference and the relative income
effect accounts for the remaining 38%, when all four frictions are included. When the Penn
Effect is ignored (see Panel B), the decomposition is virtually unchanged.
Turning to the cross-country differences in diffusion (relative to the US), in Panels C andD, the standard deviation is about 10%. About 80% of this is accounted for by prices and about
20% by income. Again, these results are not materially affected by the inclusion of a Penn
Effect.

7. Conclusion
This paper has investigated the diffusion of automobiles in the U.S. versus the rest of the world
between 1913-1940. Since virtually all automobiles were produced in the U.S. (and exported to
the rest of the world) during this period, the U.S. exports and the corresponding source prices,
together with data on various trade frictions, have been investigated.
The results based on a diffusion model with CES preferences and non-unitary income
elasticities have shown that about 62% of the gap in diffusion levels between the U.S. and therest of the world is due to price frictions such as markups, tariffs, and trade costs (with almost
equal contributions of about 20%), while the remaining 38% is due to income effects.

18

References[1] Anderson, James E., Mario Larch, and Yoto V. Yotov. 2015. “Growth and Trade with Frictions:
A Structural Estimation Framework,” NBER Working Papers, No. 21377.
[2] Baldwin, Nick, G. N. Georgano, Michael Sedgwick, and Brian Laban. 1987. The World
Guide to Automobile Manufacturers. Facts on File Publications.
[3] Bresnahan, Timothy F. and Daniel M.G. Raff. 1991. “Intra-Industry Heterogeneity and theGreat Depression: The American Motor Vehicles Industry, 1929-1935,” Journal of Economic History, 51: 317-331.
[4] Chari, V.V., Patrick J. Kehoe and Ellen R. McGrattan. 2007. “Business Cycle Accounting ”
Econometrica, 75(3):781-836.
[5] Bond, Eric W., Mario J. Crucini, Tristan Potter, and Joel Rodrigue. 2013. “Misallocation
and Productivity Effects of the Smoot-Hawley Tariff,” Review of Economic Dynamics, 16: 120-134.
[6] Comin, Diego A. and Bart Hobijn. 2009. “The CHAT Dataset,” NBER Working Paper, No. 15319.
[7] Comin, Diego, Danial Lashkari and Marti Mestieri. 2018. “Structural Change with Long-run
Income and Price Effects,” mimeo.
[8] Crucini, Mario J. and Christopher I. Telmer. 2019. “Microeconomics Sources of Real Exchange
Rate Variation,” National Bureau of Economic Research Working Paper No. 17978.
[9] Disdier, Anne-Célia and Keith Head. 2008. “The Puzzling Persistence of the Distance Effect on
Bilateral Trade,” Review of Economics and Statistics, 90(1): 37-48.
[10] Hummels, David. 2001. “Toward a Geography of Trade Costs,” mimeo, Purdue University.
[11] Irwin, Douglas A. and Randall S. Kroszner. 1996. “Log-rolling and Economic Interests in the
Passage of the Smoot-Hawley Tariff,” Carnegie-Rochester Conference Series on Public Policy, 45:
173-200.
[12] Jovanovic Boyan and Glenn M. MacDonald. 1994. “The Life Cycle of a Competitive Industry,”
Journal of Political Economy, 102(2): 322-347.
[13] Lee, Changkeun. 2016. “Was the Great Depression Cleansing? Evidence from the American
Automobile Industry, 1929-1935,” mimeo, University of Michigan.
[14] Onley, Martha. 1985. “Advertising, Consumer Credit, and the “Consumer Durables Revolution”
of the 1920s,” Ph.D. Dissertation, University of California, Berkeley.
[15] Romalis, John. 2007. “NAFTA’s and CUSFTA’s Impact on International Trade,” Review of Economics and Statistics, 89(3): 416-435.
[16] Simonovska, Ina and Michael E. Waugh. 2014. “The Elasticity of Trade: Estimates and Evidence,” Journal of International Economics, 92(1): 34-50.

19[17] Vickers, Chris and Nicolas L. Ziebarth (2017). “The Census of Manufactures: An Overview,”
Work in Progress, Auburn University.

20

Table 1. Bilateral Trade in Automobiles (1923-1928)
Non-US exporters
Importer

UnitedUnitedCountryStatesCanadaKingdom

France

Other

Total

Argentina

87.0

11.5

0.2

1.3

0.0

100

Brazil

92.0

6.9

0.1

0.9

0.0

100

Canada

93.4

4.9

1.7

0.0

0.0

100

Columbia

86.7

13.1

0.0

0.0

0.2

100

France

85.7

2.2

12.0

0.0

0.0

100

Greece

100

0.0

0.0

0.0

0.0

100

Italy

82.8

0.0

0.6

16.6

0.0

100

Norway

81.8

12.2

2.5

3.6

0.0

100

Peru

100

0.0

0.0

0.0

0.0

100

Philippine Islands

100

0.0

0.0

0.0

0.0

100

Portugal

90.7

0.0

9.3

0.0

0.0

100

Sweden

93.3

6.5

0.2

0.0

0.0

100

Uruguay

90.2

9.8

0.0

0.0

0.0

100

Venezuela

85.6

13.4

0.0

0.0

1.0

100

Average

90.7

5.8

1.9

1.6

0.0

100

Australia

75.8

21.7

2.5

0.0

0.1

100

Japan

74.8

14.7

2.9

7.6

0.0

100

New Zealand

46.5

43.6

9.9

0.0

0.0

100

Spain

54.1

0.9

1.1

43.9

0.0

100

Switzerland

31.8

0.0

0.8

67.4

0.0

100

United Kingdom

44.2

29.2

0.0

26.6

0.0

100

Average

54.5

18.4

2.9

24.2

0.0

100

Notes. The upper panel of the table list countries for which the United States accounts for
80% of more of their automobile imports. The lower panel are countries that source moresignificantly from Canada, France or the United Kingdom. See the data appendix for detailsof original data sources.

21

Table 2. Tariffs on Passenger Automobiles
Country

Average

1920

1921

Panel A: Constant Tariffs
Argentina

0.320

0.320

0.320

Canada

0.388

0.425

0.350

Chile

0.239

0.238

0.239

Colombia

0.012

0.012

0.011

France

0.450

0.450

0.450

New Zealand

0.200

0.200

0.200

Norway

0.150

0.120

0.180

Philippine Islands

0.000

0.000

0.000

Sweden

0.150

0.150

0.150

Switzerland

0.084

0.084

0.084

United Kingdom

0.333

0.333

0.333

Uruguay

0.265

0.240

0.290

Venezuela

0.017

0.017

0.016

Mean

0.201

0.199

0.202

Standard Deviation

0.149

0.148

0.151

Panel B: Escalating Tariffs
Australia

0.322

0.100

0.543

Brazil

0.207

0.158

0.257

Denmark

0.076

0.029

0.123

Greece

0.120

0.090

0.150

Italy

0.373

0.154

0.591

Japan

0.425

0.350

0.500

Mexico

0.179

0.000

0.358

Peru

0.246

0.110

0.382

Portugal

0.768

0.196

1.339

Spain

0.470

0.077

0.863

Mean

0.319

0.126

0.511

Standard Deviation

0.204

0.098

0.365

22

Table 3. Variance Decomposition of Diffusion and Theoretical Wedge (percentage)
Cross

Time

SectionSeries

Total

Total

7.18

4.64

8.55

70.6

σ=9

12.2

7.3

14.2

73.9

σ=6

18.3

10.5

21.1

75.1

Relative Diffusion

Cross-section

Theoretical Wedge

Notes. The theoretical wedge is backed out using:(1 + τ∗j,t ) =· ¡(1+(RP A )σ )¡ ωu,t ¢−1¢ ¸ σ1
u,t

ω j,t

A )σ
(RP u,t, where ωu,t and ω j,t are

diffusion ratios and measured using estimated stocks per capita for the foreign countries (foreign production
combined with US export flows) and registration per 1,000 population for the US case.

23

Table 4. Substitution and Income Elasticity Estimates
Homothetic CES
Substitution Elasticity
SampleNon-homothetic CES
Substitution Elasticity

Relative Income Elasticity

Time

PooledTime

PooledTime

PooledAveraged

Cross-sections

Averaged

Cross-sections

Averaged

Cross-sections

Panel A: NLS with All Four Empirical Frictions
1928-1930

1913-1940

5.385

5.387

7.644

7.622

1.579

1.563

(0.355)(0.222)(1.916)(1.185)(1.21)(0.748)

5.621

6.124

7.269

8.257

1.177

1.573

(0.317)(0.101)(1.388)(0.429)(0.892)(0.275)

Panel B: NLS with Four Empirical Frictions (Weak Penn Effect)
1928-1930

1913-1940

6.805

6.81

7.457

7.447

0.365

0.357

(0.579)(0.359)(1.932)(1.17)(0.993)(0.601)

7.092

7.637

7.256

8.257

0.094

0.371

(0.528)(0.158)(1.477)(0.431)(0.780)(0.228)Panel C: NLS with Three Empirical Frictions (No Penn Effect)
1928-1930

1913-1940

9.142

9.157

7.307

7.307

-0.777-0.782(1.158)(0.707)(1.962)(1.171)(0.799)(0.476)

9.464

10.04

7.254

8.286

-0.969-0.810(1.078)(0.293)(1.566)(0.437)(0.668)(0.190)Panel D: NLS with Only Export Markups
1928-1930

1913-1940

20.40220.74917.22517.56-0.595-0.571(4.016)(2.727)(7.448)(4.945)(1.308)(0.848)21.07321.94316.22917.623-0.946-0.891(2.772)(1.15)(4.037)(1.624)(0.747)(0.311)

Notes. Standard errors are in parentheses.

24

Table 5. Decomposition of Frictions(Homothetic CES Preferences, Time Averaged Data, 1928-1930)
Theoretical

Empirical

ExportAd-Valorem

Penn

Trade

Wedge

Friction

MarkupTariffEffectCost

Residual

Panel A. Analysis of the Mean Across Countries(Four Empirical Frictions, σ = 5.385)
Mean

0.731

0.790

0.190

0.161

0.299

0.140

-0.059Proportions

1.000

1.081

0.260

0.221

0.409

0.192

-0.081

1.000

0.240

0.204

0.378

0.177

Proportions

Panel B. Analysis of the Mean Across Countries(No Penn Effect, σ = 9.142)
Mean

0.432

0.491

0.190

0.161

NA

0.140

-0.060

Proportions

1.000

1.138

0.440

0.374

NA

0.324

-0.138

1.000

0.386

0.329

NA

0.285

Proportions

Panel C. Analysis of the Variance Across Countries(Four Empirical Frictions, σ = 5.385)
Std. dev.

0.262

0.280

0.189

0.108

0.194

0.000

0.270

Proportions

1.000

0.539

0.186

-0.174

0.527

0.000

0.461

1.000

0.511

0.032

0.457

0.000

0.505

0.257

-0.421

0.711

0.000

0.448

Proportions
Corr (τ∗j , τ i j )1.000

Panel D. Analysis of the Variance Across Countries(No Penn Effect, σ = 9.142)
Std. dev.

0.154

0.211

0.189

0.108

NA

0.000

0.260

Proportions

1.000

0.020

0.315

-0.295

NA

0.000

0.980

1.000

0.769

0.231

NA

0.000

0.014

0.257

-0.421NA

0.000

Proportions
Corr (τ∗j , τ i j )

1.000

25

0.583

Table 6. Decomposing Diffusion into Price and Income Effects
Non-homothetic CES Preferences, Time Averaged Data 1928-1930
Relative

Price

IncomeDiffusion

EffectEffectPanel A. Analysis of the Mean Across Countries(Four Empirical Frictions, σ = 7.644, ² N A − ² A = 1.579)
Mean

0.055

0.034

0.021

Proportions

1.000

0.619

0.381

Panel B. Analysis of the Mean Across Countries(No Penn Effect, σ = 7.307, ² N A − ² A = −0.777)
Mean

0.055

0.037

0.018

Proportions

1.000

0.677

0.323

Panel C. Analysis of the Variance Across Countries(Four Empirical Frictions, σ = 7.644, ² N A − ² A = 1.579)
Std. Dev.

0.100

0.081

0.024

Proportions

1.000

0.802

0.198

Cross-country Corr.

1.000

0.988

0.842

Panel D. Analysis of the Variance Across Countries(No Penn Effect, σ = 7.307, ² N A − ² A = −0.777)
Std. Dev.

0.100

0.085

0.020

Proportions

1.000

0.840

0.160

Cross-country Corr.

1.000

0.988

0.777

26

1600

Passenger automobile prices relative to CPI (1940=100)

U.S. average wholesale price
U.S. average export unit value
1400

1200

1000

800

600

400
1913

1916

1919

1922

1925

1928

1931

1934

1937

1940

Year

Figure 1. US Price and Export Unit Value (Value of sales divided by quantity sold).

27

250

25

200

20

150

15

100

10

50

5

0
1913

1916

1919

1922

1925

1928

1931

1934

1937

ROW passenger vehicle registrations per 1,000 population

U.S. passenger vehicle registrations per 1,000 population

U.S. passenger vehicle registrations
ROW passenger vehicle registrations

0
1940

Year

Figure 2. US and ROW Passenger Vehicle Registrations per 1000 Population.

28

ROW Long Run with All Wedges: (σ,τ)=(5,79%)575

ROW Long Run with Trade Cost Only: (σ,τ)=(34,15%)

Relative Price

900

US Long Run
500

0

20

50

100

150

200

Quantity Ratio

Figure 3. Identification Issues: Demand Elasticities and Trade Frictions.

29

250

UK

150

Autos per 1,000 population

Autos per 1,000 population

Canada

120
90
60
30
0
1913

1918

1923

1928

1933

40
30
20
10
0
1913

1938

1918

1923

Year
France

40
30
20
10
0
1913

1918

1923

1928

1933

1938

Italy

10

Autos per 1,000 population

Autos per 1,000 population

50

1928

Year

1933

8
6
4
2
0
1913

1938

Year

Registration
Est. Stocks w/o Home Production
Est. Stocks w/ Home Production

1918

1923

1928

1933

1938

Year

Figure 4. Registration and Stock-Flow Estimates (Automobile Producers).

30

Philippine Islands

2.5

Registration
Est. Stocks w/o Home Production

Autos per 1,000 population

2

1.5

1

0.5

0
1913

1916

1919

1922

1925

1928

1931

1934

1937

1940

Year

Figure 5. Registration and Stock-Flow Estimates (Automobile Non-producer).

31

Passenger automobile export unit value relative to CPI (1940=100)

75th quantile of export unit value
Median of export unit value
25th quantile of export unit value

1600

1200

800

400
1913

1916

1919

1922

1925

1928

1931

1934

Year

Figure 6. US Export Unit Values by Country.

32

1937

1940