Voluntary Export Restraints on Automobiles: …perso.unifr.ch/david.stadelmann/course/aussenwirtschaft1...Rodrik, Steve Stern, David Weinstein, Marina V.N. Whit-man, Frank Wolak, and

Voluntary Export Restraints on Automobiles:Evaluating a Trade Policy

By STEVEN BERRY, JAMES LEVINSOHN, AND ARIEL PAKES*

We evaluate the voluntary export restraint (VER) that was initially placed onexports of automobiles from Japan in 1981. We evaluate the impact this policy hadon U.S. consumer welfare, firm profits, and forgone tariff revenue from its initiationthrough 1990.(JEL F13)

In May 1981, a voluntary export restraint(VER) was placed on exports of automobilesfrom Japan to the United States. Our primarygoal in this paper is to provide some econo-metric evidence on the welfare implicationsof the VER. We evaluate the impact of thispolicy on the United States through 1990. Weestimate the policy’s impact on both con-sumer welfare and, since the auto industry isan oligopoly, U.S. auto producer profits. Wealso estimate the potential impact this policymight have had on U.S. government revenuehad the policy been implemented differently.As such, we provide (what we believe is) thefirst complete evaluation of a strategic tradepolicy. In the course of evaluating the VERs,we also address the issue of when the policysignificantly impacted prices. We find that thepolicy mattered in some years, but not inothers. We now provide an overview of ourresults on each of these issues.

I. The Voluntary Export Restraint onAutomobiles

A. The Policy and the Magnitudeof Its Impact

As noted above, the VER was initiated inMay 1981, and at that point Japan agreed tolimit total Japanese exports of passenger cars tothe United States to 1.68 million cars.1 Theenforcement mechanism was up to the Ministryof Trade and Industry (MITI) and was rein-forced by U.S. political pressure. MITI gaveeach Japanese manufacturer a separate sub-quota, allegedly based on past sales. If a firmviolated its allocation, there was no clear en-forcement mechanism in place. Cars made inthe United States by Japanese firms (e.g., Hon-das made in Ohio) did not count against thelimits, although cars imported from Japan andsold under a U.S. brand were counted againstthe VER. These so-called captive imports werecars usually produced by Mitsubishi, Suzuki,and Isuzu and sold under the Dodge/Chrysler orGeo labels by Chrysler and General Motorsrespectively.

The agreement was initially scheduled to ex-pire after three years. In 1984, though, the VERwas extended and the 1.68 million car figurewas increased to 1.85 million.2 As the economyrecovered, the Reagan administration dropped

* Berry and Pakes: Department of Economics, YaleUniversity, 37 Hillhouse Avenue, New Haven, CT 06520(e-mail: [email protected]; [email protected]);Levinsohn: Department of Economics, University of Mich-igan, Ann Arbor, MI 48109 (e-mail: [email protected]).We are grateful to Jagdish Bhagwati, Alan Deardorff, Rob-ert Feenstra, Gene Grossman, Mustafa Mohatarem, DaniRodrik, Steve Stern, David Weinstein, Marina V.N. Whit-man, Frank Wolak, and five anonymous referees for helpfulcomments. Ms. Laura Polly at the International Trade Com-mission (ITC) helped sort out data issues. We gratefullyacknowledge funding from National Science FoundationGrant No. SES-9122672.

1 Japan also agreed to limit exports to Puerto Rico to70,000 cars and to limit sport utility vehicle (SUV) exportsto 82,500. This gave a total limit on U.S. imports fromJapan of 1,832,500 vehicles.

2 When exports to Puerto Rico and SUVs are included,the figure is 2.016 million.

400

its support for the VER. In 1985, Japan agreedto extend its already nominally voluntary exportrestraint. From 1985 through early 1992, ex-ports to the United States were limited to 2.30million passenger cars.3 In 1988, MITI an-nounced that for the first time, the quota had notbeen met. However MITI stated that the VERwould be maintained because it was not clearthat imports would stay low in 1988–1989.

To the extent that the VERs impacted pricesin the auto industry, consumer welfare and firmprofits change. We examine the magnitude ofthe VER’s impact on U.S. welfare. In so doing,we address the following “big-picture” ques-tions. First, how much did the VERs benefit thedomestic producers and how much did they hurtJapanese producers? Also, how were Europeanfirms affected by the policy? Second, were theVERs sound domestic public policy and, if not,could they have been if they had been imple-mented differently? The point estimates of ourmodel imply that: (1) summing over the yearsfor which the VER’s raised Japanese prices, theVERs increased the profits of U.S. producers byabout ten billion (1983) dollars, and this esti-mate has a standard error of about seven billiondollars. We also find that U.S. producers re-sponded to the VERs by selling more cars, butthey did not significantly raise prices as it wastypically the price-sensitive consumer whoswitched from Japanese to domestic cars; and(2) the VERs resulted in moderate net welfarelosses to the United States (our point estimate ofthe loss is close to $3 billion, but it has astandard error of $7.5 billion).

We also compute what would have happenedto U.S. welfare had the VERs instead beenimplemented as tariffs or quotas. However, thiscalculation requires us to assume that the tariffswould not cause any change in the cars mar-keted in the United States or lead to trade retal-iation of any form. Under these questionableassumptions, replacing the VERs with a tariffwould have enhanced U.S. welfare by about 8.3billion (1983) dollars with a standard error of8.3 billion dollars, leaving open the possibilitythat strategic trade policy could have actuallyworked. This change in welfare is comprised of

three components—the above-mentioned in-crease in domestic profits, the forgone tariffrevenue, and the change in consumer welfare.We estimate that the revenue forgone by usinga VER instead of a tariff was 11.2 billion dollars(with a standard error of 3.1 billion dollars).This forgone revenue almost equals the loss inconsumer welfare of 13.1 billion dollars (with astandard error of 2.5 billion dollars).

B. The Policy and the Timing of Its Impact

As a reasonable first pass at the data, weexamine figures on U.S. imports from Japanduring the VER years. Table 1 provides suchdata. The second column lists imports as re-ported by the U.S. International Trade Commis-sion (ITC). These figures are for the April1–March 31 “VER year” and include sport util-ity vehicles as well as sales to Puerto Rico.4

These ITC figures are comparable to the VERlimit listed in the second column.5 (This columnalso includes the SUV’s and Puerto Ricansales.) Column 3 lists the difference. Accordingto the official U.S. statistics, imports exceededthe VER in 1981 (barely) and in 1983–1986. In1987–1990, imports fell short of the limit. Untilthe 1988 VER year, the difference between theimports and their limit was relatively small.

Table 1 might lead one to believe that theVERs were responsible for limiting imports inthe early years of the policy (leading to higherprices for Japanese cars), and that the VERs hadno impact on imports in the later years (andhence no impact on prices). However, therewere differences of opinion on this matter, andthese manifested themselves in newspaper ac-counts of the period.6 In particular, there are at

3 This figure rises to 2.506 million when SUVs andshipments to Puerto Rico are included.

4 Neither the sport utility vehicles nor Puerto Rican salesare in theAutomotive News Market Data Book(Crain Com-munications, 1984–1988) data set we use below.

5 We are grateful to a referee as well as Ms. Laura Pollyof the ITC for clarifying the VER limits.

6 The Reagan administration gave conflicting predictionsabout the impact of the VERs, asserting that they wouldhelp the domestic industry but would not restrict car sales“enough to affect the price.” (U.S. Trade Representative BillBrock in the May 2, 1981,New York Times.) Trade Repre-sentative Brock claimed that the VERs would facilitate U.S.firms attempts to obtain financing for several billion dollarsof needed new investment by providing a stable short-termfuture for the domestic industry. Roger Smith, the Chairman

401VOL. 89 NO. 3 BERRY ET AL.: VOLUNTARY EXPORT RESTRAINTS ON AUTOMOBILES

least five somewhat interrelated reasons fordoubting what might seem, at first glance, to bethe obvious implications of Table 1.

(i) The VER year typically spanned twomodel years. Since cars can be invento-ried, and since there was a reported large

inventory of Japanese cars in stock in1981, it is possible, indeed perhapslikely, that firms may have decided to useup their allocation in order to obtain theoption value conferred by the inventoryshould demand pick up later. For exam-ple, if it looked like Nissan would not beable to sell its 1981 allocation, Nissanmight still opt to export the cars to theUnited States. Late in the 1981 VERyear, Nissan would be selling its 1982model cars, and these cars could, if de-mand picked up, then be sold during the1982 VER year (even though they wereshipped during the 1981 VER year). Thisprocedure can be shifted forward until ayear when demand is sufficiently high.

(ii) The strategy of maintaining an ability tomeet future increased demand when theneed arose might have looked particu-larly attractive in the early years of theVER. In the early 1980’s, demand forcars was well below trend due to veryhigh consumer interest rates and the re-cession. With a prime interest rate ofalmost 19 percent in 1981, demand forcars was just not strong. As late as 1985,the prime rate was still about 10 percentwith consumer rates yet higher. This hada substantial dampening impact on thedemand for autos. This too suggests theJapanese would not have sold more carsin the early 1980’s had the VER not beenthere.

(iii) It was clear that MITI’s allocations werebased, at least loosely, on existing marketshares. Hence, during the recession of theearly 1980’s, Japanese firms may haveshipped cars to the United States in anattempt to fill their allocations and hencepreserve those allocations for future usewhen demand would presumably behigher. This strategy would implylowerprices as Japanese firms tried to fill theirallocations.

(iv) There is the question of why MITI agreedto the VERs at the outset. Politics and thethreat of other alternative policies mayhave played a role. Still, the quantity dataare consistent with the view that the limitswere set sufficiently high so that they hadno effect whatsoever. Under this view, Jap-

of General Motors, stated that “in a 10 million car market, adecline of 140,000 vehicles will have little immediate impact”(United Press International, May 2, 1981). Smith also claimedthat Japanese firms were sitting on an inventory of 500,000vehicles that would buffer the impact of the VER. News storiesfollowing the announcement generally adopted the tone thatthe short-term impact was expected to be small, although manyof those quoted were not disinterested parties. United AutoWorkers (UAW) President Douglas Fraser predictably claimedthe 1.68 million figure was too high to have much of an impact,while on the other side of the Pacific, Japanese newspaperswere critical of the accord and were skeptical that it would domuch to help the American industry. (See the May 3, 1981,New York Timesquotes from theTokyo Shimbun.) On the otherhand, there were many accounts of the difficulty of obtainingspecific base models of Japanese cars in the period followingthe VER.

TABLE 1—U.S. AUTOMOBILE IMPORTS FROMJAPAN

Year International TradeCommission data

U.S. imports fromJapan including

Puerto Rico

VER limit Difference

(Imports-VER)

1981 1,833,313 1,832,500a 8131982 1,831,198 1,832,500 21,3021983 1,851,694 1,832,500 19,1941984 2,031,250 2,016,000b 15,2501985 2,605,407 2,506,000c 99,4071986 2,518,707 2,506,000 12,7071987 2,377,383 2,506,000 2128,6171988 2,115,304 2,506,000 2390,6961989 2,015,920 2,506,000 2490,0801990 1,911,828 2,506,000 2594,172

Sources:The ITC figures are for “VER years” which ranfrom April 1 to March 31. The ITC data are from the Mayissue ofThe U.S. Automobile Industry: Monthly Report onSelected Economic Indicators,published annually by theU.S. International Trade Commission.

a Computed as 1.68 million autos to the United States;82,500 “utility” vehicles to the United States, and 70,000vehicles to Puerto Rico.

b Of the 2.106 million total, 1.85 million were autos soldto the United States.

c Of the 2.506 million total, 2.30 million were autos soldto the United States.

402 THE AMERICAN ECONOMIC REVIEW JUNE 1999

anese firms were in fact not constrained,and the limits in the first several years wereset at about market demand anyway. In-deed, it is perhaps because the limits wereset so high that the Japanese agreed tothem.

(v) During the late 1980’s, when the recessionhad ended and the interest rates had de-creased, the demand for new cars in-creased. The Japanese, though, may havebeen hesitant to increase shipments. Ifthere was a significant inventory of carswhen demand first picked up [see point (i)above and footnote 6], this would havebeen the time to “clean off the shelves.”Also, the Reagan administration neveragreed to the higher limits, having publiclydropped its support for the VER, and thereremained substantial pressure from theUAW, some automakers, and some sectorsof Congress to keep Japanese imports low.Japan may have elected not to push toohard, and instead used some self-restraintafter the limits were raised to 2.3 million.Some industry observers thought that ifJapan’s market share topped 25 percent,the U.S. would put up new protection.Rather than run into the “buzzsaw of pro-tection,” the Japanese may have elected tokeep imports below their announced VERlimits. Hence, while MITI might have beenhesitant to formally commit to a lower ag-gregate limit, it may have pressured firmsin subtle ways to keep prices high and saleslow.

And, as noted above, it may instead be thatthe Japanese sold about their limits during theearly years of the VER because the constraintprevented them from selling more and that theydid not sell their limits in the later years becausedemand was insufficient. The important point isthat one cannot simply examine the VER limitsand exports and then “know” when the VERimpacted prices.

Hence, it seems it is insufficient to merelyexamine VER limits and recorded data on ex-ports to the United States and then deduce whenthe VER led to higher prices. Rather, an eco-nomic model of the impact of the VER needs tobe analyzed. Our strategy is to specify an equi-librium model of the auto industry. We are very

explicit on exactly what assumptions we make,and we engage in extensive sensitivity analysis.Our results concerning the timing of the impactof the VER are as follows. We find that theVERs did not significantly raise prices whenthey were first initiated, but they were respon-sible for higher prices of Japanese cars in thelater 1980’s. Accounting for direct foreign in-vestment by the Japanese auto producers intothe United States does not really change thisconclusion. In particular, we find that the VERsfirst contributed to higher Japanese prices in1986, and that they continued to contribute tohigher prices throughout the rest of the decade.This concludes our review of the results. (Read-ers interested only in a fuller discussion of theresults, but not the methodology used to obtainthem, can skip to Section V.)

This paper has, of necessity, a large method-ological component. This is due to some largediscrepancies between the standard theoreticalmodels and the actual structure of the automo-bile market. While theory is typically con-structed around models with two countries,symmetric firms each producing one product, aconstant elasticity of demand between differen-tiated products (or homogeneous products), arepresentative consumer with a love of variety,and observed marginal cost, empirical workmust confront a very different situation. In thecase of the U.S. automobile market, there aremultiple firms of vastly different sizes, almostall of which produce multiple products. Thesefirms are from about a half dozen differentcountries. There are, in any given year, roughly20,000 unknown elasticities and they are notequal. These elasticities play a key role in de-termining the Nash equilibrium prices firmscharge. There are over 90 million householdspotentially in the market and they are quiteheterogeneous. Finally, marginal cost is unob-served. Dealing carefully with these facts andconstraints, while still obtaining explicit guid-ance from an equilibrium oligopoly model, re-quires new methodological tools, which we takelargely from Berry et. al. (1995b) (henceforthBLP).

As in any policy analysis of the VERs, inorder to arrive at our conclusions we have tomake a host of very detailed assumptions aboutfunctional form and behavior. We are expliciton exactly what these assumptions are, hence


allowing other researchers to evaluate andexpand our analysis.7 We also provide extensivesensitivity analyses investigating how changesin these assumptions impact results.

This paper is organized into seven sections.In Section II, we review some of the existingempirical literature examining the VERs on au-tomobiles. In Section III, we outline the under-lying theoretical model used here to evaluate theVERs, while Section IV discusses the method-ology used to estimate this model. Section Vpresents a discussion of the data and the basecase results, while Section VI is focused ondetermining how robust our results are to sev-eral alternative theoretical and econometricspecifications. Conclusions and caveats aregathered in Section VII.

II. The Previous Literature

At the most general level, we hope this papermight contribute to the debate on the applica-bility of the insights of the strategic trade policyliterature. On the one hand, some of the econ-omists most responsible for the development ofthe theory of strategic trade policy have arguedeloquently against its use in the public policyarena. See, for example, Paul Krugman’s (1994)Peddling Prosperity: Economic Sense and Non-sense in the Age of Diminished Expectations.On the other hand, the insights from the strate-gic trade policy literature appear to have strucka chord with some currently powerful policymakers and advisors.

Since the early theoretical models are nowover a decade old, one might have expected thatthere would be several econometric studies in-vestigating exactly this question in a multitudeof industries. We know of no econometric stud-ies of strategic trade policy. This absence isdocumented in the recent review of empiricalstudies of trade policy by Robert C. Feenstra(1995). As noted in Feenstra’s survey, the em-pirical studies of strategic trade policy havebeen simulation models in which simple theo-retical models are parameterized and experi-ments run.

While we know of no econometric studiesinvestigating the efficacy of an implemented(possibly) strategic trade policy, there havebeen several studies of international trade andthe U.S. automobile industry. While a completesurvey of this literature is beyond the scope ofthis paper, we provide an overview of some ofthis work. (See Levinsohn [1994] for an ex-tended survey.)

Some of the first studies of the effects ofVERs on the U.S. automobile industry were byFeenstra (1984, 1988). These studies focused onthe phenomenon now referred to as quality up-grading. Feenstra documented that when theVERs were implemented, the list prices of Jap-anese cars as well as the base-model character-istics of those cars increased. Using data from1979 to 1985,8 he showed that some of theobserved price increases in Japanese cars couldbe accounted for by corresponding increases in“quality,” such as more horsepower, larger ve-hicle size, and the like. Hence, if one onlylooked at the change in prices, without adjustingfor the concurrent change in quality, one wouldoverestimate the price rise due to the VERs.

Avinash K. Dixit (1988) constructed a simplesimulation model of the U.S. automobile indus-try in which there were two types of products,U.S. and Japanese. Assuming linear inverse de-mands and constant marginal cost, Dixit cali-brated his model to perfectly fit data that wereaggregated in this way. This was done for theindustry in 1979 and again for 1980. Drawingon elasticities and estimates of marginal costfrom various sources, Dixit computed theopti-mal strategic trade policy and compared thewelfare gain this would have yielded relative tothe simpler policy of levying a standard most-favored-nation tariff of 2.9 percent. Dixit foundthat the gains from employing strategic tradepolicy would have been very small—on theorder of 17 to 300 million dollars depending onthe policy tools adopted and the parametersselected.

Elias Dinopoulos and Mordechai Kreinin(1988) treat the U.S. automobile industry as ahomogeneous product perfectly competitive in-dustry with linear supply and demand schedules

7 To facilitate this, all of our data and programs will bemade available on the web at http://www.econ.lsa.umich.edu/j˜amesl.

8 Not all the Feenstra papers used all these years of data,but Feenstra (1988) uses all years.


and compute the triangles that comprise thedeadweight loss from the quality-adjusted priceincrease the VER induced.

A more recent and more sophisticated em-pirical investigation of the effect of the auto-mobile VERs on the United States is PinelopiGoldberg (1995).9 In that paper, Goldbergestimates a structural oligopoly model of theU.S. automobile industry using both product-level data and consumer-level data from theConsumer Expenditure Survey(CES). Her an-nual data cover 1983 to 1987. Goldberg firstestimates a logit-based demand system fromthe consumer data in the CES. This yieldsdemand elasticities that feed into the oligopo-listic firms’ profit maximizing first-order con-ditions. These first-order conditions resultfrom multiproduct firms maximizing profits ina Bertrand fashion. Goldberg finds that theVERs were binding in 1983, 1984, and again,but much less so, in 1987. A principal mes-sage of Goldberg’s paper is that the maineffect of the VERs came immediately afterthey were imposed and that in later years thepolicy had little or no effect. Goldberg reportson the profit-shifting aspect of the trade pol-icy, but notes that “the objective of our anal-ysis is not to compute national welfare, but toassess the quota impact on prices, productionand market shares ... .” We return to her con-clusions after presenting our results.

We address the broader question of whetherthe VERs were sound U.S. public policy. Inparticular, when the entire picture of U.S. firmprofits, consumer welfare, and government rev-enues are considered, who were the winners,who were the losers, and what was the magni-tude of these gains and losses? To address thesequestions, we use a structural model of staticoligopoly. This model is presented in the nextsection.

III. A Model of VERs in Oligopoly

To proceed we need a model of demand andsupply for the new car market. The model weuse has four primitives: (i) a distribution for

consumer utility functions; (ii) a distribution forproducer cost functions; (iii) a specification forthe rules governing the impacts of the VER’s;and (iv) a behavioral assumption which deter-mines equilibrium. We take our specificationfor the distribution of the utility and cost sur-faces from our earlier work (BLP, 1995b) whichwe review briefly now. We next provide ourspecification for the VERs and then consideralternative equilibrium concepts.

A. Utility and Demand

Our demand system is obtained by explicitlyaggregating over the discrete choices of indi-viduals with different characteristics.10 The util-ity that a consumer derives from a given choicedepends upon the interaction between the con-sumer’s characteristics, to be denoted byn, andthe product’s characteristics. Thus the prefer-ence for a car of a particular size may depend onfamily size, while price trade-offs may dependon family income. We distinguish betweenthree kinds of product characteristics; those thatare observed by the econometrician but deter-mined before the current period (such as horse-power and vehicle size) to be denoted byx,price, orp, which is also observed but may bechanged in every period, and unobserved (byus) product characteristics, denoted byj. Thevectorj is meant to take account of character-istics that are observed by market participants,but are either inherently difficult to measure(such as “prestige”) or are potentially measur-able but are not included in our specifications(usually because of a lack of data).

The consumer hasJ 1 1 choices. She canchoose to purchase one of theJ cars marketed,or she can choose not to purchase a new car. Welet the (indirect) utility derived by consumerifrom choosing alternativej be

U~n i, pj, xj, j j; u!,

where u is a vector of parameters to be esti-mated. Consumeri chooses alternativej if andonly if

9 A less technical paper that also addresses many of theseissues is Goldberg (1994).

10 For a discussion of the advantages of demand systemsobtained in this way, and a review of the relevant literature,see BLP (1995b) and the literature cited therein.


U~n i, pj, xj, j j; u! $ U~n i, pr, xr, j r; u!,

for r 5 0, 1, ...,J,

where alternativesr 5 1, ..., J represent pur-chases of the competing differentiated products.Alternative zero, or the outside alternative, rep-resents the option of not purchasing any of thoseproducts and allocating all expenditures to othercommodities. It is the presence of this alterna-tive that allows us to model changes in the totalquantity of automobile purchases.

Let A j(u) be the set of values ofn that inducethe choice of goodj when the parameter vectoris u:

(1) A j~u! 5 $n : U~n, pj, xj, j j; u!

$ U~n, pr, xr, j r; u!,

for r 5 0, 1, ...,J%.

The market share,sj, of a product is given bycomputing the fraction of the population withn[ Aj. That is,

(2) sj~p, x, j; u! 5 En[A j~u!

P0~dn!,

whereP0 provides the distribution ofn.A note on functional forms is appropriate

here. Computational constraints have frequentlyinduced the traditional discrete-choice literatureto analyze models in which utility is additivelyseparable into a component that depends onlyon product-level attributes, sayd j, and a distur-bance, say« ij ; i.e., U(n i, pj, xj, jj; u) 5 d j 1« i , j. The « i , j are assumed to be independentlyand identically distributed (i.i.d.) acrosschoices, as the specification then enables one tocompute market shares from the solution to aunidimensional integral (if, in addition, the« aredistributed multivariate extreme value, theneeded integral has an analytic form). However,the computational simplicity that these assump-tions produce comes at a large cost. These as-sumptions result in a model which, no matterthe parameter estimates (or the precise values ofthed j), implies that when consumers substitute

away from one product they will not substitutetowards products with similar characteristics,but rather to products with large market shares;a fact which leads to counterintuitive cross-price elasticities (see BLP, 1995b).11

To enable richer substitution patterns we al-low different consumers to have different inten-sities of preferences for different characteristics.We do this in a tractable way via a randomcoefficients utility specification. The utilityfunction for consumeri , considering productsindexed byj , is

(3) uij 5 xjb# 1 j j 2 a ipj

1 Skskxjkn ik 1 « ij

for j 5 1, ..., J,

while ui0 5 s0n i0 1 « i0.

The « ij are traditional i.i.d. extreme value(“logit”) draws, which capture an idiosyncratictaste of this consumer for this product. The termxjb# 1 j j, whereb# is a parameter to be esti-mated, is common to all consumers. This termallows the mean level of utility to vary withobserved and unobserved characteristics. Con-sumers then have a distribution of tastes foreach of the product characteristics. For eachcharacteristick, consumeri has a tasten ik,which is drawn from an i.i.d. standard normal.The parameterssk capture the variance in con-sumer tastes. Similarly, the parameters0 cap-tures additional variance in consumers’ tastesfor the outside good. Because the outside goodis in fact a broad category including, e.g., all

11 Related properties of the standard assumptions havebeen noted by several authors and have led to severalalternative modeling assumptions. Probably the most wellknown of the modifications is the nested logit. In the nestedlogit the researcher provides an a priori classification ofproducts into groups and then has substitution patternsconstrained only between members of the same group andbetween a member of one group and members of any othergroup (see N. Scott Cardell [1991] for an intuitive discus-sion). An alternative, and one which is closer to our spec-ification, is the random coefficients model used by JerryHausman and David Wise (1978). This specification doesnot produce an analytic integral for the shares. However, ifthe dimension of the random coefficients is small enough(as it was in the Hausman and Wise case), numerical inte-gration can be used to solve for those shares.


used cars and public transport, we expect theidiosyncratic variance for this alternative to belarger than the variance for the “inside” goods.

The terma i is the consumer’s distaste forprice increases. As in BLP, we assume that thedistribution of a i varies with income. Accord-ingly, we assume thatai has a time-varyingdistribution that is a lognormal approximationto the distribution of income in U.S. householdsin each year. Ifyi is a draw from this lognormalincome distribution, then

a i 5a

yi,

wherea is a parameter to be estimated. In thisway, price sensitivity is modeled as inverselyproportional to income.12

Because the utility specification in (3) allowsconsumers to differ in their preferences forproduct attributes, consumers who substituteout of, say, a large car will tend to be consumerswho like large cars and, precisely because ofthis preference, will substitute disproportion-ately to other large cars. As a result, the speci-fication in (3) allows for a much richer set ofsubstitution patterns than does the traditionallogit model.

The random coefficient generalization of thelogit model does, however, carry the cost of anincreased computational burden. Now, to obtainthe market shares implied by the model we willneed to evaluate ak 1 1-dimensional integral.As shown in Pakes (1986), this aggregationproblem can be solved by simulation.

The other novel feature of our model is theallowance for unmeasured product attributes,the j j. Just as with the disturbances in the ho-mogeneous goods supply and demand model,these unobserved characteristics are not inte-grated out in computing aggregate demand.Hence, they are a real source of difference be-tween the aggregate predictions of the modeland the actual data. As one might suspect, how-ever, thej j also generate a differentiated prod-uct analogue to the econometric endogeneityproblem we are familiar with from the homo-

geneous goods model. That is, unmeasuredcharacteristics, such as perceived reliability orprestige, are likely to be determinants of andhence correlated with the product’s price. If theeconometric endogeneity of price is unac-counted for in the estimation algorithm, it willgenerate inconsistent estimates of the demandelasticities. Berry (1994) suggests using an in-version routine to solve for thej, and theninstrumental variable techniques to estimate theparameters, and BLP provides a simple way ofimplementing these suggestions (see below).BLP also shows that the bias generated by theeconometric endogeneity of price is likely to beempirically important.13

This completes the discussion of the utilityside of our model. We now turn our attention tothe firm’s problem.

B. Firms, Costs, and Equilibrium Prices

The firm side of the model is straightforward. Inany given year, there areF firms, each of whichproduces some subset of theJ products,Jf. Thedecision of which products (bundles of character-istics) are produced in any year is assumed to bepredetermined outside of our model.14

Marginal costs are assumed to depend onobserved product attributes, country-specificcost shifters such as wages and exchange rates,and an unobserved productivity variable. Theproduct attributes that enter marginal cost maybe the same as those that determine utility(though this is not necessary), and the unob-served productivity term may be correlated withthe unobserved product attributes (or thejj).Note that we assume that marginal costs areindependent of output levels. The decision tomodel a product’s marginal cost as constant isthe result of our data limitations. We do notobserve worldwide output of foreign modelsand this, not just sales in the United States, is

12 This functional form for the interaction between in-come and price can be derived as a first-order Taylor seriesapproximation to the “Cobb-Douglas” utility function usedin BLP.

13 As an example, when we do not account for theendogeneity of price, several products are estimated to faceinelastic demands; this is problematic in an oligopolymodel.

14 Modeling the firm’s decision of which products toproduce conditional on its beliefs about the products otherfirms will produce and the state of future demand in amultidimensional differentiated products oligopoly is animportant and very difficult problem that is beyond thescope of this paper.


what marginal cost might vary against (see thediscussion in BLP). In addition, almost all re-searchers since Timothy Bresnahan (1981) haveadopted the constant marginal cost assump-tion.15 Using a logarithmic specification then,the marginal cost of productj is written as:

(4) ln~mc! j 5 wjg 1 v j,

where g is a vector of parameters to be esti-mated,wj is a vector of observed marginal costshifters, andv is the unobserved productivityterm.

To move from demand and costs to industryequilibrium requires two modeling decisions.First, how should the VER be modeled? Sec-ond, what is the equilibrium concept—Cournot,Bertrand, or something yet different?

When Japan “voluntarily” agreed to reduceautomobile exports in May 1981, the agreementpertained to total exports from Japan. Thesewere to be limited to 1.68 million units (a figurethat increased in later years). The Ministry ofTrade and Industry in Japan then essentiallydivided this limit across the Japanese automak-ers. It has been suggested that a firm’s alloca-tion depended in various ways on past sales ormarket shares, and this is surely true, but thereis not a (publicly available) hard and fast for-mula used by MITI.

Modeling the VER raises several issues.There is a large literature discussing tariff-quota equivalences or nonequivalences in thepresence of imperfect competition, and thelessons from that literature might, at firstglance, appear relevant here. For example,Jagdish N. Bhagwati (1969) showed that in alinear monopoly model, tariffs and quotasmight be nonequivalent. In an oligopoly set-ting, Kala Krishna (1989) has demonstratedthat when firms compete by setting quantities(as in Cournot), the quota and an appropri-ately set specific tariff are equivalent, in thatthey yield the same equilibrium. This is notthe case when firms set prices. Krishna notesthat with a VER or quota on the foreign firm,the home firm’s best-response function is dis-

continuous, and there need not be an equilib-rium in pure strategies.

However, in light of how the VER was actu-ally implemented, we believe that the targetlevels of exports MITI allocated to the firmsshould not be viewed as firm specific quotas.Failure to meet the target presumably impactednegatively on the firm’s relationship with MITIand probably on the firm’s future allocations. Itdid not prevent an additional unit from beingexported. Indeed, as shown in Table 1, aggre-gate exports exceeded the limit in five of thefirst six years of the policy. Rather, the firmwould have to evaluate these costs and decideon a course of action. As a result we choose tomodel the impact of the firm-specific limits as atax on exports in excess of that limit. The taxrate is the implicit unit cost of exceeding MITI’slimits, and becomes a parameter to be esti-mated.

For simplicity, we begin with the case inwhich the VER is implemented as an implicittax on every unit exported. If the tax per unit isdenoted byl, the firm’s profits are given by

(5) p f 5 Oj[Jf

~pj 2 mcj 2 lVERj!

3 Msj~p, x, j; u! 2 Oj[Jf

Fixed Costsj,

whereM denotes the market size andVER is adummy variable that is set to one if the car issubject to the tax.

Initially assume that the equilibrium is Nashin prices, i.e., at equilibrium each firm is settingeach of its product prices to maximize total firmprofits conditional on the prices charged by theother firms and the characteristics of all the carsmarketed. Provided such an equilibrium exists,the resulting prices must satisfy the first orderconditions:

(6) sj~p, x, j; u!

1 S r[Jf~pr 2 mcr 2 lVER!

3sr~p, x, j; u!

pj5 0.

15 The importance of the constant marginal cost assump-tion in the analysis of trade policy in the auto industry isexplored, using a partially calibrated model, in Melvin Fusset. al. (1992).


In the simple case where there is one productper firm, equation (6) sets a price equal tomarginal cost plus the tax (where applicable)plus a markup equal to the inverse of the elas-ticity of demand for that product. For our mul-tiproduct firms the markup is more complicatedas the firm takes account of the effect of achange in the price of one of its product on theprofits earned from all of its products. In par-ticular if we let the vector of markups for themultiproduct firm case beb(p, x, j; u), then

(7) b~p, x, j; u!

; D~p, x, j; u!21s~p, x, j; u!,

whereD is aJ by J matrix whose (j , r ) elementis given by:

D jr 5 52sr

pj,

0,

if r andj are produced bythe same firm;

otherwise.

Given the markups, orb(p, x, j; u), and ourmodel for marginal costs, (4), the first-orderconditions can be rearranged to yield

(8) ln~mcj!

5 ln~pj 2 bj~p, x, j; u! 2 lVERj!

5 wjg 1 v j.

Note that in (8), the VER, as modeled, lookslike a specific (as opposed to an ad valorum)tariff. That is, the VER raises prices by anamount in excess of cost plus markup. It is thisaspect of the VER that may have led firms toadjust their product mix by upgrading [as doc-umented empirically by Feenstra, and as mod-eled theoretically by Satya Das and ShabtaiDonnenfeld (1987) and Krishna (1987)].

The first-order condition in (8) is restrictive inseveral ways. First, it assumes that the same tax isplaced on each firm. It has been suggested thatsince the VERs were allocated according to aformula that placed heavy weight on past marketshares, it penalized the smaller upstart firms moreheavily. Honda, in particular, claimed that it wasmore constrained in the early years of the VER,

while other firms were less so. To investigate thispossibility, our robustness analysis includes runsthat estimate separate tax rates for large and smallJapanese firms (where the division is admittedlysomewhat arbitrary).

Note, however, that the first-order conditionin (8) does not require that the tax be placed oneach unit produced, but only on the marginalunits. MITI might exempt some initial level ofproduction from any political pressure. For ourpurposes, the level of the exemption might varyacross firms, as long as the marginal tax ratewas the same. Depending on how we modeledexemptions, they might once again place a dis-continuity in the firms’ reaction functions whichmight in turn lead to existence problems. Weassume that either the exemptions do not causeproblems or else that the tax rate is in factapplied to all units of production.

We also investigate the robustness of ourresults to the assumption that equilibrium isNash in prices. The effect of any change in theequilibrium assumption will be to change thedefinition of the markups, orb(p, x, j; u), inequation (7). One familiar alternative to ourBertrand assumption (Nash in prices) is to as-sume that firms play a Cournot game (Nash inquantities). The problem with this is that few, ifany, industry observers seem to believe that, inthe automobile industry, firms really set quan-tities and let the Walrasian auctioneer set theprices that clear markets. From Bresnahan(1981) on, researchers have modeled imperfectcompetition in the automobile industry in a Ber-trand fashion. One might, however, posit a Nashgame in which Japanese firms set quantities(subject to the export limits set by MITI), butthe rest of the firms set prices. This is an ap-proach empirically adopted by Feenstra andLevinsohn (1995) and coined “Mixed Nash.”Another possibility is that the VER somehow“taught” the Japanese firms to collude, andthese colluding firms played a Bertrand gamewith the rest of the world. In Section VII, weexamine the robustness of our results by esti-mating the model under the Cournot, the MixedNash, and the collusion assumptions.16

16 Readers interested in the derivation of the Mixed Nashfirst-order conditions and the resulting markups are referredto Appendix I of the National Bureau of Economic Researchworking paper version of this paper (1995a). The markups


In concluding, we would like to stress thatour estimates do not assume the VER raisedprices in every year. If it had no effect onprices in a particular year, we ought to esti-mate al which is within estimation error ofzero in that year.

This completes the discussion of the theoryunderlying our structural model. The key param-eters to be estimated are those characterizing thedistribution of tastes in the population,b# , s, anda, those determining marginal costsg, and the taxrates associated with the VERs, thel’s. The pa-rameters on the demand side will permit us toevaluate how consumer welfare changes with theVER. These plus the cost-side parameters allowus to estimate the effect of the VERs on thedistribution of profits. Thel’s measure the im-plicit tax on Japanese cars and allow us to com-pute the revenue forgone by the implementation ofa VER (modeled essentially as an export tax byJapan) instead of a tariff imposed by the UnitedStates (assuming a tariff could be implementedwithout changing any of the other details of theproblem, including the cars that are marketed inthe United States). One needs these pieces ofinformation, or something very close to them, toevaluate this strategic trade policy.

IV. Estimation and Computation

We closely follow the estimation methods de-tailed in BLP. Here we outline those methodsreferring the interested reader to BLP for details.

A. Overview

As in an OLS or two-stage least-squares es-timation procedure, we base our estimates on aset of moment restrictions. In particular, weassume that the unobservables defined by themodel, evaluated at the true values of the pa-rameters, are mean independent of a set of ex-ogenous instruments,z. Formally,

(9) E@j j~u0!|z# 5 E@v j~u0!|z# 5 0.

Equation (9) implies that the unobservables areuncorrelated with any function,Hj[, of theinstruments. Defining

(10) GJ~u! 51

J Oj51

J

EFHj~z!S jj~u!vj~u! DG ,

equation (10) implies

GJ~u0! 5 0.

Following the literature on Generalized Methodof Moments (GMM) (see Lars Hansen, 1982)then, we choose as our estimate ofu that valuethat comes “closest” to setting the sample ana-log of the moments in equation (9) to zero. Thissample analogue is

(11) GJ~u! 51

J Oj51

J

Hj~z!S jj~u!vj~u! D .

The GMM estimator then minimizes

(12) \GJ~u!\AJ,

where for any vectory, \y\AJ5 y9AJy, and

where the matrixAJ converges in probability tosome positive definite matrixA [we use thesample analogue ofEGJ(u1)GJ(u1)9, whereu1is an initial consistent estimate ofu0, as ourAJ].Under suitable regularity conditions this esti-mate is consistent and asymptotically normalwith covariance matrix detailed below.

To make use of the method, we must be able tocalculate the unobservables as functions of thedata at different values of the parameter vector.BLP provides a simple method for doing thiscomputation and we follow this method exactly.

We turn next to the choice of instruments,z.

B. Instruments

The estimation method as outlined requiresus to find a vector of observables, thez vector,that are mean independent of the unobservables(and are in that sense “econometrically exoge-nous”), and then use functions of them, theHj( z), as instruments. Since all the equilibriumnotions discussed above imply that thep andqof every product are functions of the (j, v)

from the Cournot game are familiar from the previousliterature.


pairs of all products, we do not want to placeprice and quantity in thez vector. This is pre-cisely the same reasoning that leads to the use ofinstruments for price and quantity in the analy-sis of demand and supply in homogeneousgoods markets.

As in the analysis of homogeneous goods mar-kets we look for observables that shift the demandand cost functions to use as the components ofz.In the differentiated products framework theseinclude the characteristics ofall the products mar-keted (their size, fuel efficiency, acceleration,etc.), or the observedx vectors, as well as thevariables, such as wage rates, that determine costsconditional on product characteristics, or the com-ponents of the observedw vectors that are notincluded inx.17

Note that the observed characteristics of allthe products marketed in a given year are in-cluded inz, and the value of the instrument forany given product, theHj[, can be any func-tion of z. In oligopolistic differentiated productsmarkets the price of each good depends on thecharacteristics and prices of all goods marketed(thus markups will be lower for products whichhave many competitors with similar character-istics). As a result the value of the efficientinstrument for any given product will be a func-tion of thex andw vectors ofall the productsmarketed (see Gary Chamberlain [1986] for adiscussion of efficient instruments given condi-tional moment restrictions). In the Appendix,we develop an easy-to-compute approximationto the efficient instruments; these are used in ourestimates.

C. Panel Data

The data set we actually use is not a singlecross section, but a panel data set that followscar models over all years they are marketed. It islikely that the demand and cost disturbances of

a given model are more similar across yearsthan are the disturbances of different models.Correlation in the disturbances of a given modelmarketed in different years will affect the vari-ance-covariance matrix of our parameter esti-mates. As a result, we use estimators that treatthe sum of the moment restrictions of a givenmodel over time as a single observation from anexchangeable population of car models. That is,replacing product indexj by indices for modelm and yeart, we define the sample momentcondition associated with a single model as

gm~u! ; O Hmt~z!S jmt~u!vmt~u! D

and then obtain our GMM estimator by mini-mizing our quadratic form in the average ofthese moment conditions across models. Asnoted in BLP, this is not likely to be the mostefficient method for dealing with correlationacross years for a given model, but it doesproduce standard errors that allow for arbitrarycorrelation across years for a given model andarbitrary heteroskedasticity across models.18

V. Data, Results, and Interpretation

This section begins with a discussion of theavailable data and some of its more importantfeatures. Next we discuss the variables includedin the utility function (3), and the marginal costfunction (4). The results of our base case sce-nario are presented next, and the section con-cludes with interpretation of these results.

A. Data

All of our product-level data are obtainedfrom the Automotive News Market Data Book(Crain Communications, annual issues). Thesedata include information on most engineeringspecifications of the automobiles marketed. Thedata span the period 1971 to 1990. In terms ofthe theory presented in Section IV, these datacomprise the product attributes. They include

17 Of course just as in the homogeneous product model,to the degree that there are unobserved cost and demandfactors that are correlated with our observed characteristics,our parameter estimates will be inconsistent. Indeed, oncewe start considering dynamic models in which productcharacteristics are endogenous, the restrictions we are cur-rently using for identification become questionable. As aresult we are exploring alternative identifying assumptionsin our current work (see the discussion in BLP).

18 Unlike BLP the standard errors we present here do notcorrect for simulation error in the computed market shares.We were able to increase the number of simulation draws tothe extent that this error should not be important.


continuous characteristics such as the car’shorsepower, weight, length, width, wheelbase,engine displacement, and EPA miles per-gallonrating. The data also include binary variablessuch as whether air-conditioning, power steer-ing, power brakes, and automatic transmissionare standard equipment. Each model is in factavailable in many variants (termed trim levels)and the list of standard equipment and specifi-cations typically varies across trim levels. Inorder to keep the number of products computa-tionally manageable, we include only the basemodel for each nameplate. It is important, then,that the price variable be that which also appliesto the base model, and this is done.

We have list prices for each product. This isnot ideal, but we think it is the best that can bedone with our present data sources. The alter-native is something akin to the average transac-tion price, where the average is taken for allpurchases of a given nameplate. Such data arein fact available (but are proprietary) for many,though not all, models in the later years of oursample. It turns out that transactions prices for agiven model are almost always higher than itslist price. This is because very few cars areactually purchased without any options, and thepurchase of options drives up the transactionprice. Without detailed information on the rela-tionship between options and transaction prices,the transactions prices are of limited use.19

We also make use of some macroeconomicdata. These variables include exchange rates,consumer price deflators (in order to put allprices into real terms), the prime interest rate,the gross national product, and foreign wages.These are obtained from annual issues of theEconomic Report of the Presidentand theOECD Main Economic Indicators.Finally, werequire information about the number of house-holds and the distribution of income in theUnited States. These data are obtained from theCurrent Population Survey.

We next consider some general trends in keyvariables. Table 2 provides some market aver-ages, while Table 3 focuses more narrowly ontrends in U.S. and Japanese competition. Table

2 lists the number of models, average sales andreal price, and four key attributes for 1971–1990. It is clear that the number of modelsclimbed fairly steadily until 1988, while theaverage sales per model declined. The deflatedprice of automobiles has risen steadily since1974, although a noticeably larger-than-averageblip appears in 1981, the year the VERs wereinitiated, and then again in 1982. Note also,however, that a smaller blip in prices occurredin 1980, a year before the introduction of theVER’s, and there is an equally large series ofincreases in real prices between 1985–1987.Moreover, an almostidentical series of in-creases occur in the variable, “Air” which pro-vides the fraction of models in which air-conditioning was standard equipment, and thissuggests that the price increases may not be“pure price increases” but rather may reflectquality upgrading.

A measure of acceleration is given by horse-power divided by weight. This variable declinedduring the 1970’s and rose during the 1980’s.Vehicle size, measured as length times width,has generally fallen. Cars have become betterequipped, and this is proxied by the inclusion ofair-conditioning as standard equipment. In1971, no car had it, while almost one-third didby 1990. Finally, we include a measure of thecost of driving: miles driven on one dollar’sworth of gas. This variable has generallytrended upwards, although the oil shocks areapparent. An important message to take fromTable 2 is that most of the variables exhibitsignificant trends—some well before theVERs—and we will want to account for thisphenomenon in our empirical work.

The first two columns of Table 3 comparesales-weighted average real list prices of Japa-nese and domestic cars. From 1973 to 1979,prices of domestic vehicles stayed relativelyconstant. Either coinciding with the impositionof the VER in 1981, or one year prior to it, U.S.prices started to increase, and they continued toincrease steadily throughout the rest of the sam-ple. Japanese prices, on the other hand, began afairly steady climb in 1976, several yearspriorto the VERs. Indeed, the largest annual jump inJapanese prices occurred between 1977 and1978, well before the imposition of the VER.This suggests the possible importance of usingdata prior to the VERs when investigating the

19 For some cursory evidence on the average transactionsprices, see Table 2 and accompanying discussion in theNational Bureau of Economic Research working paper ver-sion of this paper (1995a).


effects of the VER. Put another way, if Table 3began with 1981 data, it would appear that theVER had very strong influences on Japaneseprices. When we note that these prices wereincreasing prior to 1981, the evidence becomesless clear. The last two columns of Table 3 givemarket shares. Prior to the imposition of theVER, the Japanese market share was rising,from 5.7 percent in 1971 to 21.3 percent in1981. This was mostly at the expense of U.S.market share which fell from 86.6 to 74.0 per-cent, a fact that led some (but not all) of the“Big Three” automakers to press for importrelief.

One message suggested by Tables 2 and 3 isthat there were many trends in the industry bothpre- and post-1981. Prices and quantities doseem to change around 1981, but they exhibit aslarge or larger changes both before and after,and around 1981 we also seem to see a largechange in the product mix.

To throw further light on the issues related tothe VER, we consider a simple OLS hedonic

regression of prices against characteristics and acombination of trends and time dummies (Table4). The regressors include four vehicle at-tributes [horsepower/weight (HP/Weight), size,miles per dollar (MP$), and air-conditioning asstandard], separate trends for the United States(the omitted region), Europe, and Japan, as wellas dummy variables for each of the three re-gions, the lagged and current exchange rate, andthe current exchange rate interacted with regiondummies. Appended to this list of regressors areyear-specific dummy variables for Japan (theVER dummies) and the United States (the DOMdummies). The estimated regression had 2,217observations and anR2 of 0.815.

All included vehicle characteristics except MP$contribute positively to ln(price) in a preciseway. The coefficient on MP$ is negative and sig-nificant. Region dummy variables suggest that,conditional on other included characteristics, Eu-ropean products sell at a premium. The preciselyestimated coefficient on the overall trend indicatesthat prices are trending upwards. We pick up very

TABLE 2—SOME DESCRIPTIVE STATISTICS

Year No. of modelsQuantity(1,000’s)

Price($’000) HP/Weight Size Air MP$

1971 92 86.892 7.868 0.490 1.496 0.000 1.8501972 89 91.763 7.979 0.391 1.510 0.014 1.8751973 86 92.785 7.535 0.364 1.529 0.022 1.8191974 72 105.119 7.506 0.347 1.510 0.026 1.4531975 93 84.775 7.821 0.337 1.479 0.054 1.5031976 99 93.382 7.787 0.338 1.508 0.059 1.6961977 95 97.727 7.651 0.340 1.467 0.032 1.8351978 95 99.444 7.645 0.346 1.405 0.034 1.9291979 102 82.742 7.599 0.348 1.343 0.047 1.6571980 103 71.567 7.718 0.350 1.296 0.078 1.4661981 116 62.030 8.349 0.349 1.286 0.094 1.5591982 110 61.893 8.831 0.347 1.277 0.134 1.8171983 115 67.878 8.821 0.351 1.276 0.126 2.0871984 113 85.933 8.870 0.361 1.293 0.129 2.1171985 136 78.143 8.938 0.372 1.265 0.140 2.0241986 130 83.756 9.382 0.379 1.249 0.176 2.8561987 143 67.667 9.965 0.395 1.246 0.229 2.7891988 150 67.078 10.069 0.396 1.251 0.237 2.9191989 147 62.914 10.321 0.406 1.259 0.289 2.8061990 131 66.377 10.337 0.419 1.270 0.308 2.852All 2,217 78.804 8.604 0.372 1.357 0.116 2.086

Notes:The entry in each cell is the sales-weighted mean. Prices are in constant 1983 dollars.Quantity is the average sales (in thousands) per model.HP/Weight is in 100’s of HP divided by 1,000’s of lbs (i.e., # HP divided by 10’s of lbs.).Size is vehicle width (in inches) times vehicle length (in inches) divided by 1,000.Air is one if air-conditioning is standard equipment and zero otherwise.MP$ is the 10’s of miles one can drive on a 1983 dollar’s worth of gasoline.


little exchange rate pass-through except in the caseof the German deutsche mark (DM).

The coefficients on the VER and DOMdummy variables address a key question athand: what was the relationship between theadvent of the VERs and prices? The estimatedcoefficients on the VER dummies in Table 4 areall negativeand some are significantly so. (In-deed, the most negative and significant coeffi-cients are in the first two years of the sample.)While we are hesitant to draw conclusions froma hedonic regression, these results are nonethe-less surprising in light of what seems to be thecommon wisdom. After accounting for trendsand changes in vehicle characteristics, Japanesepricesfell or at least did not seem to rise duringthe VER years. The regression results of Table4 speak to what happened to thepricesof Jap-anese cars during the VER years conditional onvehicle characteristics, trends, and exchangerates. The data reported in Table 1 speak towhat happened toquantities of Japanese im-ports during the VER years. Both Table 1 andTable 4 are reasonable first passes at analyzingthe impact of the VER. Just as Table 1 does notconclusively show that the VERs raised pricesin certain years, Table 4 does not conclusively

show that the VERs did not raise prices. Per-haps any fall in Japanese prices would havebeen greater absent the VER. During the sameperiod, the coefficients on the domestic dummyvariables are usually positive (and often signif-icantly so). The bottom line is that simple leastsquares analysis yields puzzling results, but,due to the lack of any underlying theory, it ishard to know what to make of them. We turnnow to results from the estimated model.

B. Results

Recall that the structural parameters to be esti-mated are the means and variances of the distri-bution of the taste parameters in the utilityfunction, the parameters of the cost function, andthe implicit taxes associated with the VERs. Weestimate means and variances of the tastes for:horsepower divided by weight (HP/Weight), ve-hicle size, whether air-conditioning is standard(Air), miles driven on one dollar’s worth of gas-oline (MP$), and for the utility associated with theoutside alternative (the constant). We have exper-imented with other vehicle attributes and, in BLP,we report that the estimated elasticities and result-ing markups are robust to reasonable changes.

TABLE 3—PRICES AND MARKET SHARES IN THE U.S. AUTOMOBILE INDUSTRY:THE CHANGING BALANCE OF U.S. AND JAPANESE FIRMS

Year

Average domestic price

($’000)

Average Japanese price

($’000)

Domestic market share Japanese market share

1971 8.204 5.147 86.633 5.6881972 8.188 5.506 89.216 4.1611973 7.540 6.248 93.221 4.0191974 7.586 6.238 88.655 4.9641975 7.900 6.136 85.348 8.2911976 7.856 6.039 87.609 8.0551977 7.687 6.106 83.702 11.2161978 7.597 6.788 85.495 10.6541979 7.494 6.965 80.326 15.8291980 7.758 6.585 77.316 19.1231981 8.263 7.096 74.098 21.3061982 8.722 7.414 71.410 23.4611983 8.735 7.270 73.424 21.4521984 8.816 7.624 78.311 17.8771985 8.648 7.882 76.086 19.1311986 9.223 8.229 73.316 21.6491987 9.821 8.765 70.218 24.5381988 9.968 8.754 71.707 23.7441989 10.147 8.808 69.008 26.0831990 10.295 9.205 68.170 27.551


One variable that doesnot appear in our list ofattributes is a measure of reliability as givenby aConsumer Reportsrating. While we havesuch data for several years, it has severe prob-lems in a time-series context since ratings arerelative to other vehicles in a given year.Hence, the definition of the variable is chang-ing year by year. Moreover inclusion of thereliability index never seemed to matter. Wenote that the problems caused by not includ-ing more characteristics are somewhat atten-uated by the fact that the model explicitly

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 regiondummies for Europe and Japan, as well astrends for the United States, Europe, and Japan.Finally, we also include the log of the exchangerate of the exporting country (lagged one year)and the log of the wage rate in the producingcountry. We experimented with the contempo-raneous exchange rate and found its effect wasalways about zero and imprecisely estimated.

We include VER dummies for each yearsince 1981, the year the policy was imple-mented. These dummy variables are set to one ifthe VER applies to that automobile model. Ourbase case assumes Japanese models produced inthe United States did not count against the VER,while captive imports did. Note that this impliesthat Japanese wages and the yen to dollar ex-change rate are determinants of costs for captiveimports while U.S. wages are determinants ofcosts for the Japanese models produced in theUnited States.

The estimates for our base case and theirstandard errors are given in Table 5. We beginwith a discussion of the demand-side parame-ters. When interpreting these parameters, it isimportant to keep in mind that demand for aparticular car is driven by the maximum, andnot by the mean, of the utilities heterogeneousconsumers place on that car. Hence, there aretwo ways to explain why cars with, say, highHP/Weight are popular. Either a high mean forthe distribution of tastes for HP/Weight or alarge variance of tastes will have a tendency toincrease the share of consumers who buy carswith large values of HP/Weight. The results inTable 5 show that the means (b# ’s) are all highlysignificant. The standard deviations of the tasteparameters for Size and MP$ are also signifi-cant. The magnitudes of the standard deviationssuggest that relative to their means, there is themost variance in the value of MP$.

On the cost side, we find that each attributecontributes positively to marginal cost and al-most all of their coefficients are quite preciselyestimated. Japanese and European cars costmore to produce and transport, even after con-ditioning on wages and exchange rates. Domes-tic marginal costs are trending upwards, while

TABLE 4—A FIRST PASS AT EXAMINING THE EFFECT OF

THE VER ON AUTOMOBILE PRICES

AN ORDINARY LEAST-SQUARES HEDONIC REGRESSION

[DEPENDENT VARIABLE IS LN(PRICE)]

VariableParameterestimater

Standarderror

Constant 2.248 0.044ln(HP/Weight) 0.593 0.027ln(Space) 1.038 0.056ln(MP$) 20.312 0.035Air 0.479 0.015Trend 0.021 0.004Japan 2.358 2.945Euro 2.357 0.436jtrend 20.006 0.018etrend 20.018 0.005ln(e-rate) 20.272 0.091Lag[ln(e-rate)] 0.258 0.089ln(e-rate)*Japan 0.295 0.300ln(e-rate)*Euro 0.374 0.070VER80 20.199 0.078VER81 20.155 0.083VER82 20.156 0.114VER83 20.099 0.121VER84 20.148 0.135VER85 20.149 0.151VER86 20.120 0.115VER87 20.122 0.118VER88 20.191 0.129VER89 20.257 0.137VER90 20.280 0.150DOM80 20.056 0.037DOM81 0.018 0.039DOM82 0.112 0.041DOM83 0.130 0.043DOM84 0.109 0.048DOM85 0.076 0.050DOM86 0.216 0.057DOM87 0.171 0.060DOM88 0.164 0.065DOM89 0.111 0.069DOM90 0.063 0.073

Note: The regression had 2,217 observations and anR2 of0.815.


Japanese and European marginal costs aretrending slightly downwards. The elasticity ofmarginal cost with respect to wages is just overa third, not unreasonable for a production pro-cess with so large a materials component, whileexchange rate pass-through is about zero. Thislast result is somewhat surprising, but experi-mentation suggests that it is robust. Exchange

rates just do not seem to matter much.This finding contrasts to other estimates ofexchange-rate pass-through (see Feenstra et. al.,1993), but our estimates are based on moredisaggregated data and on a more detailedmodel of the industry.

There are several ways to interpret the mag-nitude of the utility and cost parameters. Oneway which is easy to understand and capturesthe information on both the utility and cost sidesof the model is to examine price-marginal costmarkups. These markups depend on the demandelasticities implied by theb# ’s ands’s as well asthe marginal cost function parameters (all ofwhich have been jointly estimated). A represen-tative sample of these markups for a handful of1990 models representing the quality spectrumis presented in Table 6.20 These estimates ap-pear quite reasonable and are generally in linewith other studies. The standard errors of themarkups are presented in column 4 and implythat the markups are quite precisely estimated.(A discussion of how the standard errors arecomputed is given below in “Implications,”subsection C.)

The coefficients on the VER dummies ad-dress the following question: Suppose the VERwas instead implemented as a specific tax onJapanese automobiles,and no other aspect ofthe model changed. What is the level of that taxthat would generate equilibrium prices equal tothose we observe when we have the VERs? Acoefficient (or tax) of zero would imply that theVER did not raise the prices of Japanese cars,while larger values correspond to a larger im-plicit tax. These coefficients are given in thebottom panel of Table 5.

In 1981, 1982, and 1983, the point estimates areabout zero with a standard error between $187 and$248. In these years, the point estimates imply thatthe VER had almost no effect on prices, and wecannot reject that the effect was nil. In 1984 and1985, the point estimates of the implicit tax rise to$403 and $361 respectively, but these estimateshave standard errors of $243 and $303. Again, wecannot reject the hypothesis that the VER did notraise Japanese prices, although it should be notedthat two standard errors encompass a wide rangeof implicit taxes; i.e., while we cannot reject that

20 All 2,217 markups are available on request.

TABLE 5—ESTIMATED PARAMETERS OF THEDEMAND AND

PRICING EQUATIONS: BASE CASE SPECIFICATION

1971–1990 DATA, 2,217 OBSERVATIONS

VariableParameterestimate

Standarderror

Demand-side parameters

Means (b# ’s) Constant 25.901 0.712HP/Weight 2.946 0.486Size 3.430 0.342Air 0.934 0.199MP$ 0.202 0.084

Standard deviations(sb’s) Constant 1.112 1.171

HP/Weight 0.167 4.652Size 1.392 0.707Air 0.377 0.886MP$ 0.416 0.132

Term on price (a)(2p/y) 44.794 4.541

Cost-side parameters

Constant 0.035 0.310ln(HP/Weight) 0.604 0.063ln(Size) 1.291 0.106Air 0.484 0.043Trend 0.018 0.004Japan 3.255 0.667Japan*trend 20.036 0.008Euro 3.205 0.525Euro*trend 20.032 0.006lag[ln(e-rate)] 0.026 0.024ln(wage) 0.356 0.079

VER dummies

VER81 20.085 0.187VER82 20.022 0.228VER83 0.001 0.248VER84 0.403 0.245VER85 0.361 0.303VER86 0.675 0.307VER87 1.558 0.353VER88 1.490 0.379VER89 1.277 0.458VER90 1.063 0.469


the VER had no effect in 1984 and 1985, neithercan we reject that the implicit tax was in the rangeof $600–$800. We adopt as our null hypothesis,though, the absence of any price effect of the VERand are unable to reject this null for 1981–1985. Itis perhaps not surprising that the VERs had noeffect in 1981, as they were not implemented untilmidyear. However, the lack of any effect on equi-librium prices in 1982 and 1983 is likely to besurprising to some observers.

As noted in the introduction, there are severalplausible reasons why the VER might not haveinitially led to higher Japanese prices. Severalof these reasons are interrelated and at the heartof several of them is the notion that the autoindustry is an extremely cyclical industry inwhich sales tend to be weak during recessionsand periods of high interest rates. The early1980’s had both. When interest rates are in the12–18 percent range, the new auto market issluggish. In this type of economic environment,Japanese auto firms may have found it difficultto raise prices. Indeed, the VERs may well havebeen agreed to by the Japanese precisely be-cause the Japanese realized that the promise ofexport restraints at the agreed level was bothpolitically expedient and economically inexpen-sive at the time the agreement was made. Wereturn to the impact of macroeconomic vari-ables on our results in the robustness discussionbelow. Also, Japanese firms may have opted tofill their allocations simply to save those allo-cations for future years when demand wouldpick up.

In 1986, the VER begins to have a statisti-cally significant effect on prices in that we canno longer reject that the implicit tax was zero. In1986, the point estimate of the implicit tax is$675 (with a standard error of $307). With anaverage price of Japanese cars at about $8,200,the VER is equivalent to about a 8.2 percent taxper Japanese car. (Recall the tax is specific, so itis much larger in percentage terms for inexpen-sive cars and less for costly ones.) The largesteffects of the VERs are from 1987 to 1989, andthis is again consistent with the notion thatbusiness cycles matter in this industry. (Discus-sions with the economics staff of General Mo-tors stressed the importance of the businesscycle in explaining why, in its view, the policydid not matter in the early years but did in thelater years.) During these years, the VER wasequivalent to a tax of between $1,277 (with astandard error of $458) and $1,558 (with astandard error of $353). In 1990, the estimatedimplicit tax falls to a still hefty $1,063. The datain Table 1, combined with the fact that ourestimate of the effect of the VER in 1990 is notvery robust, lead us to interpret the 1990 coef-ficient with great caution. (For a more extensivediscussion of this point, see Section VII.)

These are large effects and, by 1989, maystrike some as somewhat surprising. For ex-ample, Nissan was almost surely not export-ing its allocation at the end of our sample.Many industry observers have noted that al-though the VERs were still in effect in 1990(they remained so until 1994), they were not

TABLE 6—A SAMPLE FROM 1990OF ESTIMATED PRICE-MARGINAL COST MARKUPS BASED ON TABLE 4 ESTIMATES

Price(in 1983 $)

Markup overmarginal cost(p 2 MC)

Standard errorof markup

Markup asfraction of price

Mazda 323 $ 5,049 $ 1,219 $164 0.241Nissan Sentra $ 5,661 $ 1,451 $171 0.256Ford Escort $ 5,663 $ 1,653 $203 0.292Chevy Cavalier $ 5,797 $ 2,127 $209 0.367Honda Accord $ 9,292 $ 2,880 $198 0.310Ford Taurus $ 9,671 $ 3,352 $216 0.347Buick Century $10,138 $ 4,057 $231 0.400Nissan Maxima $13,695 $ 4,343 $255 0.317Acura Legend $18,944 $ 6,487 $383 0.342Lincoln Town Car $21,412 $ 8,206 $457 0.383Cadillac Seville $24,353 $10,231 $486 0.420Lexus LS400 $27,544 $ 9,973 $646 0.362BMW 735i $37,490 $13,521 $692 0.361


important due to the increased direct foreigninvestment by the Japanese into the UnitedStates. Our base case results suggest other-wise. What might be going on here? There aremultiple mutually nonexclusive explanations.Note that the VER dummies enter the firms’first-order conditions such that the VER cap-tures price increases above those explained bymarginal cost (including region dummies andregion-specific trends) and the markup. A sig-nificant VER dummy would occur if Japanesefirms were induced, either by MITI, or by theUnited States, or by cartelization to keepprices high and sales low relative to the no-VER Bertrand equilibrium. Another possibleexplanation is that while some firms may nothave been constrained by the VER, otherswere. For example, while Nissan probablywas not constrained, Mitsubishi (due to themany captive imports supplied to Chrysler)almost certainly was. Indeed, one reason ex-ports under the VER were increased in themid-1980’s was probably the increase in cap-tive imports. We return to the possibility thatsome firms were constrained while otherswere not in the sensitivity analyses. A thirdexplanation is that some of the large esti-mated VER dummies in the later 1980’s andespecially 1990 are not always robust to spec-ification testing. We return to a more detailedexamination of these alternatives below. Afourth explanation relates to the politics of theVER. The Japanese government raised theVER limit to 2.3 million cars beginning in1985. This was apparently a unilateral an-nouncement. By 1985, the Reagan adminis-tration had dropped its support for the VERs.The announced increase to 2.3 million causedsubstantial anger among U.S. auto firms andpoliticians that traditionally supported the in-dustry. Indeed, many traditional supporters ofthe U.S. auto industry were already angry thatthe Japanese exceeded the VER limits (albeitnot by much) in five of the first six years ofthe policy. Insofar as the Japanese may havebeen responding to the fear of future protec-tion, the Japanese may have deemed it appro-priate to limit exports to a level below thepublicly announced 2.3 million level. Our re-sults suggest, in any case, that the VER in-duced firms, either on their own or withMITI’s pressure, to keep prices higher (and

sales lower) than would have otherwise beenthe case.

Thus far, all description of the VERs hasbeen positive, not normative. Prices went up,but this is not all that surprising (though thetiming and magnitude of the rises might be).Insights from the strategic trade policy theoret-ical literature suggest that the profit-enhancingeffect of the VER might make protection wel-fare enhancing in spite of the concurrent loss ofconsumer welfare. We turn now to a fullerinvestigation of the implications of our esti-mates on both profits and on consumer welfare.

C. Implications

In order to investigate the effects of the VER onprofits and consumer welfare, we need to knowwhat the industry equilibrium would have been inthe absence of the VER. To determine that equi-librium, we setl (the implicit tax) to zero, andsolve for the vector of prices and vector of quan-tities for which the firms’ first-order conditionshold and for which consumers maximize utilityconditional on those prices. This assumes boththat the equilibrium without the VER is also Nashin prices and that the equilibrium is unique (or atleast that we solve for the relevant one). It furtherassumes that the distribution of automobile char-acteristics would not have changed in the absenceof the VER. This last assumption is probably morereasonable in the short run and less so in thelonger run, since the time needed to change mod-els is typically measured in years, not months. Weonly recompute the equilibrium for years in whichl was significantly larger than zero. This is admit-tedly a somewhat arbitrary choice, but computa-tional constraints played a role in this decision.

When we solve for the equilibrium that wouldobtain whenl is set to zero, we implicitly aremaking use of estimated parameters. Since theestimated parameters have standard errors associ-ated with them, so does the new equilibrium. Wecompute these standard errors when evaluatingpolicy implications of our estimates. Doing so isnontrivial. The ability to put standard errors onpolicy implications is one great advantage ofeconometric methods over the calibration meth-ods that are commonly used in evaluating tradepolicy. However, because the policy implicationsare typically complicated nonlinear transforma-tions of the parameters, computational constraints


have limited the extent to which standards errorshave been presented.

One solution (the “delta method”) is to lin-earize the policy implications in the parameters.We avoid this linearization and instead take amore direct Monte Carlo approach. To imple-ment this, we taken 5 175 draws of parame-ters from the estimated asymptotic normaldistribution of the parameters.21 For each ofthese draws, we resolve the entire model andthen calculate the implied policy implications.The empirical standard deviation of these policyimplications, across then draws, is then a con-sistent estimate of the true standard error of thepolicy implications.

We first turn our attention to the profit-shift-ing side of the story. The effects of the VER onprices and profits are given in Table 7. There,we report the sales-weighted average price ofJapanese, American, and European cars as wellas profits with and without the VER, the differ-ence between the VER and no VER cases, andthe standard error of this difference. These fig-ures are given for each year in which we esti-mated a statistically significant VER coefficient.As expected, the prices of Japanese cars weredriven up by the VER.22 Note that in a Nashpricing game, when at least some of the prod-ucts are strategic complements, prices can riseby either more or less than the amount of thetax. Our estimates indicate that both occur.

The issue of strategic complements and sub-stitutes is an important one in this study. Indifferentiated products price-setting models, itis usual to think of prices as being strategiccomplements. In these cases, an exogenous risein a competitor’s price will raise own-firmprices. The intuition that price-setting modelsyield strategic complements comes from linearmodels in which the competitor’s price affectsthe intercept, but not the slope, of the own-product demand curve. However, in typical dis-crete-choice models both the intercept and the

slope change as the rivals prices change: thedemand curve shifts out and becomes moreprice sensitive. The change in the slope canoccur because those customers who shift awayfrom the rival product are those who are moreprice sensitive than average. These price-elasticconsumers might induce adecreasein own-firmprices in response to a rival’s price increase.Thus, we can obtain either strategic comple-ments or substitutes.23

The VER increased Japanese prices fairlydramatically. Prices increased by around $750in 1986 and this figure rose to $1,687 in 1987.The increase then fell to around $800 by 1990.These changes in prices are measured with stan-dard errors of $35 or less.

We find that the prices of U.S. autos werelittle affected by the VER. U.S. prices rose byonly about $200 in 1987 and 1988 due to theVER. In other years the increase was less thanabout $80 and the standard error was nevermore than $28. Recall that in our model, con-sumers are heterogeneous. Our results suggestthat as Japan raised prices, price-sensitive con-sumers switched to U.S. automobiles and, as aresult, markups did not increase much. How-ever, while prices of domestically produced carswere not much changed due to the VER, salesincreased significantly, and this is reflected inthe increased profits earned by U.S. firms. Thesecond set of columns in Table 7 indicates thatU.S. profits increased by about $3.09 billion in1987 and by $2.76 billion in 1988. Even in1986, when we find the VER had a relatively

21 We experimented with more draws but found thatcomputational time went up linearly while standard errorsremained stable. With substantially fewer draws, estimatesbecame noisy.

22 Note that since the VERs induce a different combina-tion of cars to be purchased, throughout this table theweights used when the VER is assumed operative are dif-ferent than the weights when it is not.

23 It is well known that prices of productsj and k arestrategic complements if and only if2pf/pjpk . 0. Thiscross-price second derivative is

sj

pk1 O

r[Jf

(pr2mcr)F 2sr

pjpkG

In our model,

pk

sj

pj5 E F sj~n!

pjsk~n! 1

sk~n!

pjsj~n!G dF~n!,

where recall thatn is the vector of consumer character-istics. Since the first term in the integrand will usuallydominate, the integrand will be large and negative when theprice-sensitive consumers are likely to shift to goodk. Ifthis effect is large enough for productsj andk, it will morethan compensate for the positivesj /pk in the expressionfor 2pf /pjpk . 0.


small effect on prices, U.S. profits increased byabout $1.6 billion due to the VER. This is theprofit-shifting aspect of a strategic trade policy.The standard errors of the difference in profits islarge (t-statistics are somewhere between 1 and2). Hence, while point estimates suggest thatU.S. profits increased, these estimates are notprecise. (Since profits depend implicitly on hun-dreds of elasticities, it may not be that surpris-ing that even if each elasticity is tightlyestimated, the change in the level of profits isnot that tightly estimated.)

While U.S. profits were much increased bythe VER, Japanese profits did not fall a corre-sponding amount. Our estimates imply that Jap-anese profits were basically unaffected by theVER. In 1986, point estimates imply that Japa-nese profits rose by $111 million while in 1988they fell by $110 million. In other years, thefigure is somewhere between these two. Theseare not large numbers. Neither are they pre-cisely estimated. The standard error of the dif-ference in Japanese profits is on the order of$300–$400 million. Two factors contributed tothe relatively small decrease in Japanese profits.First, apparently a large fraction of consumershad relatively inelastic demands for the Japa-nese models; these consumers preferred payingthe increased Japanese prices to shifting theirdemand to other models. Second, with the VER,as opposed to a tariff, the Japanese firms did nothave to pay the implicit tax. Instead they kept

the “revenue” such a tax would have generatedand this is reflected in the higher prices. VERsare sometimes referred to as bribes to the for-eign firm, for Japanese profits might have beenlower had the VER instead been implementedas a tariff or regular quota.24

The theoretical literature has recognized thata quota (or, in this case, VER) might act to raiseindustry profits. Our point estimates imply thiswas indeed the case, although our estimates ofthe change in profits resulting from the VERhave relatively large standard errors.

Profits are only part of the economic welfareequation. Another key component is consumerwelfare. We compute the compensating varia-tion in the following way. First take a drawfrom the estimated distribution of tastes and thedistribution of income. This draw can bethought of as a simulated household. Next, com-pute which product gives the highest utility atthe VER (i.e., the actual) prices and the result-ing utility. Now find the income which gener-ates the same level of utility at the non-VERprices (i.e., the prices we obtained when wesolved for the industry equilibrium in the ab-sence of the VER). The change between this

24 It should be noted, however, that Japanese profits areactually somewhat lower than what is reported in Table 7.This is because some of the difference between price andcost is kept by the dealer, and these dealers are typicallydomestically owned.

TABLE 7—THE EFFECT OF THEVER ON PRICES AND PROFITS

Average price in $1,000’s Total profits in $ millions

With VER No VER DifferenceStandard errorof difference With VER No VER Difference

Standard errorof difference

1986 Japan 8.253 7.506 0.747 0.017 6334 6222 111 351United States 9.107 9.074 0.034 0.009 27551 25927 1623 1662Europe 17.079 17.170 20.091 0.013 3040 2974 66 171





Notes:Average prices are sales-weighted averages. (Average prices do not match those on Table 2 due to treatment of directforeign investment and captive imports.)


income and the initial draw on the household’sincome is the compensating variation.25 To es-timate the expected compensating variation fora randomly chosen household, we do this alarge number of times and take the average.Multiplying this expectation by the number ofhouseholds in the economy gives the total com-pensating variation. The estimates in Tables 7and 8 use 10,000 draws (though we have con-ducted much of the exercise with 100,000 drawsand the results only change in the third decimalpoint).

Table 8 provides estimates, for 1987, ofhow household-level compensating variationchanges with the imposition of the VER. Thistable begins to address the question of whobears the burden of the VER. The first two rowslook at the economywide aggregates. The firstrow gives the average change in the price of thegood actually purchased. There we note thatprices rise on average $18. Most households(about 90 percent) did not purchase a car in agiven year, and for these households, the pricechange was zero. Hence the average figurehides a great deal of variation. The standarddeviation of the change in the price of the goodpurchased under the VER is $277, while at leastone product’s price rose by $2,369 and anoth-er’s fell by $499. The latter is due to the pres-ence of strategic substitutes. The economywideaverage compensating variation figure impliesthat the VER cost the household, on average,$41, although this figure was as great as $2,366for some households. Again due to the strategicsubstitutes, some households were made $483better off by the VER.

The next three pairs of lines in Table 8 decom-pose the economywide averages. We estimate thatthe imposition of the VER would, on average,leave those households which (under the VER)purchased a car $317 worse off. This figure re-flects the twin facts that auto purchasers wereadversely affected by a significant amount andthat most households in a given year arenot autopurchasers. The $317 figure is aggregated overhouseholds which purchased a Japanese car (whenthe VER was imposed) and those that purchased adomestic car. These two groups fared quite differ-

ently under the VER. On average the VER costhouseholds that bought a Japanese car $1,242. Onthe other hand, the VER cost households thatpurchased a domestic car only about $30. Con-sumers of domestic cars themselves were not thatadversely affected by the VER.

Table 9 gives the bottom line on our evaluationof the VERs as a strategic trade policy. There, wecompute the components of aggregate welfare foreach of the years in which the VER was estimatedto be binding in our base case. The first columngives the change in domestic profits. The secondcolumn gives the compensating variation and isnegative since the protection harmed domesticconsumers. The third column gives the sum of thefirst two columns and represents the net change inwelfare for the VERas it was actually imple-mented.The fourth column presents the forgonetariff revenue (had an import tariff been usedinstead of the implicit export tax we model). Thefifth column then lists the welfare gain that wouldhave resulted if the VER were instead imple-mented as a tariff,andno other change occurred inthe nature of the equilibrium. The bottom row ofthe table gives the cumulative totals over the mul-tiple years, and that is the row on which we focus.Standard errors of all figures are given in paren-theses. All figures are in 1983 dollars. In 1996dollars, the amounts would be inflated by around50 percent.

The first effect of the VER was to increasethe pure profits of U.S. firms by about 10.2billion dollars. It is hard to evaluate the magni-tude of this figure. To put it into some perspec-tive, though, our estimates imply that the pureprofits (not including fixed costs) from Japaneseautomobile sales in the U.S. in 1990 were about7.6 billion (1983) dollars, while the profits ofU.S. firms in 1990 were about $23.1 billion. Itseems that the profit-shifting effects of theVERs was not negligible.

On the other hand, the burden placed on U.S.consumers was not negligible either as the com-pensating variation of the VERs was just over$13.1 billion. The standard error of this figure is$2.48 billion. The net change in welfare due tothe VERs was about2$2.9 billion. Due to thelarge standard error on the change in profits, thenet change has a relatively large standard er-ror—$7.56 billion.

When one evaluates the typical trade policy,the welfare components number three: profits,

25 A further discussion of this method and other appli-cations is found in Pakes et. al. (1993).


consumer welfare, and tariff revenue. The VERwas implemented such that it gave the latter ofthese back to the Japanese firms or government.Suppose the United States had instead opted forthe tariff that would have resulted in the sameindustry equilibrium observed under the VER.We assume that all imports from Japan generatetariff revenue, and this includes captive importsas well as the made-in-Japan portion of produc-tion of models which were also produced in theUnited States (i.e., Camrys made in Japan raisetariff revenue while those made in Kentucky donot). This policy would have generated almost$11.2 billion dollars in revenue for the U.S.government. The forgone revenue with a VERis sometimes referred to as the bribe paid inorder to induce Japan to agree to the policy inthe first place. Our (precise) estimates suggestthis was a hefty bribe. When this figure is addedto the net change computed in the third columnof Table 9, the welfare gain from the VERstotals $8.34 billion. Our point estimates suggestthat if the government been able to impose atariff without changing any of the other condi-tions in the market, the implied protection of theautomobile industry could have enhanced U.S.welfare for exactly the sort of reasons that cameout of the early theoretical models of trade

policy and imperfect competition. Nonetheless,this net figure has a standard error as large as thenet figure itself. In terms of whatwaspreciselyestimated, we conclude that the decrease in con-sumer welfare was about equal to the forgonetariff revenue.

Does this suggest that tariffs on Japaneseautomobiles would be in the U.S. economicinterest? There are several reasons why thismight not be so. For example, we do not modelretaliation (nor, though, do most theoreticalmodels of strategic trade policy). Surely onereason to implement a VER instead of an out-right tariff or quota was that the VER bribed theJapanese government into not retaliating. Fur-thermore, a tariff directed solely at Japaneseproducts would violate the GATT. Also, we areassuming that the imposition of a tariff wouldnot cause Japanese firms to stop marketingsome of their models in the United States. Ifmodels were pulled off the U.S. market thenconsumers with inelastic, as well as those withelastic, demand for that model would be ad-versely affected.

Just as there are good reasons, though, towonder whether the $8.341 billion figure mightbe unrealistically high, there are also good rea-sons to believe it is too low. First, we have

TABLE 8—DECOMPOSING THECOMPENSATING VARIATION

RESULTS FROM1987

MeanStandarddeviation Minimum Maximum n

All households:

Average change in price of originally purchased good 0.018 0.277 20.499 2.369 10,000Compensating variation 20.041 0.300 22.366 0.483 10,000

Only households which purchased a car:

Average change in price of originally purchased good 0.161 0.814 20.499 2.369 1,120Compensating variation 20.317 0.817 22.366 0.483 1,120

Only households which purchased Japanese car:

Average change in price of originally purchased good 1.208 1.149 20.432 2.369 266Compensating variation 21.242 1.012 22.366 0.426 266

Only households which purchased non-Japanese car:

Average change in price of originally purchased good 20.165 0.098 20.499 20.013 854Compensating variation 20.030 0.457 22.063 0.483 854

Note: The “originally purchased good” refers to the good purchased when the VER was in place.


estimated the welfare effects of the VERs asactually implemented, and there is no reason tobelieve that they were set to optimize welfare.Second, our theoretical and empirical work didnot account for monopoly rents accruing to U.S.workers in the automobile industry.

VI. Sensitivity Analyses

Along the way to the punchlines provided in thelast section, we have made several possibly objec-tionable assumptions. For example, we assumedthe firms played a Bertrand game, that firms’underlying cost functions were the same, and thatthe export limits were either binding or not bind-ing on all firms in any given year. We chose not toignore direct foreign investment (DFI) or captiveimports (CI), but did ignore some key ways inwhich the macroeconomy might affect automobiledemand. We also assumed that quality changeswere exogenous. In this section, we ask: dochanges in these assumptions affect our majorconclusions?26

Table 10 provides results from seven of thealternative specifications we tried. The basecase was estimated under a Bertrand assump-tion. We investigate how robust our results areto a Cournot as well as to a Mixed Nash as-sumption. We also investigate the possibilitythat the VER led to collusion among Japanesefirms while the Japanese firms collectivelymaintained a Bertrand strategy vis-a`-vis non-Japanese firms.

There are many ways to compare re-sults across specifications: demand elastici-ties, markups, profits (which use informationfrom each of the previous two), and the co-efficients on the VER dummies. Since thefocus of this study is on trade policy, we optfor the latter.

The first column of Table 10 replicates theVER multipliers from our base case. The sec-ond column has the estimates obtained underthe assumption of Cournot behavior. Theseestimates are obtained from a structural

26 There is also the issue of the shape of our objectivefunction, in particular the presence of local minima, and theability of our numerical procedures (which includes achoice of starting values and of stopping tolerances) to findits overall minimum. We experimented with alternate start-ing values and tolerances and sometimes found the minimi-zation algorithm stopping at local minima that were slightlydifferent than the overall minima reported in the text. Inparticular some of these alternate runs indicated that the

VER had a larger effect in 1985 and a smaller effect in 1990than the results reported in the text suggest (though thesedummies wereneversignificant in 1981 to 1984, and werealways significant between 1987 and 1989). The VERdummy coefficients on 1985 and especially 1990 are leaststable. Our selected base case is the most representative ofour results, but it may be that the VER had a larger effect in1985 and a smaller effect in 1990 than the base case resultssuggest. The results for these years, then, should be inter-preted with caution.

TABLE 9—AGGREGATE WELFARE AND THE VER(ACCOUNTING FORDIRECT FOREIGN INVESTMENT BY JAPANESE FIRMS)

[IN $ BILLION (1983)]

YearChange in

domestic profitsCompensating

variation Net changeForgone tariff

equivalentWelfare gain fromequivalent tariff

1986 1.623 21.636 20.013 1.337 1.323(1.662) (0.316) (1.654) (0.566) (1.792)

1987 3.085 24.019 20.934 3.266 2.332(1.467) (0.797) (1.617) (0.677) (1.770)

1988 2.764 23.338 20.574 3.012 2.437(1.568) (0.710) (1.664) (0.692) (1.838)

1989 1.583 22.505 20.921 2.131 1.209(1.410) (0.470) (1.464) (0.708) (1.641)

1990 1.151 21.635 20.484 1.521 1.037(1.317) (0.360) (1.371) (0.611) (1.556)

Total 10.207 213.135 22.928 11.269 8.341(7.350) (2.480) (7.556) (3.096) (8.311)

Note: Standard errors are in parentheses.


model in which the firms’ first-order condi-tions and resulting markup have beenamended to reflect the Cournot assumption.27

With the Cournot assumption, we find that themultiplier on the 1990 VER dummy variableis less precisely estimated, and we can nolonger reject the hypothesis that the VER did notbind that year. On the other hand, the dummyvariable for the VER in 1985 becomes statisticallysignificant. Other than 1985 and 1990, the VER isfound to be binding in the same set of years aswhen price setting was assumed to be Bertrand(though the magnitude of the VER multiplier wasquite a bit larger in 1986, and somewhat smaller inthe other years than in our base case).

A possibly more realistic alternative toBertrand is the Mixed Nash case. Here theJapanese firms set quantities while other firms

set prices.28 If one believed that there werestrict export limits given to the Japanesefirms, a model where these firms set quantitiesseems more plausible. The VER multiplierswe obtained when we reestimated our modelunder the Mixed Nash assumption are givenin the third column of Table 10. They are, interms of magnitudes of estimates and stan-dard errors, very close to those obtained un-der the Bertrand assumption. The VERs bindin all the same years and the implied specifictax is about the same across the two specifi-cations. We conclude that while it may bereasonable to estimate the model under alter-native static equilibrium concepts, it does notreally seem to impact the policy conclusionsdrawn. A caveat is in order, though. While theresults are robust to the various specificationsof the equilibrium, it remains the case in allresults presented that the demand and pricingsides of the model have been estimated simul-taneously. In principle, one could estimate the

27 All else is as in the base case, i.e., we use the same: (i)starting values, and (ii) model for direct foreign investmentand captive imports; (iii) simulation draws as in the basecase.

28 Once again, we are simply assuming that such anequilibrium exists and then showing that it does exist at theestimated parameter values.

TABLE 10—SENSITIVITY ANALYSES

Base case Cournot Mixed Nash Collusion No DFI No CI Macro Fixed effects

VER81 20.085 20.255 20.001 20.075 20.098 0.111 20.080 0.014(0.187) (0.201) (0.205) (0.203) (0.227) (0.208) (0.144) (0.167)

VER82 20.022 20.347 0.000 20.094 0.033 0.083 20.144 20.197(0.228) (0.251) (0.248) (0.246) (0.281) (0.225) (0.178) (0.204)

VER83 0.001 20.423 0.117 20.152 0.434 0.193 20.183 20.232(0.248) (0.256) (0.261) (0.233) (0.381) (0.274) (0.179) (0.220)

VER84 0.403 0.069 0.542 0.323 0.374 0.577 0.177 0.204(0.245) (0.279) (0.255) (0.223) (0.309) (0.294) (0.200) (0.217)

VER85 0.361 1.378 0.515 0.603 0.677 0.845 0.443 0.438(0.303) (0.359) (0.309) (0.228) (0.361) (0.293) (0.222) (0.241)

VER86 0.675 1.301 0.883 0.490 0.555 0.769 0.304 0.212(0.307) (0.369) (0.318) (0.253) (0.412) (0.328) (0.228) (0.268)

VER87 1.558 1.152 1.433 1.302 1.129 1.361 1.004 0.659(0.353) (0.411) (0.351) (0.296) (0.431) (0.394) (0.288) (0.336)

VER88 1.490 1.184 1.579 1.494 1.184 1.635 0.906 1.378(0.379) (0.443) (0.391) (0.343) (0.518) (0.459) (0.313) (0.382)

VER89 1.277 0.891 1.462 1.232 1.041 1.554 0.828 1.170(0.458) (0.479) (0.513) (0.377) (0.533) (0.499) (0.373) (0.441)

VER90 1.063 0.570 1.231 1.248 0.837 1.156 0.403 1.259(0.469) (0.517) (0.502) (0.387) (0.564) (0.517) (0.399) (0.430)



demand side of the model alone and then usethe estimated elasticities to investigate thecost side of the model. This would be moreflexible and would impose less structure onthe utility function parameter estimates. Wehave tried to do this, and are unable to obtainprecise estimates of many of the parametersof interest. We conclude that, absent moredata, the equilibrium first-order conditions onthe pricing side contribute to the precision ofthe demand-side estimates. We are currentlyworking on developing methods, using con-sumer-level data, that might allow one to es-timate the demand-side independently of anyequilibrium assumptions. (See, for example,Berry et. al., 1998.)

The fourth column of Table 10 presents theVER multipliers from the collusion case. Thethought experiment here is that the VER inducedJapanese firms to collude. From a modeling per-spective, this essentially changes the firms’ first-order conditions such that all Japanese firms actlike a single multiproduct oligopolist. The esti-mated VER multipliers are quite similar to thebase case, although the 1985 coefficient becomesstatistically significant while the 1986 coefficientbecomes statistically insignificant. All point esti-mates, though, are within one standard deviationof the base case estimates.

The VER was structured such that cars pro-duced by Japanese firms in the United States didnot count against the VER.29 In our base case, weaccordingly assumed that the VER did not applyto Japanese models that had production facilitiesin the United States, although the profits accruingto these models were classified as Japanese profits.For cars produced in both Japan and the UnitedStates (and prominent examples of this for thelatter part of our sample period are the HondaAccord and the Toyota Camry), this amounted toassuming that the marginal car sold was producedin the United States.30 Since DFI production wasnot subject to any restraints, one would expect the

presence of DFI to diminish the trade restrainingaspect of the VERs. On the other hand, we wouldnot necessarily expect DFI to render the VERsineffectual for three reasons. First, it takes time tobuild an automobile plant and bring it up to ca-pacity. Second, the amount of capacity built in theUnited States is determined by perceptions of thefuture implications of that capacity, including itspotential political ramifications, and there is goodreason to believe that the U.S. capacity of Japa-nese models was not built up as fast as otherwisewould have been expected. For example, althoughproduction costs in 1994 were widely believed tobe lower in the United States than in Japan for thesame vehicle, there were no major new plants onthe drawing boards, and this is due in part topolitical concerns. (Restrictions on Japanese ca-pacity in the United States were reported to bediscussed during President Bush’s “auto” trip toJapan.) Third, if production costs were lower inJapan than in the United States, the VER mightstill bind even with the presence of DFI. To in-vestigate how treating DFI differently (and effec-tively ignoring it) might alter our results, themodel is reestimated ignoring the effects of DFIon the underlying structural model. These resultsare presented in the fifth column of Table 10.

The general pattern is one in which the VERdummies are similar to the base case, with a fewexceptions. When we ignore DFI, the VER ap-pears to be binding in 1985 and not binding in1986 or 1990. More importantly, ignoring DFIdoes not affect our finding that the VER con-tributed to higher prices for Japanese cars in thelater 1980’s, but not in the first four years of thepolicy. Although the coefficient estimates of theVER dummies are not that different from thebase case, the welfare implications are. This isbecause the implicit tariff revenue forgone ismuch higher when DFI is ignored, since no-DFIassumption would attribute forgone tariff reve-nue to all the cars actually produced by Japa-nese firms in the United States.

The next column of Table 10 gives theresults when we ignore the role of captiveimports. This specification is estimated in or-der to determined whether ignoring captiveimports (as previous studies have) matters toour main results. We find that the results ofthe no-captive imports specification are quitesimilar to the base case. The main differenceis that by ignoring captive imports, it appears

29 This production via direct foreign investment was anempirically important phenomenon. Beginning with Hon-da’s Marysville plant in 1982, Japanese firms responded tothe VER by producing in the United States. By 1990,Honda, Nissan, Toyota, Mazda, and Mitsubishi were pro-ducing in the United States.

30 For a more detailed examination of how DFI works ina model of oligopoly and quotas, see Levinsohn (1989).


that the VER significantly raised prices in1985, and possibly also in 1984, while ourbase case indicates the contrary. Although thecoefficients are not that different for the no-captive imports case, the welfare conse-quences of ignoring the captive imports arelarge. Like the story with DFI, this occursbecause with captive imports, the conse-quences for forgone tariff revenue are large.

The next-to-last column of Table 10 presentsthe VER dummies when an attempt is made toaccount for macroeconomic influences on thedemand system. These runs included GNP andthe prime interest rate as linear terms in theutility function. These terms do not have ran-dom coefficients. The GNP variable had a pos-itive coefficient on it (with at-statistic of around2) while the prime interest rate had a negativecoefficient on it (with at-statistic of around210). Including these variables is quite ad hoc.In principle, one can argue that shifts in incomeare already captured by the inclusion of house-hold income in the utility function. Also, whilethe interest rate certainly matters, it just as cer-tainly would not enter a structural dynamicmodel of automobile demand in the simplemanner with which we experiment. We includethese variables, though, to investigate, albeitloosely, whether including some macroeco-nomic demand shifters substantively alters ourconclusions about the VERs. As VER dummiesin the last column indicate, our results are notthat different. We find that the 1985 coefficientbecomes significant, while the 1986 and 1990coefficients become insignificant, and the othercoefficients are slightly smaller in magnitude.This suggests that ignoring macroeconomic in-fluences may make the VER look slightly morebinding than in fact it was.

Finally, we investigate the robustness of ourresults to the implicit assumption that all firmshave the same underlying cost function. There areof course many ways in which cost functionsmight differ across firms. As a first pass at thisissue, we allow firm-specific fixed effects in thecost function and reestimate the model with these26 fixed effects. The estimated VER multipliersfrom this experiment are given in the last columnoff Table 10. The main difference between thiscase and the base case is that the 1986 coefficientbecomes statistically insignificant.

We also conducted some sensitivity analyses

in which more than just yearly VER dummieswere estimated. Recall that the base case im-posed that the export limits were either bindingor not binding on all Japanese firms in a givenyear. Anecdotal evidence suggests that perhapsthe smaller Japanese firms were more con-strained by the VER (at least in the early years).An approach which would be robust to this andother contingencies would be to estimate sepa-rate VER dummies for each firm in each year.This, though, is computationally infeasible andwould, in any case, generate imprecise esti-mates. A middle ground between the infeasibleideal and the base case is to estimate one mul-tiplier for the “Big Two” in Japan (Toyota andNissan) and another for the other Japanesefirms. The results suggested that the smallerfirms might have been more constrained in thefirst few years of the VER, although the effect isimprecisely measured. The anecdotal evidencemay have a grain of truth to it.

One possible problem with grouping Japan’s“Big Two” together is that while Toyota’s for-tunes were rising, Nissan’s were sagging. We alsodivided the Japanese firms into two groups, one ofwhich consisted of Toyota and Honda, and theother included all other Japanese firms. If lumpingNissan and Toyota together might have con-founded the results, putting Honda with Toyotamay be expected to yield a clearer picture, for bothfirms were doing very well over the 1980’s. Theresults are given in Table 11. There we find that inevery year save 1982 (when the policy had noappreciable impact) the VER coefficient is alwayslarger for the Toyota-Honda group. Indeed, wefind that the VER led to statistically higher pricesfor Toyota and Honda in 1984 and 1985, as wellas in the remaining years of the sample. On theother hand, we also find that the VER did notcontribute to significantly higher prices for theother firms in 1990. These results are consistentwith the fact that the base case results meld to-gether into one coefficient the “average” impact ofthe VER, while specific firms were, to varyingextents, more or less impacted by the VER.

The VER, as modeled, enters costs as a year-specific dummy variable for Japanese firms be-ginning in 1981. There are myriad stories thatmight lead to an observationally equivalent es-timating equation. The VER effects show up asdeviations from costs, conditional on trends andcost shifters, in the very particular way implied


by the firms’ first-order conditions. We esti-mated the model with quadratic region-specifictrends instead of the linear ones. The VERcoefficients for 1986 and 1990 cease to be sig-nificantly different from zero.

As a “common sense” test of our results,we reestimated the model with two other setsof country-year dummy variables. Each enterthe cost function just as the VER did. In onespecification, the model was reestimated us-ing “VER” dummies for every year, eventhose prior to the VER. If we were to consis-tently find significant effects of the “VERs” inthe years prior to 1981, one might wonderwhether the results for the years after 1980were really picking up the trade restraints orsomething altogether different. The coeffi-cients on the VER dummy variables wereinsignificantly different from zero throughoutthe 1970’s. During the years that the VERwas actually in place, the only changes rela-tive to the base case are that the coefficientson the VER in some years were slightlysmaller and usually less precisely estimated.

The model was also estimated with year-specific dummy variables for domestic firmsduring the 1980’s. Again, had these dummyvariables matched the pattern of the Japanese

VER multipliers, one might wonder whethersomething other than the VER might be moti-vating the base case results. We found that onlyone of the 10 year-specific dummy variables fordomestic firms was significantly different fromzero—about what we would expect if all werezero at the 90-percent level of statistical signif-icance. The point estimates were all quitesmall.31

The model was estimated allowing tastes todiffer in the 1970’s. This was done by allowingthe means of the tastes distributions to differ inthe 1970’s while constraining the variances ofthe taste distributions to remain constant overthe sample. This was required in order to keepthe estimation computationally feasible. The re-sults suggest that the marginal utility of size andair-conditioning was lower in the 1970’s, a pe-riod during which gas prices were high. We canreject that tastes were constant over the sample.The estimated VER coefficients, though, remainsubstantively the same as the base case.

Finally, we have assumed that quality changesare exogenous. That is, while upgrading occurred,we do not model this as a policy-induced re-sponse. Our results, then, are conditional on theexogeneity of the existing product attributes.

From Table 10 and our other sensitivity anal-yses, we conclude that our base case results arereasonably robust to several plausible alterna-tive specifications. Because the results seem sorobust, it is natural to question why they do notreplicate the messages of the existing literatureon the effect of the VER. Our results are notvery much at odds with Feenstra’s and the dif-ferences are explainable. Feenstra (1988) foundsubstantial quality upgrading, and we also findthis in our data. Feenstra found that the VERwas initially binding. His methods and data,though, were quite different. He did not use datafor the decade prior to the VERs, and he esti-mated separate sets of coefficients for Japanesecars. Finally, his methods are much more in thespirit of a reduced form, and the underlyingframework is not nearly as structural as ourequilibrium oligopoly model. (His work also

31 We do not report the full results here, because this wasthe one specification for which we had troubles in reliablyminimizing the objective function. This problem appearedto arise because of the large number of nonlinear cost-sideparameters being estimated.

TABLE 11—MORE SENSITIVITY ANALYSIS

Toyota andHonda

All otherJapanese firms

VER81 0.214 20.149(0.238) (0.258)

VER82 20.135 20.020(0.293) (0.258)

VER83 0.162 0.034(0.293) (0.266)

VER84 0.611 0.372(0.352) (0.315)

VER85 0.790 0.498(0.387) (0.338)

VER86 0.935 0.383(0.425) (0.368)

VER87 1.725 1.046(0.556) (0.394)

VER88 1.627 1.252(0.642) (0.444)

VER89 1.702 1.151(0.711) (0.489)

VER90 2.766 0.872(0.867) (0.534)



predates ours by about a decade, and many ofthe econometric tools at our disposal were notavailable then.) When we use the same years ofdata as Feenstra and employ simple hedonicregressions as he did, we find that we replicatethe gist of his results. The VERs appear bindingin the early years, but their magnitude is smalland not always precisely estimated. When weadd our oligopoly structure, but continue toallow Japanese cars to have different cost func-tions, we no longer find that the VERs wereinitially binding. We conclude that what differ-ences there are between our results and Feen-stra’s emanate from different interpretations tothe hedonic regression; we have a model whichallows us to impute changes in that regressionto changes in underlying costs, in markups, andin the implications of trade policy (the VERdummies).

Though Goldberg’s (1995) methods are alot more similar to ours than Feenstra’s, herresults (unlike those of Feenstra) are, in somerespects, quite different from ours. In partic-ular, as noted earlier, Goldberg finds that theVER was binding in the early years. We in-vestigated several possible sources of this dif-ference but could not account for it. Goldbergdid not use data from years prior to the VER,had fewer years of data for the later 1980’s,and made use of consumer-level data usingthe Consumer Expenditure Survey.When weestimate our model using only the same yearsof data as Goldberg, we continue to find thatthe VER did not initially bind. We allowedfor trends in the data that Goldberg does notaccount for. We again reestimate our modelexcluding all trends. Again, our results re-main at odds with Goldberg’s. As notedabove, ignoring or including macroeconomicvariables, direct foreign investment, and/orcaptive imports do not substantively changeour results, and hence could not reconcilethem with those reported by Goldberg. Wespeculate on two possible reasons for the dif-ference. We account for the econometric en-dogeneity of price, while Goldberg does not.Using consumer-level automobile purchasedata (not used in the analysis of this paper;see Berry et. al., 1998), we find that ignoringthis endogeneity substantially biases the esti-mates and that the resulting elasticities areaffected. Since these elasticities are key to the

analysis, this may account for the difference.Secondly, the demand structures in this studyand in Goldberg’s are quite different and thistoo may matter.

VII. Conclusions and Caveats

Our estimates indicate that the VERs affectedprices, although not necessarily in the yearsmost expected. They raised Japanese prices anddomestic sales. The profits of domestic firmsincreased substantially while those of Japanesefirms were less affected. Domestic consumerwelfare fell, also quite significantly, and thisburden fell disproprotionately on consumerswith relatively inelastic demands for Japaneseproducts. The “giveaway” to Japan in terms offorgone tariff revenue was very large. In sum,our point estimates imply that if tariffs couldhave been instituted without setting off otherchanges in the market (in particular with nochanges in the cars marketed in the UnitedStates and no retaliatory responses by the Jap-anese), strategic trade policy could have en-hanced U.S. economic welfare.

When the first economic models of strategictrade policy were being introduced, most of thefounders of that literature went to some lengthto make clear that their models did not mean thetraditional arguments for free trade had becomeinapplicable. This paper may be the first de-tailed econometric study of a strategic tradepolicy and similar caveats are in order.

We have computed the standard errors aroundeach of these policy implications. These suggestresearchers ought to be circumspect about makingpolicy conclusions even when the individual pa-rameters of the structural model are themselvesprecisely estimated. We are unable to preciselyestimate the impact of the VER on profits. Theforgone tariff revenue and the compensating vari-ation, though, are precisely estimated and our es-timates suggest that these two components ofwelfare about cancel each other out.

Standard errors around policy conclusionsare only one reason to view the results in thispaper with care. The underlying model is not adynamic model (nor are any of the models withwhich we compare ours) and this has multipleimplications. First, automobiles are a durablegood and expectations about how long the VERwas expected to last surely impacted production


and consumption decisions. Second, as notedearlier, we take as exogenous both the set ofproducts firms bring to the market and the at-tributes of those products. A more involveddynamic model would allow one to model theseendogenously. Third, we do not model myriadother aspects of the dynamics of automobilepurchases such as financing, expected depreci-ation, and resale value. Fourth, on the demandside, we have usually assumed that the under-lying distributions of tastes are constant. Iftastes changed over time due for example tolearning, these changes might impact our re-sults. In sum, we realize these dynamic issuesare important, and this too adds to our caution ininterpreting the results.

APPENDIX: AN APPROXIMATION TO “OPTIMAL”INSTRUMENTS

Following Chamberlain (1986), the efficient setof instruments when we have only conditionalmoment restrictions is:

(A1) Hj~z! 5 EFj j~u0!

u,

v j~u0!

uuzGT ~zj!

; Dj ~z!T ~zj!,

whereT( zj) is the matrix that normalizes theerror matrix, i.e.,

T ~z!9T ~z! 5 V~z!21

; E~~j, v!~j, v!9|z!21.

This formula is very intuitive: larger weightsshould be given to the observations that generatedisturbances whose computed values are very sen-sitive to the choice ofu (atu 5 u0). UnfortunatelyDj (z) is typically difficult to compute. Since therequired derivatives are a function of prices, tocalculateDj (z) we would have to calculate thepricing equilibrium for different {jj, vj} se-quences, take derivatives at the equilibrium prices,and then integrate out over the distribution of suchsequences.

We propose to replace the expectationDj (z)

with the appropriate derivatives evaluated at theexpectation of the unobservables. To constructsuch derivatives, we take the following steps:

(i) Obtain an initial estimateu from an initialrun using cruder instruments.

(ii) Use u to construct exogenous estimates ofd andmc: d 5 xb and mc 5 wg.

(iii) Solve the first-order conditions of themodel for equilibrium prices, p, andshares,s, as a function ofu, d, mc, andx.

(iv) Construct the functions defining the unob-servables of the model evaluated at theexogenous predictions:j(u) 5 j(p, s, d,x, u) and v(u) 5 v(p, s, d, mc, x, u).Then use as our (admittedly biased) esti-mate of the optimal instrument vector

Dj ~z! 5 Sj j~u!

u,

v j~u!

u D .

Further detail and some intuition for a simplermodel can be found in the 1995 National Bureauof Economic Research version of this paper.

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