The Gravity Model

AGRODEP Technical Note TN-05April 2013Hands-on gravity estimation with STATAVersion 2Maria Cipollina and Luca SalvaticiHands-on gravity estimation with STATAIn this document we give several examples of hands-on estimation to familiarize yourself with the gravity equation methodological choices highlighted in the literature review. This guide provides an illustrative dataset with alternative Stata codes presenting the different possible estimation strategies.Part 1 describes how estimations are carried out with panel data and are directed to show the relevance of the multilateral resistance term as well as the modeling of the (trade) policy variables. In Part 2, cross-sections estimations show the importance of working with disaggregated data. Finally, Part 3 shows how you can solve the ‘zero (trade flows) problem’ using either Heckman or Poisson estimators.As you read this guide, you will use STATA to carry out estimations designed to familiarize you with the software and, more importantly, the gravity model. STATA is a statistical software program and we assume that you have a recent version of STATA (version 11.2 or later). The instructions in this guide are quite detailed. Our aim is to give sufficient detail to enable a new user of this software to follow the examples relying solely on this guide. On the other hand, the guide is strictly related to the literature review that highlights the main theoretical and methodological issues illustrated in the regressions.Data filesThere are two Data files:∙dataset_def.dta: it contains all the essential variables used in the regressions using panel data (Part 1). The dataset covers the period from 1996 to 2006 and includes 154 developed and developing countries.∙us_agr.dta: it contains all the essential variables used in the regressions using cross-section data (Part 2 and Part 3). It refers to year 2004 US agricultural imports from 226 countries. Data are disaggregated at the most detailed level allowed by the international Harmonized System (HS) classification (6 digits) and include 689 products.The variable names are largely self-explanatory and are described when the labels are created: their generation and construction can thus be directly inspected. The data sources are described in the Appendix.Do filesThere are three Do files:∙regressions aggregated data.do: it runs regressions using panel, aggregated data (Part1).∙regressions disaggregated data.do: it runs regressions using cross-section, disaggregated as well as aggregated data (Part 2).∙regressions zeroes treatment.do: it runs regressions using non-linear estimators (Heckman or Poisson) dealing with ‘zero’ trade flows (Part 3).Part 1: Aggregated dataA.Variable Generation.Part A brings in the data and generates the variables used in the analysis:(a)We use the data file dataset_defuse dataset_def.dta(b)We take the logs of all continuous variables included in the regressions:g limports=ln(imports)g lgdp_o=ln(gdp_o)g lgdp_d=ln(gdp_d)g ldist= ln(distw)g ltariff=ln(1+s_average)(c)We label the variables to be included in the tables.l a var limports “Ln(Imports)”la var colony “Colonial link”la var comlang_off “Common language”la var contig “Border”la var ldist “Ln(distance)”la var lgdp_d “Ln(GDP_importer)”la var lgdp_o “Ln(GDP_exporter)”la var rta “Regional Trade Agreement”la var ltariff “Ln(1+Tariff)”(d)Finally, we generate the different fixed effects.qui tab imp, g(dimp)qui tab exp, g(dexp)qui tab pair, g(dpair)qui tab year, g(dyear)B. Regression SpecificationsPart B runs panel regressions with aggregated data, and the dummy RTA (i.e., Regional Trade Agreements) as (trade) policy variable. Regressions are based on equation (2) with time, importer, exporter and country-pair fixed effects.We start by declaring data to be panel.tsset pair yearIn order to show the consequences of ignoring the multilateral resistance term, we firstly estimate equation (2) without fixed effectseststo: reg limports lgdp_d lgdp_o ldist contig colony comlang_off rta, robust Then, we introduce the different types of fixed effects:eststo: reg limports lgdp_d lgdp_o ldist contig colony comlang_off rta dyear*, robust eststo: reg limports lgdp_d lgdp_o ldist contig colony comlang_off rta dimp* dexp*, robusteststo: reg limports lgdp_d lgdp_o ldist contig colony comlang_off rta dimp* dexp* dyear*,robusteststo: reg limports lgdp_d lgdp_o ldist contig colony comlang_off rta dpair* dyear*, robustThe dummy for pair effects is equal to 1 for all observations of trade occurring between a given pair of countries, for all pairs. Country dummies remove cross-section, but not time-series biases. The latter is a serious shortcoming since omitted factors affecting bilateral trade costs often vary over time. Pair dummies cannot be used in cross-section data since the number of dummies would be equal to the number of observations.The command “esttab” creates the regression table in a file regressions1.docesttab using regressions1.doc, title (aggregate-dummy policy) se ar2 label replace rtf b(2) star (* 0.10 ** 0.05 *** 0.01) se(2) mti drop (dexp* dimp* dyear* dpair*)TABLE: Panel results with different fixed effectsModel 1and 2 report the base regression. Column (1.1) reports results without fixed effects. Column (2.1) reports results where time dummies are added to the regression, to account forthe changing nature of the relationship over time. Column (2.2) and (2.3) show results for time invariant importer and exporter fixed effects and for time varying exporter and importer fixed effects, respectively. Finally, column (2.4) presents a specification where pair effects are also added.* p < 0.10, ** p < 0.05, *** p < 0.01All coefficients have the expected signs, the only exception is the coefficient of the colonial links that seem to have a negative impact if we do not consider country fixed effects (columns 1.1 and 2.1). Focusing on the most widely used specification (column 2.3), the estimated coefficients should be interpreted as follows: size of importer country has a positive and significant impact with an elasticity of 0.91, so that an increase in GDP of 10% increase trade by 9.1%; an increase in distance of 10% reduce trade by around 15%; the existence of border and language links imply an increase in trade of 72% and 118% (e0.54-1=0.72; e0.78-1= 1.18), respectively; the estimated coefficient of dummy for RTA of 0.62 implies that regional trade agreements increase trade of 86% (e0.62-1=0.86).Finally, in order to show the relevance of an actual measure we estimate equation (3) using a continuous variable for trade policyreg limports lgdp_d lgdp_o ldist contig colony comlang_off ltariff dimp* dexp* dyear*, robustThen we create the results tableesttab using regressions1.doc, title (aggregate-tariff) se ar2 label replac rtf b(2) star (* 0.10 ** 0.05 *** 0.01) se(2) mti drop (dexp* dimp* dyear*) appendTABLE: Panel results with continuous policy variable* p < 0.10, ** p < 0.05, *** p < 0.01All coefficients have the expected signs. Trade policies have a negative and significant impact on trade, a tariff factor increase by 10% leads to a 6% reduction of trade.Part 2: Disaggregated dataA.Variable Generation.(a)We use the data file us_agruse us_agr.dta(b)We take the logs of all continuous variables included in the regressionsg limports=ln(trade)g lgdp_o=ln(gdp_o)g lgdp_d=ln(gdp_d)g ldist= ln(distw)g ltariff=ln(1+tariff)(c)We label the variables to be included in the tables.la var limports "Ln(Imports)"la var colony "Colonial link"la var comlang_off "Common language"la var contig “Border”la var ldist "Ln(distance)"la var lgdp_d "Ln(GDP_importer)"la var lgdp_o "Ln(GDP_exporter)"la var ltariff "Ln(1+Tariff)"(d)We generate the exporter and product fixed effectsqui tab exp, g(dexp)qui tab hs6, g(dhs6)B. Regression Specifications(a)As in Part 1, we firstly estimate equation (2) using the OLS estimator without fixedeffectseststo: reg limports lgdp_o ldist contig colony comlang_off ltariff, robust(b)Then, we introduce the different types of fixed effects:eststo: reg limports lgdp_o ldist contig colony comlang_off ltariff dhs6*, robusteststo: reg limports contig colony comlang_off ltariff dexp* dhs6*, robust(c)Finally, we collapse the dataset in order to obtain aggregated data for a robustnessanalysis.collapse (sum) trade (mean) tariff gdp_o distw contig colony comlang_off, by(exp)g limports=ln(trade)g lgdp_o=ln(gdp_o)g ldist= ln(distw)g ltariff=ln(1+tariff)(d)and we run again the regression to highlight the relevance of the aggregation issueeststo: reg limports lgdp_o ldist contig colony comlang_off ltariff, robust(e)The command “esttab” creates the regression table in a file regressions2.docesttab using regressions2.doc, title (dati_us_agr) se ar2 label replac rtf b(2) star (*0.10 ** 0.05 *** 0.01) se(2) mti drop (dexp* dhs6*) appendeststo clearTABLE: Cross-section results with different fixed effects and different levels of aggregation Cross-sectional model covering imports in 689 agricultural commodities from 227 countries to US in 2004.Columns (1) to (3) show results with disaggregated data using different fixed-effects specifications. Column (4) reports result of aggregated data.* p < 0.10, ** p < 0.05, *** p < 0.01Most empirical analyses use gravity models with aggregated data, but using aggregate trade flows to analyze the effects of trade policies applied at product level seems misleading. As a matter of fact, the estimated coefficient related to trade policy, namely Ln(1+tariff), is not significant in column (4).Part 3: Zeroes treatmentA.Variable Generation(a)We use the data file us_agruse us_agr.dtaWe take the logs of all continuous variables included in the regressionsg limports=ln(trade)g lgdp_o=ln(gdp_o)g lgdp_d=ln(gdp_d)g ldist= ln(distw)g ltariff=ln(1+tariff)(c)We label the variables to be included in the tables.la var limports "Ln(Imports)"la var colony "Colonial link"la var comlang_off "Common language"la var ldist "Ln(distance)"la var lgdp_d "Ln(GDP_importer)"la var lgdp_o "Ln(GDP_exporter)"la var ltariff "Ln(1+Tariff)"(d)We generate the exporter and product fixed effectsqui tab exp, g(dexp)qui tab hs6, g(dhs6)B. Regression Specifications(a)We firstly run the regression using the Heckman estimatoreststo: heckman limports contig colony comlang_off ltariff , select(contig colony ltariff) mills(lambda)(b)Then we run the regression using the Poisson Pseudo-Maximum Likelihood estimatoreststo: ppml trade contig colony comlang_off ltariff(c)The command “esttab” creates the regression table in a file regressions3.docesttab using regressions3.doc, title (treatment of zeros) se ar2 label replace rtf b(2) star (* 0.10 ** 0.05 *** 0.01) se(2) mtiTABLE: Results with different estimators: Heckman and PoissonModel (1) reports results obtained using the Heckman two-step procedure. The first column shows the second stage estimates of the trade flow, whereas the second column reports the first-stage Probit selection equation. Model (2) shows results obtained using Poisson Pseudo-Maximum Likelihood estimator.The use of disaggregated data raises the “zero trade flows” issue, which introduces obvious problems in the log-linear form of the gravity equation. Several authors consider the Heckman two-step estimator as the best procedure, others argue that gravity type models should be estimated in multiplicative form, and recommend the Poisson Pseudo-Maximum Likelihood (PPML) estimator to deal with the problem of zeros in the trade matrix, in order to achieve unbiased and consistent estimates. The significant coefficient of the Mills ratio confirms that correcting for sample selection bias is justified, however, because of the presence of heteroskedasticity, estimates of the log-linear form of the gravity equation are biased and inconsistent, and this may lead to prefer the Poisson specification of the trade gravity model.APPENDIX: Data SourceDataset_def.dta: Dataset is building on extraction from WITS (/wits/index.html) and on information provided by the CEPII dataset (http://www.cepii.fr/).The WITS application gives access to international trade statistics of UN COMTRADE (The United Nations Commodity Trade Statistics database) and tariff database of UNCTAD-TRAINS (Trade Analysis and Information System).The Cepii dataset includes data on GDP and distances between countries and dummies for contiguity, common language, and former colonial links.Us_agr.dta: Data on trade and tariffs at the HS6 level of detail are taken from the MAcMapHS6-V2 database (/publication/picture-tariff-protection-across-world-2004). MAcMapHS6 provides a consistent worldwide assessment of protection, including ad valorem equivalent rates of specific duties and tariff rate quotas (including those introduced at the end of the Uruguay Round), for 2004. Data for the remaining explanatory variables are from the Cepii dataset.。

Chapter 2World Trade: An Overview⏹Chapter OrganizationWho Trades with Whom?Size Matters: the Gravity ModelThe Logic of the Gravity ModelUsing the Gravity Model: Looking for AnomaliesImpediments to Trade: Distance, Barriers, and BordersThe Changing Pattern of World TradeHas the World Gotten SmallerWhat Do We Trade?Service OutsourcingDo Old Rules Still Apply?Summary⏹Key ThemesBefore entering into a series of theoretical models that explain why countries trade across borders and the benefits of this trade (Chapters 3–11), Chapter 2 considers the pattern of world trade which we observe today. The core idea of the chapter is the empirical model known as the gravity model. The gravity model is based on the observations that: (1) countries tend to trade with other nearby economies and (2) countries’ trade is proportional to their size. The model is called the gravity model as it is similar in form to the physics equation that describes the pull of one body on another as proportional to their size and distance.The basic form of the gravity equation is T ij=A⨯Y i⨯Y j/D ij. The logic supporting this equation is that large countries have large incomes to spend on imports and produce a large quantity of goods to sell as exports. This means that the larger either trade partner, the larger the volume of trade between them. At the same time, the distance between two trade partners can substitute for the transport costs that they face as well as proxy for more intangible aspects of a trading relationship such as the ease of contact for firms. This model can be used to estimate the predicted trade between two countries and look for anomalies in trade patterns. The text shows an example where the gravity model can be used to demonstrate the importance of national borders in determining trade flows. According to many estimates, the border between the U.S. and Canada has the impact on trade equivalent to roughly 2000 miles of distance. Other factors, such as tariffs, trade agreements, and common language can all affect trade and can be incorporated into the gravity model.The chapter also considers the way trade has evolved over time. While people often feel that the modern era has seen unprecedented globalization, in fact, there is precedent. From the end of the 19th century to World War I, the economies of different countries were quite connected. Trade as a share of GDP was higher in 1910 than 1960, and only recently have trade levels surpassed the pre World War trade. The nature of trade has change though. The majority of trade is in manufactured goods with agriculture and mineral products (and oil) making up less than 20% of world trade. Even developing countries now export primarily manufactures. In contrast, a century ago, more trade was in primary products as nations tended to trade for things that literally could not be grown or found at home. Today, the reasons for trade are more varied and the products we trade are ever changing (for example, the rise in trade of things like call centers). Th e chapter concludes by focusing on one particular expansion of what is “tradable”—the increase in services trade. Modern information technology has greatly expanded what can be traded as the person staffing a call center, doing your accounting, or reading your X-ray can literally be half-way around the world. While still relatively rare, the potential for a large increase in service outsourcing is an important part of how trade will evolve in the coming decades. The next few chapters will explain the theory of why nations trade.Answers to Textbook Problems1. We saw that not only is GDP important in explaining how much two countries trade, but also,distance is crucial. Given its remoteness, Australia faces relatively high costs of transporting imports and exports, thereby reducing the attractiveness of trade. Since Canada has a border with a largeeconomy (the U.S.) and Australia is not near any other major economy, it makes sense that Canada would be more open and Australia more self-reliant.2. Mexico is quite close to the U.S., but it is far from the European Union (EU). So it makes sense thatit trades largely with the U.S. Brazil is far from both, so its trade is split between the two. Mexico trades more than Brazil in part because it is so close to a major economy (the U.S.) and in partbecause it is a member of a free trade agreement with a large economy (NAFTA). Brazil is farther away from any large economy and is in a free trade agreement with relatively small countries.3. No, if every country’s GDP were to double, world trade would not quadruple. One way to see thisusing the example from Table 2-2 would simply be to quadruple all the trade flows in 2-2 and also double the GDP in 2-1. We would see that the first line of Table 2-2 would be—, 6.4, 1.6, 1.6. If that were true, Country A would have exported $8 trillion which is equal to its entire GDP. Likewise, it would have imported $8 trillion, meaning it had zero spending on its own goods (highly unlikely). If instead we filled in Table 2-2 as before, by multiplying the appropriate shares of the world economy times a country’s GDP, we would see the first line of Table 2-2 reads—, 3.2, 0.8, 0.8. In this case, 60% of Country A’s GDP is exported, the same as before. The logic is that while the world G DP has doubled, increasing the likelihood of international trade, the local economy has doubled, increasing the likelihood of domestic trade. The gravity equation still holds. If you fill in the entire table, you will see that where before the equation was 0.1 ⨯ GDP i⨯ GDP j, it now is 0.05 ⨯ GDP i⨯ GDP j. The coefficient on each GDP is still one, but the overall constant has changed.4. As the share of world GDP which belongs to East Asian economies grows, then in every traderelationship which involves an East Asian economy, the size of the East Asian economy has grown.This makes the trade relationships with East Asian countries larger over time. The logic is similar for why the countries trade more with one another. Previously, they were quite small economies, meaning that their markets were too small to import a substantial amount. As they became morewealthy and the consumption demands of their populace rose, they were each able to importmore. Thus, while they previously had focused their exports to other rich nations, over time, they became part of the rich nation club and thus were targets for one another’s exports. Again, using the gravity model, when South Korea and Taiwan were both small, the product of their GDPs was quite small, meaning despite their proximity, there was little trade between them. Now that they have both grown considerably, their GDPs predict a considerable amount of trade.5. As the chapter discusses, a century ago, much of world trade was in commodities that in many wayswere climate or geography determined. Thus, the UK imported goods that it could not make itself.This meant importing things like cotton or rubber from countries in the Western Hemisphere or Asia.As the UK’s climate and natural resource endowments were fairly similar to those in the rest of Europe, it had less of a need to import from other European countries. In the aftermath of the IndustrialRevolution, where manufacturing trade accelerated and has continued to expand with improvements in transportation and communications, it is not surprising that the UK would turn more to the nearby and large economies in Europe for much of its trade. This is a direct prediction of the gravity model.。

The Gravity Model∗James E.AndersonBoston College and NBERJanuary18,2011AbstractGravity has long been one of the most successful empirical models in economics.In-corporating deeper theoretical foundations of gravity into recent practice has led toa richer and more accurate estimation and interpretation of the spatial relations de-scribed by gravity.Wider acceptance has followed.Recent developments are reviewedhere and suggestions are made for promising future research.JEL Classification:F10,R1.Contact information:James E.Anderson,Department of Economics,Boston Col-lege,Chestnut Hill,MA02467,USA.Keywords:Incidence,multilateral resistance,trade costs,migration.∗This review was prepared for Annual Review of Economics,vol.3.I thank Jeffrey H.Bergstrand,Keith Head,J.Peter Neary and Yoto V.Yotov for helpful comments.The gravity model in economics was until relatively recently an intellectual orphan,un-connected to the rich family of economic theory.This review is a tale of the orphan’s reunion with its heritage and the benefits that continue toflow from connections to more distant relatives.Gravity has long been one of the most successful empirical models in economics,order-ing remarkably well the enormous observed variation in economic interaction across space in both trade and factor movements.The goodfit and relatively tight clustering of coeffi-cient estimates in the vast empirical literature suggested that some underlying economic law must be at work,but in the absence of an accepted connection to economic theory,most economists ignored gravity.The authoritative survey of Leamer and Levinsohn(1995)cap-tures the mid-90’s state of professional thinking:“These estimates of gravity have been both singularly successful and singularly unsuccessful.They have produced some of the clearest and most robust empiricalfindings in economics.But,paradoxically,they have had virtually no effect on the subject of international economics.Textbooks continue to be written and courses designed without any explicit references to distance,but with the very strange im-plicit assumption that countries are both infinitely far apart and infinitely close,the former referring to factors and the latter to commodities.”Subsequently,gravityfirst appeared in textbooks in2004(Feenstra,2004),following on success in connecting gravity to economic theory,the subject of Section3.Reviews are not intended to be surveys.My take on the gravity model,thus licensed to be idiosyncratic,scants or omits some topics that others have found important while it emphasizes some topics that others have scanted.My emphases and omissions are intended to guide the orphan to maturity.An adoptive parent’s biases may have contaminated my judgment,caveat emptor.My focus is on theory.Incorporating the theoretical foundations of gravity into recent practice has led to richer and more accurate estimation and interpretation of the spatial relations described by gravity,so where appropriate I will point out this benefit.The har-vest reaped from empirical work applying the gravity model is recently surveyed elsewhere (Anderson and van Wincoop,2004;Bergstrand and Egger,2011).From a modeling standpoint,gravity is distinguished by its parsimonious and tractable representation of economic interaction in a many country world.Most international economic theory is concentrated on two country cases,occasionally extended to three country cases with special features.The tractability of gravity in the many country case is due to its modularity:the distribution of goods or factors across space is determined by gravity forces conditional on the size of economic activities at each location.Modularity readily allows for disaggregation by goods or regions at any scale and permits inference about trade costs not dependent on any particular model of production and market structure in full general equilibrium.The modularity theme recurs often below,but is missing from some other prominent treatments of gravity in the literature.1Traditional GravityThe story begins by setting out the traditional gravity model and noting clues to its union with economic theory.The traditional gravity model drew on analogy with Newton’s Law of Gravitation.A mass of goods or labor or other factors of production supplied at origin i,Y i, is attracted to a mass of demand for goods or labor at destination j,E j,but the potential flow is reduced by the distance between them,d ij.Strictly applying the analogy,X ij=Y i E j/d2ijgives the predicted movement of goods or labor between i and j,X ij.Ravenstein(1889) pioneered the use of gravity for migration patterns in the19th century UK.Tinbergen(1962) was thefirst to use gravity to explain tradeflows.Departing from strict analogy,traditional gravity allowed the exponents of1applied to the mass variables and of−2applied to bilateral distance to be generated by data tofit a statistically inferred log-linear relationship betweendata onflows and the mass variables and distance.Generally,across many applications,the estimated coefficients on the mass variables cluster close to1and the distance coefficients cluster close to−1while the estimated equationfits the data well:most data points cluster close to thefitted line in the sense that80−90%of the variation in theflows is captured by thefitted relationship.Thefit of traditional gravity improved when supplemented with other proxies for trade frictions,such as the effect of political borders and common language.Notice that bilateral frictions alone would appear to be inadequate to fully explain the effects of trade frictions on bilateral trade,because the sale from i to j is influenced by the resistance to movement on i’s other alternative destinations and by the resistance on move-ment to j from j’s alternative sources of supply.Prodded by this intuition the traditional gravity literature recently developed remoteness indexes of each country’s‘average’effectivedistance to or from its partners(id ij/Y i was commonly defined as the remoteness of coun-try j)and used them as further explanatory variables in the traditional gravity model,with some statistical success.The general problem posed by the intuition behind remoteness indexes is analogous to the N-body problem in Newtonian gravitation.An economic theory of gravity is required for an adequate solution.Because there are many origins and many destinations in any application,a theory of the bilateralflows must account for the relative attractiveness of origin-destination pairs.Each sale has multiple possible destinations and each purchase has multiple possible origins:any bilateral sale interacts with all others and involves all other bilateral frictions.This general equilibrium problem is neatly solved with structural gravity models.For expositional ease,the discussion focuses below on goods movements except when migration or investment is specifically treated.2Frictionless Gravity LessonsTaking a step toward structure,an intuitively appealing starting point is the description of a completely smooth homogeneous world in which all frictions disappear.Developing the implications of this structure yields a number of useful insights about the pattern of world trade.A frictionless world implies that each good has the same price everywhere.In a homoge-neous world,economic agents everywhere might be predicted to purchase goods in the same proportions when faced with the same prices.In the next section the assumptions on pref-erences and/or technology that justify this plausible prediction are the focus,but here the focus is on the implications for trade patterns.In a completely frictionless and homogeneous world,the natural benchmark prediction is that X ij/E j=Y i/Y,the proportion of spending by j on goods from i is equal to the global proportion of spending on goods from i,where Y denotes world spending.Any theory must impose adding up constraints,which for goods requires that the sum of sales to all destinations must equal Y i,the total sales by origin i,and the sum of purchases from all origins must equal E j,the total expenditure for each destination j.Total sales andexpenditures must be equal:i.e.,iY i=jE j=Y.One immediate payoffis an implication for inferring trade frictions.Multiplying both sides of the frictionless benchmark prediction X ij/E j=Y i/Y by E j yields predicted friction-less trade Y i E j/Y.The ratio of observed trade X ij to predicted frictionless trade Y i E j/Y represents the effect of frictions along with random influences.(Bilateral trade data are notoriously rife with measurement error.)Fitting the statistical relationship between the ratio of observed to frictionless trade and various proxies for trade costs is justified by this simple theoretical structure as a proper focus of empirical gravity models.Thus far,the treatment of tradeflows has been of a generic good that most of the literature has implemented as an aggregate:the value of aggregate bilateral trade in goods for example.But the model applies more naturally to disaggregated goods(and factors)becausethe frictions to be analyzed below are likely to differ markedly by product characteristics. The extension to disaggregated goods,indexed by k,is straightforward.X kij =Y kiE kjY k=s kib kjY k.(1)Here s ki =Y ki/Y k is country i’s share of the world’s sales of goods class k and b kj=E kj/Y kis country j’s share of the world spending on k,equal to the world’s sales of k,Y k.The notation and logic also readily apply to the disaggregation of countries into regions, and indeed a prominent portion of the empirical literature has examined bilateralflows between city pairs or regions,motivated by the observation that much economic interaction is concentrated at very short distances.The model can interpreted to reflect individual decisions aggregated with a probability model;see section5.1below.In aggregate gravity applications(i.e.,most applications),it has been common to use origin and destination mass variables equal to Gross Domestic Product(GDP).This is con-ceptually inappropriate and leads to inaccurate modeling unless the ratio of gross shipments to GDP is constant(in which case the ratio goes into a constant term).A possible direction for aggregate modeling is to convert trade to the same value-added basis as GDP,but this seems more problematic than using disaggregated gravity to explain the pattern of gross shipments and then uniting estimated gravity models within a superstructure to connect to GDP.That is the strategy of the structural gravity model research program reviewed here.Equation(1)generates a number of useful implications.1.Big producers have big market shares everywhere,2.small sellers are more open in the sense of trading more with the rest of the world,3.the world is more open the more similar in size and the more specialized the countriesare,4.the world is more open the greater the number of countries,and5.world openness rises with convergence under the simplifying assumption of balancedtrade.Implication1,that big producers have big market shares everywhere,follows because, reverting to the generic notation and omitting the k superscript,the frictionless gravity prediction is that:X ij/E j=s i.Implication2,that small sellers are more open in the sense of trading more with the rest of the world follows fromi=jX ij/E j=1−Y j/Y=1−s jusingjE j=iY i,which implies balanced trade for the world.Implication3is that the world is more open the more similar in size and the more special-ized the countries are.It is convenient to define world openness as the ratio of internationalshipments to total shipments,ji=jX ij/Y.Dividing(1)through by Y k and suppressingthe goods index k,world openness is given byji=jX ij/Y=jb j(1−s j)=1−jb j s j.Using standard statistical propertiesj b j s j=Nr bsV ar(s)V ar(b)+1/N,where N is the number of countries or regions,V ar denotes variance,r bs is the correlationcoefficient between b and s and1/N=is i/N=jb j/N,the average share.This equationfollows from the shares summing to one and using standard properties of covariance.Here, V ar(s)and V ar(b)measures size dis-similarity and the correlation of s and b,r bs,is aninverse measure of specialization.Substituting into the expression for world openness:ji=jX ij/Y=1−1/N−Nr bsV ar(s)V ar(b)(2)Implication3follows from equation(2)because on the right-hand side the similarity of country size shrinks the variances while specialization shrinks the correlation r bs.The country-size similarity property has been prominently stressed in the monopolistic competition and trade literature.(It is sometimes taken as evidence for monopolistic com-petition in a sector rather than as a consequence of gravity no matter what explains the pattern of the b’s and s’s.)The specialization property has also been noted in that liter-ature as reflecting forces that make for greater net international trade,the absolute value of s j−b j.Making comparisons across goods classes,variation in the right-hand side of(2) results from variation in specialization and in the dispersion of the shipment and expenditure shares.Notice again that the cross-commodity variation in world openness arises here in a frictionless world,a reminder that measures of world home bias in a world with frictions must be evaluated relative to the frictionless world benchmark.Country-size similarity also tends to increase bilateral trade between any pair of countries, all else equal.This point(Bergstrand and Egger,2007)is seen most clearly with aggregate trade that is also balanced,hence s j=b j.Equation(1)can be rewritten asX ij=s iji s ijj(Y i+Y j)2Y,where s iji ≡Y i/(Y i+Y j),the share of i in the joint GDP of i and j.The product s ijis ijjis maximized at s iji =s ijj=1/2,so for given joint GDP size,bilateral trade is increasingin country similarity.(With unbalanced trade or specialization,an analogous similarity property holds for the bilateral similarity of income and expenditure shares.Letγj=E j/Y j. Then the same equation as before holds with the right-hand side multiplied byγj.)A more novel implication of equation(2)is implication4,that world openness is ordinarilyincreasing in the number of countries.Increasing world openness due to a rise in the number of countries reflects the property that smaller countries are more naturally open and division makes for more and smaller countries.This effect is seen by differentiating the left-hand side ofji=jX ij/Y=1−jb j s j,yielding−j(b j ds j+s j db j).Increasing the number of countries tends to imply reducingthe share of each existing country while increasing the share(from zero)of the new country. The preceding differential expression should thus ordinarily be positive.The qualification‘ordinarily’is needed because the pattern of share changes will depend on the underlying structure as revealed by the left-hand side of equation(2).On the one hand,the average share1/N decreases as N rises,raising world openness.On the otherhand,the change in the number of countries will usually change r bsin waysthat depend on the type of country division(or confederation)as well as indirect effects on shares as prices change.(The apparent direct effect of N in thefirst term on the right-handside of equation(2)vanishes because1/N scalesV ar(b)V ar(s).)A practical implication of this discussion is that inter-temporal comparisons of ratios of world international trade to world income,to be economically meaningful,should be con-trolled for changes in the size distribution and the number of countries,a correction of large practical importance in the past50to100years.Alternatively,measures of openness meant to reflect the effects of trade frictions should be constructed in relation to the frictionless benchmark.Applied to aggregate trade data,gravity yields implication5,that world openness rises with convergence under the simplifying assumption of balanced trade for each country,b j= s j,∀j.The right-hand side of equation(2)becomes NV ar(s)+1/N under balanced trade, and per-capita income convergence lowers V ar(s)toward the variance of population.Baier and Bergstrand(2001)use the convergence property to partially explain postwar growth in world trade/income,finding relatively little action,although presumably more recent data influenced by the rise of China and India might give more action.Pointing toward a connection with economic theory,the shares s i and b j and the plau-sible hypothesis of the frictionless model must originate from an underlying structure of preferences and technology.Also,the deviation of observed X ij from the frictionless pre-diction reflects frictions as they act on the pattern of purchase decisions of buyers and the sales decisions of sellers,which originate from an underlying structure of preferences and technology.3Structural GravityModeling economies with trade costs works best if it moves backward from the end user. Start by evaluating all goods at user prices,applying demand-side structure to determine the allocation of demand at those prices.Treat all costs incurred between production and end use as being incurred by the supply side of the market,even though there are often significant costs directly paid by the user.What matters economically in the end is the full cost between production and end use,and the incidence of that cost on the producer and the end user.Many of these costs are not directly observable,and the empirical gravity literature indicates the total is well in excess of the transportation and insurance costs that are observable(see Anderson and van Wincoop,2004,for a survey of trade costs).The supply side of the market under this approach both produces and distributes the delivered goods,incurring resource costs that are paid by end users.The factor markets for those resources must clear at equilibrium factor prices,determining costs that link to end-user prices.Budget constraints require national factor incomes to pay for national expenditures plus net lending or transfers including remittances.Below the national accounts,individual economic agents also meet budget constraints.Goods markets clear when prices are found such that demand is equal to supply for each good.The full general equilibrium requires a set of bilateral factor prices and bilateral goods prices such that all markets clear and all budget constraints are met.This standard description of general economic equilibrium is too complex to yield some-thing like gravity.A hugely useful simplification is modularity,subordinating the economic determination of equilibrium distribution of goods within a class under the superstructure determination of the distribution of production and expenditure between classes of goods. Anderson and van Wincoop(2004)call this property trade separability.Observing that goods are typically supplied from multiple locations,even withinfine census commodity classes,it is natural to look for a theoretical structure that justifies grouping in this way. The structural gravity model literature has uncovered two structures that work,one on the demand side and one on the supply side,detailed in sections3.1and3.2.Modularity(trade separability)permits the analyst to focus exclusively on inference about distribution costs from the pattern of distribution of goods(or factors)without having to explain at the same time what determines the total supplies of goods to all destinations or the total demand for goods from all origins.This is a great advantage for two reasons.First, it simplifies the inference task enormously.Second,the inferences about the distribution of goods or factors is consistent with a great many plausible general equilibrium models of national(or regional)production and consumption.Modularity also requires a restriction on trade costs,so that only the national aggregate burden of trade costs within a goods class matters for allocation between classes.The most popular way to meet this requirement is to restrict the trade costs so that the distribution of goods uses resources in the same proportion as the production of those same goods.Samuel-son(1952)invented iceberg melting trade costs in which the trade costs were proportional to the volume shipped,as the amount melted from the iceberg is proportional to its volume. The iceberg metaphor still applies when allowing for afixed cost,as if a chunk of the ice-berg breaks offas it parts from the mother glacier.Mathematically,the generalized iceberg trade cost is linear in the volume shipped.Economically,distribution continues to require resources to be used in the same proportion as in production.Fixed costs are realistic and potentially play an important role in explaining why many potential bilateralflows are equalto zero.More general nonlinear trade cost functions continue to satisfy the production propor-tionality restriction and thus meet the requirements of modularity,but depart from the iceberg metaphor.Bergstrand(1985)derived a joint cost function that is homogeneous of degree one with Constant Elasticity of Transformation(CET).This setup allows for substi-tution effects in costs between destinations rather than the cost independence due tofixed coefficients in the iceberg model.Bilateral costs have a natural aggregator that is an iceberg cost facing monopolistically competitivefirms.A nice feature of the joint cost model is its econometric tractability under the hypothesis of profit maximizing choice of destinations. Although potentially more realistic,the joint cost refinement turns out to make relatively little difference empirically.Arkolakis(2008)develops a nonlinear(in volume)trade cost function in which hetero-geneous customers are obtained byfirms with a marketing technology featuring afixed-cost component(running a national advertisement)and a variable-cost component(leafletting or telemarketing)subject to diminishing returns as the less likely customers are encountered. Because of the Ricardian production and distribution technology,resource requirements in distribution remain proportional to production resource requirements.Arkolakis shows that the marketing technology model can rationalize features of thefirm-level bilateral shipments data that cannot be explained with the linearfixed-costs model.His setup is not economet-rically tractable but is readily applicable as a simulation model.In all applications based on the preceding cost functions,proxies for costs are entered in some convenient functional form,usually loglinear in variables such as bilateral distance,con-tiguity,membership of a country,continent or regional trade agreement,common language and common legal traditions.See Anderson and van Wincoop(2004)for more discussion.More generality in trade costs that violates the production proportionality restriction comes at the price of losing modularity.See Matsuyama(2007)for recent exploration of the implications of non-iceberg trade costs in a2country Ricardian model.See Deardorff(1980)for a very general treatment of the resource requirements of trade costs as a setting for his demonstration that the law of comparative advantage holds quite generally.3.1Demand-Side StructureThe second requirement for modularity can be met by restricting the preferences and/or technology such that the cross effects in demand between classes of goods(either interme-diate orfinal)flow only through aggregate price indexes.This demand property is satisfied when preferences or technology are homothetic and weakly separable with respect to a par-tition into classes whose members are defined by location,a partition structure called the Armington assumption.Thus for example steel products from all countries are members of the steel class.Notice that the assumption implies that goods are purchased from multiple sources because they are evaluated differently by end users,and goods are differentiated by place of origin.It is usual to impose identical preferences across countries.Differences in demand across countries,such as a home bias in favor of locally produced goods,can be accommodated, understanding that‘trade costs’now include the effect of a demand side home bias.In practice it is very difficult to distinguish demand-side home bias from the effect of trade costs, since the proxies used in the literature(common language,former colonial ties,or internal trade dummies,etc.)plausibly pick up both demand and cost differences.Henceforth trade cost is used without qualification but is understood to potentially reflect demand-side home bias.Declines in trade costs can be understood as reflecting homogenization of tastes.Separability implies that each goods class has a natural quantity aggregate and a nat-ural price aggregate,with substitution between goods classes occurring as if the quantity aggregates were goods in the standard treatment.The separability assumption implies that national origin expenditure shares within the steel class are not altered by changes in the prices of non-steel products,though of course the aggregate purchase of steel is affected by the aggregate cross effect.Homotheticity ensures that relative demands are functions onlyof relative aggregate prices.Thefirst economic foundation for the gravity model was based on specifying the expendi-ture function to be a Constant Elasticity of Substitution(CES)function(Anderson,1979). Expenditure shares in the CES case are given byX ij E j =βi p i t ijP j1−σ(3)where P j is the CES price index,σis the elasticity of substitution parameter,βi is the ‘distribution parameter’for varieties shipped from i,p i is their factory gate price and t ij>1 is the trade cost factor between origin i and destination j.The CES price index is given byP j=i(βi p i t ij)1−σ1/(1−σ).(4)Notice that the same parameters characterize expenditure behavior in all locations;prefer-ences are common across the world by assumption.Notice also that the shares are invariant to income,preferences are homothetic.With frictionless trade,t ij=1,∀(i,j)and therefore all the buyers’shares of good i must equal the sellers share of world sales(at destination prices),Y i/Y.Thus the frictionless benchmark is justified by assuming identical homothetic preferences.For intermediate goods,the same logic works replacing expenditure shares with cost shares.The‘distribution parameters’βi bear several interpretations.They could be exogenous taste parameters.Alternatively,in applications to monopolistically competitive products,βi is proportional to the number offirms from i offering distinct varieties(Bergstrand,1989). Countries with more activefirms get bigger weights.In long run monopolistic competition the number offirms is endogenous.Due tofixed entry costs,bigger countries have more active firms in equilibrium,all else equal.The number of activefirms contributes to determining the Y i’s that are given in the gravity module.The other building block in the structural gravity model is market clearance:at deliveredprices Y i=jX ij.Multiplying both sides of(3)by E j and summing over j yields a solutionforβi p1−σi,βi p1−σi =Y ij(t ij/P j)1−σE j.Define the denominator asΠ1−σi.Substituting into(3)and(4)yields the structural gravity model:Xij =EjYiYtijPjΠi1−σ(5)(Πi )1−σ=jtijPj1−σEjY(6)(Pj )1−σ=itijΠi.1−σYiY.(7)The second ratio on the right-hand side of(5)is a decreasing function(under the empirically valid restrictionσ>1)of direct bilateral trade costs relative to the product of two indexes of all bilateral trade costs in the system.Anderson and van Wincoop(2003)called the terms P j andΠi inward and outwardmultilateral resistance respectively.Note that{P1−σj ,Π1−σi}can be solved from(6)-(7)forgiven t1−σij’s,E j’s and Y i’s combined with a normalization.1Under the assumption of bilateral trade cost symmetry t ij=t ji,∀i,j and balanced trade E j=Y j,∀j,the natural normalization isΠi=P i.Anderson and van Wincoop estimated their gravity equation for Canada’s provinces and US states with a full information estimator that utilized(7)withΠi=P i. Subsequent research has focused mostly on estimating(5)with directional countryfixedeffects to control for E j/P1−σj and Y i/Π1−σi.Multilateral resistance is on the face of it an index of inward and outward bilateral trade costs,but because of the simultaneity of the system(6)-(7),all bilateral trade costs in the world contribute to the solution values.This somewhat mysterious structure has a simple1For any solution to the system{P0j ,Π0i},{λP0j,Π0i/λ}is also a solution.Thus a normalization is needed.Anderson and Yotov(2010a)find that the system(6)-(7)solves quite quickly,not surprisingly because it is quadratic in the1−σpower transforms of the P’s andΠ’s.。

国际贸易引力模型1.什么是国际贸易引力模型？国际贸易引力模型（Gravity Model）是一种用于描述贸易量之间的关系的经济模型，基本思想是：根据经济理论中因素互相作用的规律，可以用一个数学方程来估算国家之间的贸易量。

国际贸易引力模型涉及到两个实体之间的主观和客观因素，它们影响两个国家或地区之间的贸易。

通俗地讲，就是根据两国的距离和经济发展水平，估算两国之间的贸易量。

2. 国际贸易引力模型的构成(1) 双方的经济规模：这是描述双方贸易量大小的最重要因素。

我们常用国民生产总值（GDP）来作为代表国家经济规模的指标，因为GDP 可以反映一个国家或地区的实力，能力以及有能力生产的商品和服务种类的多少。

(2) 交通距离：这是描述两个国家贸易关系的重要因素之一，主要是反映货物的运输成本以及货物的流动性。

根据经济学的理论，贸易成本随着距离的增加而增加，而距离的递增会减少两国之间的贸易。

(3) 两国的相似性：从文化角度看，语言和宗教有可能影响两国之间的贸易关系，所以把这种相似性也作为一个重要因素。

(4) 贸易条件：贸易条件指的是两个国家之间有关贸易的政策、协议、许可证等等，这也可能影响两国之间的贸易量。

3. 国际贸易引力模型的优点(1) 它提供了一种统一的框架，可以客观准确地衡量两个国家贸易关系的状态，可以从宏观上了解国际贸易的发展情况，看出全球经济的大致态势。

(2) 通过该模型，对于促进国际贸易合作与发展也具有很好的策略指导意义，可以通过调整政策组合，从而有效地控制双方的贸易量的大小。

(3) 模型具有良好的可预测性、模型简洁，可以快速拟合和计算，可以预测和分析国际贸易水平运动趋势。

4. 国际贸易引力模型的局限性(1) 双方的经济规模不等：每个国家的经济规模和货物的需求量大小不同，通过国际贸易引力模型可能会忽略到这一点的影响。

(2) 单一货币条件：国际贸易引力模型假定货币是单一的，没有货币差异或汇率重估等，实际情况中现实是复杂合共性，国际贸易涉及到多种影响因素，可能破坏模型的正确性。

第一次课堂测试（ch01-ch03）1) Historians of economic thought often describe ________ written by ________ and published in ________ as the first real exposition of an economic model.A) "Of the Balance of Trade," David Hume, 1776B) "Wealth of Nations," David Hume, 1758C) "Wealth of Nations," Adam Smith, 1758D) "Wealth of Nations," Adam Smith, 1776E) "Of the Balance of Trade," David Hume, 17582) The United States is less dependent on trade than most other countries becauseA) the United States is a relatively large country.B) the United States is a "Superpower."C) the military power of the United States makes it less dependent on anything.D) the United States invests in many other countries.E) many countries invest in the United States.3) Which of the following is not a major concern of international economic theory?A) protectionismB) the balance of paymentsC) exchange rate determinationD) Bilateral trade relations with ChinaE) None of the above4) Who sells what to whomA) has been a major preoccupation of international economics.B) is not a valid concern of international economics.C) is not considered important for government foreign trade policy since such decisions are made in the private competitive market.D) is determined by political rather than economic factors.E) None of the above5) International economics can be divided into two broad sub-fieldsA) macro and micro.B) developed and less developed.C) monetary and barter.D) international trade and international money.E) static and dynamic.6) The gravity model offers a logical explanation for the fact thatA) trade between Asia and the U.S. has grown faster than NAFTA trade.B) trade in services has grown faster than trade in goods.C) trade in manufactures has grown faster than in agricultural products.D)Intra-European Union trade exceeds International Trade of the European Union.E) None of the above.7) Why does the gravity model work?A) Large economies became large because they were engaged in international trade.B) Large economies have relatively large incomes, and hence spend more on government promotion of trade and investment.C) Large economies have relatively larger areas which raises the probability that a productive activity will take place within the borders of that country.D) Large economies tend to have large incomes and tend to spend more on imports.E) None of the above.8) Since World War II, the relative importance of raw materials, including oil, in total world tradeA) remained constant.B) increased.C) decreased.D) fluctuated widely with no clear trendE) both A and D above.9) In the current Post-Industrial economy, international trade in services (including banking and financial services)A) dominates world trade.B) does not exist.C) is relatively small.D) is relatively stagnant.E) None of the above.10) In the pre-World War I period, the United Kingdom exported primarilyA) manufactured goods.B) services.C) primary products including agricultural.D) technology intensive products.E) None of the above.11) In the pre-World War I period, the United Kingdom imported primarilyA) manufactured goods.B) services.C) primary products including agricultural.D) technology intensive products.E) None of the above.12) In the present, most of the exports from China are inA) manufactured goods.B) services.C) primary products including agricultural.D) technology intensive products.E) None of the above.13) Which of the following does not explain the extent of trade between Ireland and the U.S.?A) Historical tiesB) Cultural Linguistic tiesC) Gravity modelD) Multinational CorporationsE) None of the above.14) Trade between two countries can benefit both countries ifA) each country exports that good in which it has a comparative advantage.B) each country enjoys superior terms of trade.C) each country has a more elastic demand for the imported goods.D) each country has a more elastic supply for the exported goods.E) Both C and D.15)Trade between two countries can benefit both countries ifA) each country exports that good in which it has a comparative advantage.B) each country enjoys superior terms of trade.C) each country has a more elastic demand for the imported goods.D) each country has a more elastic supply for the exported goods.E) Both C and D.16) In order to know whether a country has a comparative advantage in the production of one particularproduct we need information on at least ________ unit labor requirementsA) oneB) twoC) threeD) fourE) five17) A country engaging in trade according to the principles of comparative advantage gains from trade becauseitA) is producing exports indirectly more efficiently than it could alternatively.B) is producing imports indirectly more efficiently than it could domestically.C) is producing exports using fewer labor units.D) is producing imports indirectly using fewer labor units.E) None of the above.18) Given the information in the table above, if it is ascertained that Foreign uses prison-slave labor to produceits exports, then home shouldA) export cloth.B) export widgets.C) export both and import nothing.D) export and import nothing.E) All of the above.19) Given the information in the table above, if the Home economy suffered a meltdown, and the Unit LaborRequirements doubled to 30 for cloth and 60 for widgets then home shouldA) export cloth.B) export widgets.C) export both and import nothing.D) export and import nothing.E) All of the above.20) The earliest statement of the principle of comparative advantage is associated withA) David Hume.B) David Ricardo.C) Adam Smith.D) Eli Heckscher.E) Bertil Ohlin.21) The Gains from Trade associated with the principle of Comparative Advantage depends onA) the trade partners must differ in technology or tastes.B) there can be no more goods traded than the number of trade partners.C) there may be no more trade partners than goods traded.D) All of the above.E) None of the above.22) The Ricardian model demonstrates thatA) trade between two countries will benefit both countries.B) trade between two countries may benefit both regardless of which good each exports.C) trade between two countries may benefit both if each exports the product in which it has a comparativeadvantage.D) trade between two countries may benefit one but harm the other.E) None of the above.23) Given the information in the table aboveA) neither country has a comparative advantage.B) Home has a comparative advantage in cloth.C) Foreign has a comparative advantage in cloth.D) Home has a comparative advantage in widgets.E) Home has a comparative advantage in both products.24) Given the information in the table above, if wages were to double in Home, then Home shouldA) export cloth.B) export widgets.C) export both and import nothing.D) export and import nothing.E) All of the above.25) Given the information in the table aboveA) neither country has a comparative advantage.B) Home has a comparative advantage in cloth.C) Foreign has a comparative advantage in cloth.D) Foreign has a comparative advantage in widgets.E) Home has a comparative advantage in both products.26) Given the information in the table above, the opportunity cost of cloth in terms of widgets in Foreign is if it isascertained that Foreign uses prison-slave labor to produce its exports, then home shouldA) export cloth.B) export widgets.C) export both and import nothing.D) export and import nothing.E) All of the above.27) Given the information in the table above, if wages were to double in Home, then Home shouldA) export cloth.B) export widgets.C) export both and import nothing.D) export and import nothing.E) All of the above.28) Given the information in the table above, if the world equilibrium price of widgets were 4 Cloths, thenA) both countries could benefit from trade with each other.B) neither country could benefit from trade with each other.C) each country will want to export the good in which it enjoys comparative advantage.D) neither country will want to export the good in which it enjoys comparative advantage.E) both countries will want to specialize in cloth.29) Given the information in the table above, if the world equilibrium price of widgets were 40 cloths, thenA) both countries could benefit from trade with each other.B) neither country could benefit from trade with each other.C) each country will want to export the good in which it enjoys comparative advantage.D) neither country will want to export the good in which it enjoys comparative advantage.E) both countries will want to specialize in cloth.30) In a two product two country world, international trade can lead to increases inA) consumer welfare only if output of both products is increased.B) output of both products and consumer welfare in both countries.C) total production of both products but not consumer welfare in both countries.D) consumer welfare in both countries but not total production of both products.E) None of the above.31) As a result of trade, specialization in the Ricardian model tends to beA) complete with constant costs and with increasing costs.B) complete with constant costs and incomplete with increasing costs.C) incomplete with constant costs and complete with increasing costs.D) incomplete with constant costs and incomplete with increasing costs.E) None of the above.32) As a result of trade between two countries which are of completely different economic sizes, specialization inthe Ricardian 2X2 model tends to beA) incomplete in both countriesB) complete in both countriesC) complete in the small country but incomplete in the large countryD) complete in the large country but incomplete in the small countryE) None of the above.33) A nation engaging in trade according to the Ricardian model will find its consumption bundleA) inside its production possibilities frontier.B) on its production possibilities frontier.C) outside its production possibilities frontier.D) inside its trade-partner's production possibilities frontier.E) on its trade-partner's production possibilities frontier.34) In the Ricardian model, if a country's trade is restricted, this will cause all except which?A) limit specialization and the division of laborB) reduce the volume of trade and the gains from tradeC) cause nations to produce inside their production possibilities curvesD) may result in a country producing some of the product of its comparative disadvantageE) None of the above.35) If a very small country trades with a very large country according to the Ricardian model, thenA) the small country will suffer a decrease in economic welfare.B) the large country will suffer a decrease in economic welfare.C) the small country only will enjoy gains from trade.D) the large country will enjoy gains from trade.E) None of the above.36) If the world terms of trade for a country are somewhere between the domestic cost ratio of H and that of F,thenA) country H but not country F will gain from trade.B) country H and country F will both gain from trade.C) neither country H nor F will gain from trade.D) only the country whose government subsidizes its exports will gain.E) None of the above.37) If the world terms of trade equal those of country F, thenA) country H but not country F will gain from trade.B) country H and country F will both gain from trade.C) neither country H nor F will gain from trade.D) only the country whose government subsidizes its exports will gain.E) None of the above.38) If the world terms of trade equal those of country H, thenA) country H but not country F will gain from trade.B) country H and country F will both gain from trade.C) neither country H nor F will gain from trade.D) only the country whose government subsidizes its exports will gain.E) None of the above.39) According to Ricardo, a country will have a comparative advantage in the product in which itsA) labor productivity is relatively low.B) labor productivity is relatively high.C) labor mobility is relatively low.D) labor mobility is relatively high.E) None of the above.40) Assume that labor is the only factor of production and that wages in the United States equal $20 per hourwhile wages in Japan are $10 per hour. Production costs would be lower in the United States as compared to Japan ifA) U.S. labor productivity equaled 40 units per hour and Japan's 15 units per hour.B) U.S. productivity equaled 30 units per hour whereas Japan's was 20.C) U.S. labor productivity equaled 20 and Japan's 30.D) U.S. labor productivity equaled 15 and Japan's 25 units per hour.E) None of the above.41) If two countries engage in Free Trade following the principles of comparative advantage, thenA) neither relative prices nor relative marginal costs (marginal rates of transformation-MRTs) in onecountry will equal those in the other country.B) both relative prices and MRTs will become equal in both countries.C) relative prices but not MRTs will become equal in both countries.D) MRTs but not relative prices will become equal in both countries.E) None of the above.42) Let us define the real wage as the purchasing power of one hour of labor. In the Ricardian 2X2 model, if twocountries under autarky engage in trade thenA) the real wage will not be affected since this is a financial variable.B) the real wage will increase only if a country attains full specialization.C) the real wage will increase in one country only if it decreases in the other.D) the real wage will rise in both countries.E) None of the above.43) In a two country and two product Ricardian model, a small country is likely to benefit more than the largecountry becauseA) the large country will wield greater political power, and hence will not yield to market signals.B) the small country is less likely to trade at price equal or close to its autarkic (domestic) relative prices.C) the small country is more likely to fully specialize.D) the small country is less likely to fully specialize.E) None of the above.44) In the Ricardian model, comparative advantage is not likely be due toA) scale economies.B) home product taste bias.C) greater capital availability per worker.D) All of the above.E) None of the above.45) If a production possibilities frontier is bowed out (concave to the origin), then production occurs underconditions ofA) constant opportunity costs.B) increasing opportunity costs.C) decreasing opportunity costs.D) infinite opportunity costs.E) None of the above.46) If the production possibilities frontier of one the trade partners ("Country A") is bowed out (concave to theorigin), then increased specialization in production by that country willA) increase the economic welfare of both countries.B) increase the economic welfare of only Country A.C) decrease the economic welfare of Country A.D) decrease the economic welfare of Country B.E) None of the above.47) If two countries have identical production possibility frontiers, then trade between them is not likely ifA) their supply curves are identical.B) their cost functions are identical.C) their demand conditions are identical.D) their incomes are identical.E) None of the above.48) If two countries have identical production possibility frontiers, then trade between them is not likely ifA) their supply curves are identical.B) their cost functions are identical.C) their demand functions differ.D) their incomes are identical.E) None of the above.49) If one country's wage level is very high relative to the other's (the relative wage exceeding the relativeproductivity ratios), then if they both use the same currencyA) neither country has a comparative advantage.B) only the low wage country has a comparative advantage.C) only the high wage country has a comparative advantage.D) consumers will still find trade worth while from their perspective.E) None of the above.50) If one country's wage level is very high relative to the other's (the relative wage exceeding the relativeproductivity ratios), thenA) it is not possible that producers in each will find export markets profitable.B) it is not possible that consumers in both countries will enhance their respective welfares throughimports.C) it is not possible that both countries will find gains from trade.D) it is possible that both will enjoy the conventional gains from trade.E) None of the above.51) If one country's wage level is very high relative to the other's (the relative wage exceeding the relativeproductivity ratios) then it is probable thatA) free trade will improve both countries' welfare.B) free trade will result in no trade taking place.C) free trade will result in each country exporting the good in which it enjoys comparative advantage.D) free trade will result in each country exporting the good in which it suffers the greatest comparativedisadvantage.E) None of the above.52) In a two-country, two-product world, the statement "Germany enjoys a comparative advantage over Francein autos relative to ships" is equivalent toA) France having a comparative advantage over Germany in ships.B) France having a comparative disadvantage compared to Germany in autos and ships.C) Germany having a comparative advantage over France in autos and ships.D) France having no comparative advantage over Germany.E) None of the above.53) If the United States' production possibility frontier was flatter to the widget axis, whereas Germany's wasflatter to the butter axis, we know thatA) the United States has no comparative advantageB) Germany has a comparative advantage in butter.C) the U.S. has a comparative advantage in butter.D) Not enough information is given.E) None of the above.54) Suppose the United States' production possibility frontier was flatter to the widget axis, whereas Germany'swas flatter to the butter axis. We now learn that the German mark sharply depreciates against the U.S. dollar.We now know thatA) the United States has no comparative advantageB) Germany has a comparative advantage in butter.C) the United States has a comparative advantage in butter.D) Not enough information is given.E) None of the above.55) Suppose the United states production possibility frontier was flatter to the widget axis, whereas Germany'swas flatter to the butter axis. We now learn that the German wage doubles, but U.S. wages do not change at all. We now know thatA) the United States has no comparative advantage.B) Germany has a comparative advantage in butter.C) the United States has a comparative advantage in butter.D) Not enough information is given.E) None of the above.56) Which of the following statements is true?A) Free trade is beneficial only if your country is strong enough to stand up to foreign competition.B) Free trade is beneficial only if your competitor does not pay unreasonably low wages.C) Free trade is beneficial only if both countries have access to the same technology.D) All of the above.E) None of the above.57) Mahatma Ghandi exhorted his followers in India to promote economic welfare by decreasing imports. ThisapproachA) makes no sense.B) makes no economic sense.C) is consistent with the the Ricardian model of comparative advantage.D) is not consistent with the Ricardian model of comparative advantage.E) None of the above.58) The Country of Rhozundia is blessed with rich copper deposits. The cost of Copper produced (relative to thecost of Widgets produced) is therefore very low. From this information we know thatA) Rhozundia has a comparative advantage in CopperB) Rhozundia should export Copper and import WidgetsC) Rhozundia should export Widgets and export CopperD) Both A and B are true.E) None of the above.59) We know that in antiquity, China exported silk because no-one in any other country knew how to producethis product. From this information we learn thatA) China enjoyed a comparative advantage in silk.B) China enjoyed an absolute advantage, but not a comparative advantage in silk.C) no comparative advantage exists because technology was not diffused.D) China should have exported silk even though it had no comparative advantage.E) None of the above.60) The pauper labor theory, and the exploitation argumentA) are theoretical weaknesses that limit the applicability of the Ricardian concept of comparativeadvantage.B) are theoretically irrelevant to the Ricardian model, and do not limit its logical cogency.C) are not relevant because the Ricardian model is based on the labor theory of value.D) are not relevant because the Ricardian model allows for different technologies in different countries.E) None of the above.61) If labor productivities were exactly proportional to wage levels internationally, this wouldA) not negate the logical basis for trade in the Ricardian model.B) render the Ricardian model theoretically correct but practically useless.C) negate the logical basis for trade in the Ricardian model.D) negate the applicability of the Ricardian model if the number of products were greater than the numberof trading partners.E) None of the above.62) The multi-good (2-country) model differs from the two country, two product model, in that in the former,A) the relative wage ratio will determine the pattern of trade ( which good is exported by which country.B) one cannot determine which country will export which product given only labor productivity data.C) full specialization is less likely to hold in equilibrium.D) All of the above.E) None of the above.63) If transportation costs are especially high for Widgets in a Ricardian 2X2 model in which Country A enjoys acomparative advantage, thenA) Country B must also enjoy a comparative advantage in Widgets.B) Country B may end up exporting Widgets.C) Country A may switch to having a comparative advantage in the other good.D) All of the above.E) None of the above.。