Why is international trade restricted

How beneficial is international trade?

Modern trade theory over the past five years has spawned a new approach to quantifying the benefits of international trade, the "new quantitative trade theory". Benjamin Jung and Wilhelm Kohler highlight the particular advantages, but also the limits of this new approach. They concentrate on the new welfare formula used in it, explain it intuitively for different model variants and apply it to the comparison between self-sufficiency and the currently observed situation. In doing so, they emphasize the difference between tariff trade barriers (import duties) and real trade costs that can arise, for example, from international regulatory differences. Jung and Kohler contrast this application with the case of trade liberalization, in which the trade barriers are reduced based on a historically given situation. The application of the welfare formula is made more difficult in this case by the need to calculate the endogenous quantities that are important for the welfare effect for a nontrivial counterfactual state with lower trade barriers. The authors contrast the unilateral with the multilateral liberalization. They present results for hypothetical scenarios and report on new literature in which the new quantitative trade theory has also been used to calculate the welfare effects of actual or specifically planned trade liberalization.

1 The propensity for counterfactual comparisons in foreign trade theory

David Ricardo's book "On the Principles of Political Economy and Taxation" was published two hundred years ago. It contained the first theoretically abstract analysis of what we now call "gains from trade", i.e. the welfare gains from international trade: Internationally free goods markets lead countries to the division of labor according to their comparative advantages, and all countries can achieve higher aggregate real incomes than in self-sufficiency. In this or a similar form, the welfare gains from international trade can still be found as a theorem in every textbook on foreign trade. But the statement seems removed from reality: What is the comparison with self-sufficiency, a state that today in the vast majority of cases is completely beyond practical relevance? Does the theorem have any economic policy relevance?

The relevance of this extreme comparison for Ricardo was its meaning as a metaphor. The real aim of the analysis in his “Principles” had to do with practical economic policy. Ricardo wanted to clarify the harmful effects of the “Corn Laws” with which the British government tried to hinder the import of grain from mainland Europe at the beginning of the 19th century, initially by restricting quantities, later by introducing tariffs. With the depiction, driven to the extreme by abstraction and thus made crystal clear, Ricardo, at the same time a man of practice, hoped to bring the costs of this policy of import protection into a sharp light. The fact that he was not referring to grain at all, but instead used cloth and wine as examples, suggests that he was concerned with a general point. The abstract analysis of economic relationships began with his “Principles”. Ricardo did not live to see the abolition of the “Corn Laws” in 1846, but with his analysis he had undoubtedly laid an important intellectual foundation for this trade liberalization.

Today, two hundred years later, we have an enormously enriched theory compared to Ricardo's cloth-wine model. But we still often make a comparison with self-sufficiency to illustrate the welfare gains from international trade. However, there has been progress here in the recent literature on two crucial points. On the one hand, one no longer compares self-sufficiency with free trade, which would be doubly counterfactual, but a factually given and therefore observable situation. On the other hand, this comparison, although still of a counterfactual nature, is made in a quantified way; the difference in real income between the factual and the counterfactual situation is not only described qualitatively, but also quantified.

For this comparison, the new literature offers a formula that appears simple at first glance, which is to a certain extent independent of the sometimes diverse mechanisms that drive international trade and cause real income effects. They include Ricardo's comparative advantages as well as the aspects of product diversity, economies of scale and the selection of more productive companies emphasized in recent literature. The sometimes confusing variety of mechanisms gives way to a single, predictable formula. In the first part of this overview, we outline the path to this new formula for welfare gains from international trade, but also its limits. We will show that, despite these limits, the formula opens up an economically relevant perspective by directing attention away from model-mechanical details to those variables that determine the extent of trade profits. The economic-political relevance of the formula consists not least in the fact that it illustrates the wrong path of that mercantilistic thinking, as it can be seen again and again in current economic policy.

Even if the perspective of welfare gains from international trade is an instructive thought experiment, it does not seem very helpful for concrete trade policy. Trade policy is mostly about relatively small steps to reduce or increase the existing trade barriers. Even seemingly dramatic trade policy scenarios like those brought into play by the newly elected President of the United States are actually marginal compared to self-sufficiency scenarios. Changes in trade barriers can also result from policies that are not actually trade in nature, such as the proposed reform of corporate taxation in the United States. The commercial reality of the present differs in several respects from Ricardo's times. First, countries are typically constrained in shaping their trade policies by international obligations, be it due to membership in the World Trade Organization (WTO) or due to regional trade agreements. However, these obligations are asymmetrical; they concern the introduction or tightening of trade barriers, but not their removal. Second, the barriers to trade have changed; The greatest importance is no longer given to quantity restrictions and tariffs, but to so-called technical barriers that result from internationally diverging regulatory standards.

This not only requires a different analytical approach in which such barriers play a more differentiated role than they did 20 years ago. In addition, it must be made clear that these barriers have fundamentally changed the subject of trade liberalization, also in terms of economic policy, both with regard to the common good and from the perspective of the political economy of particular interests. As trade policy focuses on technical barriers, the international coordination of regulatory policy becomes a core issue. And as the negotiations between the European Union (EU) and Canada on the Comprehensive Economic and Trade Agreement (CETA) and between the EU and the United States on the Transatlantic Trade Agreement (TTIP) have shown, trade liberalization is of this type, i.e. the reduction of technical Barriers faced with new challenges. This area is still largely untouched by theoretical analysis.

In this article we offer two different perspectives on gains from trade. On the one hand, we compare the status quo with self-sufficiency. Some authors equate this with a summary ex-post analysis of a large number of liberalization steps that have led from self-sufficiency to the current situation. As we shall show, this interpretation is misleading. Nonetheless, this analysis is interesting because it gives an impression of how great the welfare gains from international trade are. It also allows to shed light on how tariff and non-tariff technical trade barriers influence the advantages of international trade differently. On the other hand, we analyze how welfare changes in more realistic scenarios in which political interventions change trade barriers, based on the current situation. In most cases, this is not about steps that have already been taken in terms of trade liberalization or protection. That is why we can speak of an ex-ante analysis, even if we are only going to consider specifically planned steps in trade policy in exceptional cases. We analyze the effects on the intervening country as well as on its trading partner.

2 welfare gains from international trade or the cost of self-sufficiency

2.1 The theorem of gains from trade: what it says and what it doesn't

Economists are probably unanimous in their conviction that the possibility of exchanging goods internationally on free markets is - at least potentially - beneficial for all countries. International exchange behaves like a new technology for obtaining goods. It works like an expansion of the production possibilities, like an alleviation of the scarcity, and that for all participating countries at the same time. In the case of well-functioning markets, this should also result in an increase in aggregate prosperity in all countries, compared to a situation without international exchange, i.e. with self-sufficiency.

Note, however, the two limitations of this statement: first, the condition of well-functioning markets, and second, the limitation to general prosperity. Poorly functioning markets, for example as a result of environmental externalities or market power, are a poor basis for realizing the welfare gains from international trade. This can increase the welfare-detrimental effect of market failure; depending on the situation, however, it can also weaken it. We have here an application of what is known as the theory of second best. And prosperity does not have to increase equally for all individuals. It has been known since the Stolper-Samuelson Theorem of 1941 that some individuals can even suffer a loss of real income through trade. Therefore, we have met the argument for welfare gains from international trade with the addition that suitable free flat-rate transfers between winners and losers would allow a Pareto improvement. This is in the above formulation with “aggregated Meant prosperity. Such income transfers are of course difficult to put into practice, and they are often politically ruled out from the outset. Then individual population groups are indeed worse off due to trade liberalization and therefore also oppose it (Jäkel and Smolka 2013).

Note also that the theorem of gains from trade does not refer to any particular cause of the comparative advantages underlying international exchange. The concept of comparative advantage cannot easily be transferred from simple models with two goods to the general case with many goods. The same applies to the explanation of comparative advantages through certain structural conditions, for example through the relative factor endowments of the various countries (Deardorff 1980, 1982). But all these difficulties do not detract from the fundamental statement about the advantages of trade. To put it somewhat casually: Well-functioning markets ensure that countries specialize in accordance with their comparative advantages, however these are precisely defined and structurally caused.

The theorem according to which international trade creates welfare gains does not from the outset refer only to free trade in the full sense. On the one hand, this is comforting, because the actual situation is mostly not free trade. On the other hand, it also goes hand in hand with the fact that the statement collapses if you allow arbitrary trade policy interventions. For example, export subsidies can generate a trade pattern in which a country produces and exports goods that it should actually import according to its comparative advantages. There may be a lot of trade then, but the “wrong” structure of the division of labor thwarts welfare gains.

But how should one recognize whether there is such a “wrong” division of labor? An old result by Ohyama (1972) gives an astonishingly simple answer: welfare gains from international trade are preserved as long as trade policy - viewed in net terms - leads to tax revenue, i.e. is not linked to government spending. When this condition is met, trade policy has “on average” hindered rather than promoted trade. These considerations make it very clear that the theorem of gains from trade does not mean that more trade - often equated in public discussion with an increase in exports - is always better.

As important as these fundamental insights may be, the counterfactual comparison with autarky seems to elude any quantification from the outset. The magnitude of the welfare gains from international trade must therefore, it initially seems, remain unclear. There are very few historical cases in which the change from self-sufficiency to trade-open borders actually took place within a short period of time. A well-known example is Japan in the 19th century. In a treaty signed with the United States in 1858, Japan promised to open its borders to international trade, which was quickly put into practice. It ended a situation of self-chosen self-sufficiency that had lasted more than 200 years. Although both states - autarky and trade - can historically be observed in direct succession, the comparison remains counterfactual. At most, it can show that Japan could have achieved a higher real income through international trade at a time when it was virtually self-sufficient. Alternatively, one can come to the conclusion that Japan would have achieved a lower real income after opening the borders if the borders had remained closed during this time.

The methodological problem that opposes a review of these counterfactual statements is closely related to the question of causality that arises almost everywhere in modern economics. In many cases this question can be solved by using a sufficiently large number of observations (for example microdata) with a randomized “treatment”. In the present case, this would mean that under otherwise identical economies, some would be allowed to trade with one another and others would experience the “treatment” of self-sufficiency. That is of course not possible and it would also be morally reprehensible.

In order to be able to draw conclusions about the magnitude of the welfare gains from international trade in the historical situation of the 19th century from the observable data from the individual case of Japan, one has to fall back on theoretical relationships. That means nothing more and nothing less than assuming the validity of a certain theory from the outset. In the case of Bernhofen and Brown (2005) it is Deardorff's (1980) generalized comparative advantages model; Their counterfactual comparison for Japan's “self-sufficiency experiment” shows welfare gains of 5 to 9 percent of the self-sufficiency domestic product.

2.2 Welfare gains from international trade in a simple formula

But how should one proceed if autarky is in no way historically observable? The empirical quantification of the welfare gains from international trade then requires a theoretical model that meets two criteria. First, it has to be plausible from the outset that one is prepared to seriously look at the situation through its lens. The current situation can then be understood as an empirical realization of the model.[1] And secondly, the model must be able to depict not only the observable, current situation but also the counterfactual, non-observable situation as a hypothetical realization. In the real case, it is about the factually observed situation with trade, whereby the empirically observed trade barriers are also taken into account as far as possible, and the counterfactual situation without any trade, viewed as a situation in which the trade barriers become prohibitively high. The comparison focuses on real income as the only measure of the country's prosperity.

Until recently, this type of counterfactual comparison was dispensed with in empirical foreign trade.[2] But in the course of the turn of economics to the quantification of theory, the measurement of trade profits was inevitable. In the past 10 to 15 years, theoretical models have emerged that enable a counterfactual analysis corresponding to the theorem of gains from trade in a very informative way. These models are now known as "New Quantitative Trade Theory". They get by with a few observable quantities. In the simplest variant of these new models, there are only two: i) the share of domestic expenditure that falls on domestic goods, and ii) the elasticity of imports in relation to real trade costs, hereinafter referred to as price elasticity of imports for the sake of simplicity.

Specifically, the first time Arkolakis et al. (2012) derived, empirically quantifiable counterfactual statement for a certain class of these new models

in which W ' or. W. represents the aggregated real income (welfare) of the economy under consideration in two different situations. We are only looking at situations that differ in terms of trade barriers and interpreting these as changes in trade policy.[3] The same applies to λ ' or. λ, the share of domestic expenditure on domestic goods. The symbol ε stands for the (positively defined) price elasticity of the demand for imported goods.

This statement applies to any two situations. The formula can be implemented empirically if one equates one of the two situations with the currently observed situation (i.e. with trade) and the other with self-sufficiency, where the share of expenditure on domestic goods is by definition 1. We follow Eaton and Kortum (2012) and mark the factual situation with an apostrophe', so that λ = 1. This then results in a trade-related increase in real income of λ '-1 / ε‒1, calculated as a percentage of self-sufficiency income. In 2015, the share of imports of goods and services in Germany’s gross domestic product (GDP) was 39.2 percent. If one corrects for the current account surplus (8.4 percent of GDP), the result is a value of λ ' = 0,572.[4] Empirically estimated values ​​for ε range between 5 and 10 (cf. Anderson and van Wincoop 2003). For the welfare gains from trade, according to the formula above, is ε = 5 a value of 11.8 percent and at ε = 10 of 5.74 percent.

That the two sizes λ and ε for which welfare gains from international trade play an important role, is obvious. Trivially, the possibility of trade only plays a role if the market participants in market equilibrium actually demand imported goods, that is, if λ ' < 1. And the lower the degree of substitutability between domestic and imported goods, the greater the difference. If they are perfect substitutes, the opportunity to trade cannot make any difference. The price elasticity of import demand then approaches infinity, and then trade cannot be advantageous, no matter how high the share of expenditure on imported goods may be.

The role of λ The formula above shows impressively the absurdity of mercantilist thinking. Krugman (1991, p. 15) describes this thinking briefly and concisely as follows: “1) Exports are good. 2) Imports are bad. 3) Other things equal, an equal increase in imports and exports is good. " He describes this thinking as "enlightened" mercantilism and regards it as the decisive driving force behind the multilateral negotiations on the General Agreement on Tariffs and Trade (GATT). Today, 25 years later, it has to be said that hardly anything has changed about that. After all, this mercantilism deserves the adjective "enlightened" - through point 3, which is ultimately the reason why the manifest result of this GATT / WTO thinking is not that bad: the relatively free world trading system. Nonetheless, the above formula shows in a simple way how much mercantile thinking is misleading: welfare gains result from a high proportion of imports in expenditure, not exports.

What is less obvious, however, is that the two sizes λ and ε should only be relevant. In fact, this is only the case for a certain class of models. The model world, to which all of the above applies, is astonishingly comprehensive. It comprises several types of models that are linked to very different assumptions at the micro level, which has been the focus of trade theory for the past 15 years. This applies to the question of market form as well as to the heterogeneity of companies. It applies equally to Ricardo's (modernized) model world with perfect competition and constant returns to scale (Eaton and Kortum 2002) as to the very widely used model with monopoly competition and economies of scale, both in the traditional variant with homogeneous companies (Krugman 1980) and in the variant with heterogeneous companies (Melitz 2003 and Chaney 2008). The amazing thing about the result by Arkolakis et al. (2012) is that all these differences between different models emphasized at the micro level have no bearing on the welfare gains from trade, provided they lead to the same value for λ and the same value for ε.[5]

However, only one of the two variables can be directly observed empirically: the share of expenditure λ. The elasticity ε must be estimated econometrically. This begs the question of whether different models for given values ​​of λ does not lead to different specifications for the econometric estimation of ε to lead. This is not the case, because it turns out that the previously outlined class of theoretical models largely contains the so-called gravitational equation for bilateral trade, which applies equally to all models as an estimation equation for ε can act:

in which Xij the country's bilateral export i to the country j is and δiX or. δjM. represent fixed effects of the countries as exporters (general export supply capacity) or importers (general import absorption capacity). The term is of crucial importance τij > 1which represents the so-called real trading costs. Accordingly, the consumer price in the country is j the τij-fold of the producer price in the country of origin i. And δij is a for country pair ij more specific (but from τij different) effect, interpreted as a preference parameter.[6]

The elasticity ε has very different economic interpretations in different models. Models in which ε closely related to the elasticity of substitution between different goods in the preferences of consumers; one speaks of CES preferences.[7] Since it is assumed that the goods do not differ at all in terms of production, there is often talk of variants of a good.

The interpretation of τij >1. These "price wedges" between the producer price in the country i and the consumer price in the country j may arise from transport costs and the cost of adapting to international regulatory differences; then they represent real resource consumption. However, an interpretation of is also conceivable τij >1 as a tariff-related increase in the price of imported goods, which arises without real consumption of resources. Below we will show that the welfare formula looks a little different in the presence of tariffs.

The model world of this simple Arkolakis formula is also limited in other points. It applies to economies with only one production factor (labor) and only one branch of the economy. In it one ignores dynamic processes such as capital accumulation, innovation and intertemporal trade. So the question arises about possible generalizations of the simple formula.

2.3 The multi-sector case

The quickest way to the case with several branches of economy is to relate the CES preferences to product variants of a sector and to nest them in a second level, which represents the preferences for the goods of different sectors. If, for the sake of simplicity, one assumes a substitution elasticity of 1 for this second level, then one arrives at a very plausible generalization of the Arkolakis formula:[8]

The index indicates s = 1... p the total of S sectors, and the parameter βs stands for the share of goods in the sector s in the total expenditure of the country under review. The share of expenditure on domestic goods is sector-specific, λs, and there is another supply-side share that comes into play, the share of within the sector s generated revenues from the total revenues of this country, rs. It applies Σ s β s= Σ sr s = 1. If the elasticity of substitution (between the sectors) is equal to 1, as assumed here, then is βs given parametrically, and thus the same for trade and self-sufficiency. Furthermore applies to self-sufficiency βs= rs. This generalized formulation applies to both types of market: With perfect competition there is δs= 0 and with monopolistic competition δs = 1.

In the case of perfect competition, the formula Π is obtained for the gains from tradeS.s=1(λs')βs/εs- 1. The advantage from trade is greater, the more the industries with a high import share (low λs') are also characterized by a low price elasticity in international trade. This is quite understandable, because a low price elasticity εs means that within the sector s the domestic goods are bad substitutes for the imported goods. Then trading is particularly beneficial. At the same time, this advantage is greater, the more the industries with a high import share are also those that are of great importance in domestic demand (measured by βs).

The situation becomes a little more complicated with monopoly competition. In our interpretation of ' as a factual situation in comparison with self-sufficiency we get

As before, a low value of λs' (high import share) ceteris paribus a major contribution from the sector s on the welfare gains from international trade for the economy as a whole. The lower the price elasticity, the greater the weight of this contribution εs the imports for the goods of this branch of industry and the larger its budget share is. With monopoly competition (δs = 1) with free market access now comes - from a formal point of view analogous to λs' - the factor βs/rs' in the game. If aggregated trade is balanced, this factor is less than 1 in export sectors and greater than 1. In import sectors, the contribution of an economic sector to the aggregated trade profits is reduced to the simple case (perfect competition) even with monopoly competition Industry balanced trade prevails. Note here that product differentiation also applies to export sectors λs <1 applies: Consumers love a variety of products and consume imported variants of all goods.

The intuition for the "correction factor" βs/rs' is pretty easy. The multi-sector case is characterized by the fact that every trade policy scenario is associated with intersectoral reallocation; some branches of production expand, others shrink. In the case of perfect competition, this reallocation per se does not play a role in measuring the trading advantages, because the allocation is efficient. In the case of monopoly competition, this allocation is no longer efficient, so that the reallocation mechanism represents an additional channel for the trading advantages.[9] The advantage of trade is particularly high if the branches of the economy with a high import share and a high share of demand are also those that expand when switching from self-sufficiency to trade. Of course, in an economy with limited resources, not all industries can expand at the same time. Obviously, it is the export industries that are growing while the import industries are shrinking compared to self-sufficiency. But also in the export sectors, a high import share is decisive for a high contribution to welfare gains.

If one compares the radically simplified model world with only one branch of the economy with the world consisting of several sectors, then one might expect that the consideration of a new adjustment mechanism, the intersectoral reallocation, increases the welfare gains from international trade. But this intuition is somewhat misleading because of the reallocation terms βs/rs' did not show up in the formula for perfect competition. Nevertheless, the trade profits do not have the same value a priori. The difference in sign, however, is not clear a priori. In the data applies λ = Σsβsλs. Viewed through the lens of a model with monopoly competition, the value of W '/W. larger if it turns out empirically that significant sectors (measured against βs) has a low value of λs as well as a low (absolute) value of ε exhibit. At first it seems open whether this is to be expected a priori, but it is consistently the case in the calculations by Costinot and Rodríguez-Clare (2014). The same is shown by the somewhat more detailed analysis of the multi-sector case by Ossa (2015).

In the multi-sector case, there is also the question of comparative advantages, which, by definition, cannot exist in the model with a single branch of industry. If the consideration of several sectors is motivated solely by the elasticity ε varies between the sectors, then the comparative advantages are not yet in the foreground.[10] If they are brought into play a little more prominently, then - as expected - the gains from trade also increase (cf. French 2016).

2.4 growth

The growth effects of trade play an astonishingly small role in the more recent literature. The great interest in dynamic trade profits generated by the theory of endogenous growth in the early 1990s has flattened somewhat.[11] In any case, dynamic effects have so far received little attention in the new quantitative trade theory. Is it to be expected from the outset that the consideration of growth effects will also increase the welfare gains from international trade? The answer is no. The increase in the capital stock or (in the case of endogenous growth) the growth rate brought about by trade liberalization only has an additional welfare effect if the capital stock or the growth rate is suboptimally low in the initial situation (cf. Baldwin 1992). And this, in turn, is only the case if the accumulation decision as such is distorted. The models with monopolistic competition of the Krugman type (1980) contain such a distortion due to the preference of consumers for product diversity, because the increase in product diversity resulting from capital accumulation is an externality (cf. Keuschnigg and Kohler 1996, 1999).

Anderson et al. (2015) examine accumulation effects in a model of the new quantitative trade theory and arrive at a simple welfare formula in which the growth effect is similar to the “multi-sector effect”. You consider the single-sector case in which there can be no reallocation effect. Nevertheless, the accumulation that takes place through trade liberalization changes the relationship between the welfare gains through trade and the import share. When comparing self-sufficiency and trade, the following now applies W '/W. := (K '/K)αλ '‒1/ε, in which α <1 in the context of a Cobb-Douglas production technology, the elasticity of the outputs in relation to the (accumulated) capital stock K indicates. Does trade lead to an increase in the capital stock, K '/K > 1, this increases the trade advantage by the factor (K '/K)α, analogous to the factor βs/rs' for an industry that is expanding from self-sufficiency to trade. The additional welfare gain comes from the previously mentioned externality (product variety), which is connected with the investment decision. If one now compares states with steady states in each case, one obtains in the general case for two states with different trade policies (with and without ') W '/W. := λ '/λ–1/[(1–α))ε]. This is a periodically recurring gain in real income in steady state. This means that the amount of capital accumulation, K '/K, ultimately depends on the two core parameters, the import share and the price elasticity of trade. There is only one additional factor here - by analogy βs in the multi-sector case - the output elasticity in relation to the capital stock.

When interpreting welfare comparisons in a dynamic context with capital accumulation, caution is advised insofar as accumulation takes time and sometimes causes “installation costs”. Both have to be taken into account. A detailed treatment of this complex of problems is provided by Keuschnigg and Kohler (1997).

2.5 Interlinkages of wholesale services and several factors

An important consequence of inter-sectoral wholesale services is that the sum of the revenues of all companies is no longer equal to the aggregated income of the economy. When the share of intermediate products in the proceeds R. is 0.4 in total, then applies to income Y = (1 ‒ 0,4)R.. With a bit of matrix algebra, this can also be transferred to the sector level, so that R. = (I.A.)–1Y, in which R. the S. × 1 vector of sectoral revenues and Y the S. × represents the vector of expenditure on final household demand for the various goods; summed up result in the elements of the vector Y the aggregated income Y. We write αks for the element in the line k and the column s the matrix (I - A)–1 (the "Leontief Inverse"). When the households take the share βs their income for goods of the sector s spend, this generates revenue for the sector k to the extent of αksβsY. These are equal to the spending of this sector under conditions of perfect competition k for wage payments and intermediate products.

Looking at the formulas for recording the welfare gains from international trade, the question now arises to what extent is the sector's expenditure k account for domestic goods. If you write for it λk, then it results:[12]

This formula assumes that the expenditure shares of a sector s for inputs from the various supplying sectors k are given parametrically. Then the values ​​of αks (they represent the inter- and intra-sectoral input-output interrelations) in the counterfactual situation (autarky) and the factually observed situation. This is analogous to the shares βs (they represent consumer preferences).

The formula is easy to interpret. Where before λs'/λs appeared, because of the inter- and intrasectoral interdependencies, the term is now found ΠS.k=1(λk'/λk)αks. This term is due to the variation of αks above s, sector-specific.[13] The sectoral share of expenditure on domestic goods results as the geometric mean of the corresponding shares in those branches of the economy from which the sector in question draws its intermediate consumption. Without inter- and intra-sectoral links, the following applies to s = kthat αks = 1, and for s k holds that αks = 0. The result is the original formula, where also λs'/λs retains its original meaning as the share of domestic goods in the demand for goods in the sector s.

The advantage of international trade results from the fact that consumed goods are cheaper or their variety is increased. In the case of input-output interlinkages, this advantage runs not only through the imported goods, but also through the imported intermediate inputs used for the production of domestic goods, with any reduction in price being increased by the input-output interlinkages. This exponentiation occurs formally in that [λs']βs/εs is replaced by the term that is greater.

Costinot and Rodríguez-Clare (2014) show with their simulation results that the difference is by no means marginal. In the case of perfect competition, there is an average increase in welfare gains from international trade of 77 percent across 33 countries (27.1 percent gains from trade with imported intermediate products versus 15.3 percent without them). If monopolistic competition and the heterogeneity of the companies are taken into account, the average value increases to 32.3 percent and 40.0 percent respectively.

2.6 Turning away from Ricardo

All previous considerations were influenced by Ricardian; they started from the idea that there is only work involved in production. To see how the welfare formula changes when we allow multiple factors, let's return to the case with no intermediate inputs. The best way to imagine the new situation is that instead of work, a bundle of production factors is used that is made up of individual factors (e.g. different types of work) in different ways in different branches of the economy. Where otherwise the wage rate simply appears, which must assume the same value in equilibrium in all sectors, there are now the minimum unit costs of the factor bundle in question, which depend on the various factor prices. Assuming intersectoral factor mobility, the price of each factor must be uniform in all branches of the economy, similar to how in the Ricardian models the wage rate must be the same in equilibrium from sector to sector.

The calculation of the welfare gains from trade is made considerably more difficult with this departure from Ricardo; additional calculations are required. You write cs(·) For the minimum unit costs as a function of the various factor prices (by · indicated), then - assuming perfect competition - a plausible generalization of the above welfare formula can be derived:[14]

In comparison between self-sufficiency and trade (') now plays in addition to the already known term (1 /λs')βs/εs the term also plays a role. But what does this term have to do with gains from trade, which are ultimately determined by the change in factor income and goods prices? And how can it be calculated?

With perfect competition cs(·)/cs(·)' the price of the good s in self-sufficiency, relative to the actual trading situation. According to the above formula, the gains from trade are high when goods have a high consumption share βs have become cheaper through trade. And they are - ceteris paribus - large when goods that are heavily discounted through trade also have a high share of consumption.

All of this is entirely intuitive, but the question remains how cs(·)/cs(·)' is to be calculated. For the sake of simplicity, let's limit ourselves to just two factors, high and low skilled work with wages wH and wL., so that cs= cs(wH, wL.). Then cs(·)/cs(·)'