Armington Elasticities in Intermediate Inputs Trade
A Problem in Using Multilateral Trade Data
Author: Mika Saito1
  • 1 https://isni.org/isni/0000000404811396, International Monetary Fund

Contributor Notes

Author’s E-Mail Address: msaito@imf.org

This paper finds that the estimates of Armington elasticities (the elasticity of substitution between groups of products identified by country of origin) obtained from multilateral trade data can differ from those obtained from bilateral trade data. In particular, the former tends to be higher than the latter when trade consists largely of intermediate inputs. Given that the variety of intermediate inputs traded across borders is increasing rapidly, and that the effect of this increase is not adequately captured in multilateral trade data, the evidence shows that the use of multilateral trade data to estimate Armington elasticities needs caution.

Abstract

This paper finds that the estimates of Armington elasticities (the elasticity of substitution between groups of products identified by country of origin) obtained from multilateral trade data can differ from those obtained from bilateral trade data. In particular, the former tends to be higher than the latter when trade consists largely of intermediate inputs. Given that the variety of intermediate inputs traded across borders is increasing rapidly, and that the effect of this increase is not adequately captured in multilateral trade data, the evidence shows that the use of multilateral trade data to estimate Armington elasticities needs caution.

I. Introduction

Neoclassical trade models have long assumed that goods are homogeneous irrespective of where they are produced. What does this mean empirically? The composite commodity theorem (Leontief, 1936) asserts that a group of commodities can be treated as a single good, if their prices move in parallel.2 In data, however, prices of goods produced in different countries do not typically move together. This behavior was first pointed out by Armington (1969). Ever since, it has become a standard practice among empirical trade researchers to treat goods produced in different countries differently and to assume a constant elasticity of substitution among them.3 Such an elasticity–for example, the elasticity of substitution between the basket of U.S. goods and that of French goods–is referred to as an Armington elasticity.

The Armington specification has played a crucial role in deriving some of the important findings in the recent empirical literature. First, Armington elasticities, as estimated by Shiells, Stern, and Deardorff (1986), Gallaway, McDaniel, and Rivera (2003), and many others, have played an important role in the welfare analysis of (as well as trade patterns predicted by) the computable general-equilibrium (CGE) models such as the Michigan Model of World Production and Trade and the Global Trade Analysis Project models. For example, McDaniel and Balistreri (2002) recently demonstrated the sensitivity of general-equilibrium models to Armington elasticities. They illustrated that unilateral trade liberalization would be harmful to Colombia with low Armington elasticities (between 1 and 3) but would be beneficial with high Armington elasticities (around 5).

Second, the gravity model has become the empirical workhorse of international trade. Most theoretical and empirical specifications of the gravity model, such as Bergstrand (1985), assume an Armington structure emphasizing imperfect product substitutability by country of origin. The implication and findings based on the gravity models are also sensitive to Armington elasticity estimates. For example, Baier and Bergstrand (2001) showed that about a third of the growth of world trade between the late 1950s and the late 1980s could be explained by reductions in tariff rates and transport costs. The contribution of these reductions in explaining the growth of world trade crucially depends on their estimate of the Armington elasticity (which was 6.4).

Third, a long-standing question in the international trade literature is the puzzlingly high U.S. income elasticity of demand for imports. Feenstra (1994) constructed a price index that took new product varieties into consideration to solve this puzzle. This key price index, the exact price index, is sensitive to the estimates of Armington elasticities. If the Armington elasticity approaches infinity, the conventional price index and Feenstra’s exact price index are no different, but if it approaches unity, two are significantly different. Feenstra’s estimates, ranging between 2.96 and 8.38 among manufactured goods, show that the variety adjustment plays an important role in explaining the high U.S. income elasticity puzzle.

Despite its role in the literature, however, alternative versions of Armington specifications are commonly used in the international trade literature without explicit tests for their validity. This paper focuses on two versions that are directly associated with the choice of trade data used in empirical studies, namely, that between multilateral and bilateral trade data.4

One version, seen in most studies mentioned above including Armington (1969), assumes that the basket of goods identified by country is weakly separable, meaning that the marginal rate of substitution between two goods from the same basket (or the same country) is separable from the rest.5 For example, the marginal rate of substitution between two goods from the basket of domestic goods does not depend on foreign goods.

The second version, the one used in Bergstrand (1985) and Feenstra (1994), assumes that the basket of goods identified by country is strongly separable, meaning that the marginal rate of substitution between two goods (not only from the same country, but also from two different countries) is separable from the rest. For example, the marginal rate of substitution between the U.S. and French products (for example, California wine and Bordeaux wine) does not depend on German products (for example, Rhine wine).

The first version is more restrictive, because the marginal rate of substitution between two goods from any combination of two different countries is assumed inseparable from each other in the first version but not in the second. It is this restriction that allows us to assume that the elasticity estimates obtained from multilateral trade data are the same as those obtained from bilateral trade data.

To use Armington elasticities estimated from bilateral and multilateral trade data interchangeably, we need to examine whether these elasticities are indeed the same. Alternatively, we need to examine whether the more restrictive (weak separability) assumption is indeed valid. To answer this question, we estimate two types of elasticities for each industry. One is the elasticity of substitution between the basket of domestic goods and that of imports as a whole (for example, the U.S. food products versus foreign food products); we call this elasticity (estimated from multilateral trade data) the intergroup elasticity. The other is the elasticity of substitution between the basket of imports from one foreign country and that from another (for example, French food products versus German food products); we call this elasticity (estimated from bilateral trade data) the intragroup elasticity.

Evidence from this analysis, which uses industry-level data at the two-digit International Standard Industrial Classification (ISIC) level from 14 industrial countries between 1970 and 1990, indicates that the elasticity estimates obtained from multilateral trade data are in most cases different from those obtained from bilateral trade data. In addition, the results suggest that the relationship between the inter- and intragroup elasticities is not uniform across industries. To make this comparison across industries, we make the following distinction: industries predominantly producing intermediate inputs are referred to as intermediate inputs industries, and industries predominantly producing final goods are referred to as final goods industries. We find that, in the intermediate inputs industries, the intergroup elasticity (estimated using multilateral trade data) tends to be higher than the intragroup elasticity (estimated using bilateral trade data), but no such evidence is found in the final goods industries. This result reveals that a potential problem (in not making the multilateral versus bilateral distinction) is more serious in the intermediate inputs sector.

Finally, we argue that some unique evidence observed in the intermediate inputs sector may be attributed to an upward bias in the intergroup elasticity (estimated from multilateral trade data) due to the growth of outsourcing and associated changes in the composition of trade that are not captured in multilateral trade data. This argument is based on the so-called variety bias of Feenstra (1994).

II. Analytical Framework

This section discusses the specification of preferences, which determines imports of consumption goods, and then of technology, which determines imports of intermediate inputs.

A. Preferences

Functional Forms We assume that multiple groups of goods identified by country (within each sector) are strongly separable. The functional form used here to describe such preferences is the two-level constant elasticity of substitution (CES) functional form introduced by Sato (1967).6 The empirically useful property of this functional form is that, together with the assumption of two-stage budgeting, where the consumer can allocate total expenditure in two stages, the utility maximization problem can be effectively separated into two stages. More specifically, the utility-maximizing problem of a representative agent in country i for a given level of total demand for goods belonging to a specific industry Yi is as follows:

Max Ui=[δiDiσi1σi+(1δi)Miσi1σi]σiσi1,  where(1)Mi=[jiϕijMijσsi1σsi]σsiσsi1
subject to Yi=piDDi+piMMi, where(2)piMMi=jipijMMij.

Note that σi, σsi ∈ {(0, 1) and (1, ∞)}, and δi, ϕij, Di, Mi, and Mij all take positive values. Ui is the industry-level utility of the representative consumer in country i. Di is the industry-specific demand for domestic goods. Mi is the industry-specific aggregate volume of imports. Mij is the industry-specific volume of imports from a foreign country j. σi is country i’s elasticity of substitution between domestic goods and aggregate imports (the intergroup elasticity), and σsi is country i’s elasticity of substitution among imports from different countries (referred to as the intragroup elasticity).7 δi and φij are the industry-specific distribution parameters.8 piD is the free-on-board (f.o.b.) price of domestic goods in country i, pijM is the price of imports from country j inclusive of the cost of insurance and freight (c.i.f.) and customs duties, and, finally, piM is the price of aggregate imports in country i.

The functional form used in Armington (1969),

Ui=[δiDiσi1σi+jiδijMijσi1σi]σiσi1,(3)

or the one more commonly used in many studies using multilateral trade data Mi,

Ui=[δiDiσi1σi+(1δi)Miσi1σi]σiσi1,(4)

can be expressed as a special case of the two-level CES functional form described in equation (1). For example, under the assumption that multiple goods are only weakly separable (σi = σsi), equations (3) and (4) can be derived from equation (1).9 In other words, all three specifications (1), (3), and (4) are equivalent, and thus the distinction between multilateral and bilateral is not necessary, if weak separability is a valid assumption.

Optimality Conditions The following optimality conditions, obtained from the utility maximization problem described above, are the bases for our regression equations:10

MiDi=(piMpiD)σi(1δiδi)σi(5)
MijMik=(pijMpikM)σsi(φijφik)σsi.(6)

Equation (5) implies that, for each 1 percent increase in the relative price of the industry-specific aggregate imports with respect to the price of industry-specific domestic goods, there is a σi percent fall in the ratio of the industry-specific aggregate volume of imports to country i’s industry-specific gross output. A similar interpretation applies to equation (6).

B. Production Technology

Let us turn to the case where the products traded are intermediate inputs. We assume analogously that the technology that the representative producer faces in its cost minimization problem has the following property: inputs from different countries are strongly separable within each sector (see Appendix I for the cost minimization problem). Under such a specification, the first-order conditions of the cost minimization problem provide the same optimality conditions as equations (5) and (6), where Di now represents domestic inputs and Mi and Mij represent imported inputs.

In the empirical part of this paper, elasticities are estimated from the same regression equations based on equations (5) and (6). The elasticities σi and σsi estimated for the intermediate inputs sectors are, however, the elasticity of technical substitution in production rather than the elasticity of substitution in consumption.11

C. Special Features in Intermediate Inputs Trade

The international trade literature refers to the growth of intermediate inputs trade in many different ways: for example, as an increase in vertical specialization of production (Hummels, Ishii, and Yi, 2001; Yi, 2003), as an increase in forward and backward linkages between firms across countries (Krugman and Venables, 1995), as an increase in the fragmentation of production processes across borders (Jones, 2000; Arndt and Kierzkowski, 2001), as an increase in outsourcing (Feenstra, 1998; Feenstra and Hanson, 2001), as the thinner slicing of the value chain (Krugman, 1995), and so on. These papers, despite the differences in terminologies used, have made and analyzed the same observation that the volume as well as the variety of intermediate inputs traded across countries has increased over time.12

What is the implication of these new varieties of intermediate inputs on the estimation of the elasticity of technical substitution? Feenstra (1994) shows that new varieties of imports can be thought of as having prices that fall from infinity (where the cross-border demand is zero) to the actual level (where the cross-border demand becomes positive). In other words, ignoring the entry of new varieties can undermine the actual fall in prices.

By ignoring new varieties in the estimation of Armington elasticities, therefore, we may be asking a smaller-than-actual fall in relative prices (for example, a smaller-than-actual fall in piMpiD or pijMpikM) to explain the observed increase in the relative demand for inputs (for example, an increase in MiDi or MijMik), and thus the elasticity estimates may be biased upward. Assuming that the rate at which new varieties are entering the international markets is similar across countries, such a bias is more likely in the intergroup elasticity estimates (obtained from multilateral trade data) than in the intragroup elasticity estimates (obtained from bilateral trade data).

For example, consider a simple scenario where the United States and France used to export only large engines for aircraft and Germany only medium-size engines for automobiles, but now all three countries export both types of engines.13 In this scenario, changes in the price of the basket of German engines relative to that of the basket of French engines (changes in pijMpikM) would be unaffected by the variety change as long as both the German and the French baskets have added the same number of new varieties each. On the other hand, changes in the price of the basket of foreign inputs relative to that of domestic inputs (changes in piMpiD) would be affected by the variety change, since the basket of foreign inputs has relatively more new varieties (for example, two new engines in the foreign basket versus one new engine in the domestic basket). Thus an upward bias in the elasticity estimates is more likely if multilateral trade data are used instead of bilateral trade data.

The variety explanation may not be a sufficient explanation, since the use of the variety-adjusted price index in Feenstra (1994) does not eliminate the intergroup versus intragroup differences.14 Nevertheless, an increase in the variety in the basket of foreign goods relative to that of domestic goods is a likely explanation for the evidence found in the intermediate inputs sector.15

III. Empirical Specifications

A. Decomposition of Prices

The key data in both of our regression equations are price data, in particular, import price data. Import price data (typically constructed by dividing the value of imports by the volume of imports) are not widely available and can be very sensitive to the quality of the volume data.

The use of import price data, therefore, tends to limit the variation in the sample–either the cross-sectoral variation, the cross-country variation, or both. For example, Feenstra (1994) covers a wide cross-country variation by using U.S. bilateral trade data, but the number of products he considers is limited. All other studies using U.S. multilateral trade data, such as Blonigen and Wilson (1999), Gallaway, McDaniel, and Rivera (2003), and Shiells, Stern, and Deardorff (1986), have wider cross-sectoral coverage, but small cross-country variations. One exception is the recent contribution by Erkel-Rousse and Mirza (2002). They use unit value indices that they have constructed from bilateral trade data from the French statistical institute INSEE. Their data have both large cross-sectional and cross-country variations, but access to these data is limited.

Many recent studies (such as Baier and Bergstrand, 2001; Head and Ries, 2001; Hummels, 1999) have turned away from price data to tariff and transport cost data to estimate Armington elasticities. These studies, however, ignore the effect of changes in productivity on prices.

Assumptions To cover a wide range of bilateral trade relations and to allow prices to reflect the cost of production in each country, we make two assumptions about the domestic price, piD, import prices, pijM, and the price of the import aggregate, piM. First, we assume that industries are perfectly competitive. This assumption is consistent with the specification that Head and Ries (2001) use for the Armington model, which is a constant-returns-to-scale model with varieties differentiated by nationality, in contrast to an increasing-returns model where varieties are linked to firms. Second, we make the standard Samuelson iceberg assumption for transport costs (Hummels, 1999; Baier and Bergstrand, 2001; and many others). The idea is that, for each unit of goods shipped from another region, only a fraction arrives, and this melting effect is captured in import prices.

Domestic Price The assumption of perfect competition allows us to let unit total costs equal prices. Unfortunately, comparable total cost data across countries and across sectors are not available. At best, the producer price indices are available, but these indices are not comparable at levels. As a second-best solution, we let domestic prices, piD, be a log-linear function of the unit labor cost, ci:16

lnpiD=γ0i+γ1i ln ci.(7)

The markup, γ1i, is the price elasticity with respect to unit labor costs in country i. Under perfect competition this markup should equal the labor cost share.17

Import Price With Samuelson’s iceberg assumption, the import price can be described as pijM=(1+tarij)(1+tranij)pjD, where pjD is the f.o.b. price of a good produced in country j, tarij is the tariff rate imposed on imports from country j, and transij is the transport cost (cost of insurance and freight) for shipping goods from country j. For simplicity, we let τij = (1 + tarij) (1 + tranij), and therefore the import price is expressed as follows:

lnpijM=γ0i+γ1ilncj+lnτij,(8)

where cj is the industry-specific unit labor cost in country j.18

Price of the Import Aggregate Finally, the price of the import aggregate, piM for all i, is assumed to take the Laspeyres price index form

ln piM=γ0i+γ1ijiωjlncj+jiωjlnτij,(9)

where the weight (ωj) is the share of imports from country j, ωj=MijpijMjiMijpijM.19

B. Regression Equations

Two regression equations are derived from the optimality conditions in equations (5) and (6). Taking the natural logarithm of both sides of equations (5) and (6) and adding time subscripts in appropriate places yields the following equations:

lnMitDit=σilnpitMpitD+σiln1δiδi(10)
lnMijtMikt=σsilnpijtMpiktM+σsilnφijφik.(11)

By substituting prices, as specified in equations (7), (8), and (9), the relative prices in the right-hand side of equations (10) and (11) take the form

lnpitMpitD=γ1ijiωjtlncjtcit+jiωjlnτij(12)
lnpijtMpiktM=γ1ilncjtckt+lnτijτik.(13)

By substituting equations (12) and (13) into equations (10) and (11), two regression equations are derived:20

lnMitDit=σiγ1ijiωjtlncjtcit+σiln1δiδiσijiωjlnτij+uit(14)
lnMijtMikt=σsiγ1ilncjtckt+σsilnφijφikσsilnτijτik+υijkt,(15)

where uit and υijkt are disturbance terms. The reduced forms of these equations are

lnMitDit=β10+β11ijiωjtlncjtcit+β12i+uit(16)
lnMijtMikt=β20+β21ilncjtckt+β22ijk+υijkt.(17)

Notice that the second term (home bias) and the third term (transport costs and customs duties) on the right-hand side of equations (14) and (15) are jointly captured by the time-invariant unobserved fixed effects β12i and β22ijk in equations (16) and (17), respectively. β12i is a fixed effect specific to each importing country i, and β22ijk is a fixed effect specific to each combination of trading partners (j and k) for each importing country i. Notice also that the slope parameters β11i and β21i in these equations are not a priori assumed to be the same across countries. That is, the inter- and intragroup elasticities (σi and σsi) are not a priori assumed to be the same across countries.

There are two points to note on the empirical specifications described above. First, the time invariance of transport costs and tariff rates is a strong assumption.21 To relax this assumption, time dummies are included in regression equation (16), which assumes that the reduction in transport costs and tariff rates is common across the industrial countries. If this assumption is valid, then the time-specific reductions in τij and τik in equation (15) should cancel out. Time dummies are therefore not included in regression equation (17).

Second, the markup (γ1i) is set to equal the labor cost share, which results from the perfect competition assumption. Identifying the size of the markup (γ1i) is critical in obtaining the structural parameters (σi and σsi) from the reduced-form parameters (β11i and β21i). It is, however, possible that the markup (γ1i) is higher than what we propose (possibly because of the presence of market power); in that case the true elasticities would be lower than the estimated ones.22 Such a bias, however, would be present in both the intergroup and the intragroup elasticities and hence is not likely to invalidate the main findings of this paper.

C. Choice of Estimators

Random effects, fixed effects, and first differencing are still the most popular approaches to estimating unobservable effects in panel data models under strict exogeneity of the explanatory variables.23 Even in the case of endogenous explanatory variables (as in the case of our model), it is common to use a transformation to eliminate the unobserved effect and then to select appropriate instruments in order to apply the instrumental variable (IV) estimator. For example, Erkel-Rousse and Mirza (2002) apply a family of IV estimators after removing the mean in the time dimension.

The estimates obtained from the IV estimator, however, can be sensitive to the choice of instrumental variables, as correctly pointed out by Erkel-Rousse and Mirza (2002). Moreover, and more important, removing the mean to eliminate the unobserved effect does not rule out serial correlation in the disturbance terms (in our regression equations, uit and υijkt). It is well known that conventional panel techniques based on the generalized method of moments (GMM) break down and produce very large biases when the data exhibit unit root behavior.24 Since our data contain unit roots, an alternative method is needed.

One alternative method is to use the GMM estimator with a proper treatment of time series (as in Feenstra, 1994). However, applying the family of GMM estimators in this paper is problematic in two dimensions. First, a rich cross-sectional variation, which is necessary to apply the GMM estimator, is available in estimating equation (17) but not in estimating equation (16). Second, the GMM estimators implicitly assume that the short-run dynamics are homogeneous across individual members of the panel. Although the short-run dynamics are not explicitly discussed in this paper, the assumption of homogeneity of the serial correlation dynamics is likely to be violated in aggregate trade data of this type.

An alternative solution to take care of unobservables, endogeneity, and serial correlation (with possible heterogeneity in the short-run dynamics) is to use the panel version of the Phillips and Hansen (1990) procedure, the panel fully modified ordinary least squares (FMOLS) estimator (Pedroni, 2000). This method fully modifies the ordinary least squares estimates (and hence eliminates the potential problem caused by endogeneity as well as serial correlation) by transforming the disturbance term (uit and υijkt) and subtracting off a parameter that can be constructed from the estimated nuisance parameters and a term from the original data; see Pedroni (2000) for more details. To apply this method, both the left-hand side and the right-hand side variables in equations (16) and (17) must be nonstationary, and there must be a cointegrating relationship between the two: that is, the disturbance terms (uit and υijkt) must be stationary. The group mean unit root tests of Im, Pesaran, and Shin (1997) and the group mean cointegration tests of Pedroni (1999) confirm that our data satisfy these time series properties.25 We therefore use the panel FMOLS estimator.

An additional important benefit of using the panel FMOLS estimator is that the inter- and the intragroup elasticities do not have to be a priori assumed to be the same across countries. The null hypothesis such as H0 : σ = σs without country subscript i could be more restrictive since it makes the a priori assumption that the elasticities are the same across countries. On the other hand, the null hypothesis using the group-mean panel FMOLS estimator is based on elasticities estimated for each i (or each ijk) and averaged together for the group mean:

H0:σ¯=σ¯s,(18)

where σ¯=1Ni=1Nσi (N is the number of i) and σ¯s=1Nsi=1Nsσsi, (Ns is the number of ijk). Our test results therefore do not rely on an a priori assumption under either the null or the alternative hypothesis.

The panel FMOLS approach does not estimate the intergroup and intragroup elasticities jointly as in the case of the maximum likelihood estimator used in Brown and Heien (1972).26 Rather, we estimate the elasticities separately for two reasons. First, the panel FMOLS estimator, although it does not minimize the residuals jointly, is a useful consistent estimator for the reasons discussed above. Second, assuming the independence of disturbances of a demand system expressed in terms of ratios, as in equations (16) and (17), is not as implausible as making that assumption for a demand system expressed in terms of levels (as in the demand system in Brown and Heien, 1972).27

D. Data

Trade and Production Data This analysis uses the International Sectoral Data Base at the two-digit ISIC level (1970-90) for the production data of 14 industrial countries.28 It also uses the International Trade by Commodities Statistics at the two-digit Standard International Trade Classification (SITC) level (1970-90) for the trade data for the same set of countries. Tables 1 and 2 show the concordance of these two data sets.

Table 1.

Concordance Between Industry Data (ISDB) and Trade Data (ITCS)

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Source: Created by author.

Goods in these classifications are allocated into two industries, agriculture and the food products industry (see Table 2).

Table 2.

Concordance Between Industry Data (ISDB) and Trade Data (ITCS): Supplement 1/

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Source: Created by author.

We need to divide import data at the two-digit SITC into two different industries at the two-digit ISIC level. For example, trade data classified as “Meat and meat preparation” (SITC 01) include both raw meat (which should be classified as agriculture) and processed meat (which should be classified as the food products industry). We take a very simply method. For example, we first compute the share of country A’s imports of processed meat products using multilateral trade data (e.g., the share of imports of meat and edible offal, salted, in brine, dried or smoked (SITC 012) and of meat and edible offal, prepared or preserved, fish extracts (SITC 014) in total imports of meat and meat preparation (SITC 01)). We then use this share to compute country A’s imports of processed meat products from country B (e.g., country A’s imports of meat and meat preparation (SITC 01) from country B times the share).

The two-digit ISIC data are highly aggregated and cover heterogeneous products. A much higher level of disaggregation would be desirable; however, as discussed in Section III.A, improving the level of disaggregation, especially of the production cost data, would come only at the cost of losing cross-sectoral variations.

Input-Output Data This study also uses the OECD Input-Output Database, which can aid the analysis in two ways. First, it allows us to obtain industry-level domestic demand Dit, which is defined as Dit=XitjiEijt, where Xit is industry-level demand for gross output (or total output) of country i and Eij is industry-level exports to foreign country j. More specifically, these data are used to obtain a proxy for industry-level gross output (Xit). The trade literature typically sets XitVit, where Vit is industry-level value added, and therefore input-output data are not used.29 This approximation, however, can grossly understate or overstate the actual value of industry-level gross output (Xit), because value added (a proxy for the supply of gross output) equals gross domestic product (a proxy for the demand for gross output) only at the aggregate level and not at the industry level.30 This paper therefore sets Xit1υi,90Vit, where υi,90 is the industry-level ratio of value added to gross output for 1990.31

Second, the OECD Input-Output Database is used to empirically distinguish the final (consumption) goods and intermediate inputs industries at the two-digit ISIC level. More specifically, the shares of intermediate and final demand in gross output are computed for 10 OECD member countries in 1990 for each industry (see Table 3 for these shares). If, for more than half of the countries in the sample, more than two-thirds of demand for the output of a given industry is for use as intermediate inputs, we classify that industry as part of the intermediate inputs sector. Final (consumption) goods industries are classified in an analogous manner.

Table 3.

The Final and the Intermediate Demand in Gross Output

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Source: Created by author using the OECD STAN Input-Output Database for 1990 for all except AUS, ITA and NLD. The input-output tables from 1989, 1985 and 1986, are used for these countries, respectively.

If an industry has more than half of the countries in the sample with the share of intermediate demand greater than 2/3, then we call such an industry as the intermediate inputs industry (see industries in bold).

If an industry has more than half of the countries in the sample with the share of final demand greater than 2/3, then we call such an industry as the final/consumption goods industry (see industries in bold).

Table 4.

Group Mean Unit Roots and Cointegration Tests for Individual Countries

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Source: Author’s estimates.

The null of unit root tests is “unit roots.” The asterisk next to the t-bar statistics indicates that the null is rejected (test statistics for the individual countries in columns 2 and 3 are not t-bar statistics, but are test statistics for individual time series). Heterogeneous lag truncation is applied (up to the maximum lag of 7). No time-specific dummies are included since there is no reasons why time-specific events such as oil shocks can affect trade patterns or labor productivity in the same manner across all countries.

The null of cointegration tests is “no cointegration.” The asterisk next to the group Augmented Dicky-Fuller (ADF) statistics indicates that the null is rejected. The cointegration tests are implemented only in cases where at least one variable is non-stationary. Heterogeneous lag truncation is applied though not reported in this table (up to the maximum lag of 3). No time-specific dummies are included.

Table 5.

The Panel FMOLS Estimates for Individual Countries

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Source: Author’s estimates.

For panel FMOLS estimations of inter-group elasticities, time-specific dummies are included since time-specific events such as transport costs and tariff rates reductions are likely to have affected the substitutability of domestic to foreign goods in the same manner across all countries. For panel FMOLS estimations of intra-group elasticities, time-specific dummies are NOT included since time-specific events such as transport costs and tariff rates reductions would cancel out if the rate of reductions are the same across all exporting countries.

The asterisk indicates that inter-group and intra-group elasticities are different with statistical significance of the 95 percent level.