Taking the measure of things: the role of measurement in EU trade

Abstract

In this paper theoretical and empirical models of intra-industry trade are developed in which economic activities, based on measurement and an associated measurement infrastructure, play a role in creating product variety. The paper discusses how the measurement infrastructure which includes institutions conducting metrological research and standard setting organization reduces transactions costs, especially in markets where differences in product characteristics are important. The theoretical analysis focuses on the public good characteristics of the measurement infrastructure, considering how the infrastructure impacts upon trade in a model based upon product differentiation under monopolistic competition. In the econometric analysis, indicators of the strength of the infrastructure within the EU, both across industries and across countries, suggest that measurement activities are important in determining the extent of bi-lateral EU intra-industry trade. Despite many common elements in the measurement infrastructure across the EU, there is also some evidence of differential access to the infrastructure among EU members.

Appendices

Data appendix

1.1 Variables used in econometric analysis

1.1.1 Dependent variable (Source: OECD Bilateral Trade Database for 1998)

Logit transformation of the Grubel-Lloyd Index (GL) (identifier IIT):

$$ {\text{GL}}_{i,j,k} = 1-\left[ {{\text{abs}}\left( {X_{i,j,k} - M_{i,j,k} } \right)/\left( {X_{i,j,k} + M_{i,j,k} } \right)} \right] $$

where i = exporting country 1, …, 13, j = importing country 1,…, 13, k = industry 1, …, 22.

The index was constructed for the following 13 countries: Austria, Belgium-Luxembourg, Germany, Denmark, Greece, Spain, United Kingdom, France, Finland, Italy, Netherlands, Portugal and Sweden.

The industries used are from the International Standard Industrial Classification Rev 2 (ISIC rev 2) and are all in manufacturing:

Other Manufacturing; Professional Goods; Other Transport Equipment; Aircraft; Motor Vehicles; Shipbuilding & Repairing; Radio, TV & Communication Equipment; Electrical Machinery; Office & Computing Machinery; Non-Electrical Machinery; Metal Products; Non-Ferrous Metals; Iron & Steel; Non-metallic Mineral Products; Rubber & Plastic Products; Petroleum Refineries & Products; Drugs & Medicines; Chemicals excluding Drugs; Paper, Paper Products & Printing; Wood Products & Furniture; Textiles, Apparel & Leather and Food, Beverages & Tobacco.

Potentially there are 13 × 12 × 22/2 = 1,767 observations.

1.1.2 Country characteristics

Average level of GDP in each country pair (la_gdpp) The logarithm of average GDP values between two countries (in PPP$ billion) (Source: OECD National Accounts).

The difference in the value of GDP in each country pair (ldiff_gdpp) The difference in the logarithm of the absolute value of the difference in GDP for each pair of countries (Source: OECD National Accounts).

The value of production by country pair and industry (la_pi).

The logarithm of the arithmetic mean of the value of production by industry for each pair of countries in 1998 (Source: OECD STAN).

The difference in the value of production by country pair and industry (ldiff_pi).

The logarithm of the absolute difference in the value of production between each pair of countries in 1998. (Source: OECD STAN).

The average level of per capita GDP (la_p_gdpp). The logarithm of average income per capita for 1998 (measured by GDP/population) between two countries and evaluated PPP$s as estimated by the OECD. (Source: OECD National Accounts).

The difference in per capita GDP between trading partners (ldiff_p_gdpp) The logarithm of the absolute different income per capita between two partner countries in 1998 as evaluated in PPP$ (Source: OECD National Accounts).

The distance between two trading partners in kilometres (ldist). The distances between the cities of corresponding regions are measured by the “great circle distance” formula based on the latitudes and longitude of each city. Therefore, All EU 15 countries are split into 206 regions and all these distances are weighted by their related GDP share calculated by GDPm/GDP, where GDPm is the GDP value of a region and GDP is at the whole country level. (source: Chen 2004).

Common Border (cb). A dummy variable = 1 if the country pair share a common border.

Common Language (lang) A dummy variable = 1 if the country pair share the same language.

Instrument Consumption Intensity (la_cinstratio) The logarithm of the average intensity of instrument consumption between two countries with intensity measured by overall instrument consumption deflated by average GDP (Source: Williams (2002) for instrument consumption data by country.

1.1.3 Industry characteristics

Industrial Concentration (identifier heu) Source: Davies and Lyons (1996).

This was constructed from an estimate of the Herfindahl Index at the EU level at the three digit NACE classification and aggregated using a geometric mean of the constituent industries.

R&D intensity (eurdpers) Business expenditure on Research and Development (measured in $ PPPs for the EU (exc Portugal) in each industry deflated by the aggregate level of employment. Source: OECD ANBERD-Analytical Business Enterprise Research and Development data for 1998 and STAN- STructural ANalysis data for employment).

Industrial Heterogeneity (lncomm) The logarithm of the number of commodity headings at the 5-digit level in each industry ource: Based upon the OECD Databases (ITCS- International Trade by commodity Statistics).

The strength of the measurement infrastructure (lsratio) This is the logarithm of a cross industry count of publicly available standards published in PERINORM© which incorporate a reference in their descriptors to both measurement and testing. Specially constructed descriptors were used to allocate standards to each industry. This count has been normalised by the number of commodities in each of the 22 industries (see above) (Source: PERINORM©, King et al. 2005).

1.2 Summary statistics

See Table 4.

Table 4 Summary data

Mathematical appendix

2.1 Section 1

Profit-maximisation requires MR = MC,

In the model MR, marginal revenue, is $P\left( {1 - \frac{1}{\eta }} \right)$, where elasticity $\eta = \frac{1}{1 - \theta }$.

MC, marginal cost, is $\beta w(1 - G)^{\alpha }$. Therefore, we can write the profit maximizing condition as $P\left( {1 - \frac{1}{\eta }} \right) = \beta w(1 - G)^{\alpha }$. Then we obtain the following pricing equation for X _i $\frac{P}{w} = \frac{{(1 - G)^{\alpha } \beta }}{\theta }$.

The mark-up is therefore dependent upon G.

2.2 Section 2

The profits the firm receives, $\pi$, can be expressed as:

$$ \pi = PX - TC $$

(26)

The first term is total revenue, and the second term is total cost.

Set $\pi = 0$, Using Eqs. (7) and (9) in the text we can now obtain

$$ \frac{{(1 - G)^{\alpha } \beta w}}{\theta }X = (1 - G)^{\alpha } [r\gamma + w\beta X_{i} ] {\text{ + rZ(G)}} $$

(27)

After rearranging Eq. 27, we finally obtain Eq. 10 in the text.

$$ X_{i} = \frac{r\theta \gamma }{\beta w(1 - \theta )} + \frac{r\theta Z(G)}{{\beta w(1 - G)^{\alpha } (1 - \theta )}} $$

2.3 Section 3

According to Eq. 11 in the text, the labour endowment in home country is:

$$ \bar{L} = L_{Y} + nX\beta = L_{Y} + n\beta X = \frac{(1 - \varepsilon )}{w}Y + n\beta X $$

(28)

$$ \bar{L} = \frac{(1 - \varepsilon )}{w}\frac{(1 - s)}{s}nXP + n\beta X $$

(29)

Rearranging, we obtain:

$$ \bar{L} = n\frac{r}{w}\left\{ {\frac{{(1 - \varepsilon )(1 - s)\gamma (1 - G)^{\alpha } }}{s(1 - \theta )} + \frac{(1 - \varepsilon )(1 - s)Z(G)}{s(1 - \theta )} + \frac{\theta \gamma }{(1 - \theta )} + \frac{\theta Z(G)}{{(1 - G)^{\alpha } (1 - \theta )}}} \right\} $$

(30)

The capital endowment in home country is:

$$ \bar{K} = K_{Y} + n\gamma = \frac{\varepsilon }{r}\frac{(1 - s)}{s}nXP + n\gamma $$

(31)

$$ \bar{K} = \frac{\varepsilon }{r}\frac{(1 - s)}{s}n\left( {\frac{r\theta \gamma }{\beta w(1 - \theta )} + \frac{r\theta Z(G)}{{\beta w(1 - G)^{\alpha } (1 - \theta )}}} \right)\frac{{(1 - G)^{\alpha } \beta w}}{\theta } + n\gamma $$

(32)

$$ \bar{K} = n\frac{{\gamma [\varepsilon (1 - s)(1 - G)^{\alpha } + s(1 - \theta )] + Z(G)\varepsilon (1 - s)}}{s(1 - \theta )} $$

(33)

After rearranging Eq. 33, we obtain Eq. 12 in the text.

$$ n = \frac{{\bar{K}s(1 - \theta )}}{{\gamma [\varepsilon (1 - s)(1 - G)^{\alpha } + s(1 - \theta )] + Z(G)\varepsilon (1 - s)}} $$

2.4 Section 4

The parameter restrictions are: $\alpha > 1$; $0 < \varepsilon < 1$; $0 < s < 1$, $0 < \theta < 1$ and $0 \le G < 1$.

Assuming $Z(G) = Q + FG$, Eq. 12 in the text becomes

$$ n = \frac{{\bar{K}s(1 - \theta )}}{{\gamma [\varepsilon (1 - s)(1 - G)^{\alpha } + s(1 - \theta )] + (Q + FG)\varepsilon (1 - s)}}, $$

(34)

$$ n = \frac{{\bar{K}s(1 - \theta )}}{{\varepsilon (1 - s)(1 - G)^{\alpha } \gamma + s(1 - \theta )\gamma + (Q + FG)\varepsilon (1 - s)}} $$

(35)

In order to simplify, let:

$$ A \equiv \bar{K}s(1 - \theta ) $$

(36)

$$ B \equiv \varepsilon (1 - s)(1 - G)^{\alpha } \gamma + s(1 - \theta )\gamma + (Q + FG)\varepsilon (1 - s) $$

(37)

So Eq. 35 becomes

$$ n = \frac{A}{B} $$

(38)

Since A Eq. 36 is not a function of G, it can be viewed as a constant. In order to simplify the mathematics, we only need to establish the relationship between B (Eq. A 2.2) and G. Note that n is inversely proportional to B, i.e. when B has a minimum point, n has a maximum point and vice versa.

The first and second derivatives of B are:

$$ B^{\prime } = - \alpha \gamma \varepsilon (1 - s)(1 - G)^{\alpha - 1} + \varepsilon (1 - s)F $$

(39)

$$ B^{\prime \prime } = (\alpha - 1)\alpha \gamma \varepsilon (1 - s)(1 - G)^{\alpha - 2} > 0 $$

(40)

Since $B^{\prime \prime } (G) > 0$, B will have a minimum point at the level of G which maximizes n (G ^* in text).

2.5 Section 5

Two steps are needed to obtain the international capital-labour ratio $\bar{k}$; the first is to get the international labour endowment.

According to Eqs. (22) and (24) in the text, the world labour stock is

$$ L_{W} = \bar{L} + \bar{L}^{*} = L_{Y} + nX\beta + L_{Y}^{*} + n^{*} X^{*} \beta $$

(41)

Since all firms are of equal size, $X = X^{*}$, Eq. 41 becomes

$$ L_{W} = (n + n^{*} )\beta X + (L_{Y} + L_{Y}^{*} ) $$

(42)

$$ L_{W} = (n + n^{*} )\beta X + \frac{(1 - \varepsilon )}{w}(Y + Y^{*} ) $$

(43)

After rearranging of Eqs. (41) and (42), international labour endowment is

$$ L_{w} = (n + n^{*} )\frac{r}{w}\frac{{s\theta [(1 - G)^{\alpha } \gamma + Z(G)] + (1 - G)^{\alpha } \{ (1 - \varepsilon )(1 - s)[(1 - G)^{\alpha } \gamma + Z(G)]\} }}{{s(1 - \theta )(1 - G)^{\alpha } }} $$

(44)

And international capital endowment:

$$ K_{W} = \bar{K} + \bar{K}^{*} = \frac{\varepsilon }{r}Y + n\gamma + \frac{\varepsilon }{r}Y^{*} + n^{*} \gamma $$

(45)

and

$$ K_{W} = (n + n^{*} )\gamma + \frac{\varepsilon }{r}\frac{(1 - s)}{s}XP(n + n^{*} ) $$

(46)

Rearranging, the amount of international capital is therefore:

$$ K_{W} = (n + n^{*} )\left\{ {\gamma + \frac{{\varepsilon (1 - s)\gamma (1 - G)^{\alpha } + \varepsilon (1 - s)Z(G)}}{s(1 - \theta )}} \right\} $$

(47)

Thus, the international capital-labour ratio $\bar{k}$ is $\bar{k} = \frac{{K_{W} }}{{L_{W} }}$

$$ \bar{k} = \frac{{(n + n^{*} )\left\{ {\gamma + \frac{{\varepsilon (1 - s)\gamma (1 - G)^{\alpha } + \varepsilon (1 - s)Z(G)}}{s(1 - \theta )}} \right\}}}{{(n + n^{*} )\frac{r}{w}\frac{{s\theta [(1 - G)^{\alpha } \gamma + Z(G)] + (1 - G)^{\alpha } \{ (1 - \varepsilon )(1 - s)[(1 - G)^{\alpha } \gamma + Z(G)]\} }}{{s(1 - \theta )(1 - G)^{\alpha } }}}} $$

(48)

Finally,

$$ \begin{gathered} \bar{k} = \frac{{[s\gamma (1 - \theta ) + \varepsilon (1 - s)\gamma (1 - G)^{\alpha } + \varepsilon (1 - s)Z(G)](1 - G)^{\alpha } }}{{[\gamma (1 - G)^{\alpha } + Z(G)][s\theta + (1 - \varepsilon )(1 - s)(1 - G)^{\alpha } ]}}\frac{w}{r} \hfill \\ \hfill \\ \end{gathered} $$

(49)

Therefore, the international wage-rental ratio is

$$ \frac{w}{r} = \frac{{[s\theta + (1 - \varepsilon )(1 - s)(1 - G)^{\alpha } ][\gamma (1 - G)^{\alpha } + Z(G)]}}{{[s\gamma (1 - \theta ) + \varepsilon (1 - s)\gamma (1 - G)^{\alpha } + \varepsilon (1 - s)Z(G)](1 - G)^{\alpha } ]}}\mathop k\limits^{ - } = \varphi \mathop k\limits^{ - } $$

(50)

where $\varphi = \frac{{[s\theta + (1 - \varepsilon )(1 - s)(1 - G)^{\alpha } ][\gamma (1 - G)^{\alpha } + Z(G)]}}{{[s\gamma (1 - \theta ) + \varepsilon (1 - s)\gamma (1 - G)^{\alpha } + \varepsilon (1 - s)Z(G)](1 - G)^{\alpha } ]}}$.

Substituting the international wage-rental ratio into Eq. 20 we obtain Eq. 25 in the text.

2.6 Section 6

Assuming that the home country’s share of world income is $\pi = z\mathop K\limits^{ - } /(\mathop K\limits^{ - } + \mathop {K^{*} }\limits^{ - } ) + (1 - z)\mathop L\limits^{ - } /(\mathop L\limits^{ - } + \mathop {L^{*} }\limits^{ - } )$, consumption of the differentiated good in home country is:

$$ \mathop X\limits^{ - } = \pi X = \left[ {\frac{{\mathop {zK}\limits^{ - } }}{{(\mathop K\limits^{ - } + \mathop {K^{*} }\limits^{ - } )}} + \frac{{(1 - z)\mathop L\limits^{ - } }}{{(\mathop L\limits^{ - } + \mathop {L^{*} }\limits^{ - } )}}} \right]*\left[ {\frac{r\theta \gamma }{\beta w(1 - \theta )} + \frac{r\theta Z(G)}{{\beta w(1 - G)^{\alpha } (1 - \theta )}}} \right] $$

(51)

On rearranging, total consumption of the differentiated good (Eq. 26 in the text)

$$ \mathop X\limits^{ - } = \frac{{\theta \mathop {\mathop L\limits^{ - } [z + (1 - z)\delta ][\gamma (1 - G)^{\alpha } + Z(G)]}\limits^{{}} }}{{\varphi \delta \beta (1 - G)^{\alpha } \mathop K\limits^{ - } (1 - \theta )(1 + a\lambda )}} $$

(52)

can be obtained.