Input Intensity: A Missing Link between Production, Trade Patterns, and Environmental Standards

1. Introduction

In the theory of international economics factor endowment is an important determinant of the pattern of production and trade. In contrast the pollution haven hypothesis (PHH) predicts that economies with strong environmental standards have high input requirements and costs associated with emission abatement resulting in lower production of the dirty goods. This paper looks at how the abatement requirement interacts with the factor-endowment effects in determining the final effect on production and trade patterns.

There have been numerous empirical studies to test the intuitive PHH idea. However, early studies based on cross-sectional analyses did not find support for this hypothesis. Tobey (1990) studied the trade patterns in five highly polluting sectors by using five cross-section regressions (one for each sector) of net exports on characteristics of 23 countries. He found that if one controls for differences in resource endowments, differences in regulatory stringency have no measurable effect on international trade patterns in these industries.

Subsequent cross-sectional analyses include additional country and industry characteristics as new explanatory variables. Birdsall and Wheeler (1993) and Lucas et al. (1992) included openness to trade as an additional country characteristic. The former looked at data from 25 Latin American countries spanning the three decades of the 1960s to 1980s, while the latter looked at 80 countries over a similar time period. Using pooled cross-sectional techniques, both studies found evidence that countries with weaker environmental stringency have a greater share of polluting industries. However, they also found that that the effect is weaker for more open economies, which should not be the case under PHH since greater international economic integration would make it easier for countries with weaker environmental stringency to attract the dirty industries. Kalt (1988) and Grossman and Krueger (1993) are examples of cross-sectional studies that regress trade flows on industry characteristics such as the cost shares of research and development (R&D), human capital, physical capital, and in some cases, the tariff rates. These studies used data on US trade flows at the industry level for the years 1977 and 1987 respectively, and found mixed evidence for the PHH with the sign of the coefficient often opposite to the expected direction.¹

More recent studies using panel data to control for country and industry heterogeneity found significant pollution haven coefficients. Ederington and Minier (2003), using industry-level US net imports data over 1978–1992, showed that the estimated effect of environmental stringency on trade volumes is stronger when it is recognized that environmental stringency itself may be simultaneously determined with trade volume. Levinson and Taylor (2008) accounted for the various types of endogeneity for the variable used to represent environmental stringency and addressed this issue by using instrumental variables in a panel data model covering the 1970s and 1980s. They found that US industries that face large increases in abatement cost also have a greater increase in import volume, indicating that these industries shifted abroad.²

Ederington et al. (2005) included additional characteristics such as the relative mobility of an industry that might affect the strength of the pollution haven impact, while Kellenberg (2009) made a distinction that the enforcement of the environmental policy rather than just the official stringency has a more significant effect on production outsourcing by US multinational corporations. Hence the newer studies explored additional country and industry characteristics to better capture the PHH effect. The model presented here contributes to this broader search by indicating that the relative input intensity of the production and abatement processes is another dimension that impacts the PHH outcome.

By incorporating pollution and abatement considerations within the standard factor-endowment framework of international trade the present author finds that whether the influence of stricter environmental policy on production will be similar or opposite to the pollution haven prediction is conditional on the factor intensities of the production and abatement activities. Two forces caused by changes in abatement requirements are identified: the first is called the “effective-endowment effect” where the abatement activity uses up some resources of the economy leaving less for the production of the final goods and the “factor-price effect” where changes in the abatement requirement affects factor prices which in turn affect production. The effective-endowment effect will increase or decrease the production of the dirty sector depending on the input intensities of the abatement and production activities while the factor-price effect is always found to act in a direction consistent with the pollution haven prediction. When the two forces reinforce each other, the pollution haven prediction emerges. However, when the effective-endowment effect works opposite to the factor-price effect, the relative strengths of the two effects determine whether pollution haven is a likely outcome or not.

2. Review of the Theoretical Literature

The empirical pollution haven prediction can be derived from theoretical models that involve a single primary factor of production. Copeland and Taylor (1994) is an important paper with this specification that incorporates abatement considerations in a Ricardian model of continuum of goods and finds that stricter environmental standard reduces the volume of dirty industries.

McGuire (1982) considered two inputs but environmental policy in the form of emission tax has the sole effect of increasing the cost and hence unambiguously reducing the production of the dirty sector. More recent models by Antweiler et al. (2001) and Copeland and Taylor (2004) allowed for two factors to allow for interaction of trade and policy effects. However their papers assumed that the abatement activity has the same factor intensity as the production activity, i.e. a firm can devote a fraction of its input to abatement activity. This assumption obscures the interesting interaction of relative factor intensities of production and abatement. Their papers identified two forces: the “trade effect” denotes specialization driven by exogenous factor endowments of the countries and the “policy effect” where increased environmental strictness unambiguously reduces production of the dirty industry. Umanskaya and Barbier (2008) followed existing literature in assuming a firm devotes a fraction of its inputs to abatement activity and using the Cobb–Douglas production function derives specific conditions when the “policy effect” dominates the exogenous endowment driven “trade effect” resulting in a “true pollution haven.” The present model is the first to find that the “policy effect” itself has production and trade implications and to show that the effect of stricter environmental standards is not as straightforward as found by the current literature.

Umanskaya and Barbier (2008) also assume exogenous difference in factor prices to motivate difference in endowment driven production. Hence their results relate to only pairs of countries with factor endowments sufficiently dissimilar to be outside the diversification cone. In Fullerton and Heutel (2007) pollutants appear as an input in the production process. The focus of their paper is on the effect of pollution policies on income distribution and not on the quantities produced and traded. The present model shows that changes in environmental strictness would endogenously cause changes in factor prices for any country creating a second force affecting production.

Hence this paper extends the existing literature in two ways: first, it finds that the “policy effect” endogenously triggers a nuanced change in production and trade under more realistic resource use assumptions, and second by endogenizing factor prices the present model shows that factor-price equalization can be violated by difference in environmental standards, resulting in a secondary effect on the composition of production and pattern of trade for a country.

3. Theoretical Model

The simplifying assumption that the abatement activity has the same factor intensity as the production activity obscures an interesting interaction of relative factor intensities of production and abatement, which is explored in this paper.³

I use a 2 × 2 general equilibrium framework. The two inputs are capital and labor. The two goods are the clean good X and the dirty good Y. The economy's environmental standard e denotes the units of abatement activity A that should accompany every unit of production of the dirty good Y.⁴a_ij represents the units of the jth input used in the ith activity where I = X, Y, A and j = K, L. Figure 1, using the simplifying assumption a_AL = 0, provides a flavor of the results to follow.

In the two panels of Figure 1, R represents the endowment points. The dashed lines capture the relative factor intensities of the vector sum Y + eA. The diagram depicts the special case where the abatement technology A uses only capital. In Panel 1 if the dirty industry Y is more K intensive than X, then stricter abatement results in an increased production of the clean good, which also implies a lower production of the dirty good. This outcome is consistent with PHH prediction. Alternatively, in Panel 2, if the dirty industry Y is more L intensive than X (the rays indicating the production activities X and Y are reversed) then stricter abatement results in increased production of the dirty good and a decreased production of the clean good. This outcome is opposite to PHH prediction.

Several simplifications are embodied in the above diagram: the factor prices and hence the production rays before and after abatement are kept unchanged and abatement is assumed to be solely capital using. A mathematical approach allows for a more comprehensive analysis. This paper uses the hat-algebra technique popularized by Jones (1965).

Equations (1) and (2) are the full employment conditions.

(1)

(2)

where a's are the input coefficients.

In order to sell at the international prices, the producers of Y must consider the abatement expenditure in addition to the direct production expenditure.⁵ The zero profit conditions under constant returns to scale take the form of (3) and (4).

(3)

(4)

where p is the price of Y relative to X.

Use of the cost minimizing envelope condition that the slope of isocost equals the slope of isoquant, reduces the percentage-change equations to the following system of equations (5)–(8).⁶ The sum of the production and associated abatement activity input coefficients for Y is denoted by b_Yjfor the jth input.

(5)

(6)

(7)

(8)

where θ_ij is the share of expenditure on jth input in the ith sector, λ_ij is the share of industry i's use of input j, s_Ai ≡ (e*a_Ai)/(a_Yi + ea_Ai) is abatement's share in total expenditure on input i for Y, and ê denotes difference in environmental standards across economies that are otherwise identical or represents a change in environmental strictness within a country. The term in parentheses in (7) can be alternately interpreted as a change in emission taxes. However, the current analysis, instead of confining the effects of environmental policy only to cost changes takes a broader view of how it also affects the resource constraints as captured by terms in parentheses in (5) and (6). ê has interesting implications for prices of inputs as shown in section 4, which in turn have an impact on production specialization as explored in sections 5 and 6.

4. Effect on Input Prices

To emphasize the effect of a difference in strictness ê, it is assumed that the constant relative world prices . The abatement activity causes a difference between the factor intensity of production of Y vs the gross input requirement for Y defined as the sum of input required for production as well as abatement. However, it is assumed that this gross input requirement does not switch the factor intensity ranking of Y with respect to X. Equations (7) and (8) provide the following solution.

(9)

If Y is K intensive, then |θ| is negative and .

The changes in the absolute prices are provided in (10) and (11):

(10)

(11)

Results from (9)–(11) can be summarized as follows. Increased environmental strictness (ê > 0), results in a lower price of the input that the dirty industry is intensive in and a higher price of the input that the clean sector is intensive in. These results are true for both absolute and relative prices of the inputs.

The explanation for these results is as follows. Starting with the original factor prices, a greater abatement requirement raises the cost of production of the dirty good. For an unchanged world price, and the economy still producing both goods, the input prices need to change to accommodate this additional component. If the dirty good is K intensive, then the price of capital goes down. Simultaneously the price of labor goes up in order to keep the total cost for the labor intensive clean good unchanged. If the dirty good is L intensive, then the additional abatement cost requires the price of labor to fall. The price of capital rises in order for the costs of the clean good to remain equal to the unchanged prices.

Under the assumption of factors immobile across countries, the above factor-price changes imply that the factor prices for the physical inputs, capital and labor, are not equalized across countries. This happens because the assumption of identical technology across countries breaks down when the environmental standards are allowed to be different. Although the production technology for X, Y, and abatement is assumed to be the same, the cost of production of Y is essentially a weighted sum of the direct production cost of Y and the indirect abatement cost. Because the weights vary across countries based on the exogenous environmental standards, the overall production technique for Y is different across countries, resulting in the violation of the factor-price equalization theorem even in the 2 × 2 model with incomplete specialization.

5. Change in Relative Production

Under the assumption of fixed endowments, the system of equations (5) and (6) takes the following form:⁷

(12)

where , are the elasticities of substitution between labor and capital in the X and Y sector and δ_L ≡ λ_LXθ_KXσ_X + λ_LYθ_KYσ_Y, δ_K ≡ λ_KXθ_LXσ_X + λ_KYθ_LYσ_Y are the percentage savings in factor use associated with a 1% rise in relative factor price.

To consider the change in relative production owing to a change in abatement strictness, is substituted in terms of ê using (9).

(13)

where .

The first right-hand side term in (13) reflects how a change in abatement requirement alters the endowment of resources available for production process and is henceforth called the “effective-endowment effect”. The second term on the right-hand side reflects how a change in abatement requirement alters the input-prices which in turn affects production and is henceforth called the “factor-price effect”.

In determining the direction of the two effects, it is found that if (a_AK/a_AL) > K/L the effective-endowment term will be lead to an increase in the production of the polluting industry Y if Y is labor intensive (i.e. |λ| > 0). Conversely if (a_AK/a_AL) < K/L the effective-endowment term will be lead to an increase in the production of the polluting sector Y if Y is capital intensive (i.e. |λ| < 0).

6. Change in Absolute Production

Having disentangled the forces underlying changes in relative production, it is more relevant for trade data to make predictions about the absolute changes in production. Equations (14) and (15) present the solution of the system of equation given by (12) for absolute changes in production specialization resulting because of alteration of environmental standard ê.

(14)

(15)

The two terms on the right-hand side of equations (14) and (15) reflect the effective-endowment and factor-price forces respectively on absolute production. As before, we analyze each of these effects in turn.

The effective-endowment effect finds that under unchanged input prices, if Y is K intensive relative to X then iff (a_AK/a_AL) < (a_XK/a_XL) and iff (a_AK/a_AL) > (a_YK/a_YL). If Y is L intensive relative to X then iff (a_AK/a_AL) > (a_XK/a_XL) and iff (a_AK/a_AL) > (a_YK/a_YL). These results are summarized in Proposition 2.

7. Conclusions

The above analysis with inputs mobile across industries demonstrates a reason why the pollution haven hypothesis has been difficult to pin down. An alteration of the environmental policy causes a reduction of the endowments left for production of final goods affecting production patterns. Difference in environmental policy also changes the factor prices causing a violation of the factor-price equalization theorem which in turn affects production patterns. These two forces work in the same or opposite direction depending on the relative factor intensities of the abatement technology and the production sectors. When these two effects work in opposite directions, if the effect of the change in endowments dominates the effect of change in input prices, then the outcome is opposite to the prediction of the pollution haven. For example if the dirty industry is labor intensive in nature and the abatement technology is capital-intensive, then for two otherwise identical economies, the one practicing stricter environmental standards would end up as the exporter of the dirty good, an outcome completely contrary to pollution haven expectation, if the effective-endowment effect is stronger that the input price effect. The current model shows how outcomes contradicting the pollution haven expectations can be explained using standard theoretical tools and provides an indication why the pollution haven effect has been relatively elusive to empirical studies.

Appendix

Derivation of Equations (5)–(8)

or, . s_AL ≡ e*a_AL/(a_YL + ea_AL) is abatement's share in total expenditure on labor for Y, reflects the partial change in only because of factor-price changes and not the part caused by the exogenous ê. Similarly where s_AK ≡ e*a_AK/(a_YK + ea_AK).

The cost minimizing envelope condition is that slope of isocost equals the slope of isoquant.

These cost minimizing conditions leave the exogenous changes ê on the right-hand side of (7).

Derivation of Equations (5)–(6)

The elasticity of substitution between labor and capital in the X and Y sector is defined as in the Jones derivation.

Change in output from (5) and (6) can be rewritten as:

The change in input requirement coefficient for the dirty industry Y is broken into the change in input requirement for production and for abatement,

The elasticity of substitution of the inputs allows the substitution of the change in input coefficients as functions of the input prices.

where δ_L ≡ λ_LXθ_KXσ_X + λ_LYθ_KYσ_Y and δ_K ≡ λ_KXθ_LXσ_X + λ_KYθ_LYσ_Y are the percent savings in factor use associated with a 1% rise in relative factor price.

Assuming fixed endowments, the above system reduces to (12).