Effective Protection Redux*

This paper rehabilitates effective protection. In general equilibrium, the usual definition (the percentage change in value added per unit induced by the tariff structure) corresponds to no economically interesting magnitude. The effective rate of protection for sector j is defined here as the uniform tariff which is equivalent to the actual differentiated tariff structure in its effect on the rents to residual claimants in sector j. This definition applies to general as well as partial equilibrium economic structures, has obvious relevance for political economy models and seems to correspond to the motivation for the early effective protection literature. Like the earlier effective rate formula, the concept is operational using the widely available set of Computable General Equilibrium (CGE) models. An example is provided for the US economy. The numerical results for the old and new concepts are not significantly correlated. JEL Classification: F13, D72. For presentation to the European Economic Association meetings, Prague, September, 1995. Communications to: James E. Anderson Dept of Economics Boston College Chestnut Hill, MA 02167 * With apologies to John Updike. According to the Oxford English Dictionary, redux: of crepitation or other physical signs, indicating the return of an organ to a healthy state. From the Latin root reducere, to bring back. Introduction Effective protection is the ranch house of trade policy construction --ugly but too useful not to be used. Building to the blueprint of theorists such as Corden (1966), a generation of applied economists have calculated effective rates of protection while cheerfully ignoring the critique of the design best summarized by Ethier (1977).1 In academic circles this work is ignored, while outside the academy it is either apologized for or trashed. Academics surveying the theory of protection (for example Dixit, 1985 and Anderson, 1994) cover effective protection since it is too practically important to ignore, but awkwardly, since the critique of the concept is so convincing. This paper rehabilitates effective protection by carefully defining the question the resulting index number is supposed to answer. The usual definition of the effective rate of protection is the percentage change in value added per unit induced by the tariff structure. The problem is that in general equilibrium this measure corresponds to no economically interesting magnitude.2 In contrast, the effective rate of protection for sector j is defined here as the uniform tariff which is equivalent to the actual differentiated tariff structure in its effect on the rents to residual claimants in sector j. This definition applies to general as well as partial equilibrium economic structures, though resulting in a different formula in each structure. The new definition has obvious relevance for political economy models and seems to correspond to the motivation for the early effective protection literature. The concept is defined for all economic structures in which sectoral residual claims exist. Like the earlier effective rate, the new definition is operational. In the last generation, Computable General Equilibrium (CGE) models have become fairly widely 1See also Anderson (1970), Ethier (1971), and Tan (1970). 2Under the restriction of value added separability, meaning attaches to the notion of protection to value added in the form of increases in a 'price' of value added. This is too restrictive to make the effective rate of protection generally useful. Moreover, there seems to be no good reason to make the protection of sectoral value added a central focus. February 12, 1996 Effective Protection Redux 2 available, and such models are readily adapted to calculate the effective rate of protection on each sector. An example is provided here using the USDA/ERS agricultural CGE model distributed in the GAMS (General Algebraic Modeling System) library. The results show that the effective rates calculated with the new and old definitions are not significantly correlated. Most important from a practical view, in 3 of 10 sectors the sign of protection is reversed, including 3 of 5 of the agricultural sectors which are the focus of the model. Several antecedents in the literature emphasize the possible usefulness of the standard measure of effective protection in analyzing sector specific factor returns. Jones (1975) characterized the loose but still useful relationship between the set of specific factor returns and the set of effective rates of protection in the Ricardo-Viner (one mobile factor and many sector specific factors) case. The theme that effective protection might usefully be linked to distribution and hence political economy was echoed by Ethier (1977) in his conclusion. Just recently, Kohler (1991) applied this idea in a study of Austrian tariff structure. Nevertheless, only in very special cases can the ranking (or sign) of the usual measure of effective protection replicate the ranking (or sign) of sector specific factor income changes. In contrast to this literature, the present paper redefines the effective protection measure to by definition avoid the problems which complicate the link between specific factor returns on the one hand and measures of effective protection on the other hand. Given a CGE model, the analyst can always compute the sector specific factor income changes due to the protection structure. Differences in these income changes across sectors reflect both the structure of protection (which the old effective protection concept tried to measure) and differences in the position of the sectoral factor in the technology. The two questions, ‘how much protection is given’ and ‘how much does income change as a result’ are distinct. The new concept gives a precise answer to the first question. February 12, 1996 Effective Protection Redux 3 The main business of the paper is to characterize the new concept and relate it to the old one. Neat and elegant results are obtained by applying modern index number and duality theory. Related work on tariff index numbers to answer different questions is in Anderson and Neary (1994, 1995). In a special case, that of partial equilibrium with fixed coefficients of production, the formula implied by the new definition is identical to the usual effective rate of protection formula. With variable coefficients but still in partial equilibrium, the formula is a simple variant on the usual formula, which can be treated as an approximation. In general equilibrium the usual formula is a component of a decomposition of the formula implied by the new definition. In general the ranking of sectors by the usual formula and the correct formula will differ, though a special case is offered in which the ranking is identical. Using the decomposition the trail leading from the general equilibrium formula to the partial equilibrium formula is clear and straight. Section I gives the partial equilibrium version of the effective protection index. The special case of fixed coefficients gives the standard formula, while substitution possibilities imply a simple variant. Section II give the general equilibrium version of the effective protection index and shows how it is related to the partial equilibrium index. Section III contrasts the effective protection index to the sector specific factor income change. Section IV takes up a number of extensions of economic structure (imperfect competition, scale economies, nontraded goods) and of the type of distortions (quotas, domestic taxes and subsidies) admitted. In each case, the set of distortions is mapped to a uniform tariff equivalent. Section V presents the empirical results of calculating US effective rates of protection based on the USDA/ERS model in the GAMS library. The old and new measures of effective protection are not significantly correlated. Section VI concludes. I. Partial Equilibrium Effective Protection A standard neoclassical convex economy is assumed here and in Sections II and III. A set of final and intermediate good prices is distorted by tariffs. In keeping with the February 12, 1996 Effective Protection Redux 4 partial equilibrium setting, all goods prices are exogenously set by the combination of perfect substitutability of foreign and domestic versions of the same good, fixed world prices and given trade policies. Non produced input prices are fixed in this section but are endogenous in Section II. The task is to evaluate the given tariff structure relative to some alternative structure with equivalent effect on rents earned in sector j. The residual payments or rents to owners of specific factors in sector j can be aggregated in a sectoral profit function πj(p,w) with the standard properties. πj should be thought of as including firm and sector specific payments to human capital.3 Here, p is the vector of goods prices, including both those for the output of sector j and the outputs of sectors from which sector j buys inputs. Since domestic distortions are absent, supply and demand prices for intermediate goods are the same. Sector j can produce a set of outputs. w is the vector of non produced input prices. The idea is to find the uniform tariff on all distorted goods which has an effect on profits of j equivalent to that of the initial tariff structure. Some goods prices are normally not distorted (e.g., those of export sectors), so this qualification matters. The undistorted prices are subsumed into the background with prices equal to one. Let the initial price vector for distorted goods be denoted p0 and the free trade price vector be denoted p1. Let the price vector for nontraded inputs be denoted w which by assumption of partial equilibrium is unchanged with respect to the change in p. The effective protection index ej for sector j in partial equilibrium is defined implicitly as: (1) e d p w p j j = − 1 1 1 0 0 / ( ; , ) , where d p w p d p d w p w j j ( ; , ) | ( / , ) ( , ). 1 0 0 1 0 0 0 = = π π The function d is the distance function (Deaton, 1979 and Deaton and Muellbauer, 1984) applied in the space of tariff distorted prices.4 Working backwards, dj is the uniform 3The profit function is usually justified by appeal to the maximization activity of an actual firm. However, the hypothesis of competition implies that the collection of interests in specific factors within each sector can be modeled as if maximizing rent. 4 In related work, Anderson and Neary apply the distance function to define a tariff index which holds real income of a representative agent constant. February 12, 1996 Effective Protection Redux 5 output price deflator which maintains profits in j.5 Since p1 is lower than p0, dj is less than one, and is equal to the inverse of a uniform tariff factor. Then ej is equal to the uniform tariff on distorted goods which has the same effect on the profits of sector j as the initial tariff vector. Several extensions of (1) are immediate. First, it is possible to define a uniform tariff (export tax/subsidy) vector which includes currently undistorted goods, but this seems much less useful for the purpose of political economy analysis, so it will be treated only as a special case. Second, the effective rate of protection defined in (1) can formally be applied to comparing any two distortion structures. If p represents a partial tariff reform price vector rather than the free trade price vector, the effective rate defined by (1) is interpreted as the uniform tariff surcharge which is required to make the new protection structure equivalent to theinitial structure in its effect on profits of sector j. Of course, the surcharge could be negative if p represents an increase in protection. This extension is practically significant, since many comparisions are in practice between one distortion structure and another. In the special case of (i) nonjoint outputs, (ii) in which all intermediate goods prices are distorted and (iii) fixed coefficients, the formula for ej is identical to the usual formula for the effective rate of protection. Elsewhere, it has a simple relationship to the usual formula. To see this it is helpful to begin with the case of small changes in the prices, due to small tariffs. (Alternatively p1 need not be interpreted as the free trade price vector, just a price vector close to p0.) The proportional rate of change of ej is equal to minus the proportional rate of change of dj. The latter is equal to 5 The existence and uniqueness of d is guaranteed if π is monotonic with respect to uniform changes in p; πpp is one-signed. For sectors which receive no output protection πp’p is negative, since πp is equal to minus the input demand vector. For sectors which receive some protection, πp’p is equal to ‘value added by undistorted’ factors. It is possible for value added to be negative at free trade prices, and positive at protected prices (see Tan, 1970), implying a sign change in πp’p. This implies there may be two solutions for d, or none. If there are two, the region of negative value added is surely also the region of negative profit. If the base profit is positive (a plausible condition) the solution for d must be sought in the region where π(p/d,w) is positive. February 12, 1996 Effective Protection Redux 6 (2) d̂ j = π π p j