Testing for market power in multi-product industries across multiple export markets.

I. Introduction

A large body of theoretical literature has developed in the past 15 years incorporating various models of imperfect competition into international trade theory.(1) Empirical work testing for imperfect competition in export markets, however, has been much more limited. In particular, the empirical evidence in support of widespread imperfect competition in U.S. export and import sectors is somewhat scant and mixed.(2) One technique for assessing the existence of market power in export markets has been developed by Knetter [33] who estimated a reduced form single equation in which the export price to a specific market for a good was a function of the exchange rate, a country specific dummy variable, and a time dummy. Knetter rejected the null hypothesis of perfectly competitive markets in nearly all of the U.S. and German export markets studied.(3) His methodology has been adopted by other researchers who have rejected the perfect competition hypothesis in other U.S. export markets.(4)

While this technique has the admitted advantage of requiring minimal data for hypothesis testing, it also suffers some shortcomings which limit the insights into an export sector's market structure that it can provide. The technique cannot distinguish between marginal cost pricing across export markets and marginal cost plus constant mark-up pricing. This limits the conclusions one can draw from such analysis. Another limitation of the analysis is that even when marginal costs are equal across markets, the results only permit one to accept or reject the hypothesis of perfect competition. No insights regarding the magnitude of the price markups, the similarity of industry pricing to monopoly pricing, the sources of the market power, or the variation in market power across destination markets are provided by the results.

This paper addresses the above issues by extending the methodologies of the "New Empirical Industrial Organization" (NEIO)(5) approach to testing for market power in domestic markets. The extension allows one to simultaneously analyze industry behavior in both domestic and export markets. This paper's specific contribution to the literature utilizing NEIO techniques to analyze international markets is the development of a reasonably straight-forward model which links an industry's factor and goods markets. A short-run multi-product, multi-factor cost function is simultaneously estimated along with multiple country-specific export demand and firm supply curves. The model permits a number of interesting market structure questions to be addressed including:

i. Testing on a destination-specific basis the hypotheses of both perfectly competitive and monopoly pricing behavior by firms in the industry.

ii. Estimates on a destination-specific basis of the degree of markup by firms over their marginal costs, and of the relative importance of the markets' demand structures (how inelastic) versus the competitive behavior of the firms in establishing the markup.

iii. Testing for changes in the degree of markup over time and for the source of the change in markup: changes in demand elasticity versus firm behavior.

Although some prior work has utilized a multi-product cost function framework, output was simply divided into domestic and aggregate export markets [9]. Existing work modelling country specific export demand and firm supply curves has not directly linked the factor and goods markets equilibrium through information on factor prices and usage levels [4; 5].

The model is used to examine the pricing behavior of the U.S. non integrated wood pulp industry (SIC 2611) over the period 1963-1987. The key results of this study relate to the different conclusions drawn about the prevalence of market power in U.S. wood pulp exports depending upon the method of analysis. Results from the single-equation analysis indicate widespread imperfect competition in U.S. exports for one of the pulp types modelled: pulp derived from dissolving chemical processes. For the other good modelled, pulp derived from sulphate based processes, the single equation analysis does not produce either a clear rejection or acceptance of the hypothesis that U.S. exporters price above marginal cost. In contrast, the structural model's estimates suggest that export pricing above marginal cost was widespread across markets for both types of pulp. Within any given export market, however, the margin on pulp derived from dissolving chemical processes exceeded the margin on pulp derived from sulphate based processes. This information on the export margin differences was not revealed by the single equation analysis.

Section II highlights important characteristics of the U.S. wood pulp export industry and reports the results of the reduced form single equation approach to testing for market power in U.S. wood pulp exports. In section III the structural model is developed which permits the econometric identification of the degree of market power in U.S. chemical pulp and sulphate pulp exports. Section IV reviews the data used in the model's estimation, results are presented in section V, and a summary of the major findings along with concluding remarks are in section VI.

II. The U.S. Wood Pulp Industry

The output from U.S. non integrated wood pulp mills (SIC 2611) can be divided into three 5 digit SIC categories: pulp from dissolving chemical processes, pulp from dissolving sulphate processes, and pulp from dissolving sulphite processes. Chemical pulp is used as an input in producing higher valued specialty papers while the sulphate and sulphite pulps are used in the production of lower valued newsprint and cardboard production. The average export prices and their share in the export bundle are shown in Figures 1 and 2 for each of the pulp types. Not surprisingly, chemical pulp prices are higher across the sample period 1963-87, but note how closely tied the sulphite and sulphate prices remain over the sample. The other key point is that sulphate pulp's share of the total export bundle steadily increased over the period as chemical pulp's share declined while sulphite pulp remained a very minor component of the bundle.

Given the shifting composition of the export bundle, estimating the industry's output as an aggregated 4-digit good could introduce estimation errors, particularly if the composition of the export bundle varies across destination markets. Consequently, in the structural model developed in section III output is divided into two types: pulp from dissolving chemical processes (hereafter chemical pulp), and pulp from either dissolving sulphate or sulphite processes (hereafter sulphate pulp). This division reflects the goods different end-product uses and effectively folds the minor sulphite pulp category in with the dominant sulphate pulp product.(6)

The non integrated wood pulp industry was selected for analysis because exports are an important share of output (approximately 35%), these exports are diversified across many markets, and the competitiveness of the industry has a number of policy implications. Perfectly competitive markets have been assumed in a number of models of global wood products trade [1; 14; 20], but the appropriateness of the assumption has been questioned by some researchers(7) so the findings of this study may be of interest to those involved in global modelling of the wood products sector.

Knetter [33] tests for imperfect competition by estimating the following equation for each good modelled:

ln [p.sub.it] = [[Theta].sub.t] + [[Gamma].sub.i] + [[Beta].sub.i] ln [s.sub.it] + [u.sub.it] (1)

where

[p.sub.it] is the pre transportation and shipping price in $'s of U.S. exports to country i at time t, [[Theta].sub.t] is a time effect,

[[Gamma].sub.i] is a country effect,

[s.sub.it] is the bilateral exchange rate in foreign currency units per $,

[u.sub.it] is the regression disturbance.

Table I. Results of Single Equation Estimation of Price
Discrimination across Export Markets

                         [[Gamma].sub.i]       [[Beta].sub.i]

Chemical Pulp

Argentina             -.504(*) (.022)          .020(*) (.004)
Austria                .013 (.021)             .189(*) (.060)
Belgium               -.358(*) (.020)          .048 (.073)
Brazil                 .084(*) (.021)          .011(*) (.005)
Canada                -.465(*) (.026)          .234 (.142)
France                 .020 (.020)            -.089 (.070)
India                 -.399(*) (.020)          .056 (.055)
Italy                  .052(*) (.023)         -.058 (.038)
Japan                 -.405(*) (.020)          .072 (.060)
Mexico                -.010 (.022)             .032 (.021)
Netherlands           -.407(*) (.021)          .054 (.070)
Spain                  .075(*) (.021)         -.074 (.042)
U.K.                  -.470(*) (.022)          .072 (.062)
West Germany                                   .081 (.053)
Yugoslavia            -.435(*) (.020)          .019 (.012)

Sulphate Pulp

Argentina              .034 (.028)             .020(*) (.003)
Australia              .050 (.026)            -.336(*) (.093)
Belgium               -.034 (.025)             .009 (.089)
Brazil                 .178(*) (.026)         -.024(*) (.006)
Canada                -.060 (.032)             .168 (.176)
France                -.011 (.044)             .013 (.089)
Italy                 -.002 (.030)            -.042 (.049)
Japan                 -.022 (.025)            -.070 (.071)
Mexico                -.041 (.027)            -.023 (.014)
Netherlands           -.024 (.028)             .005 (.007)
South Korea           -.141(*) (.025)         -.044 (.037)
Spain                  .012 (.027)             .024 (.053)
U.K.                   .002 (.027)            -.083 (.076)
Venezuela             -.099(*) (.025)          .034 (.061)
West Germany                                   .031 (.063)

* Indicates significance at the 5% level

Standard errors in parentheses. Parameter estimates are from
estimating equation (1) in paper.

Under the assumption of constant marginal cost for a good across destination markets, three different market structure hypothesis can be tested using equation (1).(8) Under the null of perfect competition, both [[Gamma].sub.i] and [[Beta].sub.i] equal zero since [[Theta].sub.t] captures all marginal cost effects over time. Under the null of imperfect competition with constant elasticity of demand, [[Gamma].sub.i] can be non zero since mark-ups can vary across markets but [[Beta].sub.i] still equals zero. Lastly, under the null of imperfect competition with non constant elasticity of demand both [[Gamma].sub.i] and [[Beta].sub.i] can be non zero.

As a point of reference for the structural model estimation, equation (1) was estimated for 15 different export markets for both chemical and sulphate pulp over the 1963-87 sample period. The 1963 time effect dummy and the West Germany country effect dummy are omitted to avoid singularity. The reported country effects, therefore, should be viewed as differentials from the omitted West Germany country effect. The parameter estimates of [[Gamma].sub.i] and [[Beta].sub.i] are listed in Table I. The chemical pulp estimates strongly support the hypothesis of imperfect competition with constant elasticity of demand as [[Gamma].sub.i] was nonzero in 11 of 14 markets, but [[Beta].sub.i] was nonzero in only 3 markets. The sulphate estimates, however, do not provide clear inferences about the prevalence of imperfect competition. In the sulphate markets [[Gamma].sub.i] was nonzero in only 3 of 14 markets while [[Beta].sub.i] was nonzero in 3 markets. Moreover, the nonzero [[Gamma].sub.i] all are for non European markets implying that none of the European nations' country effects ([[Gamma].sub.i]) were statistically different from the omitted West German market. This result could be due to perfect competition in the European markets, or alternatively, U.S. sulphate pulp exports to the European markets all could have the same mark-up over marginal cost which would generate zero [[Gamma].sub.i]'s in this model. Without an estimate of marginal cost, the two possibilities cannot be differentiated. Thus, while the single equation analysis does provide some insights into the likely market structure of U.S. wood pulp exports across pulp types, the findings are inconclusive with regards to sulphate pulp in particular.

III. The Model

Since the early 1980s, a literature has developed in Industrial Organization which tests for the presence of firm market power through the use of a complete structural model of an industry. One of the more popular methodologies has been to estimate a system composed of factor demand, market demand, and market supply equations. Applebaum [3] is an early standard example of this approach. Two key extensions of that approach in this work are that total output is modelled as selling in multiple markets, domestic plus several export, instead of in a single market; and, that a multi-product cost function is utilized. Consequently, the model specification has the following form:

i. A short run variable cost function is estimated with labor and materials as variable factors, capital as a fixed factor, and chemical pulp and sulphate pulp as the two products.

ii. Using Shepard's lemma, the materials factor demand equation is estimated along with the variable cost function.

Then, for each destination market for a given pulp type two additional equations are estimated.

iii. A demand equation for exports of the pulp to that destination market.

iv. A supply equation in which firms equate perceived marginal revenue to marginal cost. In the remainder of this section, the functional form of each equation will be presented along with a discussion of the hypothesis testing to be done with the completed model.

Factor Markets

A short run specification is used for the cost function so that the assumption of long-run equilibrium does not have to be imposed upon the data. The practice of altering capacity in the wood pulp industry through infrequent large changes in mill capacity makes it unlikely that the size of the capital stock undergoes continuous adjustments to equate capital's marginal revenue product to the current rental rate. This view is supported by Bernstein [8] who models the Canadian pulp and paper mill industry at the 3 digit level and finds that the industry is not in long-run equilibrium in its factor market for capital.(9) If information on factor prices and usage levels was available at the 5 digit SIC level, then the market equilibriums for the different types of wood pulp could be modelled independently of one another. Unfortunately, the factor price and usage data is not available at the 5 digit level. Data on factor prices and usage levels within the industry are given at the 4 digit level whereas data on the quantity and value of exports to various destination markets is available at the 5 digit level. To minimize distortions from either data aggregation or omission, a multi-product multi-factor cost function is estimated in which factor inputs and prices are at the 4 digit level and total output is the sum of its associated 5 digit sectors' output. The functional form selected for the short run cost function follows from Hall's specification of a Hybrid Diewert Joint Cost Function(10) [22] and is constructed as:

[VC.sub.t] = [B1[WL.sub.t] + B2[WM.sub.t] + 2B3[(W[L.sub.t] x [WM.sub.t]).sup.1/2]] ([YCHEM.sub.t]/[KSTOCK.sub.t]) + [B4[WL.sub.t] + B5[WM.sub.t] + 2B6[([WL.sub.t] x [WM.sub.t]).sup.1/2]]([YSULP.sub.t]/[KSTOCK.sub.t]) (2)

where

VC is real variable cost (1972 $'s),

WL is real wage rate (1972 $'s),

WM is index of real input materials' cost,

YCHEM is total production of chemical pulp in tons,

YSULP is total production of sulphate pulp in tons,

KSTOCK is the real capital stock (1972 $'s).

The materials factor demand equation is then derived from (2) via Shepard's lemma:(11)

[XM.sub.t] = [B2 + B3[([WL.sub.t]/[WM.sub.t]).sup.1/2]]([YCHEM.sub.t]/[KSTOCK.sub.t]) + [B5 + B6[([WL.sub.t]/[WM.sub.t]).sup.1.2]]([YSULP.sub.t]/[KSTOCK.sub.t]) (3)

where XM is real expenditure on materials (1972 $'s), and all other variables as defined above.

The original intent when modelling the cost function and associated factor demands was to permit the marginal cost of each pulp type to vary across markets. Unfortunately, the data lacked sufficient independent variation in sales quantities across markets over time to permit meaningful estimation when output was disaggregated any further than simply chemical pulp and sulphate pulp.

Supply Relationship

If firms are not price takers, their supply relationship is characterized by the equating of their perceived marginal revenue to marginal cost for any given good. The marginal revenue will depend upon the degree of competitiveness between producers in a market and the export good's demand elasticity. A well established literature in Industrial Organization [10] expresses this supply relationship for any given market as:

[P.sub.t](1 + [[Lambda].sub.t]/[[Eta].sub.t]) = [MC.sub.t]

or

[P.sub.t] = [MC.sub.t][[[Eta].sub.t]/[[Eta].sub.t] + [[Lambda].sub.t])] (4)

where

[[Eta].sub.t] is market demand elasticity,

[P.sub.t] is price of good,

[MC.sub.t] is marginal cost of good,

[[Lambda].sub.t] is an "index of competitiveness" which nests the two extreme market structures: perfect competition ([Lambda] = 0) and monopoly ([Lambda] = 1).

Adopting this methodology creates the following supply equations for each chemical pulp destination market i:

[P.sub.it] = MCCHE[M.sub.t][[[Eta].sub.i]/([[Eta].sub.i] + [[Lambda].sub.i])] (5)

where

[P.sub.it] is the pre transportation and shipping U.S. $ price of exports to market i at time t,

[[Eta].sub.i] is the elasticity of demand for U.S. goods in market i,

[[Lambda].sub.i] is the index of competitiveness of U.S. firms in market i,

[MCCHEM.sub.t] is the marginal cost of chemical pulp production, derived as [Delta][VC.sub.t]/[Delta][YCHEM.sub.t] from equation (2).

For the sulphate pulp markets, the supply equations are modelled as in (5) except that [MCCHEM.sub.t] is replaced with [MCSULP.sub.t]: [Delta][VC.sub.t]/[Delta][YSULP.sub.t] from equation (2).

In this study, as in most others, equation (5) will be estimated using market level data in which case [Lambda] can be viewed as a measure of the deviation of average price from marginal cost in a market which will narrow as competition between producers intensifies.(12) This can be seen by manipulating (4) to construct a Lerner Index:

L = (P - MC)/P = -[Lambda]/[Eta]. (6)

Equation (6) shows two sources of profit margin for an industry: noncompetitive behavior by firms ([Lambda] approaches 1) and/or inelastic demand ([Eta] approaches zero). One of the benefits of this study's estimation procedure is that it indicates how much of the pricing margin, or lack thereof, can be attributed to firms' noncompetitive behavior and how much arises from consumers' demand preferences.

There has been considerable policy interest in recent years regarding the impact of large exchange rate movements upon exporting firms' profit margins and pricing behavior in both the short and the long-run [6; 11; 13; 16; 19; 21; 27]. In this study, the impact of the large appreciation of the dollar upon U.S. exporters of wood pulp is examined by testing for statistically significant shifts in the value of [Lambda] or [Eta] over time. Equation (5) is modified through the use of a dummy variable interacted on either or both [Gamma] and [Eta] to test for structural breaks in the values of [Gamma] and [Eta] in the 1982-85 period.(13)

Demand Functions

For the chemical pulp markets, the demand for U.S. firms' goods in market i is modelled as (all variables in natural log form):

[Y.sub.it] = [[Omega].sub.i] + [[Beta].sub.i] x [Z.sub.it] + [[Eta].sub.i] x [p.sub.it] (7)

where

[y.sub.it] is quantity of sales in market i during period t,

[p.sub.it] is the pre transportation and shipping dollar price of U.S. pulp sold in market i during period t, deflated by the price of imported printing and writing paper,

[Z.sub.it] is a vector of exogenous market i demand shifters which includes-real GDP index, market i production of printing and writing paper, the pre transportation and shipping dollar price of non-U.S. chemical pulp imports in market i, deflated by the price of imported printing and writing paper, index of the nominal U.S./market i exchange rate in foreign currency units per $,

[[Beta].sub.i] is a vector of parameter coefficients associated with [Z.sub.it].

For the sulphate pulp markets, the demand for U.S. firms' goods in market i is modelled again as in (7) except that in the [Z.sub.it] vector of exogenous demand shifters the production of newsprint in market i is substituted for the production of printing and writing paper in market i; the sulphate pulp prices are deflated by the price of imported newsprint instead of imported printing and writing paper; and, the dollar price of non-U.S. sulphate pulp imports is substituted for its chemical pulp counterpart. Since the demand for wood pulp is a derived demand, the pulp prices are deflated by a proxy for the price of the final goods produced by each pulp type. Also, because of the log linear demand specification in (7), the elasticity of demand for U.S. pulp in market i is estimated as the parameter [[Eta].sub.i].

Thus, the complete structural model to be estimated is composed of the variable cost and materials factor demand equations (2) and (3), along with the market demand equations (7), and supply equations (5) for each destination market i which is modelled. Cross equation restrictions on parameter values link the supply equations with the factor market equations through the marginal cost estimates while the demand and supply equations are linked through the estimates of demand elasticity [[Eta].sub.i].

IV. Data

The data sources for each variable in the model are outlined in Appendix Table I.A. A detailed discussion of the data set's construction is available from the author upon request, but two points merit highlighting. First, insufficient independent variation in export quantities across markets over time precluded leaving each nation for which data was available to stand as a separate market. Instead, several key national markets were selected for each pulp type and the remaining national markets were then aggregated into regional markets using export quantities to each nation as the weight when constructing the regional variables.

A second potential concern was the issue of missing values for the export quantity series. This problem was addressed by only including a nation in the study if data on U.S. chemical pulp or sulphate pulp exports was available for every year from 1963-87. If there was no record of U.S. exports to the nation for any year in the sample period, the nation was not included in the study. Fortunately, the export country mix has been quite stable over time and this very restrictive assumption has had minimal effects on the final data set. In fact, the percentage of total exports actually included in the data set each year is approximately 90% as those nations which did not receive exports from the U.S. each year were very minor markets for U.S. exporters of wood pulp. Since the domestic sales quantity for each pulp type is calculated as the total production of pulp less exports accounted for by nations in the model, the domestic sales quantity is slightly overstated each year. The nations included in the analysis are listed in Appendix Table I.A.

V. Results

In order for the estimation of the econometric model developed in section III to be valid, the data itself must be stationary. Potential problems associated with estimating econometric models on non stationary data have been well documented and can include inflated [R.sup.2] and t-statistics as well as autocorrelation in the error terms [30, 247]. The results from Augmented Dickey-Fuller (ADF) tests, not reported here, indicated non stationarity was present in the original data series. To correct for autocorrelation problems with initial estimates using the original data, the data was quasi-differenced(14) and all reported results utilize the transformed data. In addition to eliminating the serial correlation in the error terms, transforming the data created stationary data series as the null hypothesis of a unit root was regularly rejected for the transformed variables in the model (ADF tests, not reported here).

Prior to estimating the complete structural model, a system comprised of the variable cost (2), materials demand (3), and supply (5) equations for each market of each product type was estimated. Eliminating the demand curves from the system permits an appreciably greater disaggregation of markets into specific country markets since both the number of parameters to be estimated and the non linearities of the system are reduced. The shortcoming of this approach, however, is that the supply equation is now [P.sub.it] = [MC.sub.it] x [MU.sub.i] where the mark-up parameter [MU.sub.i] is a function of both [[Eta].sub.i] and [[Lambda].sub.i] as described previously but the actual values of [[Eta].sub.i] and [[Lambda].sub.i] cannot be estimated. For both the chemical pulp and sulphate pulp markets, three different cases were estimated: 1) [MU.sub.i] is held constant across the entire sample for each market i but can vary across markets; 2) [MU.sub.i] can differ in the 1982-85 period in each market i and both the original mark-up and its change in 1982-85 can vary across markets; and, 3) alternative change in mark-up periods were tested to see if results are sensitive to the time period specification in part 2.

Thirteen chemical and ten sulphate markets are modelled. The system of factor market and quasi-supply equations was estimated using three stage least squares (3SLS) with White's correction for heteroscedasticity [53]. Table II contains the mark-up parameter estimates for the case where the mark-up was held constant over time. The mark-ups were statistically greater than one, implying pricing above marginal cost, in every market for both chemical and sulphate pulp exports. This result suggests that in the single equation analysis of sulphate pulp exports the lack of nonzero country effects in the European markets was due not to perfectly competitive pricing, but instead to a similar mark-up over marginal cost across the European markets. While export price mark-ups were greater than zero for each pulp type, within any given export market the margin on chemical pulp exports was greater than the pricing margin on sulphate exports. For chemical pulp, the Lerner index varied from 32%-42% in the European markets, from 30%-35% in the Latin American markets, and was 33% in the Japanese market. The sulphate margins were appreciably lower as the Lerner index varied from 14%-19% in the European markets, from 12%-30% in the Latin American markets, and was 19% in the Japanese market. It is possible that the above findings are not due to imperfect competition but to capacity constraints during high demand periods leading to pricing in excess of marginal cost.(15) To test for the role of capacity constraints in generating the positive pricing margin estimates, the model summarized in Table II was modified to allow shifts in the mark-up parameters during high capacity utilization periods.(16) These shift parameters, however, never were significant, implying that the mark-up estimates in the paper are not inflated by infrequent high prices during tight capacity periods.

Table III contains the key parameter results from the modified model where the mark-up [TABULAR DATA FOR TABLE II OMITTED] parameter could differ in the 1982-85 period of the high U.S. dollar. In this case, the results differ significantly for the two pulp types. For chemical pulp, the residual export market was the only market in which the reduction in the mark-up parameter was statistically significant. In the sulphate markets, however, the reduction in pricing margins was significant in eight of the ten markets. Moreover, the magnitude of the pricing margin reductions imply that during this period the entire margin was eliminated for U.S. sulphate pulp exporters who were pricing at marginal cost over this period. The ability of U.S. chemical pulp exporters to maintain their pricing margins during such an adverse exchange rate shock suggests greater market power for these firms than for those U.S. firms exporting sulphate pulp. The findings of significant reductions in mark-up in sulphate markets but not chemical markets was robust to minor changes in the mark-up period. If the period is made 1981-85, only two of the thirteen chemical markets, but six of ten sulphate markets, show a significant margin decline. For the 1982-86 period only one chemical market, but six sulphate markets, have a significant contraction of their export margins.

[TABULAR DATA FOR TABLE III OMITTED]

Initial specifications of the complete structural model included the variable cost and factor demand equations (2) and (3), several country specific market demand equations for both chemical pulp and sulphate pulp (7), and the associated country specific supply equations for both chemical pulp and sulphate pulp (5). Unfortunately, the data lacked sufficient country specific independent variation in export quantities and prices to permit estimation of such a large nonlinear system. Instead, the chemical pulp and sulphate pulp markets were analyzed independently of one another. In the chemical pulp analysis, the model was composed of the factor market equations and several country specific chemical pulp markets while the sulphate pulp markets were simply divided into domestic and total export markets. In this manner the model was closed as the sum of all sales quantities of chemical pulp and sulphate pulp equalled the total production of chemical pulp and sulphate pulp used in the factor market equations. The individual nations included in the chemical pulp markets are the dominant U.S. chemical pulp export markets with chemical pulp exports to these nations accounting for approximately 65% of total U.S. chemical pulp exports each year. The sulphate pulp markets were modelled in a manner similar to the chemical pulp analysis. The model included the factor market equations, several country specific sulphate pulp markets, a "residual" export market aggregating the remaining sulphate pulp export markets, and the chemical pulp markets which were divided into domestic and total export. While U.S. sulphate pulp export markets are more diffused than U.S. chemical pulp export markets, the individual sulphate pulp country markets do account for the major destination markets and represent approximately 40% of total sulphate pulp exports each year.

The model itself was estimated via three stage least squares with White's adjustment for heteroscedasticity to account for the obvious endogeniety problems in the estimating equations [53]. The endogenous variables were [y.sub.it] and [p.sub.it] for all i markets, YCHEM, YSULP, VC, and XM while the instruments in the 3SLS procedure were all of the exogenous variables: WL, WM, KSTOCK, and for each destination market i the various demand equation variables.

The key results of the basic model's chemical pulp market analysis are contained in Table IV where the parameter estimates for the demand elasticity [[Eta].sub.i] and the index of competitiveness [[Lambda].sub.i] are listed. The hypothesis of monopoly pricing behavior by firms, [[Lambda].sub.i] = 1, is rejected in every destination market. The hypothesis of perfect competition, however, also is rejected in six of the seven chemical pulp export markets and in the domestic chemical pulp market by the finding of nonzero [[Lambda].sub.i]'s. The implied Lerner index values are consistent with the prior findings from the joint factor market/quasi-supply analysis. As in the previous results, U.S. chemical pulp export margins were highest in the European markets with Lerner index values from 33%-56% while the Latin American margin was 26%, and the Japanese margin was 30%.

Next, the model was modified to permit [[Lambda].sub.i] to differ in the 1982-85 period. No evidence was found of a significant shift in [[Lambda].sub.i] for any of the markets so the results are not reported here. Similarly, the model was modified to permit [[Eta].sub.i] to vary in the 1982-85 period, but again no evidence of significant shifts was found. These results are consistent with the findings in Table IV.

The primary results of the sulphate pulp structural model analysis are listed in Table V for the basic model in which [[Eta].sub.i] and [[Lambda].sub.i] are constant over time. As in the chemical market analysis, the hypothesis of monopoly pricing by firms ([[Lambda].sub.i] = 1) is rejected in all markets. The evidence in support of widespread imperfect competition is weaker than in the chemical pulp markets though, as the null hypothesis of perfect competition ([[Lambda].sub.i] = 0) cannot be rejected in four of the five sulphate export markets modelled. One should be cautious, however, in drawing too many inferences from these results as the variance of the parameter estimates for [[Lambda].sub.i] are significantly larger than in the chemical pulp structural model results. Any conclusions to be drawn regarding the market structure of the sulphate pulp export markets largely should be confined to the results of the simpler joint factor market/quasi-supply system estimation in Table II.

VI. Summary and Conclusions

Based upon the results of a single-equation analysis of market power in U.S. wood pulp export markets, representative of prior work testing for imperfect competition in export markets, one would conclude that widespread imperfect competition exists in chemical pulp export markets. The single-equation analysis, however, does not provide clear support for either perfect competition or the presence of market power in U.S. sulphate pulp export markets. The difficulty is that [TABULAR DATA FOR TABLE IV OMITTED] the single-equation technique cannot differentiate price equals marginal cost pricing from price equals marginal cost plus a constant mark-up across markets pricing. Another weakness is that the results provide no evidence regarding the size of, or changes in, the export margins across markets.

In this study, the industry's factor and goods markets are modelled simultaneously by extending techniques first used in the domestic industrial organization literature. The findings indicate that export market power exists for both chemical pulp and sulphate pulp products, but that the chemical pulp export markets are less competitive. While positive export margins are found in each destination market for both pulp types, the chemical pulp margins exceed sulphate pulp margins in each case. In addition, chemical pulp exporters largely maintained their margins during the high dollar period from 1982-85 whereas sulphate pulp exporters entire pricing margin was eliminated during that time.

[TABULAR DATA FOR TABLE V OMITTED]

The findings of higher export margins for chemical pulp are consistent with other anecdotal evidence suggesting greater potential market power for U.S. chemical pulp exporters than for sulphate pulp exporters. First, fewer firms are involved in chemical pulp production. The 1987 Census of Manufactures reports only six firms engaged in chemical pulp production and eighteen firms engaged in sulphate pulp production within SIC 2611. In addition, strategic behavior by U.S. chemical pulp exporters is more likely because in most cases the U.S. share of total imports in any given market is appreciably higher for the chemical pulp exports than for the sulphate pulp exports. The U.S. quantity share of total chemical pulp and sulphate pulp imports for several major U.S. export markets are listed in Table VI for a few representative years. From the data it is clear that not only are there fewer U.S. chemical pulp exporters, but that they typically control upwards of twice as much market share in their export markets as compared to U.S. sulphate pulp exporters. Hence, the likelihood of U.S. firms engaging in various forms of strategic imperfectly competitive behavior seems more likely in the chemical pulp export markets.

Unfortunately, while the structural model estimated in this paper provides greater information regarding export market power than can be obtained from single-equation estimation, data limitations precluded using demand and cost specifications with nonconstant demand elasticities and marginal costs. Future work in this area should include efforts to develop data sets which permit marginal costs to vary across markets, and the elasticity of demand to vary with the exchange rate while simultaneously modeling the factor and goods markets equilibrium.

Table VI. U.S. Share of Total Imports by Pulp Type in Several Major
U.S. Pulp Export Markets

                   1970              1980              1987
Market         Chem   Sulphate   Chem   Sulphate   Chem   Sulphate

Belgium         11%     23%       34%     22%       13%      11%
France          45%     14%       38%     15%       58%      15%
U.K.            16%     13%       20%     15%        *       16%
W. Germany      49%     13%       63%     16%       56%      17%
Japan           80%     28%       85%     26%       67%      34%

While the above findings are most relevant to researchers studying wood products markets, the methodology developed contributes more generally to the literature testing for market power in export/import markets. This study shows that techniques developed in single market studies of market power can be adapted to a multiple markets framework. With multiple export markets, the model's structure is by necessity simpler than in many single market models, but reasonable estimates of the pricing margin over marginal cost can still be obtained. Moreover, the results suggest that the multi-product cost function may be useful when modelling other manufacturing export sectors. Trade data often is available at a level of disaggregation greater than the available factor market information for any given industry. Thus, modelling the sector with multiple outputs may provide more information on the competitiveness of an export sector than can be obtained from estimates based on more aggregated data. This study shows significant variation in pricing margins can exist across products within even a relatively homogenous disaggregated industry. In such cases, the multi-product approach reveals market structure insights missed when a more aggregated approach is used.

The author is indebted to Eric Bond, Mark Roberts, and an anonymous referee for many quality-enhancing comments on an earlier version of this paper. All remaining deficiencies are attributable solely to the author.

1. See Helpman and Krugman [24; 25] and Helpman [23] for an overview and synthesis of early work in this literature. For more recent work containing reviews of the literature, see Baldwin [6], Ethier, et al. [15], Krugman and Smith [37], Markusen [40], and Tybout [49].

2. One research tact has been to test if the degree of exchange rate pass-through in a market varies with the market's characteristics in a manner consistent with various theories of imperfect competition. Kreinen, Martin and Sheehey [34] examined, at the 4 digit SIC level, the change in U.S. import prices and quantities in response to exchange rate movements and found that market structure variables such as market concentration or advertising expenditures had little significance in determining the degree of pass-through. These results were consistent with Feinberg [17] and Fisher [18].

Another approach searches for evidence of price discrimination by firms across export markets. As noted by Krugman [36], some degree of imperfect competition must be present, along with sufficient barriers to arbitrage, if firms are able to price discriminate across various export markets for the same good, a practice known as 'Pricing to Market' (PTM). Studies by Krugman [36], Ohno [47], Hooper and Helkie [26], and Marston [41] find evidence of PTM by Japanese exporters but the results are much more ambiguous for the U.S. and European exporters.

3. Knetter examined exports of six different U.S. industries at the 7-digit level:

Dried and dehydrated onions, Breakfast cereal prepared for serving, Orange juice, not concentrated, Bourbon in containers less than 1 gallon, Snap-action switches, Refrigerator freezers over 13.5 cubic feet for household use.

4. See Pick and Park [48] for an application of Knetter's technique to U.S. exports of cotton, corn, soybeans, and wheat. See also related work by Knetter [31; 32].

5. Bresnahan [10] provides a review of developments in this area.

6. Efforts to model sulphite pulp as a separate output were not successful due to the high collinearity between sulphate and sulphite pulp prices and quantities.

7. Uusivuori and Buongiorno [52] examined the pass through of changes in the U.S. dollar to the prices of U.S. exports of 11 different wood products, including chemical pulp and sulphate pulp, to several major European countries and Japan. They conclude that it is an oversimplification to assume a competitive market structure in international forest products trade.

8. Knetter [33] contains a complete discussion of the hypothesis testing which can be done based on equation (1).

9. Bernstein and Mohnen [9] also reject long-run equilibrium in factor markets for capital when modelling the Canadian non-electrical machinery, electrical products, and chemical products industries. In this work, the industry is modelled by treating capital as a quasi-fixed input in the cost function and by also estimating a Euler equation for the accumulation of capital when there are adjustment costs incurred in changing the size of the capital stock. Morrison is a good source for a more complete discussion of this technique [42; 43; 44]. This approach was not adopted in the present paper because its parameter estimation requirements were too large for the data set given the emphasis on multiple export markets.

10. Hall's proposed specification of the multi-product multi-factor cost function was:

[Mathematical Expression Omitted]

where [y.sub.k] and [y.sub.t] give the output of goods k and l with T different types of goods so total output [Mathematical Expression Omitted], and [w.sub.i] and [w.sub.j] give the price of factor i and j with S different factors. Note that imposing separability upon the cost function sets [b.sub.ijkl] = 0 unless k = 1. Separability has been imposed on equation (2) which reduces the number of parameters to an estimatable level, but forces constant marginal cost upon the model. Alternative estimates of the cost function, however, always rejected the hypothesis of non constant marginal cost.

11. The labor factor demand equation is omitted from the model because specifying factor market behavior via the VC and XM equations yielded regression results superior to specifications which included the labor demand equation.

12. An alternative interpretation of [Lambda] is provided by Cowling and Waterson [12] who show that [Lambda] may be viewed as the market-share weighted sum of firm level conjectural variations over all firms in the market.

13. Ideally, [Lambda] and [Eta] would be nonconstant and functions of the exchange rate or other exogenous variables. No specifications were found, however, which were superior to simply assuming [Lambda] and [Eta] constant while allowing for a one-time shift in their values.

14. The procedure for generating the transformed data variables was:

i. Use the parameter estimates from the initial 3SLS estimation to generate the error residuals [e.sub.it] for each equation i.

ii. For each equation i, then estimate the correlation coefficient for the error terms as: [e.sub.it] = [[Rho].sub.i] x [e.sub.it-1]

iii. Then transform every variable [x.sub.i] in each equation i into: [Mathematical Expression Omitted].

iv. Use the transformed variables for estimating the system of equations.

See Judge, et al. [29] for a more complete discussion of the correction procedure.

15. Thanks are owed to a referee for developing this point.

16. The chemical and sulphate quasi-supply equations for each destination market i were changed to:

[P.sub.it] = [MCCHEM.sub.t] x ([MUCHEM.sub.t] + [Beta][1.sub.i] x [CHEMCAP.sub.t])

and

[P.sub.it] = [MCSULP.sub.t] x ([MUSULP.sub.t] + [Beta][2.sub.i] x [SULPCAP.sub.t])

respectively, where

[MCCHEM.sub.t] and [MCSULP.sub.t] as defined previously,

[MUCHEM.sub.i] ([MUSULP.sub.i]) are parameter estimates of the mark-up for chemical (sulphate) pulp in market i during non capacity constrained periods.

[Beta][1.sub.i] and [Beta][2.sub.j] are parameter estimates of the change in the mark-up for chemical (sulphate) pulp in market i during capacity constrained periods.

[CHEMCAP.sub.t] ([SULPCAP.sub.t]) is a dummy variable = 1 during "high" capacity utilization years for chemical (sulphate) pulp.

Various definitions of "high" capacity utilization were used such that CHEMPCAP and SULPCAP would = 1 for between 3 and 7 years in the sample (12%-28% of sample). Regardless of the capacity utilization cut-off used to designate capacity constrained years, one could never reject the hypothesis (5% level) that [Beta][1.sub.i] = 0 and [Beta][2.sub.i] = 0 for all i markets.

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