Life Expectancy of International Cartels: An Empirical Analysis

International Finance Discussion Papers Number 439

December 1992

LIFE EXPECTANCY OF INTERNATIONAL CARTELS: AN EMPIRICAL ANALYSIS

Jaime Marquez

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors.

ABSTRACT

This paper examines the empirical relation between market structure and life

expectancy for cartels that were active in international commodity markets

throughout this century. I consider two alternative empirical formulations and

estimate their parameters recognizing that durability cannot take negative

values. Both formulations predict that increases in either market shares or

intercartel concentration prolong life expectancy but disagree in the relative

importance of these two factors. The application of tests to discriminate among

the two formulations does not support constant-elasticity models.

Life Expectancy of International Cartels: An Empirical Analysis

1 Jaime Marquez

1. Introduction That cartels are short-lived is one of the most robust predictions of economic theory. Cheating is too great a temptation to resist and the ensuing price instability brings the coalition to an end. But why is it that some cartels last longer than others? Can cartels prolong their existence by increasing their share of the market and if so by how much? How important is cartel concentration in determining cartel durability? I address these questions using Griffin's data (Griffin, 1989) matching durability with indicators of market structure for international cartels.

The analysis begins in section 2 with a description of the data. Section 3 models a cartel's life expectancy as a function of its performance which is then linked to cartel concentration and market share. Section 4 describes the method for parameter estimation and offers an alternative specification to assess the sensitivity of the results. The evidence, shown in section 5, suggests that increases in market shares and cartel concentration prolong a cartel’s life expectancy. The relative importance of these two factors is model dependent but test results do not support constantelasticity models.

These findings are of interest because very little is known about the

relation between market structure and life expectancy. Indeed the reviews of

The calculations in this paper use LIMDEP version 5.0. I am grateful to William Greene for clarifying some of the functions of his software; to participants in seminars at the Federal Reserve Board and the U.S. International Trade Commission; to Paul Streaker for research assistance; and to Jon Faust, Michael Gibson, James Griffin, William Helkie, Dale Henderson, Doug Irwin, Michael Leahy, Matthew Pritsker, Stephen Salant, and Janice Shack-Marquez for several suggestions. The author is a staff economist in the Division of International Finance. The views expressed in this paper are solely the responsibility of the author and should not be interpreted as reflecting those of the Board of Governors of the Federal Reserve System or other members of its staff.

3 performance. First, advances in telecommunications could reduce cartels’ operational costs by facilitating the coordination of international activities. Second, United Nations’ programs stabilizing export revenues of developing countries could enhance cartel profitability by either controlling production (Adams and Behrman, 1978) or inducing free-rider effects.

Many of the historical cartel collapses shown in table 1 are followed by the emergence of another cartel in the same market. This phenomenon raises the question of whether cartels can improve their performance by avoiding previous mistakes made in their line of activity. Finally, the sample includes cartels that ended their operations in 1939 raising the question of whether the onset of worldwide hostilities, besides raising transportation costs and operational risks, brought a premature ending to these cartels.

To examine the role of these cartel-specific attributes, I add four dummy variables to the data set: DR which equals one for renewable products; DWII which equals one for cartels that initiated their operations before 1945; D39 which equals one for cartels expiring in 1939; and REPEAT, which equals K- 1 for cartels with K previous episodes of cartelization.-

Taking the dates of cartel activity as given, table 2 offers summary statistics for the full sample and the sub-groups mentioned above. On average, cartels last seven years but, as the moments of the distribution of durability indicate, this estimate is not representative of life expectancy. Cartels also differ in their performance and market structure. For example, the Lerner index varies from minus twelve percent to eighty percent with a mean of twenty-nine percent. Similarly, the average market share is sixtyone percent and varies from nine percent to one-hundred percent. Finally, the

Herfindahl index varies from twenty-nine percent to one-hundred percent.

The first observation of REPEAT is set to zero to treat uniformly the first episode across cartels regardless of their number of cartelization efforts.

3. Empirical Formulation :

I assume that cartels’ incentives to remain active are directly related to the gap between their profitability and the return on an alternative activity. Thus I postulate that

(1) E 5; — Bo + By E (my - Ry) 2 0,

where E denotes the expectation operator, 8, is the number of years of activity for the ith cartel, B, > 0, ms is the Lerner index of profitability, and R; is the rate of return of an alternative activity. I measure R, as the 4-6 month rate for U.S. commercial paper (see table 1), a choice based on the availability of 19th-century data. In all but five cases, the cartels listed in table 1 have Lerner indexes exceeding the alternative rate of return; for the five exceptions, durability is below its sample mean.

Ideally, equation (1) should relate life expectancy to the expected excess return over the life of the association -- that is, a lifetime analogue to m-R. The absence of such data precludes testing directly the validity of (1). As a result, appendix A develops testable assumptions showing a link between the ideal lifetime excess return and the observable excess return 7-R.

Even in the absence of these complications, estimating the parameters of (1) is difficult because no agreement exists on how to measure n (Weiss, 1971; Griffin, 1989; Schmalensee, 1989); the presence of cartels in table 1 with negative Lerner indexes underscores these measurement difficulties. To bypass them, I follow the work initiated by Bain (1951) and assume that a cartel’s performance depends linearly on its ability to coordinate production,

its price elasticity of demand, and idiosyncratic attributes:

(2) E T;, = A + aH? + ale, + a,DWII + a,DR + a,REPEAT + a,D39,

Investing in financial assets and earning R; is not the only alternative

to cartel members. For example, they might abandon the association and keep their line of business active. The rate of return in that alternative activity, however, should not be less than R, systematically.

5 where H, is the degree of cartel concentration (Herfindahl index) and 3 is the cartel’s demand price elasticity measured in absolute terms (see Geroski, 1988; Scherer and Ross, 1990). Greater cartel concentration facilitates coordinating the production levels needed to increase prices above marginal costs (a@,>0). Increases in €y> stemming from either the entrance of new firms or the introduction of substitute products, force cartel members to lower their prices and induce a decline in their profitability (a,<0).

Substituting (2) into (1) yields

bg (3) £E é, = 6, + 6,H, + One, + 6,DWII + 6,DR + 6,REPEAT + 6,D39 - A,R,,

which links life expectancy to market structure: If increases in cartel concentration or declines in price elasticity prolong life expectancy, then §,>0 and 6,<0. If developments in the postwar period expand cartel longevity, then @,<0. If having exploitation rights to sites of non-renewable products extends life expectancy, then 6,<0. If learning from previous cartel failures prolongs life expectancy, then 6,>0. Finally, if the onset of hostilities in 1939 forced cartels to end their operations, then 6,<0.

Estimating the parameters of (3) requires data on cartels’ demand price elasticities, which are either unavailable or measured very imprecisely. Recognizing that a cartel's price elasticity is inversely related to its share of the market, S;5 and that data on market shares are easier to obtain than data on price elasticities, I assume that é; 7 100/S, . This formulation allows €,; to be large for small cartels (S; + 0) and unity for large cartels

(S; +> 100). Substituting this assumption into (3) gives

(4) E 6, = 6, + 0,H. + 6,100/S; + @,DWII + 6,DR + 0,REPEAT + 6,D39 - A,R,.

Increases in market shares, by lowering the cartel’s demand price elasticity, widen the gap between prices and marginal costs enhancing the cartel's incentives to remain active (6,<0). The elasticities of life-expectancy with

respect to market share and cartel concentration are ~9,100/(5,S;) and

6 (04/2) (He /55), respectively. Because these elasticities vary with durability

and market structure, I report percentiles from their empirical distributions.

4. Econometric Estimation

Given that durability cannot be negative, I estimate the parameters of (4) using Amemiya's maximum likelihood estimator for truncated samples (Amemiya, 1973). This estimator rests on three assumptions. First, the

conditional life expectancy is a linear function of its determinants:

(5) E(6,1X,) = @'X, = Oo+ 0 His 6,100/S,+ @,DWII+ 0,DR+ 0,REPEAT+ 0,D39- £,R,,

where x, is the vector of explanatory variables and @’ = (6, ... 0, -B,) is a vector of unknown parameters.

Second, the dispersion of durability increases with life expectancy: (6) var(s,|X,) - [exp(o') - 1] [@’X,]’, where o is an unknown parameter. Third, the conditional distribution of durability is (7) . Iné, ~ N(uy, 0), where By = 1n(@’X,) - bs 0. Other distributions are available (see Amemiya, 1973), but the log-normal has a tractable likelihood function that facilitates

testing whether the estimation residuals are normal (Jarque and Bera, 1980),

and it ensures that estimates of life expectancy are positive: A A A2 A A = -_ , = , E(6;|X,) exp(u; +o) = exp[1n(6 X,)] @'X, > 0. To examine the robustness of the results to model formulation, I use (8) 1né,= not ny 1nH*+ N21n(100/S;)+ mgDWII+ 9,DR+ ,REPEAT+ ,D39+ 9,1nR,+ v,,

2 where v7 NCO, o,,)- Equation (8) retains the assumed normality of the logarithm of durability to avoid negative estimates of life expectancy. But,

in contrast to the log-normal formulation, (8) assumes constant elasticities.

I estimate the parameters of (8) with ordinary least squares (OLS).

5. Empirical Results

The coefficient estimates from the log-normal formulation (eqs. 5-7) reveal several features. First, increases in market shares and cartel concentration have positive, significant, and robust effects on cartels’ life expectancy (table 3); increases in the interest rate lower life expectancy but this effect is not very significant. Second, life expectancy is significantly shorter for cartels that initiated their operations before 1945 than for those that initiated operations afterwards. Similarly, life expectancy is shorter for cartels in renewable products than for those in non-renewable products; other cartel-specific attributes are not significant. Third, the estimation residuals are consistent with normality. Finally, predicting life expectancy using only the mean of durability (model 6) entails a loss of information relative to models allowing a role for economic theory. But as found before (Weiss, 1971), the models’ explanatory power is low; model 3 has the largest R’ (0.29) and the smallest number of parameters supported by the data.

The OLS estimates from (8) suggest that increases in market shares have positive and significant effects on life expectancy (table 4), which is consistent with the evidence from the log-normal formulation. Increases in cartel concentration also increase life expectancy, but this effect is not very significant. Similarly, increases in interest rates do not have a significant effect on life-expectancy. The postwar dummy DWII has a negative sign and is the only cartel-specific attribute with a significant effect. The estimation residuals are consistent with normality but the Rs are lower than those of the log-normal specification; model 4 has the largest R’ (0.18) and the smallest number of parameters consistent with the data.

The evidence shown thus far indicates that both formulations predict a direct association between life expectancy and either market share or cartel concentration. Stated in terms of elasticities, however, the results suggest that market shares are relatively more important in the log-linear case than in the log-normal formulation (table 5). Moreover, the log-linear

specification suggests that the relation between life-expectancy and

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Table 5 Life-Expectancy Elasticities

Log-linear ——________Log-normal

25% Median 15% Market Share 0.678 0.177 0.354 0.863 cartel concentration 0.348 0.351 0.519 1.090 Degree of Homogeneity 1.026 0.528 0.873 1.953

Source: model 4 for log-linear (table 4) and model 3 for log-normal (table 3).

its determinants is homogeneous of degree one whereas the degree of homogeneity for the log-normal case varies from 0.53 to 1.95.

Choosing between log-normal and log-linear formulations needs to recognize that the models do not nest each other because the logarithm of a sum (log-normal) is not equal to the sum of the logarithms (log-linear). Thus

I apply MacKinnon’s method (MacKinnon, 1983) to

>

(9) 5 > Fo? = Fo ig ~ S41) + Fig ¥o9 + Kio »

(10) Ce Hy (iq - by) + Fy Yor * a>

where by is the prediction from the jth formulation (j=0 for the log-normal, j=l for the log-linear); Py is a vector of partial derivatives of bij with respect to 8; evaluated at 953 and “ij is a disturbance.

MacKinnon's method focuses on the informational content of each formulation. Thus if the log-linear specification adds information to that already embodied in the log-normal formulation, then 410 ~ 0. Alternatively, if the log-normal formulation adds information to that already present in the log-linear specification, then Yi ~ 0. Based on least squares, the tstatistic for the null hypothesis that 410 -0 is 0.5 which means that the loglinear specification does not add information to that already contained in the log-normal formulation. The t-statistic for the null hypothesis that Yi =0 is 1.8 which indicates that the log-normal formulation has information not

contained in the log-linear specification, This result suggests against

explaining life expectancy with a constant-elasticity model.

6. Summary

This paper offers an empirical analysis of the relation between life expectancy and market structure for a sample of cartels operating in international commodity markets throughout the last one-hundred years. The evidence suggests that increasing market shares and cartel concentration prolongs life expectancy, a finding robust to model specification. The relative importance of these two factors is model dependent, but the evidence

does not support constant-elasticity models.

10 Appendix A: Derivation of Equation (1) I assume that cartels are active for as long as they perceive the association to be profitable:

(Al) E6,=6) +6, EN, ,

where E denotes the expectation operator, 85 is the number of years of activity for the ith cartel, and ql, is the associated present, discounted value of excess profits per unit of output (excess relative to the return of an alternative activity). By being an ex-ante and lifetime measure of excess profitability, I is hard to measure and data for it are not publicly available. Thus what is needed is a list of testable assumptions that allow linking the ideal II to the observable excess return used in equation (1), m-R. To this end, let P be the present, discounted value of the stream of

excess profits over time:

(a2) Pm TCP - me - oc), /(1+p)" , t=

where Qe is the quantity of output sold at time t, Py is the price charged by

the cartel, mc, is the cartel’s aggregate marginal cost, oc, is the

opportunity cost per unit of output, and » is the constant discount rate. To

simplify the analysis, I express (A2) as ~ t o« t (A3) P ~ 2 ee me, [(p, - mce,)/me, - oc,/me,}/(1+9) = Fe me, ("-R),/(1+9) ",

I also assume that the cartel’s

where m7 (p,-mc,)/me, and R. = oc, /me

taggregate production function exhibits constant returns to scale, implying

that marginal costs are constant and equal to mc. Moreover, I assume that

foe)

(a4) Pomme Y (CEQ + u,)(E(r - R) + e.)1/(+@)", t=

where EQ is the per-period, expected level of sales, E(m - R) is the expected excess profit rate per period; and both uw. and e, are random disturbances with

the following properties: E(u, e,) = 0 Viet; E(e, e,) = 0 Vjxt; E(u, u,) = 0 Vjxt;

E(u, e,) = 9; E(e, e,) =o, 7 E(u, u.) = a.

11 Both the nature of the cartel's aggregate production function and the assumptions about the time series of output and prices. can be tested although

I do not have the necessary data.

‘Given these assumptions, the expected value of P equals

(A5) B(P) = me E{ } EQ E(n-R)/(14p)* + T BQ ep/(1+)" + t= t=

+ LY ue(e - R)/(+~)" + Y ue /(1t9)*) t=0 t=0

-mce J EQ E(m-R)/(1+9)" + JY E(u,e,)/(1+9)* t=0 t=0

= mc [(1l+p)/p] EQ [E(x-R) + p/EQ]. The expected, present discounted value of excess profits per unit of output is (A6) E(P)/EQ = EM = me [(1+p)/p] [E(x-R) + p/EQ]. If p/EQ is close to zero, then (A7) . EW= me [(1+~)/p] E(x-R). Substituting (A7) into (Al) yields (A8) E 6; = Bo + B, me [(1+p)/p] E (x, - Ry)= Bo + By E (m, - Rj), which is equation (1).

To assess the extent to which the data in table 1 support the view that 8B, > 0, I apply Amemiya’s maximum likelihood method for truncated samples (see section 4) to (A8) and find that 8, = 0.088 with a t-statistic of 2.03,

which is statistically significant.

12 References

Adams, F. G. and J. Behrman, 1978, Econometric Modeling of World Commodity Policy (Lexington, MA: Lexington Books).

Amemiya, T., 1973, "Regression analysis when the variance of the dependent variable is proportional to the square of its expectation," Journal of the American Statistical Association, 68, 928-934.

Bain, J., 1951, "Relation of profit rate to industry concentration: American manufacturing, 1936-1940," Quarterly Journal of Economics, 65, 293-324.

Baxter, N. and J. Cragg, 1970, "Corporate choice among long-term financing instruments," Review of Economics and Statistics, 52, 225-235.

Bothwell, J., T. Cooley, and T. Hall, 1984, "A new view of the market structure-performance debate," The Journal of Industrial Economics, 32, 397-417.

Cave, J. and S. Salant, 1992, "Cartel quotas under majority rule," mimeo.

Eckbo, P., 1976, The Future of the World Oil Market (Cambridge, MA: Ballinger).

Geroski, P., 1988, "In pursuit of monopoly power: Recent quantitative work in industrial economics," Journal of Applied Econometrics, 3, 107-123.

Griffin, J., 1989, "Previous cartel experience: Any lessons for OPEC?," in L. Klein and J. Marquez (eds.) Economics in Theory and Practice: An Eclectic Approach (Dordrecht: Kluwer Academic Press).

Jacquemin, A. and M. Slade, 1989, "Cartels, collusion, and horizontal merger," in R. Schmalensee and R. Willig (eds.) Handbook of Industrial Organization, vol. II (Amsterdam: North-Holland).

Jarque, C. and A. Bera, 1980, "Efficient tests for normality, homoscedasticity, and serial independence of regression residuals," Economic Letters, 7, 149-160.

MacKinnon, J., 1983, "Model specification tests against non-nested alternative," Econometric Reviews, 2, 85-110:

Miller, J. (ed.), 1962, Competition, Cartels, and Their Regulation (Amsterdam: North-Holland).

Scherer, F. and D. Ross, 1990, Industrial Market Structure and Economic Performance (Boston: Houghton Mifflin Company).

Schmalensee, R., 1989, "Studies of structure and performance," in R. Schmalensee and R. Willig (eds.) Handbook of Industrial Organization, vol. II (Amsterdam: North-Holland).

Suslow, V., 1991, "Cartel contract duration: Empirical evidence from international cartels," RAND Journal of Economics, forthcoming.

U.S. Department of Commerce, 1989, Historical Statistics of the United States: Colonial Times to 1970 (New York: Kraus International).

Weiss, L., 1971, "Quantitative studies of industrial organization," in M.

Intriligator (ed.) Frontiers of Quantitative Economics (Amsterdam: North-Holland).

IFDP NUMBER

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International Finance Discussion Papers TITLES

1992 Life Expectancy of International Cartels: An Empirical Analysis

Daily Bundesbank and Federal Reserve Intervention and the Conditional Variance Tale in DM/$-Returns

War and Peace: Recovering the Market’s Probability Distribution of Crude Oil Futures Prices During the Gulf Crisis

Growth, Political Instability, and the Defense Burden

Foreign Exchange Policy, Monetary Policy, and Capital Market Liberalization in Korea

The Political Economy of the Won: U.S.-Korean Bilateral Negotiations on Exchange Rates

Import Demand and Supply with Relatively Few Theoretical or Empirical Puzzles

The Liquidity Premium in Average Interest Rates

The Power of Cointegration Tests

The Adequacy of the Data on U.S. International Financial Transactions: A Federal Reserve Perspective

Whom can we trust to run the Fed? Theoretical support for the founders views

Stochastic Behavior of the World Economy under Alternative Policy Regimes

Real Exchange Rates: Measurement and Implications for Predicting U.S. External Imbalances

Please address requests for co

13

AUTHOR(s)

Jaime Marquez

Geert J. Almekinders Sylvester C.W. Eijffinger

William R. Melick Charles P. Thomas

Stephen Brock Blomberg

Deborah J. Lindner

Deborah J. Lindner

Andrew M. Warner

Wilbur John Coleman II Christian Gilles Pamela Labadie

Jeroen J.M. Kremers Neil R. Ericsson Juan J. Dolado

Lois E. Stekler Edwin M. Truman Jon Faust

Joseph E. Gagnon Ralph W. Tryon

Jaime Marquez

pies to International Finance Discussion Papers,

Division of International Finance, Stop 24, Board of Governors of the Federal

Reserve System, Washington, D.C.

20551.

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International Finance Discussion Papers

TITLES 1992

Central Banks’ Use in East Asia of Money Market Instruments in the Conduct of Monetary Policy

Purchasing Power Parity and Uncovered Interest Rate Parity: The United States 1974 - 1990

Fiscal Implications of the Transition from Planned to Market Economy

Does World Investment Demand Determine U.S. Exports?

The Autonomy of Trade Elasticities: Choice and Consequences

German Unification and the European Monetary System: A Quantitative Analysis Taxation and Inflation: A New Explanation

for Current Account Balances

1991 A Primer on the Japanese Banking System Did the Debt Crisis Cause the Investment Crisis?

External Adjustment in Selected Developing Countries in the 1990s

Did the Debt Crisis or the Oil Price Decline Cause Mexico's Investment Collapse?

Cointegration, Exogeneity, and Policy Analysis: An Overview

* The Usefulness of P Measures for Japan and Germany

Comments on the Evaluation of Policy Models

Parameter Constancy, Mean Square Forecast Errors, and Measuring Forecast Performance: An Exposition, Extensions, and Illustration

Explaining the Volume of Intraindustry Trade: Are Increasing Returns Necessary?

14

AUTHOR(s)

Robert F. Emery

Hali J. Edison William R. Melick

R. Sean Craig Catherine L. Mann

Andrew M. Warner

Jaime Marquez

Gwyn Adams Lewis Alexander Joseph Gagnon

Tamim Bayoumi Joseph Gagnon

Allen B. Frankel Paul B. Morgan

Andrew M. Warner

William L. Helkie David H. Howard

Andrew M. Warner

Neil R. Ericsson

Linda S. Kole Michael P. Leahy

Clive W.J. Granger Melinda Deutsch

Neil R. Ericsson

Donald Davis