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Estimation of price policies in Senegal An empirical test of cooperative game theory
Journal of Development Economics 35 (1991) 49-67. North-Holland
Estimation
of price policies in Senegal
An empirical test of cooperative game theory* John C. Beghin North Carolina State University, Raleigh, NC 27695-8110, USA
Larry S. Karp University of California, Berkeley, CA 94720, USA Received April 1989, final version received September 1989 Abstract: A game-theoretic framework rationalizes the political economy of food and agricultural price policies in Senegal. Policies are the outcome of a cooperative bargaining process among three archetypal players: a farmer growing cash and staple crops, an urban consumer buying imported cereals, and a government marketing board intervening in agricultural markets. The game is estimated and the bargaining strength of the players is recovered. The axioms underlying the game are tested to discriminate among various bargaining game solutions. The symmetry and efftciency axioms are rejected.
1. Introduction Many African countries are characterized by highly distorted agricultural and food markets. Typically, urban staples are subsidized, and producers of export crops are taxed on their output and subsidized for their input purchases. These policies have been criticized because of their negative impact on economic efficiency and growth [Scandizzo and Bruce (1980), Agarwala (1983)]. The standard recommendation involves removal of agricultural distortions and an alignment on world prices. African governments have not followed these policy recommendations because of their high political cost [Cleaver (1985), Bates (1981)]. Many countries that tried to reduce food subsidies faced political unrest, and have had to compromise with urban groups. The analysis on which the proposed reform is based fails to incorporate the political economy of food and agricultural price policies. The assumption of free manipulation of these policy instruments is inappropriate in most African countries. Bates argues that many governments (e.g., Ghana, Senegal) compromise with different social groups to gain their legitimacy. Agricultural policies are *We thank John Harsanyi and Irma Adelman for their comments. 0304-3878/91/%03.50 0 1991-Elsevier
Science Publishers B.V. (North-Holland)
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J.C. Beghin
and L.S. Karp,
Estimation
of price
policies
in Senegal
affected by the relative political strength of social groups, resource constraints, and government objectives. Policy decisions attempt to reconcile the conflicting interests of urban consumers, farmers, and bureaucratic institutions. The resulting policy mix creates inefficiencies and undermines growth. Bates’ thesis, implicitly game-theoretic, is supported by detailed descriptions of the policies in specific countries but lacks a formal model and quantification. Policies in African countries may appear more coherent when viewed in a political-economic framework. Price policies generate revenues needed to sustain governments and their large administrations. These governments do not use their monopoly/monopsony power fully, since retaliation by socioeconomic groups can destroy the rent-generating mechanism. Farmers can respond by changing their output and crop patterns, smuggling, and defaulting on debt payments as potential threats against low producer prices. Urban consumers can retaliate against high food prices, undermining the government through voting, rioting, and labor unrest. Market interventions, essential to the survival of the government, reflect the relative political strength of the economic groups affected by the policies. We develop and test a model of endogenous food and agricultural price policies that rationalizes the distortions observed in many African countries. The theory is based on a game-theoretic bargaining model and is applied to the political economy of the agricultural and food price policy regime that prevailed in Senegal from 1960 to the early 1980s.’ The model is applicable to other countries with institutions similar to those of Senegal. The game involves three representative players: farmers producing export and staple crops, urban dwellers consuming imported cereals, and a small set of institutions intervening in agricultural and food markets. The Senegalese case illustrates an archetypal situation, since farmers are taxed on their cash crop, fertilizer use is subsidized, taxes on urban cereal consumption have been moderate or negative, and food and agricultural export and import markets are entirely controlled by a few governmental institutions. The model is based on the theory of cooperative bargaining games [Harsanyi (1977), Thomson (1981)]. The first-order conditions for solution of the game are used to derive and estimate econometrically the endogenous bargainingpower coefficients of the three players. These bargaining-power coefficients can be interpreted as the weights a fictitious social planner puts on the welfare of pressure groups when making policy decisions. A number of solutions to bargaining games have been proposed. Their underlying axioms are different but most seem reasonable. The axioms underlying the class of solutions used in our model are examined and tested empirically. This ‘In the early 1980s international donors imposed structural reforms that changed Senegalese public institutions and policies. Cash crop prices were increased and private groundnut traders were allowed, and urban consumer prices were raised.
J.C. Beghin and L.S. Karp, Estimation ojprice policies in Senegal
51
provides evidence to distinguish which type of cooperative equilibrium is more likely to describe a particular situation. Theoretical comparison of the candidate solutions is inconclusive [Friedman (1986)]. Our empirical results suggest that the symmetry axiom common to many solutions does not hold for Senegal. This provides support for asymmetric bargaining models [Roth (1979), Binmore, Rubinstein and Wolinsky (1986)]. The asymmetric game enables us to decompose the bargaining power of the players into endogenous (determined within the game) and exogenous (predetermined by factors independent of the game) bargaining power. We interpret the asymmetry of the Senegalese game as indication of urban bias of the policies. The urban consumer has a stronger exogenous bargaining power but weaker endogenous bargaining power than the farmer. Price policies appear to have favored the urban sector compared to agriculture. The concept of endogenization of market interventions is not new. The revealed preference approach [Rausser and Freebairn (1974), McFadden (1975, 1976), Sarris and Freebairn (1983)] explicitly acknowledges the existence and influence of pressure groups in the policy decision-making process. The government maximizes a weighted objective function reflecting the welfare of lobbying groups, and reveals its preferences (the weights) through its choice of policies. The revealed preference approach does not offer a formal structure of the political economy on which the government objective function is based. Game theory remedies that shortcoming by modelling the bargaining process among social groups [Harsanyi (1963), Zusman (1976)]. The weighted objective function of the revealed preference model is intrinsic to the cooperative bargaining game solution; the weights express the bargaining power of the players. The game-theoretic model provides more structure and therefore more prior information than the revealed preference model. This is a practical advantage in empirical work. The first-order conditions of both the cooperative game and the weighted objective function can be estimated in a system in which restrictions can be imposed and tested. The game-theoretic framework is instrumental in investigating the issue or urban bias of the policies implemented in Senegal. The next section describes the relevant Senegalese markets and policies and motivates the game-theoretic approach. The third section presents the cooperative bargaining model with its axioms. Complementarity between the game theoretic and the revealed preference approaches is emphasized. Econometric estimation of the game follows in the next section. The bargaining power structure is recovered, We also test the axioms of symmetry and joint efficiency. Symmetry is rejected; the asymmetry of the game is associated with the urban bias of the policies. In the same section we test the efficiency of the price policies and propose more effective interventions. Conclusions summarize the contribution of the paper. An appendix, available upon request, contains the time series data, estimation of the
52
J.C. Beghin
and L.S. Karp,
players’ payoff functions, policies.
Estimation
of price
and their derivatives
policies
in Senegal
with respect to the price
2. Trade and price policies in Senegal This section summarizes the major policies that affected the production of groundnuts and millet and the urban consumption of wheat and rice for the period 1960 to 1980. Groundnuts and millet are the major crops of Senegal. Production of rice, maize and cotton is marginal compared to that of groundnuts and millet. Groundnuts are the largest agricultural source of foreign exchange for Senegal; millet is the principal rural staple crop; rice and wheat products are the major urban staples. Other commodities (sugar, oil) are also important but have much smaller expenditure shares than rice and wheat and are not exclusively urban. Farmer cooperatives, used to modernize groundnut production and marketing, have been active since the early 1960s. During the same period, private groundnut traders were rapidly replaced by a monopsonistic marketing board. In 1980 France insisted on dissolution of the marketing board as a condition to providing financial assistance to Senegal. From 1962 to 1980 the marketing board announced ofIicia1 prices to the farmers before the beginning of the planting season. The producer price has been stabilized below world price. The estimated groundnut export tax averaged 46 percent of the world price for the period 1960-1980. The prices are decided by the Comitt des Grands Produits, a government committee on which cooperatives are represented. Political stability in rural areas relies on the hegemony of Moslem leaders who are important groundnut producers. Their strong and organised political power (Mouride and Tidiane brotherhoods) helps the farm sector to obtain more favorable prices than those corresponding to full monopsony power of the marketing board. Millet and groundnut production compete for the land and labor, for which there are virtually no markets [Braverman and Hammer (1986)]. The marketing board had no substantial involvement in millet, which is essentially a non-traded staple crop consumed in the countryside. Producers make simultaneous decisions concerning the supply of groundnuts and millet and the demand for fertilizer. From 1964 to 1980 the marketing board was in charge of the agricultural credit system, selling fertilizer and equipment at subsidized prices to farmers. Input subsidies were made to offset the effects of the output tax on groundnut supply. The credit system was abolished in 1980 when the marketing board was dissolved. The average subsidy on fertilizer was 56 percent of the factory unit cost for the period considered in the paper. Rice is the major imported cereal and is consumed in urban areas. Its retail price is fixed by law; although in most years the price has been
J.C. Beghin
and L.S. Karp,
Estimation
of price
policies
in Senegal
53
moderately above import cost, rice has been subsidized when unexpected increases in world prices occurred. These sudden increases have been passed on progressively to consumers. From 1960 to 1980, the estimated average tariff on rice was 19 percent of the import unit cost. Wheat is not produced in Senegal; it is imported by two authorized millers. The annual quota for wheat imports has never been binding. The two millers were subsidized enabling them to sell flour below cost to bakers until 1977. The price of bread is also fixed by law at a very low level. Wheat consumption, which is exclusively urban, received an average subsidy of 13 percent for the 20-year period. The threat of political unrest is a primary reason for these low urban consumer prices in Senegal [Bates (1986, p. 33) Waterbury and Gersovitz (1987, ch. 7)]. Three important interest groups have been regularly consulted on consumer price policies. These groups, CNTS (workers’ union), CES and GBES (economic groups linked to the main political party), represent private and parapublic urban workers and employees. 3. A cooperative game-theoretic framework A n-person cooperative game is assumed for two reasons. First, despite its simplicity, this type of game is appropriate to approximate more elaborate sequential bargaining games [Binmore, Rubinstein and Wolinsky (1986)]. The bargaining process between pressure groups and the policy maker often leads to enforceable agreements that render the bargaining process cooperative [Shubik (1982)]. The repeated nature of political-economy games strengthens the use of cooperative solutions. Fudenberg and Maskin (1986), and Friedman (1986, ch. 3) have shown that the cooperative outcome is plausible in repeated non-cooperative games because the repetition induces a self-enforcement mechanism. The second reason is due to the informal and institutional evidence provided by the Senegalese case to make the use of cooperative bargaining games justifiable. Senegalese society is based on a social consensus (‘la paix sociale’ dear to Senegalese policy makers) without overt coercion. The economic game among the three players has been repeated over the years with no indication of players breaking the consensus. As mentioned above, the price policies have been negotiated with formal consultation of interest groups and have been respected. This negotiation process suggests that all agents behave strategically and that none of them is in a position to set policy unilaterally. Therefore a cooperative bargaining model seems more appropriate than a Stackelberg-Cournot approach. Several solution concepts exist for cooperative games. We use the class of solutions based on reference points [Thomson (198 l)] defined as payoffs to which players find it natural to compare any proposed compromise. The
54
J.C. Beghin
and L.S. Karp,
Estimation
of price
policies
in Senegal
Nash conflict point is an example of reference point. Players might compare proposed compromises not only to the conflict point but also to other potential payoffs such as the point of minimum expectation or a convex combination of the two. To keep the empirical study flexible, we do not specify which reference point the players use. We assume that the payoff set and its frontier depend on a vector, z, of exogenous variables (e.g., world prices, exchange rate). Changes in the economic environment cause changes in the welfare possibilities, the players’ bargaining power, and the equilibrium strategies. The game can be seen as a sequence of static cooperative games with a different payoff set at every period. However, we assume that the reference point is not affected by exogenous shocks. This asumption is necessary because of the small size of the data set but is not extremely restrictive. For instance, the payoff frontier, H, may shift without affecting the point of minimum expectation or the disagreement point, d. Thomson (1981) and Friedman (1986) discuss the four axioms underlying the game; these are analogous to the axioms underlying the Nash game (1953) but are defined with respect to reference point rather than conflict point. The axiom of joint efficiency, or strong rationality, requires that the solution to the game, CV* =(CV:, CVY, . . . , CVX), lie on the upper boundary, H, of the payoff space, P; CL’: is defined as the utility of player i in equilibrium. The axiom of linear invariance states that the solution to the game obtained by a positive a&e transformation of players’ utility functions is the positive affine transformation of the solution to the original game. The axiom of symmetry insures that indistinguishable players receive the same payoff. The last axiom, the independence of irrelevant alternatives, says that excluding a point from P other than the solution or the reference point, does not alter the solution to the game. If the reference point, g(P, d), satisfies certain regularity conditions [Thomson (1981)], the solution to the cooperative game maximizes the modified Nash product
(1) where CV=(CV,,CV,,..., CV,) is an element of the set P(z). If P is compact and convex, the solution, CV*, is on the frontier, H, and satisfies dZ)i(CJ’:
-g(P, d)i) =~(z)j(CVr
-g(P, d)i)
for
all i, j;
(2)
where a(~)~= aH(CV*, z)/aCI$ The functions a(~)~ denote the bargainingpower coefficients of the players. They are normalized to sum to one. If the payoff set, P, is convex, maximizing the Nash product is equivalent to maximizing the weighted sum of utilities, w
J.C. Beghin
and L.S. Karp,
Estimation
of price
policies
in Senegal
55
(3)
First-order conditions in strategy space can be derived by maximizing either the welfare function (3) or the Nash product (1). Define sf as the kth strategy available to the players, then the necessary conditions for a solution are ,$i a(z),T=O
for
all k.
(4)
Urban consumers and farmers are utility maximizers; the negative of the compensating variation is used as their money metric utility function. The marketing board maximizes net tax revenues from the sales of rice, wheat and fertilizer and from purchases of groundnuts. Its payoff function is the change in tax revenues from the current level to the level in the reference period, 1960. The indirect utility function of the representative farmer is Ul
= ~,hll,
P-m
MP,,
Pm,
Pf,
ZJ
-
Cl),
(5)
pg, and pt are the price of millet, the price vector for where P,,,, P-,,,, consumption goods other than millet, the producer price of groundnuts, and the producer price of fertilizer. The restricted profit function, m,, minus the cost of implementing conflict strategies, CL, constitutes the net income of the farmer. At the cooperative solution C, is equal to zero, since conflict strategies are not used. The cooperative strategy involves political support; no monetary reward is given to the policy maker. The vector zl, a subset of z, contains exogenous variables affecting the profit function. We obtain the supplies of groundnuts and millet, qi, and qk, and the demand for fertilizer, qt, b y applying Hotelling’s lemma to the profit function, m,. The farmer does not consume groundnuts. Roy’s identity gives the farmer’s demand for millet, 4:. The negative of the compensating variation is
(6)
where m, and pm refer to the current period, and rn: and p: are their counterparts in the reference period; el is the expenditure function of the farmer. We do not consider changes in the price p-,,, and assume that the compensating variation and millet demand depend only on the price of millet
56
J.C. Beghin
and L.S. Karp,
Estimation
of price
policies
in Senegal
and income.* Millet supply equals demand, since millet is a non-traded commodity. The millet market equilibrium condition is totally differentiated with respect to changes in price policies ps and pf to yield the comparativestatics of the millet equilibrium price for changes in price policies (dp,,,/dp, and dp,,,/dp,). These general equilibrium effects are included when considering the impact of the policies pg and Pf on the payoff functions. A typical urban consumer has an indirect utility function, U,, with consumption prices and income as arguments:
with pr, pw, ~t-~, -WI defined as the prices of rice, wheat products, and other goods. Income of the urban consumer is equal to wage income m2, assumed exogenous, minus the cost of applying conflict strategies C2 (e.g., cost of rioting or striking). At the cooperative equilibrium, C2 is equal to zero because the threat strategies are not implemented. We assume that the demands of rice and wheat depend on rice and wheat prices and on income, and are independent of P[-~, +. Roy’s identity yields cereal demands, q:, and q$ The negative of the compensating variation is
(8)
-mm,+C,+m”,],
with superscript o corresponding to the reference period and e2 denoting the expenditure function of the urban consumer. The marketing board maximizes the sum of net tax revenues in the four markets under the constraint of the bargaining process. This assumption does not specify how the surplus generated through taxes is allocated (e.g., investment or maintenance of bureaucracy). The marketing board can both extract and transfer surplus under this assumption depending on the power structure among players.3 The tax revenue function, TR, is TR = (v,
- p&q; + (pf - w&G + (P, - wp&:
+ (P, - WpJd - & -
B2,
(9) where
wpI,
wpr,
wp,
are the world prices of groundnuts,
rice and wheat, and
ZThe compensating variation of the farmer is independent of p-,,, under the assumption of separability in utility derived from millet and all other goods. For the urban consumer, we assume that the marginal rate of substitution between rice and wheat does not depend on other prices. Under this assumption the urban consumer’s compensating variation depends on wheat and rice prices and income. 3We tried alternative specifications in which the marketing board cares about income distribution as well as its tax revenues. Estimation of this specification gave nonsensical econometric results (i.e., some bargaining power coefftcients were negative).
J.C. Beghin
and L.S. Karp,
Estimation
of price
policies
in Senegal
51
wp, is the ex-factory price of fertilizer. Variables B, and B, represent the cost to the marketing board of being in conflict with farmers (B,) and urban dwellers (BJ. The payoff function of the marketing board, CV,, is the change in tax revenues when prices move from their reference to their current level or Cv,
= Wpg,
pf, pr, P,)
- TR(P;,
PP, P;, ~3.
The necessary and sufficient conditions for a solution are applied to the Senegalese case. The strategies of the marketing board are the four price Farmers and urban dwellers have political policies pg, pf, pr, and pw. strategies that are not observed but that influence the behavior of the marketing board. The price policy decisions are the cooperative outcome of the bargaining game. The different utilities of payoff are expressed by CV,, CV,, and CV,. The frontier, H, represents the welfare tradeoffs between the farmer, the urban consumer and the marketing board. For instance, higher agricultural tax revenues increase the welfare of the marketing board and possibly the urban consumer through transfers, but leave the farmer worse off. First-order conditions (4) become a(?,~)+~(&(~)=0
for
i=g,f;
a(,&(~)+a(r),(~)=O
for
k=r,w.
and
(11)
(12)
Functional forms are chosen for utility functions U1, and UZ, and the profit function m,, and we estimate the supplies (q;, q;) and demands (qf, q& qf, qt) with time series data from 1960 to 1980. Then we obtain closed-form expressions for the payoff functions (U/s) and their derivatives and compute their values. This step is included in the appendix.
4. The game estimation
Because the payoff functions and their derivatives are endogenous variables, and instrumental variable technique is required. The values of the payoff functions and their derivatives are determined by the equilibrium outcome of the game; hence, they are simultaneously determined. We present the results of the estimation using iterative two-stage least squares. Twostage and three-stage least squares yield comparable results. We approximate the ratios of the bargaining coefficients as linear functions of exogenous
58
J.C. Beghin
and L.S.
Karp, Estimation
of price
policies
in Senegal
variables, and retain the variables having statistically significant impacts on the bargaining coefficients. The following specification is chosen: a2h)
-=a23+a231ws,
and
a3(4
where pop is the total population of Senegal, and do1 is the exchange rate (CFA frank per U.S. dollar). The bargaining coefficients are recovered as follows. First, the bargaining coefficients are normalized to sum to one. Combined with (13) and (14), the normalization yields .
I
1
44 1=
(15)
(1+(1+a23+a23lwP,)(a3l+a3llwP,+a3l2do1+a3l3~o~))’
(a23+a231w~,)(a31+a311w~r+a312do~+a313~~~) 442
(16)
= t1 +tl
+a23+a231w~,)(a31
(l
+a23+a231w~,)(a31
+a311w~r+a312do~+a313~od)’
and (a31+a31,w~r+a312do~+a313~o~) a(z)3
(17)
= +fl
+a311wi%+a312do~+a313~o~))’
Eqs. (13) and (14) are substituted in (2), (1 l), and (12) to form the estimated equations (18)
(19) dCVr -= dpi
-ta31
+a3,,w~,+~3,2~~~+~3,3~~~)
F
I
for
i=g,f,
(20)
and
acv,ah
-(a23+a231wp,)-
acv, for k=r,w. ah
(21)
The intercept terms a23b23 and a31b3, include the reference payoffs (g,‘s),
J.C. Beghin
Estimation of price policies
and L.S. Karp,
in
Senegal
59
Table 1 Estimation of the game (iterative 2SLS regression). Estimate
Parameter
Std. error
0.01070 1.71E-07 - 1.99E-05 - 67.82677 - 2.38443 1.14048 - 4.25E-06 -42.57444
aj12 a313 ajll b 31 a3, a23 a231
b 231
Asympt. t ratio
0.00244098 6.92E-08 2.96E-06 30.02419 0.77917 0.20794 4.64E-06 17.81021
4.38 2.47 -6.74 - 2.26 -3.06 5.48 - 0.92 -2.39
Bargaining coefficients Variable
Mean
Std. error
aI
0.54794175 0.22082935 0.23122890
0.13172115 0.06522543 0.06676633
a2
a3
which are not identified. We are interested primarily in the bargaining-power structure, which can be recovered without the reference point. The parameter estimates and the associated bargaining-power coefficients are presented in table 1. At the sample mean the bargaining coefficient estimates are a, = 0.5478, a, = 0.2209, a3 = 0.23 13, respectively, for the farmer, urban consumer, and the marketing board. The relative magnitude of a, with respect to a2 is counterintuitive, since the Senegalese government price policies favor urban consumers over farmers. When we relax the symmetry assumption below, we note that the data are consistent with urban groups having more political power than farmers. Location of the threat points (and hence the reference points) provides partial explanation for the degree of political power that farmers appear to possess. In case of conflict, farmers can grow their subsistence crop as an alternative; the marketing board and urban consumers do not have such an option. [See Thomson (1987) for a discussion of the relation between conflict point and cooperative equilibrium.] 4.1. Testing the symmetry axiom
The solution product ifit
(cV-dp,
to the asymmetric
4iY;
game maximizes the asymmetric
Nash
(22)
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J.C. Beghin
and LX
Karp,
Estimation
of price
policies
in Senegal
where yi is the exogenous bargaining power of the ith player. The first-order conditions to maximize the Nash product include the y;s to reflect the asymmetry of the game,
yJ F (CWl -g(P,41)=‘O’(CV(Z)j-g(P,d)j)
for
j=2,3
(23)
Asymmetric games differentiate between exogenous (the y,‘s) and endogenous (the a,‘~) bargaining power coefficients. 4 The endogenous bargaining power is determined by the position of reference point g, by the shape of payoff set P and its frontier H, by the utility function of the player, and by exogenous bargaining power coefficients yi. The latter, which are exogenous to the game, depend on institutional factors. Axioms underlying the asymmetric Nash product are similar to those previously introduced, omitting the symmetry axiom. The symmetry axiom implies that yi=yj for all i and j. In the asymmetric case the player with a larger exogenous bargaining power coelkient obtains a larger payoff, other things equal. We test the symmetry axiom by relaxing the restriction of equal parameters between the first-order conditions to maximize the Nash products and those to maximize the criterion function W; that is, we estimate the system
C~=(C23+C231WPg)(C1/2+b23),
(24)
cv,=h +c,,,wP,+c,,*do~+c,,,Pop)(C~++b,,),(25) dch’, dPi
$$
-(a31 +a,,,wp,+a,,,dol+a,,,pop)
for
i=g, f,
(26)
I
and
xv,
-= 8Pk
-(a2,+%,,wP,)p
acv, ah
for
k=r,w.
The unrestricted model differentiates between the parameters in (24) and (25), %I a more general formulation, the y’s can be made to depend on exogenous variables. Given the limited amount of data, this alternative is not practical here. This observation seems to make the distinction between endogenous and exogenous bargaining power somewhat arbitrary. However, a change in an exogenous variable such as the world price of groundnuts changes the payoff frontier and thus, necessarily changes the tangent plane (the a’s) at a bargaining equilibrium but need not change the y’s.
J.C. Beghin and L.S. Karp, Estimation of price policies in Senegal
61
Table 2 Estimation of the asymmetric model (3SLS estimates)P. Parameter a31 a23 h aJll a312 a313
b 31 b 23 c31 c311 c312 c313 C23 c231
Estimate
Std. error
- 2.84444 0.66005 - 9.37E-06 - 1.66E-05 O.OO!M48 3.55E-07 - 17024.88 -427470 - 1.77409 - 1.82E-05 0.01013 5.74E-08 0.94678 9.31E-07
Asympt. t ratio
1.31042 0.39031 5.62E-06 9.41E-06 0.00359218 l.l3E-07 30098.11 307976 0.71243 2.46E-06 0.00215709 6.82E-08 0.007614 1.72E-06
-2.17 1.69 - 1.67 - 1.76 2.63 3.16 -0.57 - 1.39 - 2.49 -7.41 4.70 0.84 12.44 0.54
Bargaining power coefficients Variable
Mean
al a2
0.53821233 0.22945472 0.23233295 0.18581598 0.67041291 0.14377112
Std. error
0.13119939 0.06516201 a3 0.06605170 Yl 0.16437738 YZ 0.21257712 Y3 0.06079777 “The error sum of squares for the unrestricted system is 90.14. The error sum of squares for the restricted system is 194.83. The computed Chi-squared test statistic is 104.69. The critical value of a Chi-squared with 6 degrees of freedom is 16.8 at the 1% significance level.
and the parameters in (26) and (27).5 We estimate the restricted and unrestricted models using three-stage least squares and construct a Chisquared test [Gallant (1987)] based on the difference of the error sum of squares of the two models. Results of the estimation and the test are presented in table 2. Symmetry is strongly rejected. An approximation of the exogenous bargaining power coefficients (the y’s) is recovered by comparing the regression estimates of the c’s of (24) and (25), and the a’s estimates obtained in (26) to (27) in the unrestricted model at their mean. The a;s are recovered as previously [see (15) to (17)]. Detine ~a~z~2~3~/~a~z~3~2~=c23+c231w~,~ and (a(z)3~I)/(a(z)I~3)=c31 +c~~~wP,+ c,,,dol + C~,~POP. Then the U;S are substituted into the two ratios, Uiyj/ajyi. Finally, the yi coefficients are normalized to sum to one. This gives the third equation needed for identification of the y’s. Results are shown in table 2. ‘The y’s can be estimated directly using (23). The test of the symmetry axiom is the test of the hypothesis yi = yj for all i and j.
J.D.E.-
c
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J.C. Beghin
and L.S. Karp,
Estimation
of price policies
in Senegal
The endogenous bargaining coefficients are equal to a, =0.5382, a2 = 0.2295, and a3 =0.2323. The exogenous bargaining power coefficients are equal to y, = 0.1858, y, =0.6704, y3 = 0.1438, respectively, for the farmer, urban consumer, and marketing board. The ai coeflicients implied by the asymmetric model are close to the ones estimated in the symmetric case (table 1). Imposing the symmetry axiom as maintained hypothesis results in a downward bias of the bargaining coefficients of players whose exogenous bargaining power is big. The first-order condition to maximize the asymmetric Nash product identifies the ratio (a,y,/a,y,). The symmetric model yields an estimate of the ratio (a2/u1)biased. By equating the two ratios it becomes clear that the ratio (u2/a1)bissedunderestimates a&z, whenever y, > y,. Exogenous bargaining power has different interpretations: the difference in the players’ beliefs about the determinants of the environment [Binmore, Rubinstein and Wolinsky (1986)]; the exogenous institutional factors influencing the relative strength of the players [Svejnar (1986)]; or ‘some other factors outside the model’ that make the players’ strengths unequal [Roth (1979)]. The exogenous bargaining power coefficients contain the residual asymmetry that is not captured by asymmetry in g, P, H, and d. In the Senegalese case we suggest that the urban bias of policies is expressed by the relative size of y, with respect to y,. Lipton (1977) defines urban bias as allocative decisions in favor of urban areas but admits the difficulty of obtaining a precise summary measure to quantify the bias. The exogenous bargaining power coefficients summarize the impacts of the different farm and urban consumption policies of the welfare of the two major social groups. The simple rural-urban dichotomy is sometimes misleading because it does not take into account the impact of policies within each group. A more disaggregated approach potentially enriches the analysis by distinguishing the rural poor and the rural wealthy from their urban counterparts. Biases against the rural poor as well as against the urban poor have been identified empirically with different methodologies [Newbery and Stern (1987)]. The lack of disaggregated data prevents us from looking at several income groups within each sector. With more disaggregated data each income group in each sector can be viewed as a distinct player. Despite our data limitation, the asymmetric game-theoretic approach permits us to identify the transfer that occurred from the rural to the urban sector in Senegal. Conclusions based solely on the endogenous bargaining coefficients (the ais) fail to identify the asymmetry associated with the price policies. This also occurs if the revealed preference approach is chosen. The symmetric cooperative game model, by imposing incorrect restrictions, ignores the exogenous bargaining structure and yields statistically biased estimates of the endogenous bargaining coefficients.
J.C. Beghin and L.S. Karp, Estimation of price policies in Senegal
63
4.2. Testing for efficiency
The axiom of efficiency states that the cooperative solution lies on the Pareto frontier of the payoff set. This requires that the derivatives of criterion function W with respect to the different price policies yield the same power structure (same a,‘~). We test whether the four first-order conditions, (26) to (27), yield the same estimates of a(&/&), and ~(z)~/u(z)~. We compare the restricted model [(26) to (27)] to the unrestricted one in which coefficients ai are allowed to differ across equations. This tests the efficiency of policies in both the farm and urban sectors. The estimated first-order conditions in the unrestricted model are (28)
dCVi -= dpr
--amat4
-ws/4m
dCV, ~ dp, ’
-(u(z)~/u(z)~) F,
r
(29)
and
(31)
The test of restrictions u3/u1 = cs/ci and u2/u3 = c2/c3 is reported in table 3. The hypothesis of efficiency is rejected. This result has several possible interpretations. Cooperative bargaining game theory may not be appropriate; perhaps players are not on the frontier, H, because the game is noncooperative. An alternative explanation recognizes that not all policies are chosen in simultaneously. Manning (1987) shows that inefficiency results in cooperative games if choices are made sequentially and bargaining power varies over time. Finally, the model neglects information problems. For instance, the marketing board is unable to predict perfectly the supply and demand responses of the other two players. In this case policy changes could bring the players to their contract curve.6 We use the estimated behavioral model to compute policy changes that move the players to the frontier. If the policies are efficient, the relative weights u1/u3 (or u2/u3) are equal in (28) and (29) [or (30) and (31)]. Assume 6This interpretation implies that the modeler knows more about agents’ responses than does the government; this is credible if the government is not econometriclaly equipped to estimate agents’ price response. The computed policy changes minimize the distance from the original equilibrium to the contract curve. They do not guarantee that all players will benefit from the move.
64
J.C. Beghin
and L.S. Karp,
Estimation
of price
policies
in Senegal
Table 3 Test of efficiency in both rural and urban markets (3SLS). Parameter c31 C3ll
C312 c314
C23 c231 a31 a311 a312 a313 a23 a231
Estimate
Std. error
-2.52431 - 1.56E-05 0.00977662 1.89E-07 1.01413 1.46E-07 -0.49314 - 1ME-05 0.00519194 - 1.23E-09 0.84340 1.46E-06
1.12467 4.29E-06 0.00370965 l.O7E-07 0.20439 4.58E-06 0.60925 2.42E-06 0.00183978 5.51E-08 0.53868 1.21E-05
Asympt. t ratio - 2.24 -3.64 2.64 1.77 4.96 0.03 -0.81 -4.29 2.82 - 0.02 1.57 0.12
‘The sum of squares of error is 94.55; the restricted sum of squares of error is 160.35. The Chi-squared test statistic is 65.79 with 12 degrees of freedom. The critical value is 26.2 at the 1% significance level.
that (28) and (29) yield different relative weights al/a3 and c1/c3. The difference of the relative weights, f, is a function of policies pg and pr (but not of policies p, and p,)
(32) Policy changes that lead to efficiency using a first-order Taylor approximation of the function f(p,, pr). Efficient policies pz and p: satisfy
/(P:,P:)=o~f(P,,Pf)+ii~~~pf)(P:-P*)+a~~~pf)(P:-Pf). B
(33) f
We assume that the optimum policy changes minimize the sum of the squared magnitudes of the policy changes subject to (33). The optimum policy changes are f(Pp
Pi*-Pi = - w-b,,
Pf) af(Pg9
Pr)laP,)2
+ (MP,,
Pf)l@i
PrY~Pf)21 for
i = gpf.
(34)
Similar optimal policy levels are derived and computed for pr, and pw. The two pairs of policies (p:, p,*), and (p,*, pc) are computed independently, since
J.C. Beghin and L.S. Karp, Estimation of price policies in Senegal
65
Table 4 Estimated relative price changes to achieve ethciency. Years 60 61 62 63 64 65 66 61 68 69 70 71 72 73 74 75 76 77 :i 80
dP&, - 0.22352 -0.24132 -0.22924 -0.18030 -0.13823 -0.09622 -0.01237 0.00109 -0.02122 -0.05314 -0.03314 0.04367 0.00252 -0.17604 -0.17513 -0.32074 -0.39040 0.12437 0.05838 - 0.00704 -0.20225
dpddp, 0.02482 0.01327 0.01329 - 0.01945 0.01081 0.00224 0.00333 0.00067 0.00608 0.00073 0.00329 - 0.00808 -0.08027 0.02875 0.00816 0.02203 - 0.22486 -0.01875 -0.00443 0.00103 0.02864
1.29830 0.53643 0.13639 0.13567 0.05417 0.02153 0.10223 0.33905 0.25524 0.14768 0.16589 0.26702 0.37820 0.43195 0.18674 0.93938 0.15535 0.47634 0.09083 -0.01291 0.06351
0.66024 0.01749 -0.03718 -0.09174 -0.01866 -0.00904 -0.04201 -0.02346 -0.04617 - 0.06628 -0.16961 0.06817 0.07411 0.08048 - 0.04829 0.63324 0.84543 -0.26139 -0.14545 0.10203 0.08149
f is not a function of the urban consumer prices. Table 4 presents the recommended relative changes in policies (in percent of the prevailing prices). These are computed with the observed differences ([(dCVJdp,)/dCV,/dp,)] [(dCI/,/dp,)/(dCVr/dp,)]). The changes are moderate, except for a few data points for which the estimated changes are large and would be difficult to implement. For the farm sector the direction of the proposed changes is plausible and implies better terms of trade. Relative price p&r has been too low for most of the observed data points. The suggested changes in urban consumer prices are mixed and depend on whether they are computed with the observed (the derivative ratios) or the predicted (the weight ratios) f. From 1980 to 1984 the World Bank negotiated policy reforms as a condition for loans to the Senegalese government; the reforms were consistent with the policy proposals mentioned in the introduction [Waterbury and Gersovitz (1987, ch. 9)] and meant an unambiguous decrease in the welfare of the urban sector. These policies were strongly opposed and partly defeated by the urban sector and state bureaucracy because they implied a redistribution of real income among Senegalese players.7 ‘An objection could be raised that the policy changes promoted by The World Bank would decrease the cost of the different subsidy programs and the taxes necessary to finance them, thus finally benefiting urban consumers. However, in the Senegalese case the tax base is the exportable agricultural output.
66
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and L.S. Karp,
Estimation
of price
policies
in Senegal
5. Conclusions We have modeled and quantified the political economy of important food and agricultural policies in Senegal using a cooperative bargaining game framework. The model explains food and price policies as the endogenous outcome of a bargaining process among three representative players: a farmer growing export and staple crops (groundnuts and millet); an urban consumer buying imported rice and wheat products; and a marketing board intervening in the agricultural and urban markets with -market power. We estimated the game and recovered its bargaining power structure. Farmers have a considerable amount of bargaining strength due to their abilities to switch from groundnut to millet production when they disagree with proposed agricultural policies. We tested the axioms underlying the cooperative game to discriminate among various cooperative bargaining game models. Symmetry and efficiency were rejected. Rejection of the symmetry axiom demonstrated the potential usefulness of asymmetric bargaining models that permit identification of differences in exogenous bargaining strength among players, We linked the asymmetry of our Senegalese game to the urban bias of the price policies that have penalized the rural sector and subsidized urban food consumption. Rejection of efficiency has significant policy implications; the bargaining power structure could be preserved, while efficiency could be improved by policy changes that implied policies more favorable to the farm sector. Validity of the axiom tests is limited by the small sample size of the data set, the choice of the functional forms and the aggregated and stylized aspects of the approach adopted. Nevertheless, the simplicity of the methodology is attractive and the method could be applied to different bargaining situations.
References Agarwala, Ramgopal, 1983, Price distortions and growth in developing countries, World Bank Staff Papers no. 575 (The World Bank, Washington DC). Bates, Robert, 1981, Markets and states in tropical Africa (University of California Press, Berkeley, CA). Binmore, Ken, Ariel Rubinstein and Asher Wolinsky, 1986, The Nash bargaining solution in economic modeling, The Rand Journal of Economics 17, 176188. Braverman, Avisnah and Jeffrey S. Hammer, 1986, Multi-market analysis of agricultural pricing in Senegal, in: I. Singh, L. Squire and J. Strauss, eds., Agricultural households models: Extensions, applications, and policy (The World Bank, Washington, DC). Cleaver, Kevin M., 1985, The impact of price and exchange rate policies on agriculture in subSaharan Africa., World Bank Staff Papers no. 728 (The World Bank, Washington, DC). Friedman, James W., 1986, Game theory with applications to economics (Oxford University Press, Oxford).
J.C. Beghin
and L.S. Karp,
Estimation
of price
policies
in Senegal
67
Fudenberg, Drew and Eric Maskin, 1986, The Folk theorem in repeated games with discounting and incomplete information, Econometrica 54, 533-555. Gallant, A. Ronald, 1987, Nonlinear statistical models (Wiley, New York). Harsanyi, John C., 1963, A simplified bargaining model for the N-person cooperative game, International Economic Review 4, 193-220. Harsanyi, John C, 1977, Rational behavior and bargaining equilibrium in games and social situations (Cambridge University Press, Cambridge). Lipton, Michael, 1977, Why poor people stay poor (Harvard University Press, Cambridge, MA). Manning, Alan, 1987, An integration of trade union models in a sequential bargaining framework, The Economic Journal 97, 121-139. McFadden, Daniel, 1975, The revealed preferences of a government bureaucracy: Theory, Bell Journal of Economics 6, 401-416. McFadden, Daniel, 1976, The revealed preferences of a government bureaucracy: Empirical evidence, Bell Journal of Economics 7, 55-72. Nash, John, 1953, Two-person cooperative games, Econometrica 21, 128-140. Newbery, David and Nicholas Stern, eds., 1987, The theory of taxation for developing countries (Oxford University Press, Oxford). Rausser, Gordon C. and John W. Freebaim, 1974, Estimation of policy preference functions: An application to U.S. beef quotas, Review of Economics and Statistics 56, 4374l9. Roth, Alvin E., 1979, Axiomatic models of bargaining, Lecture notes in Economics and Mathematical Systems no. 170 (Springer-Verlag, New York). Sarris, Alexander H. and John Freebairn, 1983, Endogenous price policies and international wheat prices, American Journal of Agricultural Economics 65, 214-224. Scandizzo, Pasquale L. and Cohn Bruce, 1980, Methodologies for measuring agricultural price interventions effects, World Bank Staff Papers no. 394 (The World Bank, Washington, DC). Shubik, Martin, 1982, Game theory in the social sciences, Concepts and solutions (The MIT Press, Cambridge, MA). Svejnar, Jan., 1986, Bargaining power, fear of disagreement, and wage settlement: Theory and evidence from U.S. industry, Econometrica 54, 1055-1078. Thomson, William, 1981, A class of solutions to bargaining problems, Journal of Economic Theory 25, 431-441. Thomson, William, 1987, Monotonicity of bargaining solutions with respect to the disagreement point, Journal of Economic Theory 42, 5c58. Waterbury, John and Mark Gersovitz, eds., 1987, The political economy of risk and choice in Senegal (Frank Cass & Co., Totowa, NJ). Zusman, Pinhas, 1976, The incorporation and measurement of social power in economic models, International Economic Review 17, 447462.
Estimation
of price policies in Senegal
An empirical test of cooperative game theory* John C. Beghin North Carolina State University, Raleigh, NC 27695-8110, USA
Larry S. Karp University of California, Berkeley, CA 94720, USA Received April 1989, final version received September 1989 Abstract: A game-theoretic framework rationalizes the political economy of food and agricultural price policies in Senegal. Policies are the outcome of a cooperative bargaining process among three archetypal players: a farmer growing cash and staple crops, an urban consumer buying imported cereals, and a government marketing board intervening in agricultural markets. The game is estimated and the bargaining strength of the players is recovered. The axioms underlying the game are tested to discriminate among various bargaining game solutions. The symmetry and efftciency axioms are rejected.
1. Introduction Many African countries are characterized by highly distorted agricultural and food markets. Typically, urban staples are subsidized, and producers of export crops are taxed on their output and subsidized for their input purchases. These policies have been criticized because of their negative impact on economic efficiency and growth [Scandizzo and Bruce (1980), Agarwala (1983)]. The standard recommendation involves removal of agricultural distortions and an alignment on world prices. African governments have not followed these policy recommendations because of their high political cost [Cleaver (1985), Bates (1981)]. Many countries that tried to reduce food subsidies faced political unrest, and have had to compromise with urban groups. The analysis on which the proposed reform is based fails to incorporate the political economy of food and agricultural price policies. The assumption of free manipulation of these policy instruments is inappropriate in most African countries. Bates argues that many governments (e.g., Ghana, Senegal) compromise with different social groups to gain their legitimacy. Agricultural policies are *We thank John Harsanyi and Irma Adelman for their comments. 0304-3878/91/%03.50 0 1991-Elsevier
Science Publishers B.V. (North-Holland)
50
J.C. Beghin
and L.S. Karp,
Estimation
of price
policies
in Senegal
affected by the relative political strength of social groups, resource constraints, and government objectives. Policy decisions attempt to reconcile the conflicting interests of urban consumers, farmers, and bureaucratic institutions. The resulting policy mix creates inefficiencies and undermines growth. Bates’ thesis, implicitly game-theoretic, is supported by detailed descriptions of the policies in specific countries but lacks a formal model and quantification. Policies in African countries may appear more coherent when viewed in a political-economic framework. Price policies generate revenues needed to sustain governments and their large administrations. These governments do not use their monopoly/monopsony power fully, since retaliation by socioeconomic groups can destroy the rent-generating mechanism. Farmers can respond by changing their output and crop patterns, smuggling, and defaulting on debt payments as potential threats against low producer prices. Urban consumers can retaliate against high food prices, undermining the government through voting, rioting, and labor unrest. Market interventions, essential to the survival of the government, reflect the relative political strength of the economic groups affected by the policies. We develop and test a model of endogenous food and agricultural price policies that rationalizes the distortions observed in many African countries. The theory is based on a game-theoretic bargaining model and is applied to the political economy of the agricultural and food price policy regime that prevailed in Senegal from 1960 to the early 1980s.’ The model is applicable to other countries with institutions similar to those of Senegal. The game involves three representative players: farmers producing export and staple crops, urban dwellers consuming imported cereals, and a small set of institutions intervening in agricultural and food markets. The Senegalese case illustrates an archetypal situation, since farmers are taxed on their cash crop, fertilizer use is subsidized, taxes on urban cereal consumption have been moderate or negative, and food and agricultural export and import markets are entirely controlled by a few governmental institutions. The model is based on the theory of cooperative bargaining games [Harsanyi (1977), Thomson (1981)]. The first-order conditions for solution of the game are used to derive and estimate econometrically the endogenous bargainingpower coefficients of the three players. These bargaining-power coefficients can be interpreted as the weights a fictitious social planner puts on the welfare of pressure groups when making policy decisions. A number of solutions to bargaining games have been proposed. Their underlying axioms are different but most seem reasonable. The axioms underlying the class of solutions used in our model are examined and tested empirically. This ‘In the early 1980s international donors imposed structural reforms that changed Senegalese public institutions and policies. Cash crop prices were increased and private groundnut traders were allowed, and urban consumer prices were raised.
J.C. Beghin and L.S. Karp, Estimation ojprice policies in Senegal
51
provides evidence to distinguish which type of cooperative equilibrium is more likely to describe a particular situation. Theoretical comparison of the candidate solutions is inconclusive [Friedman (1986)]. Our empirical results suggest that the symmetry axiom common to many solutions does not hold for Senegal. This provides support for asymmetric bargaining models [Roth (1979), Binmore, Rubinstein and Wolinsky (1986)]. The asymmetric game enables us to decompose the bargaining power of the players into endogenous (determined within the game) and exogenous (predetermined by factors independent of the game) bargaining power. We interpret the asymmetry of the Senegalese game as indication of urban bias of the policies. The urban consumer has a stronger exogenous bargaining power but weaker endogenous bargaining power than the farmer. Price policies appear to have favored the urban sector compared to agriculture. The concept of endogenization of market interventions is not new. The revealed preference approach [Rausser and Freebairn (1974), McFadden (1975, 1976), Sarris and Freebairn (1983)] explicitly acknowledges the existence and influence of pressure groups in the policy decision-making process. The government maximizes a weighted objective function reflecting the welfare of lobbying groups, and reveals its preferences (the weights) through its choice of policies. The revealed preference approach does not offer a formal structure of the political economy on which the government objective function is based. Game theory remedies that shortcoming by modelling the bargaining process among social groups [Harsanyi (1963), Zusman (1976)]. The weighted objective function of the revealed preference model is intrinsic to the cooperative bargaining game solution; the weights express the bargaining power of the players. The game-theoretic model provides more structure and therefore more prior information than the revealed preference model. This is a practical advantage in empirical work. The first-order conditions of both the cooperative game and the weighted objective function can be estimated in a system in which restrictions can be imposed and tested. The game-theoretic framework is instrumental in investigating the issue or urban bias of the policies implemented in Senegal. The next section describes the relevant Senegalese markets and policies and motivates the game-theoretic approach. The third section presents the cooperative bargaining model with its axioms. Complementarity between the game theoretic and the revealed preference approaches is emphasized. Econometric estimation of the game follows in the next section. The bargaining power structure is recovered, We also test the axioms of symmetry and joint efficiency. Symmetry is rejected; the asymmetry of the game is associated with the urban bias of the policies. In the same section we test the efficiency of the price policies and propose more effective interventions. Conclusions summarize the contribution of the paper. An appendix, available upon request, contains the time series data, estimation of the
52
J.C. Beghin
and L.S. Karp,
players’ payoff functions, policies.
Estimation
of price
and their derivatives
policies
in Senegal
with respect to the price
2. Trade and price policies in Senegal This section summarizes the major policies that affected the production of groundnuts and millet and the urban consumption of wheat and rice for the period 1960 to 1980. Groundnuts and millet are the major crops of Senegal. Production of rice, maize and cotton is marginal compared to that of groundnuts and millet. Groundnuts are the largest agricultural source of foreign exchange for Senegal; millet is the principal rural staple crop; rice and wheat products are the major urban staples. Other commodities (sugar, oil) are also important but have much smaller expenditure shares than rice and wheat and are not exclusively urban. Farmer cooperatives, used to modernize groundnut production and marketing, have been active since the early 1960s. During the same period, private groundnut traders were rapidly replaced by a monopsonistic marketing board. In 1980 France insisted on dissolution of the marketing board as a condition to providing financial assistance to Senegal. From 1962 to 1980 the marketing board announced ofIicia1 prices to the farmers before the beginning of the planting season. The producer price has been stabilized below world price. The estimated groundnut export tax averaged 46 percent of the world price for the period 1960-1980. The prices are decided by the Comitt des Grands Produits, a government committee on which cooperatives are represented. Political stability in rural areas relies on the hegemony of Moslem leaders who are important groundnut producers. Their strong and organised political power (Mouride and Tidiane brotherhoods) helps the farm sector to obtain more favorable prices than those corresponding to full monopsony power of the marketing board. Millet and groundnut production compete for the land and labor, for which there are virtually no markets [Braverman and Hammer (1986)]. The marketing board had no substantial involvement in millet, which is essentially a non-traded staple crop consumed in the countryside. Producers make simultaneous decisions concerning the supply of groundnuts and millet and the demand for fertilizer. From 1964 to 1980 the marketing board was in charge of the agricultural credit system, selling fertilizer and equipment at subsidized prices to farmers. Input subsidies were made to offset the effects of the output tax on groundnut supply. The credit system was abolished in 1980 when the marketing board was dissolved. The average subsidy on fertilizer was 56 percent of the factory unit cost for the period considered in the paper. Rice is the major imported cereal and is consumed in urban areas. Its retail price is fixed by law; although in most years the price has been
J.C. Beghin
and L.S. Karp,
Estimation
of price
policies
in Senegal
53
moderately above import cost, rice has been subsidized when unexpected increases in world prices occurred. These sudden increases have been passed on progressively to consumers. From 1960 to 1980, the estimated average tariff on rice was 19 percent of the import unit cost. Wheat is not produced in Senegal; it is imported by two authorized millers. The annual quota for wheat imports has never been binding. The two millers were subsidized enabling them to sell flour below cost to bakers until 1977. The price of bread is also fixed by law at a very low level. Wheat consumption, which is exclusively urban, received an average subsidy of 13 percent for the 20-year period. The threat of political unrest is a primary reason for these low urban consumer prices in Senegal [Bates (1986, p. 33) Waterbury and Gersovitz (1987, ch. 7)]. Three important interest groups have been regularly consulted on consumer price policies. These groups, CNTS (workers’ union), CES and GBES (economic groups linked to the main political party), represent private and parapublic urban workers and employees. 3. A cooperative game-theoretic framework A n-person cooperative game is assumed for two reasons. First, despite its simplicity, this type of game is appropriate to approximate more elaborate sequential bargaining games [Binmore, Rubinstein and Wolinsky (1986)]. The bargaining process between pressure groups and the policy maker often leads to enforceable agreements that render the bargaining process cooperative [Shubik (1982)]. The repeated nature of political-economy games strengthens the use of cooperative solutions. Fudenberg and Maskin (1986), and Friedman (1986, ch. 3) have shown that the cooperative outcome is plausible in repeated non-cooperative games because the repetition induces a self-enforcement mechanism. The second reason is due to the informal and institutional evidence provided by the Senegalese case to make the use of cooperative bargaining games justifiable. Senegalese society is based on a social consensus (‘la paix sociale’ dear to Senegalese policy makers) without overt coercion. The economic game among the three players has been repeated over the years with no indication of players breaking the consensus. As mentioned above, the price policies have been negotiated with formal consultation of interest groups and have been respected. This negotiation process suggests that all agents behave strategically and that none of them is in a position to set policy unilaterally. Therefore a cooperative bargaining model seems more appropriate than a Stackelberg-Cournot approach. Several solution concepts exist for cooperative games. We use the class of solutions based on reference points [Thomson (198 l)] defined as payoffs to which players find it natural to compare any proposed compromise. The
54
J.C. Beghin
and L.S. Karp,
Estimation
of price
policies
in Senegal
Nash conflict point is an example of reference point. Players might compare proposed compromises not only to the conflict point but also to other potential payoffs such as the point of minimum expectation or a convex combination of the two. To keep the empirical study flexible, we do not specify which reference point the players use. We assume that the payoff set and its frontier depend on a vector, z, of exogenous variables (e.g., world prices, exchange rate). Changes in the economic environment cause changes in the welfare possibilities, the players’ bargaining power, and the equilibrium strategies. The game can be seen as a sequence of static cooperative games with a different payoff set at every period. However, we assume that the reference point is not affected by exogenous shocks. This asumption is necessary because of the small size of the data set but is not extremely restrictive. For instance, the payoff frontier, H, may shift without affecting the point of minimum expectation or the disagreement point, d. Thomson (1981) and Friedman (1986) discuss the four axioms underlying the game; these are analogous to the axioms underlying the Nash game (1953) but are defined with respect to reference point rather than conflict point. The axiom of joint efficiency, or strong rationality, requires that the solution to the game, CV* =(CV:, CVY, . . . , CVX), lie on the upper boundary, H, of the payoff space, P; CL’: is defined as the utility of player i in equilibrium. The axiom of linear invariance states that the solution to the game obtained by a positive a&e transformation of players’ utility functions is the positive affine transformation of the solution to the original game. The axiom of symmetry insures that indistinguishable players receive the same payoff. The last axiom, the independence of irrelevant alternatives, says that excluding a point from P other than the solution or the reference point, does not alter the solution to the game. If the reference point, g(P, d), satisfies certain regularity conditions [Thomson (1981)], the solution to the cooperative game maximizes the modified Nash product
(1) where CV=(CV,,CV,,..., CV,) is an element of the set P(z). If P is compact and convex, the solution, CV*, is on the frontier, H, and satisfies dZ)i(CJ’:
-g(P, d)i) =~(z)j(CVr
-g(P, d)i)
for
all i, j;
(2)
where a(~)~= aH(CV*, z)/aCI$ The functions a(~)~ denote the bargainingpower coefficients of the players. They are normalized to sum to one. If the payoff set, P, is convex, maximizing the Nash product is equivalent to maximizing the weighted sum of utilities, w
J.C. Beghin
and L.S. Karp,
Estimation
of price
policies
in Senegal
55
(3)
First-order conditions in strategy space can be derived by maximizing either the welfare function (3) or the Nash product (1). Define sf as the kth strategy available to the players, then the necessary conditions for a solution are ,$i a(z),T=O
for
all k.
(4)
Urban consumers and farmers are utility maximizers; the negative of the compensating variation is used as their money metric utility function. The marketing board maximizes net tax revenues from the sales of rice, wheat and fertilizer and from purchases of groundnuts. Its payoff function is the change in tax revenues from the current level to the level in the reference period, 1960. The indirect utility function of the representative farmer is Ul
= ~,hll,
P-m
MP,,
Pm,
Pf,
ZJ
-
Cl),
(5)
pg, and pt are the price of millet, the price vector for where P,,,, P-,,,, consumption goods other than millet, the producer price of groundnuts, and the producer price of fertilizer. The restricted profit function, m,, minus the cost of implementing conflict strategies, CL, constitutes the net income of the farmer. At the cooperative solution C, is equal to zero, since conflict strategies are not used. The cooperative strategy involves political support; no monetary reward is given to the policy maker. The vector zl, a subset of z, contains exogenous variables affecting the profit function. We obtain the supplies of groundnuts and millet, qi, and qk, and the demand for fertilizer, qt, b y applying Hotelling’s lemma to the profit function, m,. The farmer does not consume groundnuts. Roy’s identity gives the farmer’s demand for millet, 4:. The negative of the compensating variation is
(6)
where m, and pm refer to the current period, and rn: and p: are their counterparts in the reference period; el is the expenditure function of the farmer. We do not consider changes in the price p-,,, and assume that the compensating variation and millet demand depend only on the price of millet
56
J.C. Beghin
and L.S. Karp,
Estimation
of price
policies
in Senegal
and income.* Millet supply equals demand, since millet is a non-traded commodity. The millet market equilibrium condition is totally differentiated with respect to changes in price policies ps and pf to yield the comparativestatics of the millet equilibrium price for changes in price policies (dp,,,/dp, and dp,,,/dp,). These general equilibrium effects are included when considering the impact of the policies pg and Pf on the payoff functions. A typical urban consumer has an indirect utility function, U,, with consumption prices and income as arguments:
with pr, pw, ~t-~, -WI defined as the prices of rice, wheat products, and other goods. Income of the urban consumer is equal to wage income m2, assumed exogenous, minus the cost of applying conflict strategies C2 (e.g., cost of rioting or striking). At the cooperative equilibrium, C2 is equal to zero because the threat strategies are not implemented. We assume that the demands of rice and wheat depend on rice and wheat prices and on income, and are independent of P[-~, +. Roy’s identity yields cereal demands, q:, and q$ The negative of the compensating variation is
(8)
-mm,+C,+m”,],
with superscript o corresponding to the reference period and e2 denoting the expenditure function of the urban consumer. The marketing board maximizes the sum of net tax revenues in the four markets under the constraint of the bargaining process. This assumption does not specify how the surplus generated through taxes is allocated (e.g., investment or maintenance of bureaucracy). The marketing board can both extract and transfer surplus under this assumption depending on the power structure among players.3 The tax revenue function, TR, is TR = (v,
- p&q; + (pf - w&G + (P, - wp&:
+ (P, - WpJd - & -
B2,
(9) where
wpI,
wpr,
wp,
are the world prices of groundnuts,
rice and wheat, and
ZThe compensating variation of the farmer is independent of p-,,, under the assumption of separability in utility derived from millet and all other goods. For the urban consumer, we assume that the marginal rate of substitution between rice and wheat does not depend on other prices. Under this assumption the urban consumer’s compensating variation depends on wheat and rice prices and income. 3We tried alternative specifications in which the marketing board cares about income distribution as well as its tax revenues. Estimation of this specification gave nonsensical econometric results (i.e., some bargaining power coefftcients were negative).
J.C. Beghin
and L.S. Karp,
Estimation
of price
policies
in Senegal
51
wp, is the ex-factory price of fertilizer. Variables B, and B, represent the cost to the marketing board of being in conflict with farmers (B,) and urban dwellers (BJ. The payoff function of the marketing board, CV,, is the change in tax revenues when prices move from their reference to their current level or Cv,
= Wpg,
pf, pr, P,)
- TR(P;,
PP, P;, ~3.
The necessary and sufficient conditions for a solution are applied to the Senegalese case. The strategies of the marketing board are the four price Farmers and urban dwellers have political policies pg, pf, pr, and pw. strategies that are not observed but that influence the behavior of the marketing board. The price policy decisions are the cooperative outcome of the bargaining game. The different utilities of payoff are expressed by CV,, CV,, and CV,. The frontier, H, represents the welfare tradeoffs between the farmer, the urban consumer and the marketing board. For instance, higher agricultural tax revenues increase the welfare of the marketing board and possibly the urban consumer through transfers, but leave the farmer worse off. First-order conditions (4) become a(?,~)+~(&(~)=0
for
i=g,f;
a(,&(~)+a(r),(~)=O
for
k=r,w.
and
(11)
(12)
Functional forms are chosen for utility functions U1, and UZ, and the profit function m,, and we estimate the supplies (q;, q;) and demands (qf, q& qf, qt) with time series data from 1960 to 1980. Then we obtain closed-form expressions for the payoff functions (U/s) and their derivatives and compute their values. This step is included in the appendix.
4. The game estimation
Because the payoff functions and their derivatives are endogenous variables, and instrumental variable technique is required. The values of the payoff functions and their derivatives are determined by the equilibrium outcome of the game; hence, they are simultaneously determined. We present the results of the estimation using iterative two-stage least squares. Twostage and three-stage least squares yield comparable results. We approximate the ratios of the bargaining coefficients as linear functions of exogenous
58
J.C. Beghin
and L.S.
Karp, Estimation
of price
policies
in Senegal
variables, and retain the variables having statistically significant impacts on the bargaining coefficients. The following specification is chosen: a2h)
-=a23+a231ws,
and
a3(4
where pop is the total population of Senegal, and do1 is the exchange rate (CFA frank per U.S. dollar). The bargaining coefficients are recovered as follows. First, the bargaining coefficients are normalized to sum to one. Combined with (13) and (14), the normalization yields .
I
1
44 1=
(15)
(1+(1+a23+a23lwP,)(a3l+a3llwP,+a3l2do1+a3l3~o~))’
(a23+a231w~,)(a31+a311w~r+a312do~+a313~~~) 442
(16)
= t1 +tl
+a23+a231w~,)(a31
(l
+a23+a231w~,)(a31
+a311w~r+a312do~+a313~od)’
and (a31+a31,w~r+a312do~+a313~o~) a(z)3
(17)
= +fl
+a311wi%+a312do~+a313~o~))’
Eqs. (13) and (14) are substituted in (2), (1 l), and (12) to form the estimated equations (18)
(19) dCVr -= dpi
-ta31
+a3,,w~,+~3,2~~~+~3,3~~~)
F
I
for
i=g,f,
(20)
and
acv,ah
-(a23+a231wp,)-
acv, for k=r,w. ah
(21)
The intercept terms a23b23 and a31b3, include the reference payoffs (g,‘s),
J.C. Beghin
Estimation of price policies
and L.S. Karp,
in
Senegal
59
Table 1 Estimation of the game (iterative 2SLS regression). Estimate
Parameter
Std. error
0.01070 1.71E-07 - 1.99E-05 - 67.82677 - 2.38443 1.14048 - 4.25E-06 -42.57444
aj12 a313 ajll b 31 a3, a23 a231
b 231
Asympt. t ratio
0.00244098 6.92E-08 2.96E-06 30.02419 0.77917 0.20794 4.64E-06 17.81021
4.38 2.47 -6.74 - 2.26 -3.06 5.48 - 0.92 -2.39
Bargaining coefficients Variable
Mean
Std. error
aI
0.54794175 0.22082935 0.23122890
0.13172115 0.06522543 0.06676633
a2
a3
which are not identified. We are interested primarily in the bargaining-power structure, which can be recovered without the reference point. The parameter estimates and the associated bargaining-power coefficients are presented in table 1. At the sample mean the bargaining coefficient estimates are a, = 0.5478, a, = 0.2209, a3 = 0.23 13, respectively, for the farmer, urban consumer, and the marketing board. The relative magnitude of a, with respect to a2 is counterintuitive, since the Senegalese government price policies favor urban consumers over farmers. When we relax the symmetry assumption below, we note that the data are consistent with urban groups having more political power than farmers. Location of the threat points (and hence the reference points) provides partial explanation for the degree of political power that farmers appear to possess. In case of conflict, farmers can grow their subsistence crop as an alternative; the marketing board and urban consumers do not have such an option. [See Thomson (1987) for a discussion of the relation between conflict point and cooperative equilibrium.] 4.1. Testing the symmetry axiom
The solution product ifit
(cV-dp,
to the asymmetric
4iY;
game maximizes the asymmetric
Nash
(22)
60
J.C. Beghin
and LX
Karp,
Estimation
of price
policies
in Senegal
where yi is the exogenous bargaining power of the ith player. The first-order conditions to maximize the Nash product include the y;s to reflect the asymmetry of the game,
yJ F (CWl -g(P,41)=‘O’(CV(Z)j-g(P,d)j)
for
j=2,3
(23)
Asymmetric games differentiate between exogenous (the y,‘s) and endogenous (the a,‘~) bargaining power coefficients. 4 The endogenous bargaining power is determined by the position of reference point g, by the shape of payoff set P and its frontier H, by the utility function of the player, and by exogenous bargaining power coefficients yi. The latter, which are exogenous to the game, depend on institutional factors. Axioms underlying the asymmetric Nash product are similar to those previously introduced, omitting the symmetry axiom. The symmetry axiom implies that yi=yj for all i and j. In the asymmetric case the player with a larger exogenous bargaining power coelkient obtains a larger payoff, other things equal. We test the symmetry axiom by relaxing the restriction of equal parameters between the first-order conditions to maximize the Nash products and those to maximize the criterion function W; that is, we estimate the system
C~=(C23+C231WPg)(C1/2+b23),
(24)
cv,=h +c,,,wP,+c,,*do~+c,,,Pop)(C~++b,,),(25) dch’, dPi
$$
-(a31 +a,,,wp,+a,,,dol+a,,,pop)
for
i=g, f,
(26)
I
and
xv,
-= 8Pk
-(a2,+%,,wP,)p
acv, ah
for
k=r,w.
The unrestricted model differentiates between the parameters in (24) and (25), %I a more general formulation, the y’s can be made to depend on exogenous variables. Given the limited amount of data, this alternative is not practical here. This observation seems to make the distinction between endogenous and exogenous bargaining power somewhat arbitrary. However, a change in an exogenous variable such as the world price of groundnuts changes the payoff frontier and thus, necessarily changes the tangent plane (the a’s) at a bargaining equilibrium but need not change the y’s.
J.C. Beghin and L.S. Karp, Estimation of price policies in Senegal
61
Table 2 Estimation of the asymmetric model (3SLS estimates)P. Parameter a31 a23 h aJll a312 a313
b 31 b 23 c31 c311 c312 c313 C23 c231
Estimate
Std. error
- 2.84444 0.66005 - 9.37E-06 - 1.66E-05 O.OO!M48 3.55E-07 - 17024.88 -427470 - 1.77409 - 1.82E-05 0.01013 5.74E-08 0.94678 9.31E-07
Asympt. t ratio
1.31042 0.39031 5.62E-06 9.41E-06 0.00359218 l.l3E-07 30098.11 307976 0.71243 2.46E-06 0.00215709 6.82E-08 0.007614 1.72E-06
-2.17 1.69 - 1.67 - 1.76 2.63 3.16 -0.57 - 1.39 - 2.49 -7.41 4.70 0.84 12.44 0.54
Bargaining power coefficients Variable
Mean
al a2
0.53821233 0.22945472 0.23233295 0.18581598 0.67041291 0.14377112
Std. error
0.13119939 0.06516201 a3 0.06605170 Yl 0.16437738 YZ 0.21257712 Y3 0.06079777 “The error sum of squares for the unrestricted system is 90.14. The error sum of squares for the restricted system is 194.83. The computed Chi-squared test statistic is 104.69. The critical value of a Chi-squared with 6 degrees of freedom is 16.8 at the 1% significance level.
and the parameters in (26) and (27).5 We estimate the restricted and unrestricted models using three-stage least squares and construct a Chisquared test [Gallant (1987)] based on the difference of the error sum of squares of the two models. Results of the estimation and the test are presented in table 2. Symmetry is strongly rejected. An approximation of the exogenous bargaining power coefficients (the y’s) is recovered by comparing the regression estimates of the c’s of (24) and (25), and the a’s estimates obtained in (26) to (27) in the unrestricted model at their mean. The a;s are recovered as previously [see (15) to (17)]. Detine ~a~z~2~3~/~a~z~3~2~=c23+c231w~,~ and (a(z)3~I)/(a(z)I~3)=c31 +c~~~wP,+ c,,,dol + C~,~POP. Then the U;S are substituted into the two ratios, Uiyj/ajyi. Finally, the yi coefficients are normalized to sum to one. This gives the third equation needed for identification of the y’s. Results are shown in table 2. ‘The y’s can be estimated directly using (23). The test of the symmetry axiom is the test of the hypothesis yi = yj for all i and j.
J.D.E.-
c
62
J.C. Beghin
and L.S. Karp,
Estimation
of price policies
in Senegal
The endogenous bargaining coefficients are equal to a, =0.5382, a2 = 0.2295, and a3 =0.2323. The exogenous bargaining power coefficients are equal to y, = 0.1858, y, =0.6704, y3 = 0.1438, respectively, for the farmer, urban consumer, and marketing board. The ai coeflicients implied by the asymmetric model are close to the ones estimated in the symmetric case (table 1). Imposing the symmetry axiom as maintained hypothesis results in a downward bias of the bargaining coefficients of players whose exogenous bargaining power is big. The first-order condition to maximize the asymmetric Nash product identifies the ratio (a,y,/a,y,). The symmetric model yields an estimate of the ratio (a2/u1)biased. By equating the two ratios it becomes clear that the ratio (u2/a1)bissedunderestimates a&z, whenever y, > y,. Exogenous bargaining power has different interpretations: the difference in the players’ beliefs about the determinants of the environment [Binmore, Rubinstein and Wolinsky (1986)]; the exogenous institutional factors influencing the relative strength of the players [Svejnar (1986)]; or ‘some other factors outside the model’ that make the players’ strengths unequal [Roth (1979)]. The exogenous bargaining power coefficients contain the residual asymmetry that is not captured by asymmetry in g, P, H, and d. In the Senegalese case we suggest that the urban bias of policies is expressed by the relative size of y, with respect to y,. Lipton (1977) defines urban bias as allocative decisions in favor of urban areas but admits the difficulty of obtaining a precise summary measure to quantify the bias. The exogenous bargaining power coefficients summarize the impacts of the different farm and urban consumption policies of the welfare of the two major social groups. The simple rural-urban dichotomy is sometimes misleading because it does not take into account the impact of policies within each group. A more disaggregated approach potentially enriches the analysis by distinguishing the rural poor and the rural wealthy from their urban counterparts. Biases against the rural poor as well as against the urban poor have been identified empirically with different methodologies [Newbery and Stern (1987)]. The lack of disaggregated data prevents us from looking at several income groups within each sector. With more disaggregated data each income group in each sector can be viewed as a distinct player. Despite our data limitation, the asymmetric game-theoretic approach permits us to identify the transfer that occurred from the rural to the urban sector in Senegal. Conclusions based solely on the endogenous bargaining coefficients (the ais) fail to identify the asymmetry associated with the price policies. This also occurs if the revealed preference approach is chosen. The symmetric cooperative game model, by imposing incorrect restrictions, ignores the exogenous bargaining structure and yields statistically biased estimates of the endogenous bargaining coefficients.
J.C. Beghin and L.S. Karp, Estimation of price policies in Senegal
63
4.2. Testing for efficiency
The axiom of efficiency states that the cooperative solution lies on the Pareto frontier of the payoff set. This requires that the derivatives of criterion function W with respect to the different price policies yield the same power structure (same a,‘~). We test whether the four first-order conditions, (26) to (27), yield the same estimates of a(&/&), and ~(z)~/u(z)~. We compare the restricted model [(26) to (27)] to the unrestricted one in which coefficients ai are allowed to differ across equations. This tests the efficiency of policies in both the farm and urban sectors. The estimated first-order conditions in the unrestricted model are (28)
dCVi -= dpr
--amat4
-ws/4m
dCV, ~ dp, ’
-(u(z)~/u(z)~) F,
r
(29)
and
(31)
The test of restrictions u3/u1 = cs/ci and u2/u3 = c2/c3 is reported in table 3. The hypothesis of efficiency is rejected. This result has several possible interpretations. Cooperative bargaining game theory may not be appropriate; perhaps players are not on the frontier, H, because the game is noncooperative. An alternative explanation recognizes that not all policies are chosen in simultaneously. Manning (1987) shows that inefficiency results in cooperative games if choices are made sequentially and bargaining power varies over time. Finally, the model neglects information problems. For instance, the marketing board is unable to predict perfectly the supply and demand responses of the other two players. In this case policy changes could bring the players to their contract curve.6 We use the estimated behavioral model to compute policy changes that move the players to the frontier. If the policies are efficient, the relative weights u1/u3 (or u2/u3) are equal in (28) and (29) [or (30) and (31)]. Assume 6This interpretation implies that the modeler knows more about agents’ responses than does the government; this is credible if the government is not econometriclaly equipped to estimate agents’ price response. The computed policy changes minimize the distance from the original equilibrium to the contract curve. They do not guarantee that all players will benefit from the move.
64
J.C. Beghin
and L.S. Karp,
Estimation
of price
policies
in Senegal
Table 3 Test of efficiency in both rural and urban markets (3SLS). Parameter c31 C3ll
C312 c314
C23 c231 a31 a311 a312 a313 a23 a231
Estimate
Std. error
-2.52431 - 1.56E-05 0.00977662 1.89E-07 1.01413 1.46E-07 -0.49314 - 1ME-05 0.00519194 - 1.23E-09 0.84340 1.46E-06
1.12467 4.29E-06 0.00370965 l.O7E-07 0.20439 4.58E-06 0.60925 2.42E-06 0.00183978 5.51E-08 0.53868 1.21E-05
Asympt. t ratio - 2.24 -3.64 2.64 1.77 4.96 0.03 -0.81 -4.29 2.82 - 0.02 1.57 0.12
‘The sum of squares of error is 94.55; the restricted sum of squares of error is 160.35. The Chi-squared test statistic is 65.79 with 12 degrees of freedom. The critical value is 26.2 at the 1% significance level.
that (28) and (29) yield different relative weights al/a3 and c1/c3. The difference of the relative weights, f, is a function of policies pg and pr (but not of policies p, and p,)
(32) Policy changes that lead to efficiency using a first-order Taylor approximation of the function f(p,, pr). Efficient policies pz and p: satisfy
/(P:,P:)=o~f(P,,Pf)+ii~~~pf)(P:-P*)+a~~~pf)(P:-Pf). B
(33) f
We assume that the optimum policy changes minimize the sum of the squared magnitudes of the policy changes subject to (33). The optimum policy changes are f(Pp
Pi*-Pi = - w-b,,
Pf) af(Pg9
Pr)laP,)2
+ (MP,,
Pf)l@i
PrY~Pf)21 for
i = gpf.
(34)
Similar optimal policy levels are derived and computed for pr, and pw. The two pairs of policies (p:, p,*), and (p,*, pc) are computed independently, since
J.C. Beghin and L.S. Karp, Estimation of price policies in Senegal
65
Table 4 Estimated relative price changes to achieve ethciency. Years 60 61 62 63 64 65 66 61 68 69 70 71 72 73 74 75 76 77 :i 80
dP&, - 0.22352 -0.24132 -0.22924 -0.18030 -0.13823 -0.09622 -0.01237 0.00109 -0.02122 -0.05314 -0.03314 0.04367 0.00252 -0.17604 -0.17513 -0.32074 -0.39040 0.12437 0.05838 - 0.00704 -0.20225
dpddp, 0.02482 0.01327 0.01329 - 0.01945 0.01081 0.00224 0.00333 0.00067 0.00608 0.00073 0.00329 - 0.00808 -0.08027 0.02875 0.00816 0.02203 - 0.22486 -0.01875 -0.00443 0.00103 0.02864
1.29830 0.53643 0.13639 0.13567 0.05417 0.02153 0.10223 0.33905 0.25524 0.14768 0.16589 0.26702 0.37820 0.43195 0.18674 0.93938 0.15535 0.47634 0.09083 -0.01291 0.06351
0.66024 0.01749 -0.03718 -0.09174 -0.01866 -0.00904 -0.04201 -0.02346 -0.04617 - 0.06628 -0.16961 0.06817 0.07411 0.08048 - 0.04829 0.63324 0.84543 -0.26139 -0.14545 0.10203 0.08149
f is not a function of the urban consumer prices. Table 4 presents the recommended relative changes in policies (in percent of the prevailing prices). These are computed with the observed differences ([(dCVJdp,)/dCV,/dp,)] [(dCI/,/dp,)/(dCVr/dp,)]). The changes are moderate, except for a few data points for which the estimated changes are large and would be difficult to implement. For the farm sector the direction of the proposed changes is plausible and implies better terms of trade. Relative price p&r has been too low for most of the observed data points. The suggested changes in urban consumer prices are mixed and depend on whether they are computed with the observed (the derivative ratios) or the predicted (the weight ratios) f. From 1980 to 1984 the World Bank negotiated policy reforms as a condition for loans to the Senegalese government; the reforms were consistent with the policy proposals mentioned in the introduction [Waterbury and Gersovitz (1987, ch. 9)] and meant an unambiguous decrease in the welfare of the urban sector. These policies were strongly opposed and partly defeated by the urban sector and state bureaucracy because they implied a redistribution of real income among Senegalese players.7 ‘An objection could be raised that the policy changes promoted by The World Bank would decrease the cost of the different subsidy programs and the taxes necessary to finance them, thus finally benefiting urban consumers. However, in the Senegalese case the tax base is the exportable agricultural output.
66
J.C. Beghin
and L.S. Karp,
Estimation
of price
policies
in Senegal
5. Conclusions We have modeled and quantified the political economy of important food and agricultural policies in Senegal using a cooperative bargaining game framework. The model explains food and price policies as the endogenous outcome of a bargaining process among three representative players: a farmer growing export and staple crops (groundnuts and millet); an urban consumer buying imported rice and wheat products; and a marketing board intervening in the agricultural and urban markets with -market power. We estimated the game and recovered its bargaining power structure. Farmers have a considerable amount of bargaining strength due to their abilities to switch from groundnut to millet production when they disagree with proposed agricultural policies. We tested the axioms underlying the cooperative game to discriminate among various cooperative bargaining game models. Symmetry and efficiency were rejected. Rejection of the symmetry axiom demonstrated the potential usefulness of asymmetric bargaining models that permit identification of differences in exogenous bargaining strength among players, We linked the asymmetry of our Senegalese game to the urban bias of the price policies that have penalized the rural sector and subsidized urban food consumption. Rejection of efficiency has significant policy implications; the bargaining power structure could be preserved, while efficiency could be improved by policy changes that implied policies more favorable to the farm sector. Validity of the axiom tests is limited by the small sample size of the data set, the choice of the functional forms and the aggregated and stylized aspects of the approach adopted. Nevertheless, the simplicity of the methodology is attractive and the method could be applied to different bargaining situations.
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J.C. Beghin
and L.S. Karp,
Estimation
of price
policies
in Senegal
67
Fudenberg, Drew and Eric Maskin, 1986, The Folk theorem in repeated games with discounting and incomplete information, Econometrica 54, 533-555. Gallant, A. Ronald, 1987, Nonlinear statistical models (Wiley, New York). Harsanyi, John C., 1963, A simplified bargaining model for the N-person cooperative game, International Economic Review 4, 193-220. Harsanyi, John C, 1977, Rational behavior and bargaining equilibrium in games and social situations (Cambridge University Press, Cambridge). Lipton, Michael, 1977, Why poor people stay poor (Harvard University Press, Cambridge, MA). Manning, Alan, 1987, An integration of trade union models in a sequential bargaining framework, The Economic Journal 97, 121-139. McFadden, Daniel, 1975, The revealed preferences of a government bureaucracy: Theory, Bell Journal of Economics 6, 401-416. McFadden, Daniel, 1976, The revealed preferences of a government bureaucracy: Empirical evidence, Bell Journal of Economics 7, 55-72. Nash, John, 1953, Two-person cooperative games, Econometrica 21, 128-140. Newbery, David and Nicholas Stern, eds., 1987, The theory of taxation for developing countries (Oxford University Press, Oxford). Rausser, Gordon C. and John W. Freebaim, 1974, Estimation of policy preference functions: An application to U.S. beef quotas, Review of Economics and Statistics 56, 4374l9. Roth, Alvin E., 1979, Axiomatic models of bargaining, Lecture notes in Economics and Mathematical Systems no. 170 (Springer-Verlag, New York). Sarris, Alexander H. and John Freebairn, 1983, Endogenous price policies and international wheat prices, American Journal of Agricultural Economics 65, 214-224. Scandizzo, Pasquale L. and Cohn Bruce, 1980, Methodologies for measuring agricultural price interventions effects, World Bank Staff Papers no. 394 (The World Bank, Washington, DC). Shubik, Martin, 1982, Game theory in the social sciences, Concepts and solutions (The MIT Press, Cambridge, MA). Svejnar, Jan., 1986, Bargaining power, fear of disagreement, and wage settlement: Theory and evidence from U.S. industry, Econometrica 54, 1055-1078. Thomson, William, 1981, A class of solutions to bargaining problems, Journal of Economic Theory 25, 431-441. Thomson, William, 1987, Monotonicity of bargaining solutions with respect to the disagreement point, Journal of Economic Theory 42, 5c58. Waterbury, John and Mark Gersovitz, eds., 1987, The political economy of risk and choice in Senegal (Frank Cass & Co., Totowa, NJ). Zusman, Pinhas, 1976, The incorporation and measurement of social power in economic models, International Economic Review 17, 447462.