Welfare Calculations in a Distributed Lag Model: Beans in Colombia

Welfare Calculations in a Distributed Lag Model: Beans in Colombia

Willem Janssen Economist, Department of Marketing and Market Research, Agricultural

University, Hollandseweg 1, 6706 KN, Wageningen, The Netherlands. Received 6 January 1992, accepted 28 September I992

Distributed lag functions are very popular for modeling supply behavior, but there is little published on their use for estimating welfare effects. A partial equilibrium model for beans in Colombia is used to derive the welfare parameters for distributed lag supply functions. Welfare calculations are made for a zero trade and a free trade scenario. The results of welfare calculations with the distributed lag supply functions are compared with the results of simple (undistributed) one-lag supply functions. Sensitivity analysis on price and lag coefficients is applied. Whereas the simple supply functions would lead to the conclusion that the free trade scenario would have brought most benefits, the distributed lag specification leads to the conclusion that for certain conditions the zero trade scenario would have been more beneficial. The reasons for the diverging results are explored.

Les fonctions a retard CchelonnC sont t r b utilisCes pour la modtlisation du comportement d’approvisionnement, mais leur utilitC pour estimer les effets sur la qualit6 de la vie est peu documentCe. Un modtele d’Cquilibre partiel pour la production des haricots en Colombie est utilisC dans le but de dCgager les paramktres sociaux pour des fonctions d’approvisionnement a retard CchelonnC. Les calculs des effets sociaux sont basks sur un scCnario de commerce extCrieur nu1 et sur un scCnario de libre-Cchange. Les rCsultats des calculs sociaux obtenus avec la fonction d’approvisionnement retard Cchelonnt sont compares avec ceux des fonctions d’approvisionnements simple (non CchelonnC) a un regard. Une analyse de sen- sibilite est faite sur les coefficient de prix et sur les coefficients de retard. Alors que les fonctions d’approvisionnement simple sembleraient indiquer que c’est le scCnario de libre- Cchange qui aurait CtC le plus profitable, l’introduction de la fonction a retard CchelonnC amkne la conclusion que dans certaines conditions le sctnario de commerce extCrieur nu1 aurait CtC plus avantageux. Les raisons de cette divergence sont examinCes.

INTRODUCTION Distributed lag functions have proven to be very popular for estimating agricultural supply behavior (Griliches 1967; Askari and Cummings 1976). They allow the modeling of the gradual reaction to price changes. These gradual reactions are often observed in agriculture because of the time needed to realize investments or because of the cautious adaptation of farmers to changing prices. The geometrically distributed lag function as defined by Koyck (1954) is especially popular. It permits the specification of supply as defined by prices in the past in a rather simple econometric procedure where each moment’s supply is a function of only one price and the last moment’s supply. Koyck’s procedure also allows estimation of short- and long-run supply elasticities. Estimation procedures for

Canadian Journal of Agricultural Economics 40 (1992) 459-474 459

460 CANADIAN JOURNAL OF AGRICULTURAL ECONOMICS

distributed lag supply functions are extensively treated in most econometric textbooks.

Although distributed lag functions are popular for modeling supply behavior, they are apparently omitted from welfare calculations, where other supply specifications are frequently found. For example, Peterson (1979) uses a log-linear supply specification to estimate the cost of cheap food policies. Edwards and Freebairn (1984) employ simple linear supply functions to analyze research in tradable commodities. Lichtenberg and Zilberman (1986) apply a constant elasticity specification of the inverse supply to estimate welfare effects of price supports in U.S. agriculture. Oehmke (1988) utilizes constant elasticity functions to study returns to research in distorted markets. Cramer et a1 (1990) estimate short-run elasticities in a constant elasticity specification to calculate the cost of regulation in the U.S. rice industry. These authors assume immediate supply reaction to changing prices and are not concerned with the slow adaptation of supply that has often been observed and measured with distributed lag functions.

The omission of distributed lag functions from welfare analysis may be due to two reasons. First, welfare analysis and supply estimation are often practiced by persons with different objectives. If the quality of supply prediction is the main interest, the supply specification becomes a very important issue and distributed lag functions may be considered. On the other hand, if the interest is the meas- urement of welfare effects of a policy or innovation, attention is centered around measuring and modeling the interventions, rather than on the specification of the supply function.

Second, as this paper illustrates, the treatment of distributed lag functions for welfare calculations is less straightforward than that of the specifications men- tioned earlier. It requires a multi-period analysis with a defined time frame as well as a number of other steps before arriving at a final welfare estimation.

A geometrically distributed lag supply function estimated for the case of beans in Colombia (1977-86) is used for welfare analysis of two alternative policies. By studying a specific rather than a generic case, the analysis reflects the insta- bility (e.g., world market prices) in which the agricultural sector tends to operate. The simulation model is presented first, followed by a specification of the time frame of analysis and alternative import policies. Applied welfare theory is used to derive the measurements of consumer and producer welfare changes, and outcomes for alternative policy scenarios are discussed. These are compared with the results that were obtained with simple lag supply functions. Sensitivity analysis on the two principal parameters of the model is applied.

MODEL SPECIFICATION Estimated equations are taken from previous research, as reported by Luna and Janssen (1990) and represent demand and supply equations for the Colombian bean market. Domestic supply is:

WELFARE CALCULATIONS IN A DISTRIBUTED LAG MODEL 46 I

Q, = 6832 + 1015 * P,-1 + 0.673 * Q,-l (1)

where Q, = estimated domestic production of beans in year t (tonnes);

P,- = retail price of beans in year t - 1 (Col. pesos/kg, deflated to 1980

Q,- = domestic production of beans in year t - 1. values) ( U S 1 = 44 Col. pesos); and

Domestic demand is:

P, = -27.10 - 14.58 * AH, + 1.18 * Y, (2)

where Pt = estimated retail price of beans in year t (Col. pesos/kg, deflated

to 1980 values); AH, = observed availability of beans per person in year t (kg); and

Y, = trend value expressed as the last two numbers of the year of estimation (e.g., 1984 = 84).

Availability per person is:

AHt = (Q,-l + M,)/POP, (3)

where Mt = imports of beans made available at retail level in year t (tonnes);

POP, = population of Colombia in year t (in thousands); and the other variables are as defined before.

Supply is specified by a distributed lag function. In the demand equation, price is the dependent variable, as market availability is defined by the quantity supplied in the previous year. The model is estimated with ordinary least squares using data from 1976 to 1986. All coefficients are significant with 95% confidence. Adjusted R2 are 0.60 for the supply equation and 0.88 for the demand equation. The relatively low R2 for the supply equation reflects weather varia- bility and price fluctuations for alternative crops. Durban-Watson coefficients do not indicate autocorrelation. For further explanation of the model, the reader is referred to the article by Luna and Janssen. Domestic production, imports, domestic retail price, CIF world market price, and population data from 1976 to 1986 are presented in Table 1.

The Time Frame of Simulation Alternative import policies are simulated from 1977 to 1986. To assure that different policies are correctly compared, conditions before and after the simulation period should be equal. Prices, production and imports for 1976 are left as they were observed and are used to start the simulation (because of the one-year


Table 1. Bean supply and prices and population, Colombia, 1976-88

Domestic Domestic CIF world production Imports retail price market price Population

Year (tomes) (Col. pesos/kg) (Col. pesos/kg) (thousands)

1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986

Average

67,600 74,900 74,823 74,707 83,356 74,100 72,900 81,800 80,155 98,964

103,943

8 1,985

23 72

3,593 250

4,568 1,486

11,376 31,115 6,675 8,893 4,584

6,603

22.88 22.23 18.62 23.95 22.92 18.33 22.44 16.67 25.71 28.05 19.23

21.82

27.98 19.12 22.61 21.67 24.48 24.08 13.75 12.76 16.21 17.62 18.85

19.12

23,672 24,183 24,707 25,245 25,794 26,355 26,929 27,515 28,110 28,774 29,310

~~ ~ ~

ahports available at retail level. b ~ S $ I = 44 Col. pesos. Sources: Domestic production: Ministerio de Agricultura, Oficina de Planeaci6n del Sector Agricola. Figures from the agricultural sector, various years, Bogot6. Imports: Depar- tamento Administrativo Nacional de Estadistica, Anuarios de Comercio Exterior, various years, Bogoti. Domestic price: Departamento Administrativo Nacional de Estadistica, Boletin mensual, various years, Bogotil. Note: Average price for red-mottled beans. CIF world market price: Small red beans, FOB, Idaho, Bean market summary. Agricultural Marketing Service, various years, Denver, Colorado. Population: Departamento Adminis- trativo Nacional de Estadistica, Boletin mensual, various years, BogotB.

lag structure, the 1976 price influences 1977 production). From 1987 onward, the same average world market price is applied to all different model runs.

Import Policy Scenarios The Colombian government followed a somewhat erratic policy of import restrictions during the period of simulation. Three factors defined the policy: the wish to increase availability of beans to consumers, the pressure by traders to allow imports, since this would provide opportunities for profits and, thirdly, the desire to protect bean producers. In some years, when domestic supply or international prices were low, sizable imports were allowed, but in other years imports were forbidden (Table 1). For simplicity, this article does not simulate the observed Colombian policy but the two extreme cases of trade policy:

Free trade: Colombia imports and exports beans according to the difference between domestic quantity supplied and demanded at the world market price. The internal price equals the world market price (CIF-Colombia).

WELFARE CALCULATIONS IN A DISTRIBUTED LAG MODEL 463

No adjustments for transaction costs are made. If the world market price is known, Eq. 2 is used to define the availability per person that can be cleared in the market. With the same world market price, the domestic quantity supplied in the following year is defined by Eq. 1. Since the quantity supplied in the year before is also known, Eq. 3 can be used to define the imports needed to arrive at the availability per person as calculated in Eq. 2. Zero trade: The Colombian bean market is completely isolated from the world market. Neither imports nor exports are allowed. In this case, the simulation starts by calculating the domestic quantity supplied in Eq. 1, on the basis of last year’s quantity supplied and price. Last year’s quantity supplied is also used to calculate the availability per person in Eq. 3. Availa- bility per person is then used to define the market price in Eq. 2.

Welfare Evaluation Parameters Welfare evaluations are made in a Marshallian surplus framework. The two alternative trade policies affect consumer and producer welfare. Calculation of welfare parameters in a simulation framework follows general theoretical concepts Oyillig 1976; Curry et a1 1971). However, in the case of producer welfare, some particular issues must be addressed. Welfare parameters throughout the simulation period have to be aggregated, which necessitates specification of a discount rate.

Consumer Welfare Calculating consumer surplus is straightforward. For each simulation and each year, it is calculated as the surface of the triangle (see Figure 1):

where Po = price at which quantity demanded is zero, and other variables are as previously defined. This value is afterward multiplied by the size of the population, POP,.

Producer Welfare The distributed lag structure of the domestic supply equation complicates the meas- urement of producer surplus. Three steps are required to calculate producer surplus. The first step concerns the short-run supply function. This function equals the marginal cost curve and forms the basis for producer welfare calculations. The short-run supply function shifts to the right (by fixing the last term of Eq. 1) if prices are high and to the left if prices are low. The short-run supply surplus for each year, SSS, is the starting point for further calculations.

The second step is to calculate the investments, I , made to shift the short-run supply function. The investments needed to realize these shifts are subtracted from


Quantity

Figure 1. Estimation of consumer surplus

the producer surplus as calculated with the short-run supply function (SSS - I). Investments can be calculated with the long-run supply function (Just et a1 1982).

The third step is to calculate the residual effect of the investment behavior after the simulation ends. At the end of the simulation, the intercept of the short- run supply function is not the same in each scenario, but depends on developments during earlier years of simulation. With a large intercept (reflecting large investment costs) the short-run producer surplus after the simulation period is larger than with a small intercept (reflecting small investment costs). A residual value, R, must be calculated to account for the difference among scenarios in producer surpluses after the simulation period. The residual value, R , is added to sss - I.

The sum of short run surplus, investments and residual value forms the total producer surplus. By comparing this between scenarios (i.e., ASSS - AZ + AR), the impact of free trade versus zero trade can be assessed. The three required steps are now explained in more detail.

Short-run Producer Surplus: This can be measured by fixing the lag component of the production equation (the last term in Eq. l), aggregating this to the


intercept, and now measuring (see Figure 2, the area enclosed by boldfaced lines):

where Z, = intercept of the short-run supply function at moment t ; 0 = origin;

and the other variables are as defined before. This surface now has to be corrected for the possible price change from year

t - 1 to year t . The correction exists in subtracting the following from Eq. 5 (see Figure 2, the shaded area):

By executing these calculations for both scenarios and subtracting one from the other, the difference in short-run producer surplus, ASSS, is obtained.

Investments: The calculation of the investment effect follows the discussion by Just et al. They define a distributed lag model with the following long-run specification:

Q, = a. + bo*P, (7)

where Q, = supply at moment t; a. = intercept; bo = supply coefficient; and P, = price in period t ;

corresponding to the following short-run specification:

Q, = (1 - e) a. + (1 - e) bo*P, + e*QtPI (8)

where e = lag coefficient, and other variables are as above.

Just et a1 define the difference in investments between scenarios 1 and 0 as:

where AZ, = difference in investments between scenarios 1 and 0 at moment t ;

ALSS,+l = difference in producer surplus between scenarios 1 and 0 as


calculated with the long-run supply function (see Eq. 7) at the expected prices for period t + 1; and

U S S , = difference in producer surplus between scenarios 1 and 0 as calculated with the long-run supply function at the prices for period f.

Interpreting this verbally, the difference in investments at moment t depends on the long-run producer surplus for scenarios 1 and 0 at the expected prices for period t + 1 and period t .

In the case of beans in Colombia, supply in year t depends on the price in t - 1. Substituting t for f + 1 and r - 1 for t in the right-hand side of Eq. 9 allows it to be reexpressed as:

Thus the difference in investments at moment I depends upon the producer surplus as observed with the prices at moment t and t - 1 for the two scenarios.

By further substituting LSS,' - LSSp for U S S , and LSS:-l - LS$- I for U S S , - I , Eq. 10 may be rewritten as:

where LSS = the producer surplus calculated with the long-run supply function, with superscripts indicating the scenario and subscripts the time period.

For the present example, the long-run supply corresponding with the short- run specification of Eq. 1 is:

The long-run producer surplus corresponding with prices of moment t can now be calculated as:

LSS, = 20894*P, + 0.5*3104*(PJ2 (13)

Calculating LSS, and LSS,-1 for the free trade and the zero trade scenario with Eq. 13 obtains All, the difference in investments between scenarios.

Residual surpluses: Now consider what happens when the simulation period ends. At the average world market price after the simulation period (see subsection on The Time Frame of Simulation), the short-run supply functions of the two scenarios start to converge to the short-run supply function as expected at the world market price. In the meantime, the short-run supply functions of the different scenarios have different intercepts, depending on the supply development in the simulation period. The intercept influences the size of producer surplus after the


0

Figure 2. Estimation of producer benefits in the case of a distributed lag function

simulation period. Since producer surplus after the simulation period depends on developments within the simulation period, a correction has to be applied.

For year 11, supply equals:

Q,, = 6832 + 1015*Pf + 0.673*&10 (14)

where P - average assumed world market price. f. - The intercept for year 11 is:

6832 + 0.673*Qlo

For year 12, the intercept equals:


6832 + 0.673*(6832 + 1015*Pf + 0.673*Q,o) (16)

After the simulation period, Pf is the same for both runs, and the difference in the intercept between scenarios is caused only by the quantity supplied in the last year of the simulation period, Qlo. All the other terms of Eq. 15 and 16 are constant between scenarios and remain so for further years.

By multiplying the short-run intercept with Pfi the contribution of the intercept to the producer surplus is measured. For scenarios 1 and 0, the difference in this contribution, AR, over the years after the simulation period equals:

m

AR = (Qto - Qyo)*0.673('-'o)*P f f = 11

which equals

(Qio - Qyo)*0.673/(1 - 0.673)*Pf (18)

Comparison of Total Producer Surplus. By adding AR (the difference in residual value) to ASSS (the difference in short-run producer surplus) and subtracting Al (the difference in investments), the final indicator for comparison of total producer surplus is obtained: ASSS - AZ + AR.

Trade Benefits In the case of free imports, domestic prices are equal to CIF prices and profits (in the neoclassical sense) in trade are zero. In the case of zero imports, trade profits cannot be made.

Aggregation throughout the Simulation Period To aggregate values from different years in the simulation period, a discount factor has to be used. In the present analysis, the discount factor is set at 7%.

SIMULATION RESULTS

Table 2 provides the principal results of the simulations for the first and second five-year periods. In the first period of analysis, a free trade policy would have stimulated production more than a zero trade policy. This is because international prices were rather high (due to the trade restrictions that the Colombian government applied, international prices were in fact above the observed domestic prices).

During this period, consumers would have obtained more benefits with the zero trade policy and producers would have lost. In the second five-year period, world prices are considerably lower and the situation changes radically. Produc- tion would now have been higher in the zero trade scenario, as would have been prices. Comparison of import and production data between the zero trade and


Table 2. Market and welfare indicators for free and zero bean trade scenarios in Colombia

Free trade Zero trade

Average production (tonnes) 1978-82" 1983-87 Average price (Col. pesodkg) 1977-81 1982-86

Average imports (tonnes) 1977-81 1982-86

Producer welfare (million pesos)b 1977-81 1982-'

Consumer welfare (million pesoslb 1977-81 1982-86

84,227 82,821 76,064 94,989

22.4 15.8

21.4 25.6

- 1,386 - 26,567 -

- 227 3,162

31 1 -2,953

Total welfare (million pesos) 1977-8 1 84 1982-' 210

'Production for 1977 is predefined by (fixed) 1976 price and production. In the different scenarios, domestic production starts to vary only from 1978 onward. Therefore, the period of analysis for production figures has been shifted forward one year.

'Contains the difference in residual surplus (see subsection on Residual Surpluses) after the simulation period.

comparison with the free trade scenario.

the free trade scenario demonstrates that for each tonne of imports, domestic production falls by some 0.7 tonne.

As would be expected, in the second period, producers gain considerably with trade elimination, and consumers lose. The overall surplus is higher for the zero trade scenario. The simulation suggests that for the period of analysis as a whole, a zero trade policy would have been more favorable than a free trade policy. This outcome deviates from the theory that countries stand to benefit from free trade.

Distributed Lag Versus Simple Supply Models The results of the distributed lag specification are compared with results of simple lag supply specifications. Two simple lagged supply functions are defined:

Q, = 59979 + 1015*Pt-1


Eq. 19 has the same price coefficient as the short-run specification of the distributed lag model used before. Eq. 20 represents a more elastic supply. The price coefficient of this equation equals the price coefficient of the distributed lag model aggregated over a three-year period (this is 1015 + 1015*0.673 + 1015*0.6732). Intercepts are chosen to assure that average production in the free trade scenario over the period of analysis is the same with both simple supply specifications and with the distributed lag specification. Eq. 19 is the “inelastic” specification and Eq. 20 is the “elastic” specification.

Model simulations and welfare calculations are made in a fashion similar to the distributed lag runs. For these simple lag supply functions, there are no investments and no residual surpluses. Consumer surpluses are calculated in the same way as for the distributed lag model.

Summary data of simulation runs for both the distributed lag and the inelastic and elastic specifications are given in Table 3. In the inelastic supply model, a zero trade policy has a more limited effect on production growth than in the distributed lag model, and prices tend to increase more. In the elastic supply model, the zero trade policy has a slightly smaller effect on production growth than in the distributed lag model. Prices increase less rapidly than for the inelastic model and also stay below the level observed in the distributed lag model.

Gains to producers in the zero trade scenario are almost two-thirds larger in the inelastic than in the elastic model, mainly due to higher producer prices. The distributed lag model shows a very interesting result: with a smaller price increase, the gains in producer surplus for the zero trade scenario are higher than for the inelastic supply model. With a somewhat larger price increase than in the elastic supply model, the gains are almost doubled. The investments in production structure that shift the short-run supply function to the right allow increased producer surpluses with a more modest price rise.

With the distributed lag specification, the total surplus for the zero trade policy is higher than for the free trade policy (as already shown in Table 2). With simple lag supply functions, the free trade policy has a higher surplus.

The Effect of Price and Distributed Lag Coefficients on Model Results To analyze the robustness of the analysis, sensitivity analysis is performed on the size of the price and distributed lag coefficients. The maximum advantage of trade restriction would be obtained with a somewhat smaller short-run coefficient of around 900, some 10% below the estimated value of 1015. The short- run supply coefficient could increase by 20 % (to a value of 12 15) or fall by 32 % (to a value of 690) without changing the conclusion that trade restriction is beneficial. Outside the range from 690 to 1215, the free trade scenario quickly becomes much more beneficial than the zero trade scenario.

WELFARE CALCULATIONS IN A DISTRIBUTED LAG MODEL 47 1

Table 3. Summary data for distributed lag, inelastic and elastic supply models ~ ~

Distributed Inelastic Elastic lag model supply model supply model

Average annual domestic supply 1978-87 (tonnes) in free trade scenario 79728 79728 79728

Average annual domestic supply increase 1978-87 (tomes)” 8760 5350 8530

Average annual price increase 1977-86

Producer surplus increase

Consumer surplus increase

(Col. pesos/kg)a.b 4.40 5.27 3.95

(million pesos)” +2935 +2480 + 1533

(million pesos)” -2642 -3001 - 1977 Total surplus increase (million pesos)” + 294 -521 - 444

aFor zero trade scenario in comparison with the free trade scenario. bPrices for 1977-86 define domestic supply for 1978-87.

A larger price coefficient would reflect a stronger and more responsive supply (at the same price, more would be supplied), while a smaller price coefficient would reflect a weaker supply. If the price coefficient were more than 20% above the estimate, the Colombian bean sector would win more through exports to the world market than through sales in a closed market with limited absorption capacity. If the price coefficient were more than 32% lower, the domestic supply would be so small that the country would gain by importing.

The sensitivity of the outcomes with respect to the lag coefficient is analyzed. The estimated value of 0.673 is very close to where the maximum advantage of zero trade can be realized. The lag coefficient can increase by 7 % or fall by 15 % without changing the conclusions. Again, outside this range, the free trade scenario quickly becomes more beneficial. This interpretation is very similar to the one given above. A larger lag implies a stronger but more slowly reacting supply sector; at a certain level of strength, more benefits can be obtained through exports than through isolation. Similarly, a smaller lag, which implies a more rapidly but weakly responding supply, suggests that more benefits can be obtained through imports than through protection.

The stability interval, as derived from the sensitivity analysis, may fall within the statistical confidence limits for the estimates of price or distributed lag coefficients (as it does in the present study). From an empirical point of view this war- rants caution when interpreting the results. From a theoretical point of view, the results of the sensitivity analysis suggest that trade restriction is relevant for supply sectors that are almost able to compete in the world market, but not for very strong or very weak sectors.


CONCLUSION As indicated in the introduction, distributed lag specifications are popular because they allow the modeling of gradual changes and they recognize the inability of the production structure to adapt itself rapidly to changing prices. They also recognize the investment nature of the supply reaction in welfare calculations. By investing in production structure (as measured in changes of the producer surplus along the long-run supply curve), the short-run supply curve shifts to the right and marginal production costs fall.

Welfare measurements obtained with distributed lag functions suggest that trade restrictions may be economically efficient for a country. If such restrictions allow investments in production structure, from a strictly welfare point of view, a country might be better off than with trade, even without considering issues such as the shadow price of foreign exchange or transaction costs. In fact, welfare calculations with the distributed lag supply function strongly support the infant industry argument for trade restrictions (Wells 1977),

For the specific case analyzed in this paper - beans in Colombia - the restrictions applied on imports may have been economically efficient. Colombia’s bean sector is close to being competitive in the world market, but has not become an efficient exporter as yet. The erratic policy of the government in responding to consumer, trader and producer interests at different moments in time may have been more efficient than a free trade policy.

Would the use of distributed lag functions then argue against free trade? The sensitivity analysis shows that trade restrictions are efficient only in certain intervals of price and lag coefficients. Free trade can remain the “default” option for policy makers. Nevertheless, the results obtained with a distributed lag specification may argue for trade restrictions in cases where a production sector is close to competitiveness. Where the supply reaction is known to be very slow but sus- tained, as in the case of tree crops, trade restrictions may also be justified.

Three issues affect the validity of this conclusion. The first one is the relevance of the long-run supply function. If producer prices in the long run are stable, it could be argued that adjustments of production capacity will not be made and that the industry will produce at average costs that are equal to the producer price (Eckert and Leftich 1988). Producers would react only to temporary short-run deviations from the long-run price expectation, and the long-run producer surplus would be zero: producer surplus could be measured completely with the short- run supply function, as done in simple (lag) supply functions. However, as the price developments in the two different scenarios show, the assumption of stable producer prices is not realistic. Rather, average producer prices over the years depend on the policies reflected in each scenario, and investment behavior will change accordingly. Exclusion of long-run producer surplus invalidates the analysis.

The second issue is the use of a partial equilibrium model. Distributed lag specifications recognize the importance of investments for production structure


and, in that respect, they are less partial than simple supply functions. Neverthe- less, a partial equilibrium model cannot be used to judge whether investments in a certain sector are better than in other sectors.

Third, by restricting trade for certain products, the search for cost-reducing technology is limited. Although the short-run supply function might shift to the right, the long-run supply function might be relatively stable and not experience the shift toward the right that improved technology might have caused. However, both the analysis made here and the infant industry argument assume only temporary isolation from the world market. Rather than providing unqualified support for trade restrictions, the distributed lag specification shows that strategic market interventions from time to time may be worthwhile.

Distributed lag specifications represent a popular econometric solution to the estimation of supply behavior. Remarkably, the welfare consequences of the assumptions behind distributed lag functions have not been addressed. Distributed lag functions assume that investments in production structure are a substantial component of the overall supply reaction. If these investments take place, production costs are reduced and producer welfare increases more than would be expected on the basis of the price change alone. Given the popularity of distributed lag functions for supply specification, it may be assumed that investment and reduc- tions in the subsequent production costs are quite usual. This would suggest that in many previous studies that applied producer surplus calculations on the basis of simple (lag) supply functions, the effect of price or policy changes on producer surplus has been underestimated.

ACKNOWLEDGMENT Research for this paper was done while the author was employed as an economist in CIAT’s Bean Program (Centro Internacional de Agricultura Tropical, A.A. 6713, Cali, Colombia). The author wants to thank Douglas Pachico, Luis Sanint, Guy Henry and two anonymous Journal referees for useful comments and suggestions on earlier drafts of the paper. The editorial support of Bill Hardy and Marnie Leybourne is highly appreciated. The author remains the only person responsible for mistakes and omissions.

REFERENCES Askari, H. and J. T. Cummings. 1976. Agricultural Supply Response: A Survey of the Econometric Evidence. New York: Praeger Publishers. Cramer, G. L., E. J. Wailes, B. Gardner and W. Lin. 1990. Regulation in the U.S. rice industry, 1965-1989. American Journal of Agricultural Economics 72: 1056-65. Curry, M., A. Murphy and A. Schmitz. 1971. The concept of economic surplus and its use in economic analysis. Economics Journal 81: 741-99. Eckert, R. D. and R. H. Leftich. 1988. The Price System und Resource Allocation. 10th ed. Chicago: Dryden Press. Edwards, G. W. and J. W. Freebairn. 1984. The gains from research into tradeable commodities. American Journal of Agricultural Economics 66: 41-49.


Griliches, Z. 1967. Distributed lags: A survey. Econometrica 35: 16-49. Just, R. E., D. L. Hueth and A. Schmitz. 1982. Applied Welfare Economics and Public Policy. Englewood Cliffs, N.J.: Prentice Hall. Koyck, L. M. 1954. Distributed Lags and Investment Analysis. Amsterdam: North Hol- land Publishers. Lichtenberg, E. and D. Zilberman. 1986. The welfare economics of price supports in U.S. agriculture. American Economic Review 76: 1135-41. Luna, C. A. and W. Janssen. 1990. El comercio internacional y la produccih de frijol en Colombia. Coyuntura Agropecuaria (BogotB, Colombia) 7 (1): 107-39. Oehmke, J. F. 1988. The calculation of returns to research in distorted markets. Agricul- tural Economics 2: 291-302. Peterson, W. L. 1979. International farm prices and social cost of cheap food prices. American Journal of Agricultural Economics 6 1 : 12-2 1. Wells, S. J. 1977. International Economics. Rev. ed. London: George Allen & Unwin. Willig, R. D. 1976. Consumer surplus without apology. American Economic Review 66: 589-97.

Documents

Welfare Calculations in a Distributed Lag Model: Beans in Colombia