Supply Response: Expectations Formation and Partial Adjustment
4. Policy Uses of Estimates
The estimated parameters are of value only in their usefulness for policy analysis. In this final section of the exercise, you will use the results recorded in Table 4E.3 to calculate short- and long-run elasticities as well as impacts from 15% increases in groundnuts and millet prices.
Calculating Elasticity Estimates
The convenient feature of the log-linear specification is that the elasticity estimates do not vary with the point at which they are evaluated, and the short-run elasticities are simply equal to the parameter estimates of the price variables: Egroundnuts
sr b2 andEmillet
sr b3. The long-run elasticities are calculated as follows:
Eilr Eisr 1b1.
Calculate the short- and long-run elasticities for your models.
Calculating Impacts from Price Changes
Consider now only the model that best explains the groundnut acreage decision.
Estimation of the impact of price changes on groundnuts production can be done by using the estimated model to predict acreage response under alternative scenarios of price changes.
Consider, for example, the following model (model (5) above):
lnAt b0b1lnAt1b2lnpgt b3lnpm,t1b4 lnRt1 b5DUMtb6St. First, create a column of estimated area in J44–J76 as follows:
ˆ ,
A t exp(b0 b1ln ˆ A t1b2 lnpgt b3lnpm,t1b4 lnRt1b5DUMtb6St)
which would serve as reference. In column K, create a new vector of real prices for groundnuts that incorporates a 15% increase in prices from 1961 to 1988. This represents a policy in which the price increase occurs in 1961 and from then on the change is maintained.
Create the corresponding variable ln and then estimate a new vector of areas:
pgt1
pgt1 A ˆ t
1 exp(b0 b1ln ˆ A t1b2 lnpgt
1 b3 lnpm,t1b4lnRt1b5DUMt b6St).
The comparison of gives you the impact of the price policy. You can compute the percentage changes (in column O), or view these on a graph. Comment.
A ˆ t1and ˆ A t
Repeat the same procedure without the variables DUM and S in columns M and N, with percentage change in column P. This tells you what would have been the impact of the price policy in the absence of a structural adjustment program. Compare these two results. What can you infer from them? Does structural adjustment make supportive price policies more or less necessary than in normal times? Explain why.
References
Anderson, Jock, John Dillon, and Brian Hardaker. 1977. Agricultural Decision Analysis. Ames: The Iowa State University Press.
Antonovitz, Frances, and Richard Green. 1990. “Alternative Estimates of Fed Beef Supply Response to Risk.” American Journal of Agricultural Economics 72:475-88.
Antonovitz, Frances, and Terry Roe. 1986. “A Theoretical and Empirical Approach to the Value of the Information in Risky Markets.” Review of Economics and Statistics 68:105-14.
Askari, Hossein, and John Cummings. 1976. Agricultural Supply Response: A Survey of the Econometric Evidence. New York: Praeger.
Behrman, Jere. 1968. Supply Response in Underdeveloped Agriculture: A Case Study of Four Major Annual Crops in Thailand. 1937–1963. Amsterdam: North–Holland.
Chavas, Jean-Paul, Rulon Pope, and Robert Kao. 1983. “An Analysis of the Role of Futures Prices, Cash Prices, and Government Programs in Acreage Response.” Western Journal of Agricultural Economics 8:27-33.
Cuddihy, William. 1980. Agricultural Price Management in Egypt. Staff Working Paper no. 388.
Washington, D.C.: World Bank.
Debertin, David. 1986. Agricultural Production Economics. New York: Macmillan.
Eckstein, Zvi. 1984. “A Rational Expectations Model of Agricultural Supply.” Journal of Political Economy 92:1–19.
Ezekiel, Mordecai. 1938. “The Cobweb Theorem.” Quarterly Journal of Economics 52:431–443.
Fisher, Brian. 1982. “Rational Expectations in Agricultural Economics Research and Policy Analysis.”
American Journal of Agricultural Economics 64:260–65.
Gardner, Bruce. 1976. “Futures Prices in Supply Analysis.” American Journal of Agricultural Economics 58:81-84.
Hartley, Michael, Marc Nerlove, and Kyle Peters. 1987. “An Analysis of Rubber Supply in Sri Lanka.” American Journal of Agricultural Economics 69:755-61.
Heathfield, David, and Soren Wibe. 1987. An Introduction to Cost and Production Functions. Atlantic Highlands, N.J.: Humanities Press International.
Henderson, James, and Richard Quandt. 1971. Microeconomic Theory: A Mathematical Approach.
New York: McGraw-Hill.
Jarvis, Lovell. 1974. “Cattle as Capital Goods and Ranchers as Portfolio Managers: An Application to the Argentine Cattle Sector.” Journal of Political Economy 82:489-520.
Judge, George, Carter Hill, William Griffiths, Helmut Lütkepohl, and Tsoung-Chao Lee. 1988.
Introduction to the Theory and Practice of Econometrics. New York: John Wiley & Sons.
Just, Richard. 1977. “Estimation of an Adaptive Expectations Model.” International Economic Review 18:629-44.
Lovell, Michael. 1986. “Tests of the Rational Expectations Hypothesis.” American Economic Review 76:110–24.
Lucas, Robert. 1976. “Economic Policy Evaluation: A Critique,” In The Phillips Curve and Labor Markets, edited by K. Brunner and A. Meltzer. Amsterdam: North–Holland.
Mundlak, Yair. 1985. The Aggregate Agricultural Supply Response. Working Paper no. 8511.
Rehovot, Israel: Center for Agricultural Economics Research.
Muth, John. 1961. “Rational Expectations and the Theory of Price Movements.” Econometrica 29:315-35.
Nelson, Gleen, and Thomas Spreen. 1978. “Monthly Steer and Heifer Supply.” American Journal of Agricultural Economics 60:117-25.
Nerlove, Mark. 1956. “Estimates of Supply of Selected Agricultural Commodities.” Journal of Farm Economics 38:496–509.
Nerlove, Mark. 1958. The Dynamics of Supply: Estimation of Farmers’ Response to Price. Baltimore:
Johns Hopkins University Press.
Paarsch, Harry. 1985. “Microeconomic Models of Beef Supply.” Canadian Journal of Economics 18:636-51.
Rao, Mohan. 1989. “Agricultural Supply Response: A Survey.” Agricultural Economics 3:1–22.
Scandizzo, Pasquale, and Colin Bruce. 1980. Methodologies for Measuring Agricultural Price Intervention Effects. Staff Working Paper no. 394. Washington, D.C.: World Bank.
Shideed, Kamil, and Fred White. 1989. “Alternative Forms of Price Expectations in Supply Analysis for U.S. Corn and Soybean Acreages.” Western Journal of Agricultural Economics 14:281-92.
Shonkwiler, Scott, and Suzanne Hinckley. 1985. “A Generalized Supply Response/Factor Demand Model and Its Application to the Feeder Cattle Market.” Western Journal of Agricultural Economics 10:245-53.
Wallis, Kenneth. 1980. “Econometric Implications of the Rational Expectations Hypothesis.”
Econometrica 48:49–73.
Waugh, Frederik. 1964. “Cobweb Models.” Journal of Farm Economics (now American Journal of Agricultural Economics) 46: 602–614.
Wickens, M.R., and J.N. Greenfield. 1973. “The Econometrics of Agricultural Supply: An Application to the World Coffee Market.” The Review of Economics and Statistics 55:433-440.
Williams, Jeffrey, and Brian Wright. 1991. Storage and Commodity Markets. Cambridge, England:
Cambridge University Press.
Wright, Brian. 1994. “Dynamic Perspectives on Agricultural Policy Issues.” American Journal of Agricultural Economics 75:1113-25.
Supply response A priori Reduced Structural
models information form parameters Restrictions Estimators Residuals
Partial adjustment and None pt –1 1, 2, 3 624523560 2(32)134 0
2wt
adaptive expectation qt –1, qt –2 , 14/(1) , 11/ , [ut(1)ut1]
zt, zt –1 22/ ,35/ [vt(1)vt1]
Adjustment and expec- 3 = 0 pt –1 1, 2 None 121/2, 2 2/(341) Same tations, restricted qt –1, qt –2 , and not estimatable
Expectations only = 1 pt –1, qt –1 1, 2, 3 6 = – 35 13 ut(1)ut1
zt, zt –1 11/,22/,35 + wt
Expectations restricted = 1 pt –1 , 2 None 13 Same
3 = 0 qt –1 11/,22/
Adjustment only = 1 pt –1, qt –1 1, 2, 3 None 13 ut + vt
zt 11/,22/,35/
Adjustment restricted = 1 pt –1 1, 2 None 13 Same
= 0 qt –1 11/,22/
Extrapolative naive = 1 pt –1 1, 2, 3 None 11,22,35 ut
= 1 zt
Extrapolative naive = 1, = 1 pt –1 1, 2 None 1 = 1, 2 = 2 ut and restricted 3 = 0
Price elasticities
Product Country Period Short–run Long–run R2
Agricultural production Argentina 1950–74 0.21 to 0.35 0.42 to 0.78 — Foodgrains India 1951–64 –0.06 to 0.42 — —
Rice Thailand 1951–65 0.39 0.31 0.48
India 1960–69 0.19 to 0.24 0.64 to 0.68 —
Pakistan 1949–68 0.12 0.17 —
Bangladesh 1949–68 0.13 0.19 —
Philippines 1972–74 0.4 to 0.7 0.7 to 1.0 —
Indonesia 1951–62 0.20 — 0.69
Malaysia 1951–62 0.23 1.35 0.61
Taiwan 1962–72 0.22 0.97 —
South Korea 1960–71 0.24 2.00 —
Sri Lanka 1953–74 0.21 0.99 —
Egypt 1953–72 0.08 0.08 0.43
Iraq 1960–71 0.66 1.57 0.59
Wheat India 1950–67 0.10 0.13 —
Pakistan 1950–68 0.07 0.21 —
Egypt 1953–72 0.91 0.44 0.83
Syria 1961–72 0.64 3.23 0.57
Iraq 1962–71 1.59 1.96 0.70
Jordan 1955–67 0.20 0.23 0.66
Lebanon 1951–72 0.56 0.58 0.29
Kenya 1950–69 0.31 0.65 —
Barley India 1951–64 0.53 0.60 0.88
Pakistan 1951–68 0.03 0.02 —
Brazil 1970–71 0.22 to 0.62 2.5 to 1.1 —
Syria 1961–72 0.27 0.40 0.50
Iraq 1951–60 0.51 0.35 0.74
Jordan 1955–67 2.85 4.04 0.52
Lebanon 1951–72 0.17 0.22 0.67
India 1960–69 0.11 to 0.13 0.14 to 0.16 —
Maize Kenya 1950–69 0.95 2.43 —
Egypt 1953–72 0.04 0.09 0.89
Syria 1947–60 0.51 0.69 0.84
Jordan 1955–66 6.13 6.40 0.60
Lebanon 1953–72 0.13 0.29 0.93
Sudan 1951–65 0.23 0.56 —
Cassava Thailand 1955–63 1.09 1.09 0.14
Millet Syria 1961–72 1.21 1.60 —
Sudan 1951–65 0.09 0.36 —
Iraq 1961–70 0.88 1.85 0.82
India 1951–65 0.83 to 0.90 — 0.49 Sorghum India 1947–65 0.02 to 0.20 0.03 to 0.28 0.70
Sudan 1951–65 0.31 0.59 —
Potatoes Syria 1950–60 0.65 1.30 0.87
Lebanon 1957–72 0.54 0.58 0.73
Source: Scandizzo and Bruce, 1980.
Expected Expected Price Yield Malaria Area Price Province Constant price yield risk risk death rate adjustment expectation R2
(a1) (a2) (a3) (a4) (a5) () ()
Nakhornsawan –3.64 a 3.04 –0.26 0.81
(2.6) (6.2) (2.9)
5.50 –0.43 –0.22 0.45
(4.2) (2.8) (2.4)
0.37 1.70 –0.95 0.20
(1.2) (1.5) (2.0)
Sara–buri –1.57 1.35 –0.07 0.92
(2.2) (2.6) (2.1)
Lopburi –8.71 0.54 4.05 –0.12 0.69 1.27 0.96 (6.6) (0.3) (10.4) (2.8) (3.8) (6.7) Nakhornratsima –5.02 0.97 3.51 –0.71 0.54 0.85
(1.6) (1.0) (2.1) (2.1) (2.3)
Phitsnulok 4.76 4.36 –0.15 0.82
(3.7) (7.6) (1.3)
Phicit 0.60 1.89 –0.40 –0.46 0.75
(0.4) (4.8) (1.6) (1.1)
7.42 –0.22 –0.46 –0.40 0.70
(5.7) (0.7) (1.0) (4.2)
Phetchabun 9.99 6.70 3.94 0.32 0.73
(1.9) (1.5) (2.8) (1.2)
Sukhothai 11.0 5.58 –0.28 –0.12 0.89
(6.1) (8.1) (2.0) (1.8)
3.8 –0.55 –0.20 –0.17 0.39
(5.2) (2.6) (1.3) (2.1)
Source: Behrman, 1968, pp. 322–23.
t-statistics in parentheses
aCorresponding variable was not used
Short-run elasticities of Long-run elasticities of planted area with respect to planted area with respect to Province Price Yield Price
risk Yield
risk
Malaria death rate
Price Yield Price risk
Yield risk
Malaria death rate
Nakhornsawan 1.92 4.88 –1.19 a –0.85 1.92 4.88 –1.19 –0.85
to to
–2.09 2.09
Sara-buri 2.24 –0.34 3.96 0.62 Lopburi 1.58 4.71 –0.30 1.81 6.83 –0.44 Nakhornratsima 0.27 1.36 –0.21 0.41 2.52 –0.40 Phitsnulok 2.44 –0.22 2.44 –0.22
Phichit 1.41 –0.16 –0.35 –12.27 1.41 –0.16 –0.35 –12.27
to to
–0.28 –0.28
Phetchabun 4.47 3.68 14.17 11.68 Sukhothai 7.73 –0.36 –0.15 –0.22 7.73 –0.36 –0.15 –0.22
to to to to
–0.70 –0.26 –0.70 –0.26 Source: Behrman, 1968, p. 325.
aCorresponding variable was not used.
Estimation of coefficients of revenues
(in LE/feddan) received from sales of Area
Crop Form of Long adjustment (feddan) equation Constant Wheat Rice Maize Cotton berseem coefficient R2
Wheat Linear 1172 25.8 –7.2 –9.6 1.1 –6.3 0.89 0.72 (3.3) (3.4) (–1.3) (–1.1) (0.4) (–2.0) (0.5)
Rice Linear 11.7 –11.7 7.5 6.2 0.7 5.0 0.30 0.78 (0.3) (–0.9) (1.0) (0.5) (0.2) (0.9) (2.9)
Maize Linear 1549 29.1 a –18.0 4.8 1.24 0.82 (6.5) (4.9) (–3.6) (2.3) (1.4) Cotton Linear 1409 3.6 –2.7 –9.5 0.69 0.34
(2.8) (0.7) (–0.7) (–1.9) (1.5) Long Loglinear 1.92 0.05 –0.11 –0.25 –0.02 0.10 0.96 berseem (2.5) (0.5) (–1.0) (–2.3) (–0.3) (7.6)
Source: Cuddihy, 1980.
t-statistics in parentheses
aCorresponding variable was not used.
Elasticities of area planted with respect to revenues
Short–run Long–run
Crop Wheat Rice Maize Cotton Berseem Wheat Rice Maize Cotton Berseem
Wheat 0.41 –0.16 –0.16 0.04 –0.12 0.46 –0.18 –0.16 0.04 –0.13 Rice –0.32 0.28 0.15 0.04 0.14 1.05 0.91 0.52 0.15 0.47 Maize 0.41 a –0.29 0.13 0.33 –0.19 0.13
Cotton 0.06 –0.09 –0.13 0.95 0.09 –0.12 –0.19 Berseem 0.05 –0.10 –0.24 –0.02 0.05 –0.11 –0.25 –0.02 Source: Cuddihy, 1980.
aCorresponding variable was not used.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
Table 4E.1. Supply response for groundnuts in Sub-Saharan Africa: Base data
Area in Current prices Consumer Real prices groundnuts Groundnuts Millet Rainfall price Groundnuts Millet Year (1,000 ha) (CFA/mt) (mm) index (1961 CFA/mt) 1960 1323 20500 22000 817 0.95 21652 23236 1961 1230 22000 22500 685 1.00 22000 22500 1962 1233 21500 23000 609 1.07 20101 21503 1963 1185 21500 25000 699 1.14 18873 21945 1964 1055 20600 25000 830 1.21 17039 20678 1965 1016 20600 25800 660 1.26 16401 20541 1966 1017 21000 22000 897 1.28 16355 17134 1967 1064 18000 23000 886 1.32 13678 17477 1968 1091 18000 23000 457 1.31 13730 17544 1969 1097 21200 24000 841 1.37 15520 17570 1970 1051 23100 23000 496 1.42 16256 16186 1971 1060 23100 29000 745 1.51 15288 19193 1972 1087 25500 22000 428 1.60 15977 13784 1973 1280 41500 37000 461 1.69 24513 21855 1974 1020 41500 35000 556 1.95 21282 17949 1975 1201 41500 42000 801 2.37 17533 17744 1976 1175 41500 55000 573 2.51 16508 21877 1977 1079 41500 65000 437 2.67 15520 24308 1978 970 41500 45000 637 2.87 14445 15663 1979 995 41500 45000 666 3.11 13344 14469 1980 1097 50000 45000 418 3.52 14209 12788 1981 1216 60000 55000 573 3.73 16100 14759 1982 1148 60000 75000 553 4.37 13730 17162 1983 925 60000 85000 337 4.88 12303 17429 1984 873 75000 95000 492 5.46 13741 17406 1985 750 75000 100000 546 6.16 12175 16234 1986 789 90000 100000 735 6.54 13761 15291 1987 823 90000 110000 809 6.82 13191 16122 1988 787 70000 115000 500 6.54 10700 17579
41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 7677 7879 80 81 82 83 84 85
Table 4E.2. Supply response for groundnuts in Sub-Saharan Africa: Data preparation and simulation results
Previous Agricultura Estimated area Estimated area in groundnuts under alternative policy Area in Lag Prices (1961 CFA) Rainfall three year structural in groundnuts High price oHigh price No High priceHigh priceHigh price groundnuts area in Last year last mean adjustment Best groundnuts with structural without with without Year (1,000 ha)groundnutsGroundnut millet year rainfall 1979 - 88 Model 1 model ? new Pgt struct. adjadjustmentstruct. adj struct. adj struct. adj
t ln At ln At-1 ln Pgt ln Pm,t-1 ln Rt-1 ln Rt-(1-3) DUM (1,000 ha) (CFA/mt) (1,000 ha)(1,000 ha)(1,000 ha) (percent change)
1960 7.19 9.98 1323
1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988
Working space for regression
Year Dependent Independent variables variable
t ln At ln At-1 ln Pgt ln Pm,t-1 ln Rt-1
1960 7.19 9.98
41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62
Table 4E.3. Supply response for groundnuts in Sub-Saharan Africa: Regression results Prices (1961 CFA) Rainfall Structural adjustment
Dependent Lag Current last Three-year 1979 - 88 Elasticities (at mean values) w.r.t.
variable Intercept area groundnut Millet year average Additive On price R2 Groundnut price Millet price ln At-1 ln Pgt ln Pm,t-1 ln Rt-1 ln Rt-(1-3) DUM DUM*ln Pgt [adjusted] Short Long Short Long
1. lnAt 1.62 0.676 .349 -.341 .09 0.82
(1.8) (5.4) (3.9) (-3.9) (1.8) [.79]
2. lnAt
3. lnAt
4. lnAt
5. lnAt
Note: t-statistics in parentheses; elasticities with structural adjustment in curly brackets.