Chapter 9
Measuring the Effectiveness of Nonprice Promotion of U.S. Agricultural
Exports
Using a Supply-side Approach
Estimation
Share equations (9.8)
and (9.9) are estimated as a separate system for each sector
using an iterative version of Hansen's generalized method of
moments procedure (GMM) available in TSP 4.3. The estimated error
structure accounts for both contemporaneous correlation among
equations and second-order serial correlation. The energy and
capital equations are omitted from the estimation system in both
sectors. Because of singularity of the covariance matrix of complete
systems of share equations, iterative three-stage least squares
(I3SLS) estimates are invariant to the equations deleted from
each system. Initial values for GMM estimation are obtained by
first estimating the system using I3SLS.
All parameters for the omitted equations are derivable from
the estimated equations through the homogeneity and symmetry
conditions. There are 144 system observations (six equations
times 24 annual observations) to estimate 33 parameters for the
farm sector and 456 system observations (six equations times
76 quarterly observations) to estimate 33 parameters for the
food processing sector. Since output prices are simultaneously
determined, Canada's GDP, Japan's GDP, the European Community's
GDP, the U.S.'s GDP, a multilateral trade weighted value of the
U.S. dollar, Moody's Aaa bond rating interest rate, import price,
energy price, hired labor or agricultural inputs price, materials
or marketing inputs price, self-employed labor or labor quantity,
capital quantity, time trend, and a constant are used as instrumental
variables in estimation.
Results
The GMM parameter estimates for
both sectors are reported in Table
9.2. Nineteen of 33 farm production sector and 21 of 33 food
processing sector parameters are significant at the 5 percent
significance level. Convexity in variable input and output prices
requires that the eigenvalues associated with rows and columns
of the Hessian matrix corresponding to outputs and variable inputs
be positive. These are computed at the data means and reported
in Table 9.3. All are positive,
so convexity is satisfied for both models. The quasifixed input
eigenvalues are also reported in Table 9.3. Their negative signs
satisfy concavity in quasifixed input quantities at the data
means for both sectors. Monotonicity requires that predicted
output and quasifixed input shares are positive and predicted
variable input shares are negative. The predicted shares have
the correct signs for all observations in both sectors.
Satisfaction of curvature and monotonicity conditions insures
that the estimated models fully conform with the underlying profit-maximization
assumption. By also testing for homothetic separability, we determine
whether either sector's output for domestic consumption and for
export can be aggregated into a single output category as is
assumed in other trade models. When data are homothetically separable
in a partition, the subset of quantities can be aggregated into
a single index and their corresponding prices into another index.
It permits consistent two-stage choice modeling. Homothetic separability
is tested with each translog variable profit function using the
following three-part hypothesis test:
Part I: Ho: biI=0, biF=0, biM=0,
YiL=0, Yit=0,biC+ biX=0,
i=C,X.
Part II: Ho: biI=0,
biF=0, biM=0,
YiL=0, Yit=0,
bC/bX=biC/ biX,
i=C,X.
Part III: Ho: bC/ bX= biC/biX, bC/bX= YCj/
YXj, i = X, I, H or A,
M, or R, and j = L, t.
To consistently aggregate domestic bound production and exports,
we must fail to reject at least one of the three parts. The calculated
likelihood ratio test statistics for the three parts of the test
for farm production are 50.92, 64.36, and 21.58, respectively.
They are 267.32, 220.26, and 149.62, respectively, for food processing.
These results indicate that consistent aggregation of domestic
bound production and exports is rejected at the 1 percent significance
level (critical values of c2.01,12=26.22
and c2.01,7=18.48)
for both sectors. Thus, they should be considered as distinguishable
outputs in both sectors, as allowed in the GNP function approach.
It should be noted that the GNP function approach is the only
one of the popular trade-oriented models that keeps domestic
bound production and exports in differentiated categories, as
required for consistency with these specification test results.
Hence, the suitability of the GNP function approach for modeling
U.S. agricultural trade for both the farm and food processing
sectors is supported by statistical performance and hypotheses
tests. In addition, about two-thirds of the estimated parameters
of each model are statistically significant.
The full matrix of the farm sector's
short-run elasticities (flexibilities) are reported in Table
9.4. They include the output supply and variable input demand
price elasticities, their cross-price elasticities with respect
to the quasifixed factor endowments (similar to the Rybczynski
elasticities from the Heckscher-Ohlin model [Kohli 1990]), and
the price and quantity flexibilities for quasifixed input prices
(the former are similar to the Stolper-Samuelson elasticities
from the Heckscher-Ohlin model). They are computed at the data
means from the estimated parameters using equation (9.4). Approximate
standard errors are computed for the elasticities using the delta
method. Nearly half of the elasticities are statistically significant
at the 5 percent level.
Consistent with the expectation of a convex profit function,
all own-price elasticities (flexibilities) have the expected
sign. In addition, all for which a standard error is computed
are significant. Export supply is barely elastic while the supply
elasticity of domestic bound production is inelastic at .48.
Except for materials, all variable input demands are inelastic.
All cross-price effects with respect to both output prices are
positive. Hired labor and energy are significant economic complements.
Self-employed labor is a significant economic complement to imports
and is an economic substitute for both hired labor and capital.
However, although a change in self-employed labor quantity has
a large relative effect on the quantity of imports, a change
in import price has a trivial effect on self-employed labor price.
Capital is a significant economic complement to hired labor and
materials and an economic substitute for self-employed labor.
Due to the maintained hypothesis of constant returns-to-scale,
the own-quantity flexibility of each quasifixed input is of equal
magnitude and opposite sign to its cross effect with respect
to the other quasifixed input's quantity.
The processing sector's short-run
elasticities (flexibilities) are reported along with their approximate
standard errors in Table 9.5.
Most of the elasticities are statistically significant at the
5 percent level. Again consistent with the expectation of a convex
profit function, all own-price elasticities (flexibilities) have
the expected sign. All for which a standard error is computed
are significant. Opposite to the farm sector, the supply of domestic
bound production in the food processing sector is highly elastic
(3.64) and export supply is inelastic (.45). Half of the variable
input demands are elastic. Except for energy's response to export
price, all significant cross-price effects with respect to both
output prices are positive. And, the response of both outputs
and all inputs to a change in the price of domestic bound production
is significant. The variable inputs are consistently economic
complements to all other inputs, both variable and quasifixed,
and most relationships are significant. The quasifixed inputs
are significant substitutes to each other. While a change in
the price of domestic bound production, agricultural inputs,
or marketing inputs generally has a significant and highly elastic
impact on all variable netput quantities and quasifixed input
prices, a change in energy price has a trivial impact on the
quantities demanded of other variable inputs and on the prices
of quasifixed inputs.
Intermediate-run own-price elasticities
computed from equation (5) are reported in Table
9.6 for both sectors.1 Capital is kept quasifixed
in the first column for each sector, and labor or self-employed
labor is quasifixed in the second column. All input demand and
output supply elasticities have the expected signs. Allowing
capital to vary has a much greater impact on the intermediate-run
elasticities than allowing self-employed labor to vary for the
farm sector. Results are mixed for the processing sector. Consistent
with Le Chatelier's principle, each of the intermediate-run variable
input demand elasticities is more elastic than in the short run.
Model Simulations
Once estimated, equations (9.8) and (9.9) can be transformed
from shares to levels by multiplying each share equation by variable
profit and dividing by the respective price. The transformed
models can then be simultaneously solved to determine welfare
effects of alternative policies on farm producers and food manufacturers.
The farm sector's nontraded output (C) and the food processing
sector's agricultural food input demand (A) explicitly link the
two U.S. sectors through supply and demand, endogenizing the
price of agricultural inputs to the processing sector and agricultural
outputs from the production sector. The model is then augmented
with additional equations representing export demand for processed
food and a market clearing identity for the world market to endogenize
export quantity and price in the food processing industry. Export
demand for processed food is specified in Cobb-Douglas form so
that the parameters are interpreted as elasticities. Export demand
for processed agricultural products is given by:
where px is export price,
pa is promotional expenditures, b is the advertising
export elasticity, and c is the price elasticity of export demand.
The intercept a is calibrated so that
model solutions are near the observed mean export value for the
food processing sector when export demand and export advertising
elasticities are equal. Simulation results indicate that changes
in producer welfare resulting from a change in Market Promotion
Program (MPP) expenditures are not overly sensitive to the point
chosen for calibrating the export demand function. Advertising
expenditures are taken as the mean MPP expenditures for the 1989-1992
period. During that period, $200 million was appropriated for
MPP activities each year (Ackerman, Smith, and Suarez 1995).
The MPP requires producer groups and food manufacturers to pay
approximately 50 percent of the total promotional cost. To assess
the welfare effects of the MPP, we compare model simulations
using alternative own-price and advertising elasticities of demand
with and without the $200 million MPP subsidy. All other exogenous
variables are set at their respective mean values. Changes in
each sector's variable profit (i.e., returns to the quasifixed
inputs) associated with alternative advertising and own-price
export demand elasticities are reported in Table
9.7.
Assuming (a) promotional activities affect demand for only
one period, (b) administrative costs for the MPP are zero, (c)
there is no free riding by competitors, and (d) tax revenue sufficient
to cover the MPP costs can be collected with no deadweight loss,
a profitable return for the program is anything above a $200
million rise in the sum of both sectors' variable profits. This
occurs in the upper right portion of Table 9.7 where the ratio
of the advertising elasticity to the absolute value of the own-price
elasticity of export demand is equal to or greater than unity.
This result coincides with the observation by Kinnucan et al.
(1995) that nonprice promotion is most effective when the advertising
elasticity is high and the export demand elasticity is low. As
the price elasticity of export demand rises, the break-even point
for MPP expenditure drops below the diagonal where the ratio
of the advertising elasticity to the absolute value of the own-price
elasticity of export demand is one. For example, when the own-price
elasticity of export demand is -0.3, an advertising elasticity
of 0.2 results in a positive return for MPP expenditures. Except
at high export demand elasticities and very low advertising elasticities,
the farm sector benefits more from the MPP than does the processing
sector. This suggests that, under certain conditions, the MPP
may provide a reasonably efficient scheme to enhance farm profitability.
Including MPP administrative costs and the deadweight loss
associated with collecting taxes to cover program costs would
shift the breakeven point in Table 9.7 further to the northeast.
Assuming that it costs $0.20 to $0.50 in deadweight loss to collect
$1.00 in tax revenues (Alston and Hurd 1990), the breakeven point
for the MPP would shift to between $240 and $300 million. Alternatively,
including long-run benefits from promotional activities would
move the breakeven point more toward the southwest part of Table
9.7. However, most evidence suggests that the benefits of advertising
are short lived (Fuller et al. 1992; Duffy 1983).
Several studies estimate advertising elasticities for specific
commodities but none for the food aggregate. Dewbre et al. (1987)
report an advertising elasticity of 0.086 for Australian wool
imported to the United States Williams (1985) reports short-
and long-run advertising elasticities for exports of soybeans
as 0.02 and 0.08, respectively. Kinnucan and Forker (1986) report
a domestic advertising elasticity of 0.056 for milk in New York
City. Solomon and Kinnucan (1993) report advertising elasticities
for U.S. exports of cotton to be 0.25 for Japan, 0.19 for Hong
Kong, and 0.12 for the Pacific Rim. Duffy (1983) reports domestic
own-price demand and advertising elasticities of -0.36 and 0.05
for beer, -0.85 and 0.11 for spirits, and -1.13 and 0.15 for
wine, respectively, in the U.K. Chang and Green (1989) report
domestic own-price demand and advertising elasticities of -0.50
and 0.103 for meats, -0.027 and 0.123 for dairy products, -0.044
and 0.035 for cereal products, -0.072 and 0.031 for fruits and
vegetables, and -0.037 and 0.240 for other foods at home for
the United States
In nearly all cases, the own-price elasticity estimate is
greater in absolute value than the associated advertising elasticity.
Duffy (1987) also concludes that advertising campaigns exert
weak effects relative to the influence of price changes. In addition,
the elasticities for aggregate food are expected to be smaller
in absolute value than for individual commodities. These estimates
suggest that the most likely combination of own-price and export
demand elasticities are in the lower left of Table 9.7, probably
below the breakeven ratio of advertising to own-price elasticity.
Interestingly, advertising and own-price elasticities in relevant
portions of this range indicate farmers receive almost no benefit
from public MPP expenditures. For example, using Chang and Green's
estimated elasticities for meat suggests agricultural producers
would receive only $2 million in benefits from a $200 million
subsidy.
Notes
1Intermediate-run elasticities with respect to
the remaining quasifixed input are all 1.0 because of the assumption
of constant returns-to-scale. Long-run elasticities are undefined
by the same assumption.
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