A General Equilibrium Model of Trade Liberalization: North Carolina Hog Pollution
Authors:
Osei-Agyeman Yeboah
Department of Agribusiness, Applied Economics & Agriscience Education
North Carolina A&T State University
Victor Ofori-Boadu
Department of Agribusiness, Applied Economics & Agriscience Education
North Carolina A&T State University
A- 29 C.H. Moore Agricultural Research Station
1601 E. Market St. Greensboro, NC 27411
Phone (336) 256 - 2259
Fax
(336) 344 - 7658
E-mail [email protected]
Edward Fosu
Department of Agribusiness, Applied Economics & Agriscience Education
North Carolina A&T State University
Selected Paper for Presentation at the 63rd Annual Professional Agricultural Workers
Conference, Tuskegee University; December 6-9, 2005.
A General Equilibrium Model of Trade Liberalization: North Carolina Hog Pollution
ABSTRACT
The study uses a specific factor model to project the magnitude of income redistribution
and output adjustments in North Carolina due to Trade liberalization. We also estimate changes
in hog waste output associated with the predicted changes in hog production. A projected 15%
change in output price due to trade liberalization results in a 0.38% increase in hog production.
In the long-run hog waste is estimated to change by 2.89 million tons. However, from statistics,
92% of North Carolina’s hog are raised by “megafarms” that are able to pursue clean
environmental practices by spreading the costs over their larger herds.
1
INTRODUCTION
North Carolina ranks as the second largest hog producer in the United States. Currently,
the state houses over 10 million hogs. The sector has experienced exponential growth in the
1990’s. Within a decade, hog population in North Carolina increased from 2.6 million hogs in
1988 to over 8 million by 1997, representing an increase of over 207%. However, the number of
hog farms in the state over the period has decreased from 15,000 in 1986 to 3,600 in the year
2000. Big hog factories have taken over the hog production business. Over 92% of the 10 million
hogs in North Carolina are raised on factory operations of at least 2,000 hogs (Environmental
Defense, 2000). The new industry structure of large, more efficient and geographically
concentrated producers has been accompanied by rising environmental concern and has resulted
in more stringent environmental regulation. An average factory in the state has about 3,700 hogs
and produces 38,480 pounds of faces and urine every day. It is estimated that about 19 million
tons of hog waste was produced in 2004 by the 10 million hogs in the state (Scorecard.com).
Figure 1 shows levels of Hog and hog waste production in the state of North Carolina. A ton of
hog waste produces 250 gallons of waste. This contains 12.29 pounds of nitrogen and 4.2 pounds
of phosphorous. 8.75 pounds of the nitrogen is lost to the atmosphere.
***Insert Figure 1***
Despite the continued increase in waste output due to increased production, concerns are
that majority of these producers have not improved their waste management practices. As a
result of these environmental concerns, the North Carolina state government passed a bill in
1997 that placed a moratorium on construction of any new farms with over 250 hogs. The bill is
in effect until September 2007. In addition, the regulation sets standards to protect ground and
surface water by controlling storage and field application of manure. Compliance to these
2
regulations is at a cost to hog producers. Metcalfe (2002) estimated the mean value of the share
of environmental compliance cost in total hog costs as 0.045. Producers argue that, an increase in
more stringent environmental regulation is unnecessary since it is likely to increase their
compliance cost without significantly affecting an improvement in waste management
(Environmental Defense, 2000). In North Carolina, it has been found out that the larger
“Megafarms” were able to pursue clean environmental practices by spreading the costs over their
larger herds of pigs. Smaller operations however tend to violate some environmental regulations
due to financial constraints (Franca, 2000).
Trade Liberalization
International trade in pork has in part contributed to these increases in pork production.
World pork consumption has been increasing over the last decade, and there has been a
concurrent increase in the quantity of pork traded internationally. Total world pork trade in the
year 2000 was approximately three million metric tons and an increase of 43% over the quantity
in 1993 (Metcalfe, 2002). The problem of hog waste pollution is even more alarming as there are
projections of continuous increase in export demand for U.S. pork due to increased trade
liberalization and access to new markets emerging from several trade agreements with the United
States. Among these are the North American Free Trade Agreement (NAFTA), the US-China
Bilateral trade agreement and the recent Dominican Republic-Central American Free Trade
Agreement (DR-CAFTA).
Several studies have examined the conflicting relationship between trade and
environmental quality using computable general equilibrium (CGE) model (Beghin et al., 1997;
Felder and Rutherford, 1993; Perroni and Wigle, 1994; Shoven and Whalley, 1984; Wajsman,
3
1995; and Yeboah, Thompson, and Mostafa , 2003). The main objective of a CGE model is that
it allows a quantitative analysis of large dimensional models (Glebe, 2003).
In this study, we examine the potential environmental impact of the expected increase in
North Carolina hog production due to trade liberalization in an applied comparative static
general equilibrium (CGE) model of production and trade. The model generates comparative
static adjustments in outputs and factor prices due to changing output prices The simulation is
based on the use of factor and industry shares, allowing for substitution between inputs across
the economy using a Cobb Douglas production function. Waste output is algebraically defined as
a function of hog production. Therefore the predicted change in Hog production is used to
estimated change in Hog waste output.
An Applied General Equilibrium Model of Production and Trade
Full employment of labor, capital, and energy is described by
v  Ax
(1)
where v is a vector of inputs, A is a matrix of cost minimizing unit inputs, and x is a vector of
outputs. Factor endowments are exogenous with perfectly inelastic supplies ensuring the full
employment in (1). Competitive pricing in each industry leads to the other major relationship in
the model
p  A w
(2)
where p is the vector of product prices and w factor prices. North Carolina’s economy is
assumed to be a price taker in markets for products including vegetables and fruits and nuts.
Emphasis is upon comparative statics starting in equilibrium. Taking the differential of (2),
dv  xdA  Adx
(3)
4
Aggregate economy wide substitution terms Sik are Sik 
 xa
j
j
h
ij
, where  aij /  wh  aijh . These
substitution terms summarize how cost minimizing firms across the economy alter their input
mix in the face of changing factor prices. If Sik is positive (negative), factors i and h are
aggregate substitutes (complements). For every factor i, dAx 

s dw, and (3) becomes
k ik
dv  Sdw  Adx .
(4)
Considering small changes, cost-minimizing behavior insures that
wdA  0.
(5)
Using (5) and taking the differential of (2),
dp  A dw.
(6)
Putting (5) and (6) together into matrix form,
 S A  dw  dv 

    .
 A 0  dx   dp
(7)
In elasticity form, the model is written
     w   v 
  0  x    p 

   
(8)
Where:
 is a 6x6 matrix and contains aggregate price elasticities factor demand,
 is a 3x5 matrix of industry shares and,
θ́ is a 5x3 transpose matrix of factor shares.
The variables are written in vectors where w represents endogenous factor prices, x
endogenous outputs, v exogenous factor endowments, and p exogenous world prices of goods
facing the economy. The ^ represents % changes.
5
Factor and Industry Shares
Factor shares are the proportion of total payments received by each productive factor
while industry shares represents, the portion each productive factor employed in each industry.
Factor and industry shares are important for estimating the substitution between inputs across the
economy, which is essential for deriving the comparative static elasticities of the general
equilibrium model (Thompson, 1996). Table 1 shows the total factor payments for North
Carolina for the year 2002. Total receipts and payments for labor in manufacturing, services
were obtained from the 2002 Economic census data by the Census Bureau. Energy spending for
the Manufacturing and Service sectors are from US Department of Energy (2001) while total
receipts, Labor and Energy in Agriculture and Hog are from the 2002 Census of Agriculture
“Summary by North American Industry Classification System (NAICS)”. Capital was plugged in
as the residual in each industry after the labor and energy bills.
***Insert Table 1 here***
The dollar value of factor i input in sector j is wij  wi vij , where wi is the price of factor i
and vij the quantity of factor i used in sector j. The share of factor i in sector j is then

ij

w y
ij
(9)
j
where yj is the value added by sector j. The data are static, taken at a single point in time as
nominal values for factor payments and value added. Index i runs across capital k, energy e, and
aggregate labor l. Equation 9 mathematically represents the calculation of factor shares. Tables 2
reports the factor shares. Gleaning through the results show that capital is the factor that receives
the greatest share of payments in each sector. The share of capital in the Hog sector is about
91%. This is evident of the new industry structure, which consist of very large automated
factories of production.
6
***Insert Table 2 here***
Table 3 presents the related industry shares. The service sector employs the most labor of
about 69% and uses the most energy. Manufacturing industry has the greatest share of capital
employed.
***Insert Table 3 here***
Specific Factor Model of Production
Substitution elasticities summarize adjustment in cost minimizing inputs when factor
prices change as developed by Jones (1965) and Takayama (1982). Following Allen (1938), the
cross price elasticity between the input factor i and the payment to factor k in sector j is written
Eijk  aij / w k   kj Sijk
(10)
where Sijk is the Allen partial elasticity of substitution. Cobb-Douglas production implies Sijk =
1. With constant elasticity of substitution (CES) production, the Allen partial elasticity can have
any positive value. Given linear homogeneity, k Eijk  0 and the own price elasticities Eiji are
the negative sum of cross price elasticities.
Substitution elasticities are the weighted average of cross price elasticities for each
sector,
 ik  a / w k    ij Eijk 
j
 
k
ij kj ij
S
(11)
j
Factor and industry shares are used to derive the Cobb-Douglas substitution elasticities in Table
4. Constant elasticity of substitution (CES) would scale the elasticities in Table 4. With CES
0.5, for instance, elasticities would be half those in Table 4.
***Insert Table 4 here***
7
The largest own substitution occurs for returns on capital to energy followed by service
and labor. Every 10% increase in interest rate of capital causes 4.97% decline in return to capital
in energy, a decline of 3.2% and 3.1% in service and labor respectively.
Comparative Static Elasticities in the Model
The model generates comparative static adjustments in outputs and factor prices due to
changing output prices. The present focus is on adjustments from price changes due to tariff
reduction. Using Cramer’s rule, the comparative static elasticities of the system are in the
inverse of the system matrix (11). Table 5 shows Elasticities of factor prices with respect to
Output Prices.
***Insert Table 5 here***
The results in table 5 shows that, every 10% increase in hog prices would result in a
10.9% increase in the return to hog capital investment. Higher prices in the service sector will
increase output, thus attracting labor from other sectors raising productivity and return to capital.
Wages depend heavily on the price in services but very little on the prices of hog and the rest of
agriculture.
***Insert table 6 here***
Table 6 reports the price elasticities of outputs along the production frontier. A higher
price raises output in that sector thus it draws labor away from other sectors and lowers output in
those sectors. The largest own output effect occurs in agriculture other than hog production,
where every 10% price increase raises output by 2.9%. Every 10% increase in hog price results
in a less than 1% increase in output.
8
Predicted Price Changes and Simulation:
We assume the US is an excess supplier for agricultural and service goods. Using
average tariff reduction from 43% to 24% based on the U.S. China bilateral trade agreement.
Pre-free trade prices is assumed to be; Pimp = 1.43Pus where Pimp = price for trade partner
With the new tariffs, Pimp = 1.24Pus* where Pus* > Pus thus the level of trade increases as
production in the US also increases due to price increases. Higher prices are expected for
exporting industries in the move to trade liberalization and the level of trade increases as
production in the US increases. Using export and import elasticities of 1 and -1 respectively, a
price increase of 15% is predicted for hog, the rest of agriculture along with service and a fall of
15% in price is predicted for the manufacturing sector.
Table 7 reports on factor and output adjustments due to the projected price change from
trade liberalization. The results show that a projected 15% change in output price will result in a
0.38% increase in the output of hog and 1.11% for the rest of agriculture. Output increases by
1.94% in services, and a decline of -4.67% in manufacturing output. At 0.38% increase in hog
output, there is a projected increase of 72,089 tons of hog waste. Nitrogen found in the hog waste
will change by 402 tons out of which 286 will be lost to the atmosphere. Amount of phosphorous
will increase by 136 tons.
***Insert table 7 here***
The predicted changes in output are not large in the short run. Therefore it is envisaged
that the hog industry can continue to meet export demands without having to incur any
significant increase in the waste management compliance cost that will make them less
competitive. In the long run, outputs adjust whenever the levels of capital adjust. In a factor
model with constant return to scale, the percentage adjustment in output and the percentage
9
change in the industry’s capital stock are about equal. Table 8 shows the approximate long run
output changes due to 15% price changes. In the long run outputs in services, the rest of
agriculture, hog are projected to increase by 16.9%, 16.11% and 15.38% respectively. Output in
manufacturing is projected to fall by 19.67% due to cheap labor from overseas. Hog waste is
projected to increase by 2.89 million tons. Nitrogen will increase by 16,133 tons, nitrogen lost to
the atmosphere will change by 11,484 and phosphorous by 5,469.
***Insert Table 8 here***
These projections are based on an initial hog production level of 9.9 million heads in
2005 for North Carolina. The relation between hog output and hog waste is 1 to 1.9.(ie one pig
produces 1.9 tons of waste). This indicates that in 2005, 1.88 million tons of hog waste was
produce. According to estimates from scorecard.com, a ton of hog waste would generate 250
gallons of liquid waste, 12.29 pounds of nitrogen, 4.2 pounds of phosphorous and will release
8.75 pounds of the nitrogen to the atmosphere. Since the rate of change for hog and hogwaste
are directly proportional, the predicted changes for hog output estimated by the model is
multiplied by the initial hog waste numbers to obtain the estimated changes in hog waste.
Conclusion
The study uses the specific factor model to project the magnitude of income
redistribution and output adjustments in North Carolina as a result of trade liberalization. The
projection is further used to estimate changes in the output of hog waste. A projected 15%
increase in price will result in a 0.38% increase in hog output. An estimated increase of 72,089
tons of hog waste is expected. The relation between hog output and hog waste is 1 to 1.9,
however the rate of increase in both hog production and hog waste output is directly
proportional. This implies that as hog production increases the share of the environmental
10
regulatory compliance costs in hog production costs remains constant. Furthermore, most
producers have already made heavy capital investments into waste management and therefore we
assume that the relative costs of additional environmental regulation for these minimal changes
in waste output will not significantly affect total cost of production.
In the long run, results from the simulation predict a significant increase in hog waste by
2.89 million tons. At this output level, there is a likelihood of enforcing more stringent
environmental regulations, which may increase compliance cost to hog producers. According to
researchers from United States Department of Agriculture/ERS, the extent to which a more
heavily regulated U.S. hog production industry can retain its international competitiveness will
depend in part on how governments in other pork producing countries choose to respond to their
own citizens’ environmental concerns (ERS/USDA, 1998). Several studies have shown that most
competing exporters in the EU and other countries currently are faced with more stringent
regulation and therefore their waste management cost is higher than that in the U.S. In addition,
the new industry structure of large producing factories is favored by efficiency and economies of
scale to produce at relatively cheaper cost. This coupled with technology, research and the
abundance of land base enhances the ability to better accommodate compliance with
environmental regulation. About 92% of North Carolina’s hogs are raised by large factory
operation “megafarms” which are capable of managing their waste based on the afore-mentioned
facts.
Furthermore, results from our shows increase in incomes due to the liberalization of
trade. This will enhance economic development in North Carolina even though it may come with
some level of pollution. It is likely that the gains in income will offset the damage envisage from
pollution. In the debate over environmental consequence of trade liberalization, Bhagwati (1993)
11
argues that environmentalists are wrong to fear the effects of free trade because both trade and
environmental protection can be advanced by imaginative solution. Bhagwati states that free
trade accelerates economic growth, which will intend provide resources for protecting and
cleaning the environment. This is also supported in a study by Grossman and Kruger (1993),
which empirically showed that some environmental quality indicators improve as income
increases. Thus, trade liberalization in the opinion of several researchers (Bhagwati, 1993;
Grossman and Kruger ,1993), should generally protect the environment rather than harm it. We
therefore do not envisage a significant negative impact from environmental regulations on the
international competitiveness of North Carolina hogs.
12
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14
Table 1. Factor Payment Matrix ($ '000)
Labor
capital
Energy
Total
Hog
148,968
Rest of
Agric
511,042
5,672,645
2,088,971
3,583,674
10,281,300
629,031
47,142
581,889
156,821,943 179,839,493
6,961,686
2,285,081
4,676,605
Mfg
20,647,572
Service
Agriculture
46,876,233
660,010
132,760,771 122,681,960
3,413,600
15
Table 2. Factor Shares,ij, 2002
Service Agriculture
0.2607
0.0948
Hog
0.0652
Rest of
Agric
0.1093
Labor
Mfg
0.1317
Capital
0.8466
0.6822
0.8148
0.9142
0.7663
Energy
0.0218
0.0572
0.0904
0.0206
0.1244
16
Table 3. Industry Shares,ij
Service Agriculture
0.6875
0.0097
Hog
0.0022
Rest of
Agric
0.0075
Labor
Mfg
0.3028
Capital
0.5084
0.4698
0.0217
0.0080
0.0137
Energy
0.2383
0.7178
0.0439
0.0033
0.0406
17
Table 4. Cobb-Douglas Substitution Elasticities,  ik
Ŵrest of
Ag.
0.0018
âLabor
ŵLabor
-0.3138
ŵEnergy
0.0469
ŵManuf
0.0465
ŵService
0.2185
ŵHog
0.0002
âEnergy
0.2231
-0.4976
0.0366
0.2281
0.0003
0.0095
âManuf.
0.1317
0.0218
-0.1534
0.0000
0.0000
0.0000
âService
0.2607
0.0572
0.0000
-0.3178
0.0000
0.0000
âHog
0.0652
0.0206
0.0000
0.0000
-0.0858
0.0000
âRest of Ag.
0.1093
0.1244
0.0000
0.0000
0.0000
-0.2337
18
Table 5. Elasticities of Factor Prices with Respect to Output Prices
^pMfg
^pS
^pHog
^pRest of Ag.
^wL
0.1479
0.8474
0.0005
0.0041
^eE
0.0988
0.8598
0.0009
0.0405
^rMfg
1.1557
-0.1539
-0.0001
-0.0017
^rS
-0.0648
1.0700
-0.0003
-0.0050
^rHog
-0.0128
-0.0798
1.0938
-0.0012
^rRest of Ag.
-0.0371
-0.2605
-0.0002
1.2978
19
Table 6. Elasticities of Output with Respect to Output Prices
^pMfg
^pS
^pHog
^pRest of Ag.
^xMfg
0.1557
-0.1539
-0.0001
-0.0017
^xS
-0.0648
0.0700
-0.0003
-0.0050
^xHog
-0.0128
-0.0798
0.0938
-0.0012
^xRest of Ag.
-0.0371
-0.2605
-0.0002
0.2978
20
Table 7. Prices and Adjustments in Hog and Hog Waste Output (Cobb-Douglas 15%)
Changes in Amounts (Tons)
Projected
Price
Changes
Mfg
Service
Hog
Rest of Ag.
-15%
15%
15%
15%
Factor Price
Adjustments
wLabor
eE
rMfg
rS
rHog
rRest of Ag.
10.56
12.04
-19.67
16.94
15.38
16.11
Output
Total Hog Nitrogen in Nitrogen lost Phosphorus in
Adjustments Waste
Waste
to
waste
atmosphere
xMfg
xS
xHog
xRest of Ag.
-4.67
1.94
0.38
1.11
72,089
402
286
136
Table 8. Long-run Adjustment in Hog and Hog Waste Output
Changes in Amounts (Tons)
Projected
Price
Changes
Mfg
Service
Hog
Rest of Ag.
-15%
15%
15%
15%
Output
Total Hog Nitrogen in Nitrogen lost Phosphorus in
Adjustments Waste
Waste
to
waste
atmosphere
xMfg
xS
xHog
xRest of Ag.
-19.67
16.94
15.38
16.11
2,893,526
22
16,133
11,484
5,469
Figure 1. Hog and Hog Waste Production
12000
20000
18000
14000
8000
12000
6000
10000
8000
4000
6000
4000
2000
2000
0
0
Years
23
Hog Waste ('000 tons)
16000
19
8
19 5
8
19 6
8
19 7
8
19 8
8
19 9
9
19 0
91
19
9
19 2
9
19 3
9
19 4
9
19 5
9
19 6
97
19
9
19 8
9
20 9
0
20 0
0
20 1
0
20 2
0
20 3
04
Hogs and Pigs ('000)
10000
Hogs and Pigs
Hog Waste