estimating disequilibrium cost elasticities in agricultural production

Estimating Disequilibrium Cost Elasticities in Agricultural Production

Gabriel Toichoa-Buahal and Jeffrey Apland2

1 Research assistant, Department @Applied Economics, University of Minnesota, Minneapolis, Minnesota.

2 Associate p Y of2 ssor, Department @Applied Economics, University @Minnesota,Minneapolis, Minnesota.

Received 17 December 1995, accepted 10 Decemer 1996

A restricted cost function is estimated using annual data for western Canadian agriculture over the period 1961-84. Using the parameter estimates, disequilibrium cost elasticities are calculated. The elasticities for the sector indicate that the ex ante market prices of quasi-fixed inputs were higher than their shadow values. That is, quasi-fured factors were underutilized during the sample period. Excess agricultural land contn’buted most to the cost of disequilibrium.

Les auteurs ont calcule une fonction de cotit restreinte utilisant les donnees annuelles concemant 1 ‘a- griculture de 1 ‘Ouest du Canada de 1961 a 1984. A partir des valeurs estimees des parametres, on a calcule les blasticites des cotits du desequilibre. Les elasticites obtenus montrent que les prix de marche ex ante des intrants quasi fuces etaient plus importants que leur valeur virtuelle. Autrement dit, les fac- teurs quasi fuces etaient sous-utilises durant la p&ode couverte par 1 ‘analyse. L ‘exces de terres agri- coles utilisees etait le facteur contribuant le plus au cotit du desequilibre.

INTRODUCTION

One of the stylized characteristics of agricultural sectors in developed countries is that farmers use more resources than needed to sustain “normal” production. It is sometimes argued (e.g., Brandow 1977; Melichar 1984) that these producers use more land and big- ger machinery than is necessary under optimal conditions, and thus chronic misallocation of resources characterizes the sector.

Disequilibrium is defined here as the difference between the shadow price and the market rental rate of a resource.’ The divergence between shadow and observed prices can be interpreted as the result of imperfect markets, government interventions and vari- ous restrictions. This divergence provides a measurement of market distortion. The shadow price is the firm’s implicit resource value, and thus reflects the current and future pro-

ductivity of the resource. Equality between the implicit and rental prices implies equilibrium. Given the above definition, one may ask the following questions: Is disequilibrium a significant problem in agriculture? If so, does it have any direct impact on production expenditures or revenue?2 In other words, does resource disequilibrium impose a large cost on agricultural producers? Although there has been no concrete evidence of the effects of disequilibrium on economic variables, one may argue that actual economic losses result from resource misallocation. The above question provides the motivation for this paper. Specifically, we focus on the direct effect of disequilibrium on production cost. We do this by estimating the cost elasticities with respect to quasi- fmed inputs. Results of this research can have significant policy implications concern- ing agricultural competitiveness, trade,

Canadian Journal of Agricultural Economics 44 (I 996) 23 7-249

237

238 CANADIAN JOURNAL OF AGRICULTURAL ECONOMICS

regional production shifts and welfare. Despite the important issues involved, research in this field is practically nil.

Previous studies of disequilibrium in agriculture and other sectors of the economy have generally followed two distinct lines. The fast is the effect of disequilibrium on productivity (e.g., Berndt et al 1990; Berndt and Fuss 1986; Hauver et al 1991; Conrad and Unger 1989; Hulten 1986; Morrison 1985, 1986, 1988, 1990) or estimation of capacity utilization (e.g., Segerson and Squires 1990, 1993). The second area of research pertains to the development and application of econometric tests of disequilibrium models (see Coyle 1991; Kulatilaka 1985; Schankerman and Nadiri 1986; Toichoa-Buaha 1993). Except Morrison (1988), none of these studies analyze the effect of resource disequilibrium on production cost. Morrison provides the conceptual basis for estimating the cost elasticities calculated in the present paper. However, our analysis uses a methodology that allows calculation of cost elasticities under a more disaggregated frame- work when compared with that used by Morrison. The methodology is applied to western Canadian agriculture for the period 196 l-84 using a restricted cost function.

This paper is organized as follows. The next section presents the theoretical background of the analysis. After this comes a description of the data and presentation of the empirical model. This is followed by the empirical results, and the final section sum- marizes the key results.

THEORETICAL BACKGROUND The agricultural sector is characterized by multi-product firms. A theoretical starting point is a specification of the technical possi- bilities that these firms face. Suppose that a firm produces M outputs by combining N variable inputs given K quasi-fixed factors at time t.3 Let T(v+~xy) be the set of all combi- nations of fixed factors, variable inputs, and outputs that is feasible given the existing technology. Here, y = (y’, . . . fl) is a nonnegative vector of outputs, x = (x1 ,. . . +P) is a nonnegative vector of variable inputs, and v

= (V’ , . . . ,vK> is a nonnegative vector of quasi- fvted factors4

Suppose that the levels of x = (xl,. . . ,_x~) are chosen by a farmer to minimize variable costs xE1 w’ xi subject to the levels of quasi- fared inputs v = (vl ,. . .,v”> and outputs y = o’,. . .,yM>:

*i*{x} i [

wixi : (y,x,v) E T(v,x,y) i=l 1

where VC&,v,w,t) denotes the firm’s short- run cost function dual to T(v,x,y). The basic properties of VC(y,v,w,t) are well known (e.g., Brown and Cristensen 198 1). Assuming Eq. 1 is differentiable with respect to w, then by Shephard’s duality theorem:

x’tjf,v,w,t) = d vctjq,w,t)lad i=l ,. . . a (2)

where xi (y,v, WJ), i = 1,. . . ,N are the restricted input demands. If the behavioral model in Eq. 1 describes the actual decision process of the multi-product firm, then the following symmetry or reciprocity conditions hold:

i3xi(y,v,w,t)lad = dxj(y,v,w,tyawi

ij= l,...,N but i *j (3)

Restrictions in Eq. 3 imply a joint test of the first-order conditions for cost minimization and the existence of a parent cost function from which the factor demand in Eq. 2 is derived (Cornes 1992).

To analyze the impact of disequilibrium on production cost, we defme the following total cost functions following Slade (1986). First, the disequilibrium cost function is defined as:

C(y,v,w,r,t)= Vc(u,.,W,t)+~~W (4) j=l

where Y = (rl,. ..,#) is a vector of strictly positive market prices for fixed factors, and C(y,v, w,r, t) is the minimum cost of produc-

ESTIMATING DISEQUILIBRIUTM COST ELASTICITIES 239

yM when some factors are fured. , Second, shadow cost function is defmed as:

C*(y,“,w,t)= VC(y,v,w,l)+~~W (5) j=l

where, by Shephard’s duality theorem, hj = - d VC(v,v,w,t)ld d (j = 1,. . .$o is the shadow price of quasi-fixed input cj. The function C* (y,v,w, t) is the cost that would be incurred if, given any level of the fured factors, the prices of those factors adjusted to make the actual levels optimal (Slade 1986, 78). Note that if all factors are in equilibrium, then the shadow cost function in Eq 5 is equal to the disequilibrium long-run total cost in Eq. 4. That is, at full equilibrium:

hi=--8 VCCy,v,w,t)ldd=rj u= l,..., IQ

Thus, C* b,v,w, t) is the minimum cost of producing vM when the fm faces prices wN and h,

The cost of disequilibrium can be evaluated using Eqs. 4 and 5. We can calculate the cost elasticities with respect to quasi- fixed factor v’(j = l,...K) as (Morrison 1988):

cp’cv = (dlc) (a VC/&J + d)

=(dlC) (d-hi) j= l,...J (6)

The last equality in Eq. 6 follows from the shadow price condition in Eq. 5. The elasticities in Eq. 6 represent the deviations between the shadow and rental values of the quasi-fixed factors. Intuitively, & (j = 1 ,...,K) can be interpreted as the proportionate increase in cost of fixed factors rk less the savings associated with variable inputs h, resulting from an increase in the stock of fmed inputs vk (Morrison 1988,504). If cp’& = 0 VjE (1,. . .,K), that is, a change in the stock of futed factors vk does not affect production cost, full equilibrium is implied. In addition, cp’c, > 0 VjE (1,. . .,K), implies that ri > hi Vje (1,. . . ,K). Therefore, there is an oversupply (excess capacity) of fixed factors relative to their optimal levels. Finally, if @&, < 0 Vje (1,. . .,K), an increase in the stock of vk

decreases the total cost of production after adjustments in the use of variable inputs. If some of these elasticities are positive and others negative, the fmal directional impact on production cost would depend on the size of the elasticities and changes in fured factors. The disequilibrium cost elasticities in Eq. 6 can also be interpreted as indicators of the firm’s incentives to invest. For example, @& > 0 implies underutilization of fmed factor v’ or excess capacity, implying that disin- vestment is desirable.

Calculation of the elasticities Cpi, in Eq. 6 requires estimates of the shadow values hi = -3 VC/d v’. With sufficient degrees of freedom, parameter estimates of the cost function, VC(y,v, w, t ), can be used to calculate the shadow values and thus the disequilibrium cost elasticities. This approach is generally not feasible because of data limitations.5 In this paper, we take the following indirect approach. The restricted, variable input demand equations xi (v,v,w, t) (i = 1,. . . ,N) in Eq. 2 are first estimated. Then, the cost minimization relationship, based on these estimates, is used to calculate ti (j = 1,. . .,K). First, note that by definition:

VC(y,v,w,t) = &vGj(y,v,w,r) (7) i=l

Furthermore, the conditional cost shares are:

sy i - w’x’(‘) i = 1 N

VC(.) ,*--, (8)

where sxi is the share of the ith input in variable cost. Estimation of the shadow prices of the quasi-futed inputs and, by implication, the disequilibrium cost elasticities are based on defmitions in Eqs. 7 and 8. Using Eq. 7, we can calculate hi as:

Q = aVCC.1 --=-

avj c N wi ax’(.) j = 1

i=l ad ,...,K (9)

The above derivative of the cost function represents the impact of a marginal increase i&o’= l,..., K) on variable cost. Now, dif-


ferentiating Eq. 8 with respect to v’ (j = l,...,K) yields:

a(s.2) avj

( i 3X’(.) . a VC(.) w - VC(.) - wix’ -

ad avj 1 = VP (.)

i= l,..., N; j = l,...,K

Then, substituting Eq. 9 into Eq (.)/a v’ and simplifying gives:

d(sx’) AJ

(10)

lOford VC

i=l ,..., N; j=l,..., K (11)

This is a key step in the calculation of the shadow prices. In particular, this substitution allows us to sidestep the estimation of the cost function VC(.) jointly with the variable cost shares. This is an important aspect of our methodology, given the degrees of freedom problem that is common in empirical studies using aggregate data. The left-hand side of Eq. 11 represents the marginal impact of changes in the stock of frxed factors on the variable cost shares. Eq. 11 can be written in matrix notation as:

qsxp -g--

a(sx*) avj

f3(sx3) avj

. . . N-l a(sx 1

&j

I-

W1 --(I-a’)

W1 ----a*

VC

W1 - -,3

VC

1..

_ w1#1

VC

w* 1

For ease of presentation, let the above equation be represented in a compact form by:

[a (SX) / d vi] = [H] [a x/d VJ]

j= l,...& (12)

where [@XV) / d d] (j = 1,. . .,K) represents the above ((N - 1) x 1) vector of derivatives of the cost shares, [fl is the ((N - 1) x (N - 1)) full rank matrix,6 and [&/a vi] (j = I,...&) is the ((N - 1) x 1) vector of derivatives of the variable input demands. Assuming [HJ is a nonsigular matrix, then the shadow value of fmed factor 9 (j = l,...,K) can be calculated by fast solving for [3x / Wj as:

[ax/avj]=[H]-1 [a(SX)/avi]

j= l,...J

and then substituting into Eq. 9 to get:

hi- dVC - ---$ = [FVJ[H-J-* [a(sX)/dvj]

j = l,...,K (13)

where [WI is a (1 x (N- 1)) vector of variable input prices. The disequilibrium cost elasticities cp’c,, (j = 1,. . . ,K) can finally be calculated by substituting Eq. 13 into Eq. 6. Note that the value of the right-hand side

w3 1 -- VC?

-- vcsx- . . .

W2 W3 _-,3 -

VC VC (I -xX3) . . .

. . . *.. ..*

W* SXN-l w3 sxN-l . . .

VC VC

j = l,...,K

,N-1

- -.sx 1

VC

WN-l

--sx 2

VC

,N-1

- -.w 3

VC

*..

,N-l

vc (1 - SP)

ax’ . avj

ax* dvj

ax3 avj

. . . ax N-1 avj

ESTIMATING DISEQUILIBRIUh4 COST ELASTICITIES 241

term of the second equality in Eq. 13 does not depend on all of the parameters of the cost function. In fact, it depends only on the subset of parameters estimated from the variable cost shares.7

THE DATA AND EMPIRICAL MODEL

The data used in the empirical application of this paper are obtained from Toichoa-Buaha ( 1993). A three-output, four-variable-input, four-fixed-input model is specified for western Canadian agriculture over 196 l-84 using annual data for the region. To make estimation feasible, outputs and inputs must be aggregated in a meaningful way. The products in this data set include: crop output (wheat, barley, rape seed, corn oats, rye and flax), livestock output (cattle, calves, hogs, sheep and lambs), and supply-managed output (dairy and poultry products). The quantities in the third category of outputs are fvted by marketing board policies. Therefore, supply- managed output is assumed exogenous in the estimating equations. The variable inputs are: crop materials (fertilizer and lime, pesticides, seeds and other miscellaneous expenditures), livestock materials (feed, feeder cattle, weanling pigs and veterinary services), hired labor and energy (petroleum, oil and lubricant and electricity). And the fixed inputs are: machinery and equipment, farm-produced durable, land and family labor. All output and input categories are aggregated using divisia indices. In addition, a linear trend variable is included to capture the potential effects of biased technical change.

Empirical implementation of the methodology developed here requires specification of a functional form for VCo/,v,w,t). We postulate a multi-product, restricted translog cost function for the western Canada agricultural sector. The translog form provides a second-order Taylor series approxi- mation to an arbitrary variable cost function. Assuming constant returns to scale (CRTS) and homogeneity of degree one in prices, this function is specified as:*

ln[VC/(w4*v4)]=ao +iailn0l,/V4)

i=l

3 3

+1/2 cc

aij lnbi / V4) ln(yj / V4)

i=l j=l

3 3

+ cc

Pih ln(JJi / V4) ln(wh / W4)

i=l h=l

+ cc y is ln(ri / v4) ln(v, / v4)

i=l s=l

+ c 6~ ln(wh / ~4)

h=l

3 3

+1/2 cc

shI ln(wh / w4)ln(w1 / w4)

h=l I=1

3

+ c

0,ln(v, / v4)

s=l

3 3

+1/2 cc

Osf ln(v, /v4)ln(vf lv4)

s=l J-=1

3 3

+ cc

ohs ln(wh / w4) ln(v, / v4)

h=l s=l

3 3

+ c

Ctit ln(_VilV4)t+ c

8ht ln(wh / w4)t

i=l h=l

+ c 8,, ln(v, lv4)1-r<,t+1/2t;,t2 (14)

s=l

where ij = 1 ,...,3 refer to crop output, livestock output and supply-managed output, respectively; h,Z = 1,...,3 denote the variable inputs crop materials, livestock materials and hired labor, respectively; w4 is the price of energy; of = 1, . . . ,3 represent quantities of machinery, farm produced durables and land; and v4 is family labor. Note that this cost function is defined at the industry level under the hypothesis of static competitive profit maximization and identical prices over firms. Cost minimization is consistent with a variety of dynamic processes of resource adjustment and with many models of output price expectations and behavior toward output price


uncertainty (Treadway 1970). Given Eq. 14 where xxh = W&~/VC. The assumption of a and using Shephard’s duality theorem, cost translog cost function in Eq. 14 and cost min- minimization implies the following condi- imization imply the following symmetry tional cost share equations for variable inputs: restrictions:

6,,= 6, h,l= 1,...,3 but h +I (16)

s.xh=8h+ on coefficients for variable cost share Eq. l=l i=l

+ c 3 Ohs Ill@ lv4)+8&

s=l

h= 1,...,3

Iv’ --(l-S?)

_ w1$ VC

Iv1 _ -&3 VC

15.9 The shadow values of machinery, farm

produced durable, and land inputs are calculated using Eq. 13 and the parameters in Eq.

(15) 15 as:

(17)

0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10

Time TiIIlC

Panel A Panel B

Figure 1. Hypothetical time paths of disequilibrium cost elasticities

where hats denote estimated values. The dise- For illustration purposes, Figure 1 depicts quilibrium cost elasticities are then calculated two different paths that these elasticities by substituting Eq. 17 into Eq. 6 as follows: could take over time. In Panel A, disequilib-

rium elasticities are consistently greater or @& = (VS / C) (I.8 -ti) less than zero. This scenario implies rigidity

s= 1 3 ,..*, (18) in the adjustment of capacity utilization.

ESTIMATING DISEQUILIBRIUM COST ELASTICITIES 243

Panel B on the other hand shows a situation of flexibility in the adjustment of capacity utilization. These illustrations will be helpful when interpreting the estimated disequilibrium cost elasticities presented in the next section.

EMPIRICAL RESULTS For econometric purposes, stochastic random errors are attached to Eq. 15. These errors are assumed to be additive and normally distrib- uted with zero means and a contemporane- ous variance-covariance matrix 0. These disturbances could simply reflect optimiza- tion errors by producers. Also, producers could be envisaged as differing from each other according to parameters known by the manager of the firm, but not observable in the aggregate (Berndt 1991).

Table 1 reports results obtained by linear, iterative, three-stage least squares (13 SLS) using Shazam, version 7.0 (White 1994). Nonrestricted outputs (crop and livestock) and quasi-fmed inputs are treated as endogenous variables in the above cost share equations. That is, all fms are assumed to be profit max- imizers. The set of instruments includes loga- rithms of an index of Canadian farm input prices, current quantities of supply-managed output, lagged quantities of quasi-fured inputs, and normalized prices of variable inputs, quasi-fixed inputs, and nonrestricted outputs. Table 1 shows estimates of the normalized cost share equations for variable inputs in Eq. 15. The symmetry or integrability conditions in Eq. 16 are initially tested. The null hypothesis that the symmetry conditions are satisfied (that is, 6,, = 6, for all h + I) is tested against the alternative hypothesis of no symmetry, i.e., unrestricted values of S,, = 6,. The null hypothesis is not rejected at a 1% level of significance (x2 value = 8.823 with 3 degrees of freedom) but it is rejected at a 5% level of significance. lo Given this result, the symmetry

i restrictions in Eq. 16 are imposed in all subse- quent calculations. Acceptance of these restrictions, as noted earlier, implies cost minimization and the existence of a restricted translog cost function. The Durbin-Watson statistics show that first-order autocorrela- tion is not a problem in these equations.’ 1

Table 2 reports estimated annual disequilibrium cost elasticities for western Canadian agriculture. These values can be interpreted as estimates of the proportionate increase in costs of fixed inputs yk = (y ‘, . . . ,y3) less the savings of variable input hk =

(A’ ,. . . ,h3) associated with an increase in the stock of quasi-fixed factors v = (vl, 3, v3). These numbers provide information on costs incurred with changes in the stock of fured inputs. For example, a 1% increase in machinery and equipment resulted in a 0.06% increase in costs net of the change in variable inputs in 1973. Similar increases in farm produced capital and land resulted in 0.25% and 0.56% increases in costs, respectively, in the same year. A result that could have policy implications is that the average impact of changes in land on production cost is signifi- cantly larger than those of machinery and farm produced capital. That is, land appears to be the most important factor affecting resource disequilibrium in western Canadian agriculture during 196 l-84. This is not entirely unexpected, since increases in land may induce additional purchases of machinery, equipment and farm-produced capital given underutilization of land. The apparent high variability in the disequilibrium cost elasticities of land (Table 2) may be partially explained by the pervasive impact that some farm policies (e.g., supply management, price support, transportation subsidies and others) have on land values. If land is a substitute for hired labor in Canadian agriculture (Lopez 1984), any technological advance that encourages an increase in agricultural land use will decrease the employment of hired labor in this sector. This fmding is consistent with the result of a labor-saving technology.

All cost elasticities reported in Table 2 are positive, suggesting that the ex ante market prices of the quasi-fixed inputs f, j =

, . . . ,3, are higher than their shadow values hi, f=l , . . .,3. This implies, as indicated earlier, that the actual usage of these factors over the sample period was higher than their optimal levels. Therefore, the existence of excess capacity in western Canadian agriculture from 1961 to 1984 is indicated by the sample

244 CANADIAN JOURNAL, OF AGRICULTURAL ECONOMICS

Table 1. 13SLS parameter estimates for western Canadian cost shares and associated statistics, symmetry

imposeda

Parameter Estimate Asymptotic

t-ratio

6 22 6 23

p21

P 22

p23

4 21

422

$23

62,

63

633

p31

p32

p33

+ 31

$32

433 6 3t

Equationb Sxl sx2 sx3 R2 0.9695 0.9315 0.9219 Durbin-Watson 1.6632 2.3880 1.9308

0.1948 7.8685 0.1888 4.867 1

-0.0502 2.1654 -0.0836 2.3517

0.0175 1.4699 0.0068 0.0972 0.0695 1.0443 0.0671 2.6196

-0.0757 1.0655 -0.0312 0.708 1

0.0475 1.8252 0.3005 15.1170 0.1830 8.4737

-0.0534 2.3853 0.0516 5.2212 0.1780 3.5118 0.0108 0.1999

-0.0264 1.2527 -0.1082 1.7716 -0.007 1 0.23 14 -0.0516 2.5192

0.3225 10.3590 0.0637 1.3515

-0.0439 3.0496 0.0978 1.0663

-0.2870 3.8326 0.0076 0.2562 0.2164 2.5318

-0.0428 0.7825 -0.0785 2.3758

a All variables are scaled by their arithmetic means. b sxl = Crop materials; sx2 = Livestock materials; sx3 = Hired labor.

data. This result conforms with the idea of asset fucity or rigidity in the adjustment of

year-to-year demand fluctuations and govern-

capacity utilization as opposed to flexible ment policies. However, this excess capacity

adjustment (see Figure 1). There are instances may impose cost penalties on farmers. In par-

where firms may overinvest in their produc- titular, a firm may not be able to easily adjust

tion capacities. For example, in response to its production scale fast enough during periods of economic slowdowns. This rigidity in


Table 2. Disequilibrium cost elasticities, western Canadian agriculture, 1961-84

Year (PC”’

1961 0.144 1962 0.137 1963 0.137 1964 0.137 1965 0.138 1966 0.126 1967 0.115 1968 0.125 1969 0.112 1970 0.101 1971 0.090 1972 0.074 1973 0.059 1974 0.083 1975 0.128 1976 0.141 1977 0.148 1978 0.150 1979 0.149 1980 0.170 1981 0.185 1982 0.198 1983 0.207 1984 0.203

Average 0.135 Standard deviation 0.039

(PC”* = cost elasticity of machinery.

‘PC” 2 = cost elasticity of farm produced durable.

%v3 = cost elasticity of land.

%“2 %v3

0.215 0.394 0.220 0.390 0.221 0.408 0.229 0.426 0.248 0.430 0.255 0.435 0.270 0.420 0.283 0.399 0.256 0.419 0.261 0.465 0.268 0.467 0.273 0.515 0.25 1 0.557 0.240 0.53 1 0.25 1 0.366 0.268 0.348 0.292 0.317 0.285 0.334 0.292 0.366 0.325 0.354 0.338 0.325 0.341 0.310 0.334 0.302 0.322 0.313

0.272 0.400 0.038 0.07 1

adjustment may have a negative impact on farmers’ long-run competitive positions. So, the size and changes over time of disequilibrium cost elasticities are useful indicators not only of the need to invest but also of farmers’ long-run competitive prospects.

One possible advantage of overinvest- ing in quasi-fixed inputs is that it allows farmers to quickly respond to increases in (domestic or foreign) demand. If capacity is small relative to market demand of the product, then the necessary adjustments in response to a rising market may not be fast enough to capture fully the potential rev-

enues implied by increases in demand. Furthermore, farmers in this situation cannot expand their market share and occasionally may even lose ground to competitors who could adjust their capacity faster. Note that there is still a cost involved in excess capacity. However, the net effect here will depend on the gains obtained during periods of high demand.

CONCLUSION

This paper has evaluated the impact of resource disequilibrium on production cost in western Canadian agriculture over the


period 1961-84. A restricted cost function is specified and estimated using annual data for this region’s agricultural sector. The parameter estimates appear to fit the data and con- form to theoretical restrictions. Using these estimates, disequilibrium cost elasticities are calculated. The elasticities for the sector suggest that quasi-fixed factors were underutilized in terms of the application of variable inputs during 196 l-84. This result implies that during the period of excess capacity, farmers should have been disinvesting in land, machinery and farm-produced durable inputs. An interesting exercise would be to analyze the actual investment decisions of producers in this region during 196 l-l 984 to see how closely the observations correspond to the above conclusion. Excess agricultural land contributed most to the cost of disequilibrium. Results obtained in this paper show that an increase in capacity may have a direct impact on production cost net of adjustments in variable inputs use. Thus, resource disequilibrium may affect the competitive posi- tion of agriculture in a particular country relative to other countries, besides having unin- tended indirect effects on the environment.

Further analysis is required to deter- mine the causal factors of disequilibrium in the western Canada agricultural sector. Potential determinants of disequilibrium include farm policies (i.e., policies affecting commodity prices, prices of inputs such as land, land retirement programs, etc.), changes in domestic and foreign demand, changes in weather, behavioral objectives of farmers and other factors. A promising future line of research in this area will be to deter- mine the relationships between disequilibrium cost elasticities and factors such as agricultural exports, import restrictions and pub- lic expenditures in agricultural research and development. Such a study will provide con- siderable insights into the linkages between these policy instruments and subequilibrium in the utilization of agricultural resources. One could also look at the speed of adjustment from one disequilibrium point to the next.

NOTES ‘Resource in this context refers to quasi-fixed factors (those inputs that cannot easily be adjusted from one time period to the next) utilized by the firm. *Resource misallocation may also have unintend- ed consequences. For example, excess capacity in agricultural land may induce increases in environ- mental externalities such as soil erosion, surface and ground water pollution, and other ambient degradation. 3The terms$xed and quasi-faed factors are used interchangeably throughout this paper. 4Following Chambers, T(v,x,y) is assumed to sat- isfy the following restrictions:

l T(.) is a nonempty, closed and convex set l if (x,v,y) E 7’(.), x1 zz x, then (xl,v,y) E Z’(.)

(free disposability of x) l if (x,v,y) E 7’(.), y1 I, y, then (x,v$) ET(.)

(free disposability of y) l for every finite x, r(.) is bounded from above l (x,v,O,) E T(.), but ify 2 0, (O,,Od) +Z r(.)

(weak essentiality). SThis is a common difficulty in aggregate time series studies involving parametric estimation of an underlying production technology. 6This is generally the case, since one of the share equations is dropped in estimating the system in Eq. 2. 7An anonymous referee has noted that shadow prices of fixed inputs cannot be recovered given only the information of estimated shares for variable inputs. However, as shown by the definition in Eq. 13, this is not necessarily correct. If one uses the standard definition of shadow prices, h = - 8 VC(.) / a V, then it is obvious that these values depend on most of the parameters in the cost function. On the other hand, by using the indirect method described by Eq. 13, namely, h = [v [ml [a (sx> / 8 v], we can recover the shadow prices

f iven only estimates of the variable cost shares. Constant return to scale is more likely to hold in

the aggregate (Morrison 1990). Imposing CRTS and homogeneity of degree one on the cost function also reduces the parameters to be estimated and hence improves degrees of freedom. ‘Another anonymous reviewer suggested we test for constant returns to scale (CRTS) before imposing this restriction. In this model, if CRTS holds, then VC t’y,v,w,t) = VC (hy,hv,w,t) for all h > 0. That is, if all outputs and fixed inputs are increased by the same proportion, variable costs will not change. Given this definition, it can be shown that under constant returns to scale, S.X~ Cy,v,w,t) = S.X~ (hy,hv,w,t), where sxh is the share


Table A-l. 13SLS parameter estimates of cost shares and associated statistics, symmetry imposed: NCRTS modela

Parameter Estimate Asymptotic

t-ratio

6, 0.1777 4.95 15 s;, 6 12

;::

p12

p13

cb 11

$2

13

::k

62 6 22

‘23

p21

;22

23 4 21

4 22

423

2:

63

633 P 31 P 32

p33 0 31 0 32

433

0.1814 4.7608 -0.0455 1.9803 -0.085 1 2.3603

0.0118 0.8089 -0.0003 0.0048

0.0200 0.2055 0.057 1 1.7782

-0.1306 1.2020 -0.0277 0.6403

0.0615 1.8509 -0.1215 0.6086

0.2757 8.9719 0.1798 8.3048

-0.0516 2.2478 0.0443 3.5661 0.1562 3.0009

-0.0345 0.4145 -0.0474 1.7331 -0.1767 1.8721 -0.0035 0.1149 -0.0305 1.0880 -0.1628 0.9466

0.3172 7.053 1 0.055 1 1.1236

-0.0466 2.6055 0.1094 1.1709

-0.3248 2.7541 0.005 1 0.1316 0.1912 1.4208

-0.0468 0.8470 -0.0757 1.8031 -0.065 1 0.2599

Equationb R2 Durbin- Watson

sxl sx2 sx3 0.9708 0.933 1 0.9208 1.7175 2.4381 1.9577

a All variables are scaled by their arithmetic means. b sxl = Crop materials; sx2 = Livestock materials; sx3 = Hired labor.

of input h (h = 1 ,. . .,3) in variable cost. The 3 3

hypothesis of constant returns to scale can be test- s.Q=8h+ c

6hl ln(wh / ~4) + c Phi ln& / ~4)

ed using the conditional cost share equations for I=1 i=l variable inputs, implied by the translog cost function and cost minimization. In this case, under + nonconstant returns to scale (NCRTS), these

c 3 $hs ln(v, /v4)+6htt+(bh4v4

s=l

equations can be defined as: h = 1,...,3


The difference between this system of share equations and Eq. 15 is that, here, family labor (~4) is added to each equation as an explanatory variable to allow for NCRTS. The null hypothesis of CRTS then implies the parametric restrictions +14 = $24 = $34 = 0. This proposition was evaluated by estimating the above system of equation by iterative, three-stage least squares given the symmetry restrictions. The null hypothesis of constant returns to scale is not rejected at either the 1% or 5% level of significance (X2-statistic = 3.867 with 3 degrees of freedom). Furthermore, the estimated coefficients of the NCRTS model are not signifi- cantly different from those in Table 1 (see Table A-l above). This result is encouraging because it suggests that the findings and implications of our paper are invariant to the model used.

It is important to note, however, that reject- ing NCRTS in this particular case should not be taken as the final evidence with regard to this issue. The outcome of the test presented here depends on the particular functional form chosen, the sample period and level of aggregation. The effect of NCRTS on disequilibrium cost elasticities is difficult to evaluate. In a related study, Morrison (1985) concluded that the compound effect of long-run scale economies on cost capacity utilization measures of the U.S. automobile industry makes interpretation complex. In the case at hand, what one can expect to see if NCRTS holds is that the magnitudes (and possibly signs) of the estimated disequilibrium cost elasticities are different under NCRTS versus CRTS. lOAdditional checks of the theoretical plausibility of the cost function in Eq. 14 were conducted. Monotonocity was satisfied, since all the fitted shares were positive at all observations. The cur- vature property (strict quasi-concavity) of the cost function did not hold for all observations. The validity of this restriction was checked using the sum of input price elasticities (Berndt). “Additional hypotheses were tested given the structure of our estimated model. The proposition of a neutral effect of supply management on farmers’ allocative decisions was evaluated by the parametric restriction & = pZ3 = p33 = 0. This hypothesis is rejected (x2 value = 16.657 with 3 degrees of freedom) at both the 1% and 5% levels of significance. However, in terms of individual parameters, changes in the level of supply-managed products affected only the demand for hired labor pj3. Previous studies of the allocative effect of supply management policies have found conflict- ing results. Moschini found that in the province of Ontario, reduction in output of supply-managed

commodities is partly offset by increased production of unrestricted output. However, this substitution is limited, since a reduction in regulated output generally reduces total input use. Schmitz concluded that there is a sizable income transfer from consumers to producers along with a misallocation of resources as a result of supply management. He further noted that one could easily reverse these conclusions by changing the assumptions upon which past research has rested. And Harling and Thompson found that intervention in Canadian agriculture is much more pervasive than is often realized, and that decisions about altering intervention must be commodity- specific because the economic situation of each is unique.

A test of the null hypothesis of no factor-aug- menting, technical change in western Canadian agriculture was also conducted using the paramet- . . ric restriction 6,, = 6 63, 2t = is rejected (x2 value

= 0. This proposition = 13.698 with 3 degrees of

freedom) at both a 1% and 5% levels of significance. Lopez (1980) did not reject this hypothesis for Canadian agriculture. However, he stated that the general conclusion is that technological progress has been important in Canadian agriculture. Continuing with the characterization of technology, parameters in Table 1 suggest that technical change is crop-materials-using, livestock- materials-saving, and hired-labor-saving.

REFERENCES

Berndt, E. R. 1991. The Practice of Econometrics: Classic and Contemporary. Massachusetts Institute of Technology and the National Bureau of Economic Research. Cambridge, Mass.: Addison- Wesley. Berndt, E. R. and M. A. Fuss. 1986. Productivity measurement with adjustments for variations in capacity utilization and other forms of temporary equilibrium. Journal of Econometrics 33: 7-29. Berndt, E. R., S. Mori, T. Sawa and D. 0. Wood. 1990. Energy price shocks and productivity growth in the Japanese and U.S. manufacturing industries. In Productivity Growth in Japan and the United States, edited by Charles R. Hulten. National Bureau of Economic Research: Studies in Income and Wealth, Vol. 53. Chicago: University of Chicago Press. Brandow, G. E. 1977. Policy for commercial agriculture. In A Survey of Agricultural Economics Literature, Vol. I, edited by L. Martin, Minneapolis: University of Minnesota.


Brown, R. S. and L. R. Cristensen. 1981. Estimating elasticities of substitution in a model of partial static equilibrium: An application to U.S. agriculture, 1947 to 1974. In ModeIing and Measuring Natural Resource Substitution, edited by E. R. Berndt and B. C. Field. Cambridge, Mass.: MIT Press. Chambers, R. G. 1988. Applied Production Analysis: A Dual Approach. New York: Cambridge University Press. Conrad, K. and R. Unger. 1989. Productivity gaps and capacity utilization in the manufacturing sectors of five OECD countries, 1963-1982. The Journal of Productivity Analysis 1: 10 l-22. Cornes, R 1992. Duality and Modern Economics. New York: Cambridge University Press. Coyle, B. T. 1991. Test of Static Equilibrium and Profit Maximization in U.S. Agriculture, 1948-79. Staff Paper, Winnipeg: University of Manitoba. Harling, K. F. and R. L. Thompson. 1983. The economic effect of intervention in Canadian agriculture. Canadian Journal of Agricultural Economics 3 1: 153-76. Hauver, J. H., J. Yee and V. E. Ball. 1991. Capacity Utilization and Measurement of Agricultural Productivity. AER-1798. Washington, D.C.: USDA, ERS. Hulten, C.R. 1986. Productivity change, capacity utilization, and the sources of efficiency growth. Journal of Econometrics 33: 3 l-50. Kulatiiaka, N. 1985. Test on the validity of state equilibrium models. Journal of Econometrics 28: 253-68. Lopez, R. E. 1980. The structure of production and the derived demand for inputs in Canadian agriculture. American Journal of Agricultural Economics 60: 3845. Lopez, R. E. 1984. Estimating substitution and expansion effects using a profit function frame- work. American Journal of Agricultural Economics 64: 354-67. Melichar, E. 1984. A financial perspective on agriculture. Federal Reserve Bulletin 70: 1-13. Morrison, C. J. 1985. Primal and dual capacity utilization: An application to productivity measurement in the U.S. automobile industry. Journal of Business and Economic Statistics 3 (4). Morrison, C. J. 1986. Productivity measurement with non-static expectations and varying capacity utilization: An integrated approach. Journal of Econometrics 33: 5 l-74.

Morrison, C. J. 1986. Subequilibrium in the North American steel industries: A study of short- run biases from regulation and utilization fluctuations. The Economic Journal 98: 390411. Morrison, C. J. 1990. Decisions of firms and productivity growth with fixed input constraints: An empirical comparison of U.S. and Japanese manufacturing. Productivity Growth in Japan and the United States, edited by Charles R. Hulten. National Bureau of Economic Research: Studies in Income and Wealth, Vol. 53. Chicago: University of Chicago Press. Moschini, G. 1988. A Model of production with supply management for the Canadian agricultural sector. American Journal of Agricultural Economics 70: 3 18-29. Schmitz, A. 1983. Supply management in Canadian agriculture: An assessment of the economic effects. Canadian Journal of Agricultural Economics 3 1: 136-5 1. Schankerman, M. and M. I. Nadiri. 1986. A test of static equilibrium models and rates of return to quasi-fixed factors, with an application to the Bell system. Journal of Econometrics 3: 97-l 18. Segerson, K. and D. Squires. 1990. On the measurement of economic capacity utilization for multi-product industries. Journal of Econometrics 44: 347-61. Segerson, K. and D. Squires. 1993. Capacity utilization under regulatory constraints. Review of Economics and Statistics 75: 76-85. Slade, M. E. 1986. Total factor productivity measurement when equilibrium is temporary. Journal of Econometn’cs 33: 75-95. Toichoa-Buaha, G. 1993. Testing for static resource and product equilibrium under output price risk: western Canadian agriculture, 1961-84. MSc thesis. Winnipeg: University of Manitoba, Department of Agricultural Economics and Farm Management, August. Treadway, A. 1970. Adjustment costs and variable inputs in the theory of the competitive firm. Journal of Economic Theory 2: 329-57. White, K. J. 1994. Shazam Econometrics Computer Program: User’s Reference Manual. Version 7.0. New York: McGraw-Hill.

estimating disequilibrium cost elasticities in agricultural production

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