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Assessing the impact of economic liberalization acrosscountries: a comparison of dairy industry efficiency inCanada and the USAMorteza Haghiri , James F. Nolan & Kien C. Tran ba Department of Agricultural Economics , University of Saskatchewan , 51 Campus Drive,Saskatoon, Saskatchewan, S7N 5A8 Canadab Department of Economics , University of Saskatchewan , 51 Campus Drive, Saskatoon,Saskatchewan, S7N 5A8 Canadac Department of Economics , University of Saskatchewan , 51 Campus Drive, Saskatoon,Saskatchewan, S7N 5A8 Canada E-mail:Published online: 02 Feb 2007.

To cite this article: Morteza Haghiri , James F. Nolan & Kien C. Tran (2004) Assessing the impact of economic liberalizationacross countries: a comparison of dairy industry efficiency in Canada and the USA, Applied Economics, 36:11, 1233-1243

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Assessing the impact of economic

liberalization across countries: a

comparison of dairy industry efficiency

in Canada and the USA

MORTEZA HAGHIRI, JAMES F. NOLAN and KIEN C. TRAN*z

Department of Agricultural Economics and zDepartment of Economics, University ofSaskatchewan, 51 Campus Drive, Saskatoon, Saskatchewan, S7N 5A8 Canada

This paper examines and compares the technical efficiency measures of Ontario andNew York dairy producers for the period 1992 to 1998. A nonparametric stochasticfrontier model is introduced to estimate technical efficiency. The backfitting algo-rithm of Breiman and Friedman is used to estimate the frontier. Empirical resultsindicate that during the period of study, New York dairy farmers produced milkmore efficiently than Ontario dairy producers, but the magnitude of the differencewas small. The estimated mean technical efficiency for the former group is 0.602 ascompared to 0.532 for the latter. The results also indicated that over time, dairyfarms in both regions improved their level of technical efficiency. Furthermore, nocorrelation was found between farm size and estimated technical efficiency.

I . INTRODUCTION

For many industries in North America, regulatory institu-tions governing the workings of the economy in Canadamirror those found in the USA. Some exceptions to this

rule can be found in those industries for which the twocountries compete in export markets, and many agricul-

tural products fall into the latter category. With respectto the production and export of dairy products, Canadahas recently implemented policies that are substantially

different from those found in the USA.Differences in dairy policy have been the source of

several recent trade disputes between the two countries.Despite efforts to the contrary by participants in the

major policy agreements governing agricultural trade (i.e.CUSTA, NAFTA, and WTOA), regulatory oversight ofthe dairy industry in Canada and the USA is still a con-

tentious issue. These policies must certainly have a directimpact on the productive efficiency of dairy farms.

Depending on the policy, there are often strong incentives

to produce output in a less-than-efficient manner.In this regard, the dairy industry in Canada and the USA

provides a natural experiment allowing us to compare the

relative performance of otherwise almost identical pro-ducers under different agricultural policies. The goal ofthis research is to estimate and compare the technical effi-

ciency of a large set of dairy producers in Canada, locatedin the province of Ontario, with their counterparts inthe USA located just across the border in the state of

New York.First, some facts are reviewed about the dairy industry in

both countries. This discussion offers some idea about the

peculiar conditions and circumstances imposed on dairyfarms in each country. Next, the measurement of technicalefficiency in the context of the diary industry is discussed

because the focal point of the research is to properly esti-mate the technical efficiency of dairy producers in bothcountries. While there have been some relevant studies of

*Corresponding author. E-mail: trank@sask.usack.ca

Applied Economics ISSN 0003–6846 print/ISSN 1466–4283 online # 2004 Taylor & Francis Ltd 1233

http://www.tandf.co.uk/journalsDOI: 10.1080/0003684042000247406

Applied Economics, 2004, 36, 1233–1243

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this industry, we have compiled a unique panel data setwhich allows us to compare the performance of dairyproducers both within and between the two countries.Subsequently, a new econometric methodology is devel-oped to estimate stochastic non-parametric frontiersusing the theory of generalized additive models (GAMs).By testing for and then imposing additive separability inthe production function, the new methodology allows oneto avoid the so-called ‘curse of dimensionality’ problem inparameter space plaguing non-parametric kernel estimatesof technical efficiency. The penultimate section presentsand discusses the findings from both the between andwithin region efficiency estimates. The final section con-cludes the paper.

II . THE DAIRY INDUSTRY INNORTH AMERICA

The Canadian dairy industry

The dairy industry is one of Canada’s larger agriculturalsectors. It operates under a supply management systemintended to protect the industry from the uncertainty ofworld markets. The Canadian Dairy Commission (CDC)acts on behalf of the federal government to implementCanadian dairy policy. Prior to 1995, dairy policy hasnot permitted substantial international trade in dairyproducts for almost three decades. During this time, theCDC enforced a price support policy with productionquota being centrally controlled.

From 1975 to 1995, Canada used an import quota policyto control the imports of all dairy products. The importquota policy allowed a pre-specified quantity of importeddairy products into the country, limiting the supply of milkproducts in Canada. After 1995, Canada’s commitmentsto the NAFTA and the WTO agreements meant that pro-duction policy and the import quota policy were eliminatedin the process of trade policy tariffication. The presentimport tariff policy (called a tariff-rate quota or TRQ)keeps lower priced imports out of the domestic market.Only minimum quantities of imports (called minimumaccess requirements or MAR) are allowed into the countryfree of tariffs. Furthermore, dairy exports by individualfarmers and processors are also restricted to relativelysmall amounts of surplus disposal.

The CDC implements dairy policies for which milkprices and quantity (quota) are the primary focus. Thepricing policy is determined domestically by heavy restric-tions placed on cross-border trade in dairy products. Thisbegins with the fluid milk price being determined in eachprovince by legislation or through direct intervention bythe associated provincial milk marketing board. The priceis subsequently increased to account for increases in thecosts of primary milk production inputs, along with other

purchased inputs. The purpose of milk quota policy is torestrict domestic production.

By design, dairy policy has had a non-trivial impact onthe efficiency of dairy production in Canada. Overcomingsuch a long-term policy objective will take some time. Inthe meantime, the US dairy sector has undergone a rela-tively recent series of major regulatory changes, movingthe industry towards increased economic liberalization.

The US dairy industry

The US dairy industry, to a large degree, is very similar tothe Canadian dairy industry (Morris, 2001). Strongsimilarities in general inputs, production technology, andclimate conditions are particularly evident in the regionsconsidered for this study: the province of Ontario and thestate of New York. However, during the latter part of the20th century, the US dairy sector transitioned from a cen-tralized market chain characterized by local and federalgovernment intervention to a more commercialized andmarket-oriented industry.

Due to overproduction and continuously increasing milkproduction costs, the US federal government gave up sup-porting the dairy industry in the mid-1980s. Instead, thefederal government implemented a series of dairy policies,including lowering output prices, to interrupt rising milkproduction. The lower output price policy brought sub-stantial pressure on dairy farms to adjust their productionstructure.

At present, the entire US dairy industry (except forCalifornia) functions under a series of mixed dairy policyregimes. They include: (1) the dairy price support pro-gramme; (2) the pooled price discrimination programme;(3) an import barriers policy; (4) an export subsidy pro-gramme; and (5) the federal milk marketing order pro-gramme. The dairy price support programme determinesthe price structure of all milk produced in the countrybased on a set of parity prices. These are adjusted so thateach farm’s milk producing units have the same purchas-ing power over time. The policy now has little impacton the US dairy industry since it has been phased downdramatically in recent years (Sumner, 1999).

The pooled price discrimination policy is an interna-tional market-oriented policy rather a domestic market-chain policy. It is designed to reduce US dairy outputprices so that they become more competitive with inter-national dairy products. Next, the import barriers pro-gramme was planned by the US government to achievesanitary and non-sanitary goals for milk products.Implementing this regulation obviously restricts theimport of dairy products within the USA; for thepast three decades, the US government allowed foreigndairy products to comprise just 2% of total domesticconsumption.

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In order to encourage more domestic production, theUS federal government has also funded a programme ofsubsidized exports for dairy products. This policy is oftenassociated with the international food aid plan, althoughsome output is released as a donation to domestic foodprogrammes. And since 1989, the Dairy Export IncentiveProgram (DEIP) has offered explicit price subsidies forcommercialized dairy products, financed as part of exportsubsidy expenditure (Ackerman et al., 1995).

The final programme to consider with respect to thepresent study is the federal milk marketing order pro-gramme. This functions as a classification pricing systemthat determines the price of each dairy product fallinginto each category. At the moment, there are four classesof milk available in the US marketing order (Outlaw andKnutson, 1996).

In sum, the majority of the US dairy industry functionsunder varying combinations of these five basic policies.Even though the US industry has tended towards a moreliberalized market chain for dairy products, we still observenew policies that might impede the efficiency of producersin the dairy industry. Recently, an adjusted model of pro-duction quota and import barriers called the tariff-ratequota (or TRQ) has become the dominant policy through-out the US industry. Under this policy, increases in thequantity of imported dairy products are permitted tosome extent (Sumner, 1999).

Regardless of what types of policies and regulations areemployed, dairy farms in North America are exposed toextensive regulations. Furthermore, the dairy industries ineach country face quite different sets of regulations.Producers in both countries will react to these policies ina manner that affects their productive efficiency, but it isclear that during the period of this study, Canadian dairyfarmers faced more stringent regulations on productionthan their US counterparts. In this regard, we expect thatthe relative performance of Canadian dairy farms will beinferior to that of their US counterparts.

In sum, one of the most important issues in studies ofagricultural production is to determine how efficiently pro-ducers combine inputs and services to obtain a given levelof output. In this light, the technical efficiency of dairyproducers in both countries will be identified and measuredusing a non-parametric stochastic frontier methodology. Abrief overview of the literature on the measurement of tech-nical efficiency in agricultural production follows.

III . THE CONCEPT OF TECHNICALEFFICIENCY

The historical discussion of efficiency measurement datesback over fifty years at a time when Debreu (1951) andKoopmans (1951) implicitly addressed this issue in the eco-nomic literature. Farrell (1957) was the first to build upon

this work and explicitly introduced the notion of efficiency

measurement. These authors defined technical efficiency as

a comparison between observed and maximum values of

firms’ inputs and outputs. This comparison can take the

form of the ratio of observed to maximum potential output

obtainable from the given input (input-oriented measure),

or the ratio of minimum potential to observed input

required to produce the given output (output-oriented

measure), or some combination of the two. Farrell also

suggested that firm efficiency consists of two components:

technical efficiency, which reflects the ability of firms to

obtain maximal output from a given set of inputs, and

allocative (price) efficiency, which reflects the ability of

firm to use inputs in optimal proportions, given their

respective prices. These two measures are then combined

to provide a measure of total (overall) economic efficiency.

Since Farrell’s work, much effort has been made to

formulate and improve measures of technical efficiency.

One commonly used method is the estimation of frontiers,

or bounding functions, which are intended to represent an

envelope of the best technology of firms within an industry.

In addition, there has always existed an intimate link

between measurement of firm-level efficiency and the esti-

mation of industry level production frontiers, because a

standard is needed against which to measure technical

efficiency (Schmidt, 1986).

The methods used to estimate frontier production or cost

functions could be classified into two basic types: para-

metric and non-parametric. Parametric frontiers rely on

the specification of a particular functional form for produc-

tion, while non-parametric frontiers have the advantage of

not being limited by a priori functional forms. Another

important distinction between these two methodologies is

based on error distributions.

Frontiers can also be either deterministic, or stochastic

(non-deterministic). In the former, any deviation from the

frontier is assumed to be due to inefficiency; while in the

latter model, a compound error term is defined to account

for inefficiency as well as random noise. A non-parametric

estimator is a robust estimator that allows the data to

determine the shape of the functional form without any

constraints derived from relevant economic theory.

The primary shortcomings of parametric frontier

estimation techniques are the need to use predeter-

mined functional forms (e.g. Cobb–Douglas, Translog,

Transcendental, etc.) and their reliance on pre-specified

types of error distributions (e.g. half-normal, truncated

normal, exponential, gamma, etc.). In contrast,

non-parametric estimators do not possess these limita-

tions because they do not rely on these same strict

assumptions. The non-parametric estimation approach

derived in this paper is referred to as stochastic because,

unlike two other popular non-parametric methods (data

envelopment analysis (DEA) and free disposal hull

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(FDH)), our approach is fully statistical and accounts forrandom noise in the data.1

Stochastic non-parametric frontier analysis is utilized inthis study for two reasons. First, efficiency scores obtainedfrom different stochastic parametric frontier functions canvary depending upon the chosen functional forms (Bravo-Ureta and Rieger, 1990; Giannakas et al., 2003). Second,distributional assumptions about technical inefficiencycan impact the computed efficiency scores. For example,Mbaga et al. (2000) showed that there exists a correlationbetween the efficiency scores and the various distributionalassumptions of error terms.2 In general, the inconsistenciesin the estimated results occur because efficiency scores aredata specific. An attempt is made to circumvent these prob-lems with the use of appropriate non-parametric econo-metric estimators.

This research proposes a new methodology to estimatestochastic non-parametric frontiers using generalizedadditive models or GAMs. The basic generalized additivemodel was first proposed by Hastie and Tibshirani (1990).A GAM is a generalization of the linear regression modelexcept that an additive unknown predictor replaces thepredetermined linear predictor. The model is designedto estimate technical efficiency of New York and Ontariodairy using a non-parametric approach, called locally-weighted scatterplot smoothing (LOWESS). LOWESS isalso referred to as the local regression model (LOESS)(Cleveland, 1979). The LOWESS model generates a robustlocal smooth of scatterplot data. One advantage of thismodel compared to the other nonparametric methods,particularly kernel estimators, is that it does not sufferfrom the problem of the ‘curse of dimensionality’ (Kneipand Simar, 1996).

But like other parametric and nonparametric econo-metric models, the generalized additive model is not with-out drawbacks. The shortcomings of this method can bedivided into theoretical and applied discussions. From atheoretical perspective, although a generalized additivemodel relaxes the linearity assumptions of the generalizedlinear models (GLMs), it maintains the additivity structureof these models. The additivity assumption of the modelmeans that the predictors must be additively separable.Thus, the use of a statistical pre-test is strongly advisedto check for the additive separability of the predictors.

The applied portion of the problem refers to the methodthat is used to estimate the mean response function andits parameters. This method, to be discussed in Section V,follows an iterative smoothing procedure. Finding theoptimal choice of smoothing degree is time consuming

and requires significant computational effort. However,methods for removing the problem have been suggested.Among them, the cross validation (CV) method waschosen, which was independently introduced by Stone(1974) and Allen (1974). The CV approach provides con-sistent estimators by leaving out an observation for eachiteration in the estimation process of the mean responsefunction. In sum, given that relatively innocuous assump-tions are made with respect to technology in the dairyindustry, it is felt that the gains from employing a general-ized additive model over the alternatives argue for its use inthe analysis.

IV. STUDIES OF EFFICIENCY IN THEDAIRY INDUSTRY

Some attempts have been made to measure the efficiency ofdairy farms in Canada and the USA using both parametricand nonparametric frontier analyses. Chronologically, theresults obtained from some of these studies are highlighted.First, Tauer and Belbase (1987) conducted a study thatmeasured technical efficiency of New York dairy pro-ducers. They estimated a deterministic Cobb–Douglas pro-duction frontier function using a corrected ordinary leastsquares (COLS) approach with cross-sectional data from1984 collected for 432 dairy farms. They found that onaverage, dairy farmers produced only 69% of potentialoutput from their use of a given set of inputs.

Kumbhakar et al. (1989) studied technical, allocative,and scale efficiency of owner-operators of Utah dairyfarmers using a stochastic production frontier function ina simultaneous equation profit maximization framework.The results indicated, respectively, positive and negativecorrelations between farmer’s education and off-farmincome with their level of efficiency. They also found thatlarge farms (more than 100 cows) were technically moreefficient than small farms (less than 50 cows). Due to allo-cative inefficiency, costs of small farms, on average, wereincreased by 5.91% whereas this factor was 3.74% and33.58% for medium- and large-sized farms, respectively.

Bravo-Ureta and Rieger (1991) extended the Kopp andDiewert (1982) deterministic methodology to a stochasticmodel that decomposes overall efficiency into its com-ponents. They used cross-sectional data for a sample of511 New England dairy farms to estimate a stochasticCobb–Douglas production frontier. Mean economicefficiency for the farmers in the sample was 70.2% andthere was little difference between technical (80.3%) and

1DEA (Charnes et al., 1978) is a linear programming methodology used to construct a piece-wise convex surface (or frontier) which‘envelops’ the data. FDH (Deprins et al., 1984) is similar to DEA, but the convexity assumption is relaxed. With both of thesedeterministic frontier methods, the distance from each observation to the computed frontier is the measure of inefficiency.2 It is intended to show the non-robustness of efficiency score estimates to the choice of various distribution assumptions of error terms inthe authors’ next research.

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allocative (84.6%) efficiency. Analyses of the relationship

between the obtained efficiencies and four socioeconomic

variables, i.e. farm size, education, extension, and experi-

ence revealed that the socioeconomic variables did not

affect the efficiency levels.

With respect to nonparametric frontier estimation of

dairy efficiency in Canada, Cloutier and Rowley (1993)

used a deterministic data envelopment analysis (DEA)

approach to estimate technical efficiency of Quebec dairy

farmers. Their results showed that the mean efficiency score

for 1989 (0.913) with minimum score of 0.683 was higher

than 1988 (0.883) with minimum score of 0.662. In addi-

tion, irrespective of the subsamples and the whole samples,

they reported that large farms were much more likely to

appear efficient than small ones.

Romain and Lambert (1995) studied the level of technical

efficiency in milk production and analysed the relationship

between production costs, the level of technical efficiency,

and farm size in two provinces of Canada (Quebec and

Ontario) by estimating a deterministic transcendental loga-

rithmic production function. They also identified socio-

economic variables that characterized the most efficient

dairy farmers who produced at lower cost. The results indi-

cated that in Quebec the level of technical efficiency

increased slightly with herd size. The level of education,

participation in a milk recording programme, expenditure

per cow for veterinary care, quality of hay, and finally the

number of years as member of a management club were all

variables that characterized efficient farms.

Finally, a recent study by Mbaga et al. (2000) measured

the technical efficiency of Quebec dairy farmers using three

parametric functional forms (Cobb–Douglas, Translog,

and generalized Leontief). The parametric results were

then compared with the results obtained using the data

envelopment analysis approach. By employing cross-

sectional data collected from 1143 specialized dairy farms

in 1996, they found that the average efficiency scores from

all models were above 0.91.

The literature review shows that the present study

makes two major contributions to the growing literature

on dairy farm efficiency. First, no studies conducted to

date have directly compared the distinct dairy regulatory

regimes in the USA and Canada as well as their potential

effects on farm level efficiency. This is able to be accom-

plished by computing efficiency scores both within and

between countries using data from similar geographic

areas in Canada and the USA Second, the research

methodology represents a major improvement over other

methods used to date to measure dairy farm efficiency.

The next section introduces and explains the econometric

framework used in this study.

V. METHODOLOGY

Model and estimation procedures

Suppose one has observed data Yit;Xitð Þ: i ¼ 1; 2; . . . ;N;�

t ¼ 1; 2; . . . ;Tg where Yit 2 <þ; and Xit 2 <d are d vectors

of random regressors. The dependent variable Yit repre-sents the output of firm i at time t, and Xit is a vector ofrandom regressors representing the inputs used. Thenonparametric stochastic production frontier can beformulated as (Kneip and Simar, 1996)

Yit ¼ fi Xitð Þ þ "it i ¼ 1; 2; . . . ;N and t ¼ 1; 2; . . . ;T

ð1Þ

where fi is a smooth and unknown production frontier and"it is the usual random noise term, typically assumed to bei.i.d. with zero mean with common distribution f, whichpossesses compact support. In addition, it is assumedthat fi, Xit and "it are independent.

For a given economic agent i, Kneip and Simar (1996)propose estimating the unknown function fi using theNadaraya–Watson kernel estimator, incorporating the Tobservations on this firm. However, it is well known thatin order to obtain a reasonable estimator of fi a minimumsample size is necessary and this requirement increasesrapidly as d increases. This problem in nonparametricregression and density estimation is known as the curseof dimensionality (see Hardle, 1990 and Silverman, 1986for a detailed discussion). To circumvent this problem, analternative model is proposed in which the structure of theproduction frontier is assumed to take the following form:3

fi Xitð Þ ¼ cþXdj¼1

fji xjit� �

ð2Þ

Thus, Equation 1 can be written as

Yit ¼ fi Xitð Þ þ "it ¼ cþXdj¼1

fji xjit� �

þ "it ð3Þ

where fji are functions of a single input with E [ fji(xjit)]¼ 0for identification purposes. Note that Hastie andTibshirani (1990) referred to Equation 3 as a generalizedadditive model (GAM). There exist various estimationalgorithms in the literature to estimate fji, (Hastie andTibshirani, 1990; Tjostheim and Auestad, 1994; Newey,1994; Linton and Nielsen, 1995; Chen et al., 1996). Thispaper, proposes to estimate fji by the backfitting algorithmintroduced by Friedman and Stuetzle (1981); this algorithmwas subsequently modified by Breiman and Friedman(1985) as an iterative smoothing process.

3 The structure of the assumed production function can be easily tested. See Section VI for more details.

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A description of the backfitting algorithm proceeds asfollows. For the sake of brevity, the discussion of estimat-ing fji for the case d¼ 2 is confined. The extension of d>2can be generalized in a straightforward manner. In addi-tion, for notational simplicity, the subscripts i and t aredropped. First note that for d¼ 2, one has:

E Y x1; x2��� �

¼ f x1; x2ð Þ ¼ cþ f x1ð Þ þ f x2ð Þ ð4Þ

Moreover, notice that

f1 x1ð Þ ¼

Zf x1; x2ð Þ g x2ð Þ dx2 ¼ E f x1; x2ð Þ½ � ð5Þ

sinceRf2 x2ð Þg x2ð Þ dx2 ¼ 0 by the assumption that

E f2 x2ð Þ½ � ¼ 0. Thus, f1 x1ð Þ can be estimated by ff1 x1ð Þ ¼

T�1 PTt¼1 ff x1; xl2ð Þ where ff x1; xl2ð Þ is some non-parametric

estimator of f x1; x2ð Þ (Chen et al., 1996). Now, given theinitial estimate of ff1 x1ð Þ, one can estimate f2(x2) by smooth-ing the partial residuals Y � c� ff1 x1ð Þ in the direction ofinterest x2. Then with the estimate of ff2 x2ð Þ in hand, onecan obtain an improved estimate of ff1 x1ð Þ by smoothingY � c� ff2 x2ð Þ on x1. The backfitting algorithm continuesthis process until convergence is reached. It is importantto recognize that this algorithm requires the initial estima-tion of ff1 x1ð Þ, and hence an estimate of ff x1; xl2ð Þ. As men-tioned above, one utilizes the locally weighted scatter plotsmoothing (LOWESS) approach to obtain the initial esti-mate of f1(x1) in the iterative smoothing process. Precisedetails about the LOWESS approach can be found inFan (1992, 1993) as well as Hastie and Loader (1993).

Measuring efficiency

Following Kneip and Simar (1996), a model that incorpo-rates a technical efficiency component can be written as

fi Xitð Þ ¼ f Xitð Þ þ �it ð6Þ

where the efficiency terms are modelled by the additiveterm �it 2 <: Equation 6 assumes that each firm possessesthe same level of technology in their production process.Differences among firms are captured by the efficiency term�it, a procedure commonly used in the frontier literaturewith panel data. Since one wants to estimate technical effi-ciencies, the following quantities will be defined as the basicelements for this purpose. Suppose,

�it ¼ fi Xitð Þ � f Xitð Þ ð7Þ

where f �ð Þ is the average production frontier with respectto the unknown density =, and

f Xitð Þ ¼ E fi Xitð Þ½ � ð8Þ

For each observation (i, t), the quantity �it represents thedistance between the average production level of the farmi and the average production level of all the technologiesbeing used (Kneip and Simar, 1996, p.195). Generally,there are two approaches to estimate the �s. The simplest

approach is to replace fi by the obtained estimators, and fby some empirical average over i and then, some inferencecould be conducted on particular structural forms ofdependence on i and/or t. However, as Kneip and Simar(1996) pointed out, the statistical performance of theobtained inference will be relatively poor unless both Nand T are large enough. Consequently, this estimator willnot be pursued here. Alternatively, by averaging the �it inEquation 7 over time produces

�i ¼1

T

XTt¼1

�it ¼1

T

XTt¼1

fi Xitð Þ �1

T

XTt¼1

f ðXitÞ ð9Þ

and replacing fi and f by their estimates, the estimates ofthe �s can be shown to have superior statistical properties(Kneip and Simar, 1996).

Now given the estimates of f and �s the individualfunctions fi, for i¼ 1, 2, . . . ,N, can be obtained as follows:

ffi ¼ ff Xitð Þ þ ��i ð10Þ

In this case, the frontier function can be defined as

FF Xitð Þ ¼ maxi¼1;...;N

ffi Xitð Þ

h i¼ ff Xitð Þ þ max

i¼1;...;N��i ð11Þ

VI. EMPIRICAL ANALYSIS

This section presents the results of the estimation proce-dure described above. The concept of measuring efficiencyonly makes sense when decision-making units are at thefirm level; otherwise the inherent problem of workingwith aggregate data prevents one from analysing theperformance of the economic unit.

This section is divided into two parts. First, it will brieflyexplain the sources and the general characteristics of thedata set followed by a description of the variablesemployed in the model. Second, the results will be pre-sented and the implications of this research discussed.

Data and variable descriptions

To estimate and compare technical efficiency between theselected regions of the Canadian and American dairy sec-tor, a farm-level database collected from Ontario and NewYork was used. The Ontario data, obtained from theAgriculture and Agri-Food Canada, were collected by theOntario dairy farm project (ODFAP). The New York datawere obtained from the dairy farm business project(DFBP), which is an integral part of Cornell CooperativeExtension’s Agricultural Educational programme in NewYork State. They were collected by the joint efforts of theDepartment of Agriculture, Resource and ManagerialEconomics of the College of Agriculture and Life Science

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at Cornell University in association with County Extension

staff.

The similar geophysical conditions for producing milk

in these two regions is the primary reason why they were

selected for comparison. One of the pitfalls of any stochas-

tic nonparametric model is the need for a large number of

agents i¼ 1, . . . ,N and time periods t¼ 1, . . . ,T to obtain

reliable estimators. However, this problem is not applicable

to the within-region results. The sample data set comprises

an unbalanced panel with 6836 observations related to

1718 dairy farms. Of these, 6085 observations represent

the information collected from 1504 New York dairy

farms within the period from 1985–1998. The remaining

751 observations contain information describing 277

Ontario dairy farms from 1992–1998. Table 1 shows the

number of farms and time periods in the within regions

data set.

Considering the curse of dimensionality problem present

in any non-parametric regression analysis whose smooth-

ing parameter is a kernel estimator, three key explanatory

variables that play important roles in dairy production

were able to be included and have been used in previous

studies. The first factor is land, measured as annual total

(owned and rented) tillable area in hectares. The second

explanatory variable is labour, measured as an annual

total equivalent worker unit. Finally, the third predictor

is annual total feed cost deflated by the appropriate

Producer Price Index (PPI). These three independent vari-

ables were used to explain the variation in the mean

response variable, annual total milk production measured

as hundredweight (cwt).

All dependent and independent variables were converted

to logarithmic form and Canadian dollars were used as the

common unit of currency. All data are adjusted for farm

size by dividing by the number of milk cows. Table 2

presents the statistical description of the variables. It is

noted that the average number of milking cows in New

York dairy farms is higher than that of Ontario dairy

farms, while the minimum size dairy farms in Ontario

are more than twice the size of the smallest New York

dairy farms. This situation is reversed in the maximum

number of milking cows: the herd size in New York is

approximately seven times greater than that of the

Ontario dairy farms. Table 2 also reveals that the average

volume of milk produced per cow in New York dairy

farms, i.e. 22 497 per hundredweight, is three times

greater than Ontario at 7167 per hundredweight. The

data also indicates that milk production in New York

is more labour-intensive than in Ontario as the average

number of workers in the former region is higher than

the latter. Finally, Table 2 shows that even though the

minimum average of total feed costs for the New York

sample data is less than the Ontario sample of dairy

farms, overall, the New York dairy farmers paid more

(per cow) than their Ontario counterparts to purchase

basic feed and other supplemental materials.

Testing the assumption of additive separability for dairy

technology. To test the assumption of additive separability

in predictors necessary to estimate this econometric model,

the residual deviance statistic is employed. The analysis of

deviance has been found to be useful for statistical infer-

ence in generalized additive models (Bowman and Azzalini,

1997; Schimek and Turlach, 2000). In this case, the value of

deviance is the logarithm of the likelihood ratio (Hastie

and Tibshirani, 1990). Therefore, the value of deviance

can be compared with the likelihood ratio (LR) statistic,

Table 2. Statistical description of the variables

Mean Std. Dev. Min. Max.

Variable NY ON NY ON NY ON NY ON

Milk output 22497 7167 32276 5806 435 1172 616321 83214Land 142 89 122 50 2 15 2119 356Labour 3.6 2.03 3.06 0.9 0.42 0.02 54 7Feed costs 99 45 158 40 2.5 7.6 3624 636No. cows 122 48 149 28 6 14 2658 382

Source: Sample data. All variables are in Canadian units. Feedcost per ($000) Canadian Dollars.

Table 1. Number of farms and time period in the sample

Region Time series Number of years Number of farms Number of obs.

New York 1985–1998 14 1504 6085Ontario 1992–1998 7 277 751Total 1781 6836

Source: Agriculture and Agri-Food Canada and Cornell University.

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which has a chi-squared distribution. To perform this test,

a new independent variable obtained from the cross-

product of land and total feed costs are first introduced,

the two independent variables that are not expected to be

additively separable.4 Then, using a likelihood ratio (LR)

statistic, the null hypothesis of holding additive separability

of the predictors in the nonparametric approach (restricted

model) is tested as opposed to the alternative hypothesis,

that the new independent variable could add more infor-

mation to the model (unrestricted model). For complete-

ness, separate statistic tests were conducted for each year in

the between-region models for 1992–1998. In all years, the

study failed to reject the null hypothesis. This means the

new variable did not add any information to the model and

that the assumption of additive separability with respect to

the predictor variables is appropriate. Now we turn to a

discussion of the empirical results.

Estimation results

Using the methodology discussed earlier, the mean

response function, f in Equation 1 is estimated.

Subsequently, technical inefficiencies of individual dairy

producers in the regions of the study were computed

based on Equations 10 to 13. Since this study covers two

different areas and contains varying time periods and

observations, two different models are constructed to esti-

mate the mean response function and obtain the technical

inefficiencies between and within the regions. The former

refers to the comparison of the estimated technical efficien-

cies between US and Canadian dairy farmers. Conversely,

the within model only computes the performance of dairy

farmers within each country.

It is clear that such a division is relevant for the within

case, but it is very important for the between case because

given a particular year, the number of the observations

must be equal for both regions. Obviously, a comparison

between Canadian and American dairy producers only

makes sense when the number of farms is equal within a

specific period of time. By doing this, one avoids obtaining

biased results for the estimated technical efficiencies attri-

butable to the impacts of large sample size, along with

other factors that might affect efficiency individually or in

combination with various policies implemented in different

times. Thus, for the between regions analysis, a sub-sample

of the data is derived to maintain equal time periods and

observations for each region.

Within-region results. Table 3 presents the estimated tech-

nical efficiencies of Canadian (Ontario) and American

(New York) dairy producers within their own regions clas-

sified by the mean performance group. No adjustments

were made to equalize the sample sizes in each year, thus

one cannot compare mean technical efficiency of the class

intervals at this point in the analysis. However, a few points

about these results are worth noting. The mean technical

efficiency of New York dairy farmers was found to be 0.675

compared to 0.640 for Ontario farmers. A two-tailed nor-

mality test and an F-test show that the differences between

means and variances in Ontario and New York are statis-

tically significant at the 0.01 level. If constant returns to

scale are assumed, this means dairy farmers in New York

and Ontario, respectively, could have produced the same

output by reducing their input usage 32.5% and 36%

respectively. In addition, it is found that the variability of

efficiency scores in both regions under study is not homo-

geneously distributed. For instance, approximately 7% of

New York dairy farms in the sample are less than 50%

efficient in producing milk, while this number for Ontario

dairy farms is 11%.

The relative inefficiency of Ontario farmers shows up in

the highest efficiency class interval as well. As Table 3 indi-

cates, almost 13% of New York dairy farmers are catego-

rized as operating at more than 80% efficiency, while the

4 The new independent variable can be introduced because with the type of methodology proposed, the problem of the curse ofdimensionality is not applicable to the model.

Table 3. Technical efficiency (within-regions)

New York Ontario

Range No.of farms Per cent Mean No. of farms Per cent Mean

<¼ 0.50 98 6.53 0.445 31 11.19 0.4520.51–0.60 278 18.48 0.559 55 19.86 0.5630.61–0.70 492 32.71 0.651 116 41.88 0.6510.71–0.80 447 29.72 0.746 64 23.10 0.739>0.80 189 12.56 0.856 11 3.97 0.866

Total 1504 100.00 0.675 277 100.00 0.640

Source: Sample data.

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percentage of their Ontario counterparts falling in the sameinterval is just 4%. It should be emphasized that thesevalues only represent the range of efficiency scores amongthe class intervals. Finally, Table 3 also shows that the vastmajority of both New York and Ontario dairy farms reside

in the category 50–70% technical efficiency, with more than50% of all farms included in this class.

Between-regions results. This section estimates technical

efficiency of dairy farms between countries, allowing us tomake direct comparisons between Canadian and Americanproducers. As mentioned earlier, the sample size had to beequalized in both regions for each year. To accomplish this,the length of time periods in the Ontario data set wereconsidered as the base line for the comparison. Using arandom generation method to choose New York farms,the number of dairy farms were narrowed down by taking

a sample equal to the Ontario data set for each year (seeTable 1). All variables in this particular estimation wereconverted to appropriate Canadian units. Figure 1 illus-trates the estimated technical efficiency of dairy producersin the between regions analysis for 1993 and 1998.

Tables 4 and 5 show the distribution of dairy farmsamong the efficiency class intervals in the between regionsmodel for the selected years. With respect to New Yorkdairy farms, it is found that in almost every year, the

majority of farms are bunched into the technical efficiency

category between 0.51 and 0.70. With Ontario dairy farms,

the results are different. It is observed that the majority of

technical efficiency scores for Ontario dairy farms fall

below 0.50. Subsequently, it is observed that the number

of New York dairy farms in the sample whose efficiency

scores are above 90% is greater than the Ontario sample

for all selected years (see Table 5).

Overall, it was found that in 1997, dairy farms in both

regions performed better in comparison to other years.

Moreover, the mean technical efficiency of New York

dairy farms (0.69) and Ontario dairy producers (0.66)

in 1997 were the highest among the years selected for

the between regions study. Finally, the percentage of

0.010.020.0

30.040.050.0

Per

cen

tag

e<=

0.500.51-0.60

0.61-0.70

0.71-0.80

> 0.80

Efficiency Scores

NY (1993, Mean=0.68)

ON (1993, Mean=0.61)

NY (1998, Mean=0.58)

ON (1998, Mean=0.53)

Fig. 1. Technical efficiency of dairy producers (between-region).Source: Sample data

Table 5. Distribution of dairy farms (between-region)

New York Ontario

Range 1992 1993 1995 1997 1998 1992 1993 1995 1997 1998

<¼ 0.50 42 0 50 8 24 90 18 89 9 440.51–0.60 57 25 28 18 42 25 31 12 22 340.61–0.70 17 48 15 35 15 3 42 2 41 140.71–0.80 1 23 8 28 15 0 17 0 24 40.81–0.90 0 13 1 18 1 0 3 0 12 2>0.90 1 3 1 3 2 0 1 0 2 1

Total 118 112 103 110 99 118 112 103 110 99

Total number of farms 542 542

Source: Sample data.

Table 4. Technical efficiency (between-regions) (per cent)

New York Ontario

Range 1992 1993 1995 1997 1998 1992 1993 1995 1997 1998

<¼ 0.50 35.6 0.0 48.5 7.2 24.2 76.3 16.0 86.4 8.2 44.40.51–0.60 48.3 22.3 27.2 16.4 42.4 21.2 27.7 11.7 20.0 34.30.61–0.70 14.5 42.9 14.6 31.8 15.2 2.5 37.5 1.9 37.3 14.10.71–0.80 0.8 20.5 7.8 25.5 15.2 0.0 15.2 0.0 21.8 4.0>0.80 0.8 14.3 1.9 19.1 3.0 0.0 3.6 0.0 12.7 3.2

Mean 0.53 0.68 0.53 0.69 0.58 0.44 0.61 0.42 0.66 0.53

Total average mean 0.602 0.532

Source: Sample data.

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dairy farms whose efficiency scores were less than 50%decreased in both countries from 1992 to 1998.

The mean technical efficiency of New York dairy farm-ers at 0.602 is, on average, higher than that of Ontariodairy producers (0.532) during the period of the study.We performed two conventional statistical tests to exam-ine whether the variances and the means, respectively, ofthe computed technical efficiencies in both regions areequal. First, an F-test rejected any discrepancies betweenthe two variances of the computed technical efficiencyin both regions at the 1% level of significance. Second,using the results obtained via the first test, a pooled-variance t-test was conducted to measure any differencesamong the mean technical efficiency of New York andOntario farms. The two-tailed pooled-variance t-testrejected any equality between the technical efficiencymeans of Canadian and American dairy producers atthe 1% level of significance. This finding strongly indi-cates that the different policies implemented in the twocountries significantly affected performance in the dairysector. Furthermore, the direction of the performanceimpact was as predicted; the tighter regulations inCanada over the sample period hurt the performanceof Ontario dairy farmers in comparison to their UScounterparts.

We also conducted several discrete multivariate anal-yses to find a relationship between technical efficiency,time period, and region (Bishop et al., 1975). A chi-squared test at the 95% confidence level rejected anykind of significant relationship between these variableswith two major exceptions. A relationship between effi-ciency class intervals and time period was found. Giventhe region, the estimated technical efficiency in a particu-lar year (on average) affected the performance of dairyfarms in the following year. It is expected that this is dueto a learning-by-doing effect in the dairy sector. And inthe time period of the study, a relationship between theefficiency class intervals and the regions of the study wasfound. Given the basic physical similarities between thedairy sector in both countries, it is believed that this lastresult is most likely attributable to those governmentpolicies that differentially affect the performance ofdairy farms in Canada and the USA.

It is cautioned that these results must be interpretedwith care. Taken at face value, the findings imply thatsupply management policy implemented in Canada sig-nificantly and adversely affected the efficiency of Ontariodairy farmers as compared to their US counterparts.This conclusion supports the conventional belief thatsupply management policies can lead to a misallocationof resources. However, it is suggested that another non-parametric stochastic frontier study is necessary to fullyverify the conclusions. Ideally, that study would containmore information from Ontario dairy farms in order tominimize any possible bias in the results due to the

reduced number of farms used in the between-regionsanalysis. As Table 5 indicates, in the between-regionsmodel, the study was only able to use 542 observationsout of a total of 6836 observations reported in Table 1for the within-regions model.

VII. CONCLUSIONS

Policy in the Canadian dairy sector has been characterizedby rules and regulations on the supply side (supply man-agement) imposed by the federal and provincial govern-ments through the Canadian Dairy Commission (CDC)and the provincial milk marketing boards. Dairy policyin the USA, to some extent, is not heavily supported bythe government as it is in Canada. The US dairy industry isoperated under a collection of different policies, which ismore market-oriented and tends to be liberalized. InCanada, such interventions of government in agriculturalpolicy could lead to inefficiencies in production and a mis-allocation of resources. Trade liberalization would exposethe Canadian producers to lower and more uncertainprices, resulting in a need to adjust production.

A stochastic nonparametric frontier model was set upto estimate technical efficiency of Ontario and NewYork dairy producers between 1992 and 1998. Themodel is based on the theory of generalized additivemodels (GAMs). This study utilized a locally weightedscatter plot smoothing (LOWESS) model to estimate themean response function in a nonparametric approach.A quadratic form of the LOWESS function was usedby implementing the backfitting algorithm.

The results showed that during the period of study,New York dairy farmers produced milk more efficientlythan Ontario dairy farmers, but the magnitude of the dif-ference is small; the estimated mean technical efficiencyfor the former group was 0.602 which was higher thanthe latter group’s, 0.532. Like several previous studies,our results also showed that over time, dairy farms inboth regions improved their level of technical efficiency.However, unlike the results of previous studies, no sig-nificant correlation was found between farm size andthe level of estimated technical efficiency. It is believedthis finding indicates that the methodology represents animprovement over the econometric methods used pre-viously to estimate efficiency frontiers in this industry.

ACKNOWLEDGEMENTS

The authors would like to thank Robert Romain to manyhelpful comments and suggestions that led to substantialimprovement of the paper. All the remaining errors aretheir own.

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