Relationship between Farm Size and TechnicalEfficiency

An empirical analysis of the oil palm sector in Colombia

Raysa Rosario Lizarraga Hernandez

June 8, 2020

Research ProgramDepartment of Economics

University of Oslo

Preface

For my thesis I was interested in studying a topic that could be related

to my homeland, Peru. During the search for a topic I came to meet my

supervisor, Henrik Wiig, who from day one gave me his full support. I

would like to thank him for his help and feedback through the ups and

downs of this process. Thanks to his support I traveled to Colombia and

visited an oil palm plantation, where I got extremely valuable first-hand

experience that complemented my knowledge for this thesis. I am forever

grateful to Henrik, and I will take his advice with me in my development

as an economist.

I would like to thank all the professors I have met at UiO, and give a

special thanks to Nils Framstad for teaching me to see mathematics in a

different light. Thanks to my dear friend Edinson Tolentino for his time

and guidance every time I needed it. Thanks to Balazs Vaghy and Laura

de Vries for their recommendations. I am grateful to all of my friends who

always had a word of support for me, and cheered me up to keep going. I

also want to thank my parents, Charo and Guillermo, for always being

there for me in every step of my life, no matter the distance. Last, but not

least, I thank Stian Hyman Berg, my partner, for his patience and love,

and for giving me his endless support in the pursuit of my professional

goals.

Raysa Rosario Lizarraga Hernandez

June, 2020

Abstract

The literature within development economics generally assumes the hypothesis

of an inverse size-productivity relationship of agriculture. Using Stochastic Fron-

tier Analysis (SFA), this thesis provides an empirical analysis of the relationship

between farm size and technical efficiency of the oil palm sector in Colombia. The

study uses data from the 3rd National Agricultural Census conducted between

2013 and 2014 by the National Department of Statistics (DANE). This study

found that farms with more than 50 hectares tend to be more efficient than

smaller farms, meaning that the sector did not show an inverse size-efficiency

relationship. The study also found that the positive relationship between farm

size and technical efficiency is partially explained by technological factors, such

as the use of machines, fertilizers, pest controls, irrigation systems, and technical

assistance. When these factors are included in the analysis, the relationship

between farm size and technical efficiency becomes negative, which is possibly

explained by the low productivity of hired labour compared to family labour, as

indicated in the theory of the principal-agent problem. The analysis has found

evidence suggesting that big farms in the oil palm sector in Colombia operate

with increasing returns to scale, and have better access to input markets, such as

fertilizers and agrochemicals. Technical assistance and irrigation systems have

the highest effect on technical efficiency among the technological factors included

in the analysis. Oil palm farms in the Orinoquia region had, on average, the

highest technical efficiency level. This thesis has found that the expansion of the

sector would be more technically efficient if it is done through large farms. The

alternative expansion through small farms should go in hand with improving the

conditions of rural input markets, and technical assistance. Finally, the results

need to be studied in more depth when more complete and disaggregated data is

available.

Contents

1 Introduction 1

2 Background 3

2.1 Agriculture in Colombia . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Palm oil industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Motivation and Research Questions . . . . . . . . . . . . . . . . . . . . 12

3 Literature Review 13

3.1 Inverse Relationship between Productivity and Farm size . . . . . . . . 13

3.2 Production Frontier and Efficiency Measures . . . . . . . . . . . . . . . 16

4 Methodology and Theoretical Framework 19

5 Data and Variables 24

5.1 Input Variables in Frontier Estimation . . . . . . . . . . . . . . . . . . 27

5.2 Presumed determinants of Technical Inefficiency . . . . . . . . . . . . . 27

5.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

6 Empirical Model 35

6.1 Estimation of inefficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 36

6.2 Hypothesis Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

7 Preliminary Analysis 42

8 Results and Discussion 46

8.1 Frontier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

8.2 Technical Inefficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

9 Conclusions 53

References 55

1 Introduction

Climate change is a global concern that has a major role in the political agenda of most

developed and developing countries. The European Union has committed to reduce

their greenhouse gas emissions by at least 40% by 2030 compared to 1990 levels, and to

supply 32% of their energy from renewable sources (European Comission, 2014).

A possible alternative to fossil fuels are biofuels. Biodiesel is a type of biofuel made

from vegetable oils, animal fats, and recycled greases. One type of vegetable oil used to

produce biodiesel is palm oil, which is derived from the fruit of the oil palm. This crop

has a global average yield of 3.2 tons of vegetable oil per hectare, which is the highest

yield among oilseeds (the 2nd highest yield is that of rapeseed with just over 0.7 t/ha)

(WWF-UK, 2020). Its high oil yield and its use in diverse supply chains have positioned

palm oil as a major world commodity. Sadly, the expansion of the industry has caused

deforestation of rainforests in various tropical regions. This is a serious problem for the

industry, which has recieved a lot of criticism for its enviromental impact. But evidence

suggests that when oil palm is grown in a sustainable way1 in degraded grasslands

instead of in rainforests, it can be a valuable feedstock to produce climate friendly

biodiesel (RSPO, 2020).

In this context, Colombia can contribute to the expansion of oil palm production without

deforestation. According to the Rural and Agricultural Planification Unit (UPRA, 2017),

the country has about 16 million hectares suitable for sustainable oil palm production (of

which only around 560 000 hectares are planted (Fedepalma, 2020)), and most of these

lands are in the Orinoquia region, which mostly consists of natural open savannahs with

extensive pasturelands. Hence, there is a big potential for expansion, and it is important

to analyse the possible variables that affect the efficiency of oil palm farms, such as farm

size. Empirical research has found evidence of an inverse size-productivity relationship

in developing economies. These findings are in line with the theory of Principal-agent

problem, in the sense that small farms that operate mainly with family labour produce

more efficiently than large farms with hired labour (Ray, 1998). On the other hand,

1The term sustainable includes social, economic, ecological, and environmental guidelines for palmoil production (RSPO, 2020).

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some authors have found that the inverse size-productivity relationship is not a general

rule for all agricultural production in developing economies, and big farms can be more

productive than small farms due to technological differences (Deolalikar, 1981), and

imperfect credit and insurance markets (Kevane, 1996).

This thesis analyses the relationship between farm size and technical efficiency at farm

level, as well as how it is affected by technological variables. The estimations are

done using the software Stata 16.1 (StataCorp, 2019). The goal of this thesis is to

contribute to the development of public policies aimed at expanding the oil palm sector

in Colombia.

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2 Background

2.1 Agriculture in Colombia

The geography of Colombia is very diverse. Its territory includes the Amazon rainforest,

extensive savannas known as ‘Los Llanos’, and the high altitude Andean Mountains.

Colombia is identified as one of the 17 megadiverse countries of the world, meaning

it is among the world’s top biodiversity-rich countries (UNEP-WCMC, 2014). The

tropical location and its good weather conditions offer a high potential for agricultural

production. In the last decade, however, agricultural production has only accounted for

roughly 6% of the GDP, and as seen in figure 1, crop production by itself represented

around 4% of the National GDP.

Figure 1: Crop production value added (% of GDP)

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2.5

3

3.5

4

4.5

5

2010 2011 2012 2013 2014 2015 2016 2017 2018

Per

cen

t o

f G

DP

1Source: DANE, Cuentas Nacionales.2The calculation is agricultural production minus forestry,cattle ranching and fishery.

The low contribution of the agricultural sector in the economy can to some extent be

explained by the predominance of low-productivity extensive livestock farming in rural

areas (an average of 0.86 heads of cattle per hectare in 2009) (PNUD, 2011). This

feature can be partially explained by the absence of the rule of law in rural areas, which

leads insecure property rights. Weak property rights restrict investment in productive

activities due to the fear of losing the land, hence pushing producers to low cost and

low maintenance activities (Wiig and Garcıa-Reyes, 2020). Furthermore, property taxes

in Colombia are relatively low in comparison to taxes on productive activities. This

has attracted investors that speculate with the value of the land, instead of using it as

a means of production (PNUD, 2011).

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Extensive livestock farming limits the amount of space for crop production and its

potential to generate profits, especially within the sector of agro-industrial farming. In

an effort to address this issue, the government has estimated the agricultural frontier.

Agricultural frontier (‘frontera agrıcola’) does not refer to the calculation of frontiers as

are known in the field of economics. It is a national reference of how much of the total

extension of the country is suitable for agricultural production (considering social and

environmental restrictions), regardless of whether it is currently used for agriculture or

not (UPRA, 2018).

In 2016, the agricultural frontier was found to be 35% of the national territory2.

Approximately 80% was used for livestock farming and pastures, leaving only 20% for

crop cultivation (UPRA, 2018). This shows how the agricultural frontier is underutilized

and that it is possible to increase crop production without deforestation by reallocating

land from low-productivity cattle ranching to agro-industries.

The agricultural sector of Colombia is characterized by a large number of small properties

and a small number of big properties. According to the National Census Report 2014

(DANE, 2014), almost 70% of the agricultural producers3 have properties with less than

5 hectares and altogether represent less than 5% of the total rural area covered by the

Census4. In contrast, 0.4% of the agricultural producers have properties of at least 500

hectares and they possess 41.1% of the total rural area covered by the Census.

The high concentration of land in the hands of a few could be a consequence of, among

other factors, the armed conflict that the country has experienced5(Corredor, 2016). The

armed conflict in Colombia can be traced back to the independency of the country in

1810. However, the conflict as we know it was shaped in the 1960’s with the foundation

2The delimitation of the agricultural frontier took into consideration legal restrictions, the protectionof natural forests and protected ethnic territories.

3It should be noted that although the Census treats people with any size of land in agricultural useas ‘agricultural producer’, some of these people with very small properties usually supply labour forceto bigger farms, and work their land as secondary activity.

4The total rural area for the census was delimited by the topographic mapping of the ColombianGeografical Institute. It covered a total of 113,008,623.9 hectares, and it included agricultural producers,non-agricultural producers and natural parks. Agricultural producers included producers (people orfirms) dedicated to crop production, cattle ranching, fishing or forestry. Non-agricultural producersincluded producers located in rural areas, but dedicated exclusively to non-agricultural activities, suchas trading, services, and transformation industries (mills, oil extraction plants, etc.).

5This study only provides general lines of the armed conflict and the following land restitution process.A detailed history of the conflict and its implications on agriculture can be found in Montana (2014).

4

of guerrilla groups, such as the Revolutionary Armed Forces of Colombia (FARC-EP)

and the National Liberation Army (ELN) (Garcıa-Godos and Wiig, 2014). The conflict

was intensified when the government incentivized the organization of self-defense groups

known as paramilitary forces to take up arms against the guerillas. The consolidation of

drug trafficking in powerful cartels during the 80’s and 90’s also played a major role in

the fight for territorial dominance between guerrillas and paramilitaries (Corredor, 2016).

The armed conflict affected primarily rural areas, where the population was forced

to leave and abandon their lands. The quantities of displaced people and abandoned

hectares vary accross sources; Corredor (2016) refers to an estimate of 3,6 millions of

displaced people and 2,5 millions of abandoned hectares, other sources have found an

estimate of more than 5 millions of displaced people and 7 to 8 millions of abandoned

hectares (Garcıa-Godos and Wiig, 2014).

The Colombian government approved the Victim’s Law (Law 1448) in 2011. The goal

of the law is to identify the victims of the conflict and offer reparations, such as land

restitutions, and to bring the rule of law to rural areas of the country. Garcıa-Godos

and Wiig (2014) analyzed the land restitution program and identified that although the

program, in theory, should contribute to the redistribution of rural property, in reality,

few of the displaced people were planning to return to the land. Furthermore, the land

restitution program creates an environment of uncertainty for current rural owners

(even for those who did not acquire the land through illegal activities), which could

discourage large investments in agricultural development6. In summary, the armed

conflict has impacted the agricultural sector in different ways, and still influences the

potential agricultural productivity.

6Wiig and Garcıa-Reyes (2020) provides an analysis of the land trials against the companyAgropecuaria, which had bought plots from local people and invested about 720,000 USD in the ElCarmen municipality between 2008 and 2012. The trials ended discouraging the company from itsinitial productive plans.

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2.2 Palm oil industry

According to the National Department of Statistics (DANE), crop production in

Colombia can be grouped in agroindustrial products7, cereals, forest plantations, tubers

and bananas, fruits, vegetables, and others8. The group that contributes the most to

crop production is agroindustry, which in the first trimestre of 2019 represented 48.7%

of the total cultivated area of the country (DANE, 2020). In agroindustrial production,

oil palm9 has the second largest extension of cultivated land after coffee .

Physical evidence suggests that oil palm is native from West Africa10. The name of

the specie is Elaeis guineensis, but it is usually known as the African palm. Industrial

plantations of oil palm began after World War I in Nigeria, Congo and French territories,

but the plantations’ success was limited by political instability. This context allowed

South-Asian plantations to become the world’s largest producers since 1938 (Corley, R.

H. V. and Tinker, P.B., 2008). Indonesia and Malaysia have consolidated themselves

as the world’s largest exporters of palm oil, with making up approximately 84% of

the market in 2019, and Colombia is positioned in 4th place, after Thailand, with 2%

(USDA, 2020).

The fruit of the oil palm can be divided into two main parts: a hard-shelled nut in the

center of the fruit, and the pulp that surrounds the nut. The pulp has a fibrous texture

that contains crude palm oil (CPO), while the nut contains a kernel from which it is also

possible to extract an oil known as crude palm kernel oil (CPKO). The residuals from

the extraction process can be used as fertilizers (residues from the pulp and skin) and

animal food (residues from the kernel) (Corley, R. H. V. and Tinker, P.B., 2008).

Oil palm gives the highest oil yield per hectare among the known vegetable oil crops.

The global average yield of CPO is about 3.2 tons per hectare11, and research has found

that under good weather conditions and appropiate management of the crop, yield of

CPO could reach levels of 7 to 10 tons per hectare (Woittiez et al., 2017). Palm oil

7It referes to crops that have an added value process after harvest, such as coffee, oil palm, sugarcane, cacao, soja and cotton.

8Others include maize, forage, flowers and herbs.9Oil palm refers to palm trees from where palm oil is extracted from.

10Some authors suggest that the origin can be traced back to South America. However, physicalevidence of pollen from Miocene sediments in Nigeria supports the African origin theory (Corley, R. H.V. and Tinker, P.B., 2008).

11Rapeseed oil and sunflower oil have an average yield of 0.7 tons per hectare (WWF-UK, 2020).

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is used in diverse supply chains, such as food production, cosmetics and biodiesel12.

The high yield of oil palms combined with the properties of palm oil13 has positioned

palm oil as the most widely used vegetable oil (Yara, 2019). However, oil palm requires

humid tropical conditions to grow, and as the demand for vegetable oils has increased,

the expansion of the industry in Southeast Asia has converted natural forests for the

purpose of oil palm plantations. This has accentuated the concerns about the negative

environmental impacts of the industry.

Koh and Wilcove (2008) estimated that at least 55% of the oil palm expansion in

Malaysia and Indonesia during the period of 1990-2005, was at the expense of natural

forest areas. Their study does not explicitly state if their calculation accounts for

direct deforestation and indirect deforestation, but it can be deduced that they refer

only to direct deforestation, meaning that calculations could be underestimating total

deforestation. Indirect deforestation occurs when oil palm displaces other types of crops,

‘pushing’ them to take over natural forests. This is known as indirect land-use change

(ILUC) (European Parliament, 2018). Hansen et al. (2014) estimated that greenhouse

gas (GHG) emissions related to the oil palm expansion in Malaysia were underestimated

if ILUC (from rubber) was not accounted for.

Deforestation is not only a source of GHG emissions, but it also poses a threat to

biodiversity, which altogether challenges the potential positive environmental and social

impacts of the industry. However, as oil palm is the most efficient vegetable oil crop,

replacing it with other oilseed crop would require using even more land in order to cover

global demand. This has led governments, NGO’s and companies to work together to

make palm oil production environmentally and socially sustainable.

To provide guidelines for sustainable production, international certifications have been

introduced, such as the Round Table on Sustainable Palm Oil (RSPO), and the Inter-

national Sustainability & Carbon Certification (ISCC). RSPO was established in 2004

and it takes into account the entire palm oil supply chain. RSPO principles and criteria

12Biodiesel is a substitute for fossil fuels, and if produced in a sustainable way, it can contribute toclimate change mitigation (Yara, 2015).

13Corley, R. H. V. and Tinker, P.B. (2008), Chapters 13 & 14, provide a detailed description of thecomposition and properties of palm oil, and its advantages in edible uses, for example “palm oil isparticularly suitable for deep frying because it is relatively stable at high temperature, compared withthe more unsaturated oils.” (Corley and Tinker (2008), p. 473).

7

include no deforestation and improving the living conditions of oil palm plantation

workers. The RSPO standard principles and criteria are further adapted by each country,

accounting for legal, cultural, and social differences through National Interpretations.

Currently, 19% of global palm oil production is RSPO certified (RSPO, 2020). ISCC

was established in 2006 with the objective to ensure environmentally, socially and

economically sustainable conditions in the supply chain of not only palm oil, but all

biomass and products derived from biomass. Although the ISCC certification follows

global standards, they have also developed a different program for small farmers of

oil palm in order to reduce the burden and costs of certification. In 2018, 1,630,084

hectares with oil palm was ISCC certified (ISCC, 2020).

In line with sustainable production goals, Indonesia and Malaysia have committed

to stop and to compensate deforestation done by the industry (RSPO, 2019)14. For

example, the Malaysian government has committed to focus on productivity growth,

and keep a fixed percentage of its land as forest (Yara, 2019). This limits the amount

of suitable land for oil palm plantations in Southeast Asia. In contrast, Colombia, as

explained in the previous section, has a high potential for crop production expansion

without deforestation.

Oil palm is not a new crop in Colombia, it was introduced to the country in the early

20th century, and its commercialization began in the 1950’s (Cenipalma, 2017). Since

the year 2000, the extension of land cultivated with oil palm has steadily increased

from 158,000 hectares to 560,000 hectares in 2019 (Fedepalma, 2020). According to

the National Federation of Oil Palm Growers (Fedepalma, 2019), the distribution of

hectares planted with oil palm in 2017 was: 41% in the East (Orinoquia region), 31%

in the Center (Andean region), 24% in the North (Caribbean region), and 4% in the

Southwest (Pacific region)15.

In a study aimed at estimating the impacts of oil palm on deforestation and biodiversity,

Vijay et al. (2016) found that 100% of the oil palm expansion between 1989 and

2013 in Colombia was done converting previously deforested land, meaning that it

14RSPO certification allows for remediation and compensation procedures (RaCP) of land clearencedone after November 2005. RaCP has been included in the National Interpreations of Malaysia andIndonesia (RSPO, 2020).

15Further detail about the characteristics of the regions is provided in the ‘Data Description’ section.

8

replaced pastures and other agricultural activities. However, these results do not provide

information on whether oil palm replaced natural forests prior to 1989. In a survey of 32

oil palm farmers conducted by Rodrıguez and Van Hoof (2003), it was found that 17.5%

of the land was declared to had been natural ecosystems prior to the establishment of oil

palm plantations. According to Castiblanco et al. (2013), about 50% of the expansion

of oil palm plantations between 2002 and 2008 was in pasturelands, and about 29% in

croplands16.

There is limited data about the historical expansion of the oil palm industry in Colombia,

which makes it difficult to estimate the total forest and biodiversity loss associated

with the industry. However, land with oil palm has an associated biodiversity that

has higher species richness than pastures, meaning that replacing pastures with oil

palm can increase biodiversity (Fitzherbert et al., 2008)17. Nevertheless, introducing

new species to pre-existing natural ecosystems can have very varying effects, and such

potential alterations to natural ecosystems should be taken into account when deciding

where to expand the industry.

As has been discussed, replacing cattle ranching and croplands with oil palm planta-

tions is a more efficient use of land, and it can also contribute to forest conservation.

However, it can have a negative impact on food production. Garcia-Ulloa et al. (2012)

remarked that to offset food production loss in Colombia due to oil palm expansion,

this should go in hand with efficiency improvements of remaining pastures and low yield

croplands.

From a social perspective, in some areas of Colombia, the expansion of oil palm has been

linked to conflict and forced displacement, especially in the Pacific region. Guerrillas,

paramilitaries and drug dealers saw oil palm plantations as an opportunity for territorial

control and money laundering. They extorted the already established oil palm farmers

that were not willing to work with them, and forced protected ethnic groups to abandon

their lands. These lands were then taken over by oil palm farmers associated to their

16Their study does not account for ILUC, but the authors point out that most of the deforestationin Colombia is due to illicit coca plantations.

17However, the authors also found that this was not the case with abandoned pastures, and that oilpalm has lower species richness than most other tree crops. Furthermore, there is limited researchabout biodiversity loss associated with oil palm plantations, which, according to the authors, might beunderestimating the loss.

9

illegal activities (Ocampo Valencia, 2009). Fedepalma established its own program of

corporate social responsability (RSE) in 2005, with the objective to reduce the link

between oil palm and illegal activities through socially and environmentally sustainable

guidelines. One of the objectives of the RSE program was to become a RSPO member,

and to develope the RSPO Principles and Criteria National Interpretation (RSPO NI)

for Colombia (Ocampo Valencia, 2009)18.

Sustainable production of palm oil has been recognized by the Colombian government

as a relevant agroindustry to fight rural poverty (Restrepo, 2000). According to the

National Survey of Direct Employment in the Palm Oil Sector conducted by DANE

(DANE, 2016a), the sector provided a total of 67,672 direct jobs, which represented

2.3% of total agricultural employment. It also found that 82.4% of palm oil workers

had a formal employment relationship, while formal rural employment as a whole is

only 18% (Observatorio Laboral LaboUR, 2018)19. Furthermore, Olivera et al. (2011)

found that the sector follows the country’s labour regulations more closely than other

agricultural sectors, meaning that it provided better and more stable salaries, shorter

working days, and labour benefits (paid vacations and labour termination compensations

(‘cesantıas’20)).

Concerns about climate change acceleration due to production and combustion of

fossil fuels, have increased the interest in alternative energy sources, such as biofuels.

Biodiesel is a liquid type of biofuel21, and it can be blended with traditional diesel to

reduce emissions of air pollutants during combustion (FAO, 2008). Biodiesel obtained

from palm oil gives the highest yield in liters of biofuel per hectare among oilseeds

(3,600 liters per hectare against 700 liters per hectare obtained from soy), and it has

one of the highest potential yield among all types of biofuels (IEA, 2011). However, as

previously explained, the potential positive environmental impact of biodiesel can be

offset if it is made from palm oil that was not produced in a sustainable fashion.

18The RSPO NI was published for public consultation in 2019. It includes the defense of humanrights, and the commitment to identify land that was taken illegally, or without previous environmentalassessment, for future remediation RSPO (2020).

19The methodology and sampling between DANE and LaboUR might differ, thus the aim is not todo a precise comparisson, but to give a general context.

20Cesantıas is a one time payment formal workers recieve at the end of their labour relationshipwith the employer, and it is proportional to their salaries and time they worked for the employer.

21Biofuels refer to any type of fuel obtained from biomass, including biodiesel, ethanol, fuelwood,charcoal, biogas and bagasse (FAO, 2008).

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In 2008, the Colombian government approved a document called Conpes 351022, which

establishes guidelines to stimulate sustainable prodution of biofuels. These guidelines

are based on the competitive advantages of Colombia, such as the production of palm oil.

Conpes 3510 recommends to begin by consolidating the domestic market of biofuels, to

set a foundation for Colombia to compete in the international market (CONPES, 2008).

In 2018, domestic producers of biodiesel represented the largest buyers of Colombian

CPO, buying 27% of total production (Fedepalma, 2019).

In summary, the agricultural sector of Colombia has potential to contribute more to GDP

by replacing pasturelands used mainly for extensive livestock farming with agroindustrial

crops, leading to a better use of the agricultural frontier. One of Colombia’s biggest

crops is oil palm. Oil palm has the highest yield of all oilseeds, and its many uses has

made it a profitable industry. However, its rapid expansion in Southeast Asia has raised

environmental concerns, especially regarding deforestation. Colombia has identified that

there are large areas of degraded grasslands, especially in the Orinoquia region, that

could be converted to oil palm production, such that the expansion of oil palm would not

be at the expense of rainforests. This complies with international regulations of palm

oil production. Currently, oil palm plantations represent a large share of the cultivated

land in Colombia, and the economical activities derived from it have created several

direct jobs with better working conditions than in other sectors of agriculture. The

production of sustainable palm oil can have positive social, economic and environmental

effects. Socially and economically, it can improve the living conditions of the rural

population, and be a driver of agroindustrial development. Environmentally, it can

contribute to climate change mitigation through the supply of palm oil for biodiesel.

However, there are still many challenges in regard to governmental regulations and

efficiency. Research on public policy and efficiency can contribute to sustainable palm

oil production and the economy.

22Conpes documents are governmental documents developed by the National Council of Economicand Social Policy (CONPES) through the National Planning Department. These documents are theroadmap of the country, and are associated with the National General Budget project that is revisedand approbed by the Parlament (ECLAC, 2020).

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2.3 Motivation and Research Questions

As previously described, the Colombian government has identified the oil palm sector

as a strategic agroindustry to fight rural poverty, and to contribute with climate change

mitigation through the production of sustainable palm oil for biodiesel. The potential

to expand the sector without deforestation has received the attention from the public

and the private sector. In line with this, the main question for this study is:

• What farming system should be favored in the planning of the expansion of the

sector?

To answer this question, this thesis analyzes the relationship between farm size and

technical efficiency of the oil palm industry. Measuring and identifying the determinants

of technical efficiency in oil palm plantations can contribute to improving yield of CPO

per hectare, meaning that the industry would need less land to cover domestic, and global

demand. Furthermore, it could make the industry more profitable, potentially improving

the living conditions of oil palm plantations workers, while indirectly improving the

livelihood of the population in the proximities of the plantations.

The empirical questions are:

• What is the relationship between farm size and technical efficiency in oil palm

production in Colombia?

• How do geographical, technological, and social variables affect technical efficiency?

These questions will be analyzed using available data at farm-level, collected by

DANE.

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3 Literature Review

3.1 Inverse Relationship between Productivity and Farm size

Ray (1998) describes two opposite forces that shape the relationship between farm

size and productivity23: technology and incentives. Technology refers to the level of

mechanization of the farm, for example through the use of tractors or animals. Although

technology can allow the farm to reach economies of scale, it can be costly to possess.

This implies that a minimum farm size is required for capital-intensive farming to

become an economical alternative, thus technology usually pulls the size-productivity

relationship towards favoring larger farms (in the worst case scenario it would make

large farms at least as productive as small farms). On the other hand, with information

asymmetries and imperfect factor markets, incentives favour small farms that rely on

family labour. The explanation of why incentives favor small farms can be found in

mechanism design theory, in particular in the principal-agent problem.

The principal-agent problem refers to a context of asymmetric information between two

parties that want to sign a contract, for example when the owner of a farm (principal)

wants to hire a worker (agent). The informational problem can be of two types: hidden

information and hidden action, the latter is also known as moral hazard. Hidden

information means that only the worker knows his/her real skills and how good they

fit the tasks given by the owner. Assuming that the hidden information problem is

solved, and a contract is reached, there would still be a hidden action problem. Hidden

action means that a worker can choose to put less effort into the task, specially if the

worker has a fixed-wage contract (Mas-Colell et al., 1995). Hidden action may hurt

both sides: being aware of the moral hazard, the owner can decide to offer a lower wage,

which would further reduce the worker’s incentives to be productive. Furthermore, the

larger the farm, the more hired labour it needs, which makes it harder and more costly

to supervise the workers’ effort24. On the other hand, with imperfect factor markets,

members of a small farm might not have better alternatives than to work their own land,

23He uses the term ‘productivity’ from the production efficiency perspective, not from the TotalFactor Productivity perspective.

24Further details and solutions to the principal-agent problem are in the field of Contract Theory(Bolton, Dewatripont, et al., 2005).

13

meaning that they would exert more effort than hired workers, thus obtaining more

output per unit of land. The incentives force makes the size-productivity relationship

negative (Ray, 1998).

In summary, the direction of the size-productivity relationship depends on which force,

technology or incentives, is stronger. Ray (1998) remarks that this is “ultimately an

empirical question”, and empirical findings suggest that it is usually the incentives

force that dominates in developing economies. This is the base of the hypothesis of an

inverse relationship between farm size and productivity, which has favored policies of

land redistribution in developing economies.

Numerous empirical studies have supported the inverse size-productivity relationship

hypothesis for developing economies, and the possible explanations found in the literature

are: imperfect factor markets, land quality, and measurement error. Some authors have

also found the opposite relationship, meaning that larger farms were more productive

than small farms (mainly explained by technological factors). The remainder of this

section will briefly discuss some of these empirical findings.

Sen (1962) observed that the hypothesis of an inverse size-productivity relationship

found in Indian agriculture, was due to the farming system, and farm size was just

incidental in the relationship. His analysis is in a context of wide-spread unemployment,

and it considers two systems of farming: family-based and waged-based. A high

unemployment rate means that it is hard for the members of a family-based farm to

find a job outside of the farm, which implies that the opportunity cost of labour is

very low. Sen (1964) argues that even if the market wage is low, it does not go below

the opportunity cost of labour, meaning that wage-based farms are more restricted

to use labour than family-based farms. In other words, family-based farms will apply

labour more liberally (even if it is not profitable) than wage-based farms, getting more

output per acre than wage-restricted farms. He concludes that the root of the inverse

size-productivity relationship in India, is the system of farming (namely due to the

cheapness of family labour), and that large cooperative farms could be as productive as

small farms.

14

Deolalikar (1981) tested two hypotheses about the inverse size-productivity relationship

using regional data from India in 1970-71. The first hypothesis is that the inverse

relationship is a general rule that applies to all Indian agriculture. The second is

that the inverse relationship doesn’t hold with technical progress (average fertilizer

application per hectare is used as a proxy for technical progress). His findings are that

in India, among farms with no technical progress, the small farm sector as a whole had a

higher productivity per unit of land than the large farm sector. However, among farms

with higher levels of technical progress, the relationship between size and productivity

became positive, i.e. the large farm sector showed bigger gains on productivity from

technical change than the small farm sector. His findings are in line with the theory that,

as previuosly described, when technology dominates incentives, the size-productivity

relationship is positive.

Kevane (1996) developed a theoretical framework showing that a positive size-productivity

relationship is possible even in the absence of technological progress. He found that

in the Sheikan district of Sudan, there was a positive relationship between wealth and

yield (output value per unit of land). Furthermore, wealthier farmers owned larger

farms, meaning that there was a postive relationship between size and productivity.

He remarked that these findings happened in a context of very little technical change,

such that technology could not be the explanation behind the results. He suggests that

the most plausible explanation for his findings is the combination of credit constraints,

absence of insurance, and risk of losing property rights. Poor farmers without access

to credit might not have the implements nor the nourishment to work their lands

intensively, which over time would increase the gap between wealthy and poor farmers,

up until the point where poorer farmers are willing to sell their lands to wealthier

farmers.

Studies that tested measurement error as a source of the inverse size-productivity

relationship propose that farms may be over-reporting some of the main variables for

the estimations, such as farm size. If over-reporting is systematic in smaller farms, the

measurement error would be negatively correlated with farm size, meaning that the

parameter of size will be downward biased (Barrett et al., 2010). Lamb (2003) tested

measurement error as a potential explanation of the inverse relationship hypothesis. He

15

used panel data information of India between 1975 and 198525. He found that land

quality and labour market imperfections explained most of the inverse size-productivity

relationship of the dataset, but that it was likely that the measurement error in farm

size was intensifying the results.

Barrett et al. (2010) used cross-sectional dataset at plot-level from Madagascar to test

whether the hypothesis of the inverse size-productivity relationship comes from market

imperfections or from omitted soil quality measurements26. They found that market

imperfections might explain a third of the inverse relation in the dataset, but they

did not find a significant difference between measuring the model with or without soil

quality controls. They concluded that neither market imperfections nor soil quality

explained most of the inverse relationship they found, and that the relationship was

likely to be driven by meassurement error (i.e. small farmers might have systematically

over-reported plot sizes) or intra-household allocative inefficiency (i.e. households might

put more effort in some of their plots based on convenience, rather than on efficiency,

and this effect would increase with farm size)27.

There is an ongoing debate about why the inverse size-productivity relationship is

usually found in developing economies, and under which circumstances it is not. The

topic has important policy implications for how to increase agricultural productivity,

while improving the social conditions of the rural population.

3.2 Production Frontier and Efficiency Measures

A production frontier is the representation of the maximum output attainable from a

given combination of inputs. If the farm produces on the frontier, it is considered to have

full technical efficiency. If production is beneath the frontier, then there is some level

of technical inefficiency, represented by the distance to the frontier. This perspective

to measure efficiency is known as output-oriented, it asks the question “how much

more output can be obtained with the same amount of inputs?”. Efficiency measures

can also be of an input-oriented perspective. The input-oriented perspective asks the

25Collected by the International Crop Research Institute for the Semi-Arid Tropics (ICRISAT).26The data they used provided detailed soil quality measures (levels of carbon, nitrogen, potassium,

clay, silt and sand, as well as soil pH) at plot level.27However, these potential explanations were not tested due to lack of data.

16

question “how can the farm produce the same level of output using less inputs?”, and

it is represented by an efficient isoquant28 (Coelli et al., 1998).

Both perspectives of efficiency-measure rely on the assumption that the level of full

efficiency is known. In practice, this is not the case, and it needs to be calculated.

Farrell (1957) proposed that a hypothetical fully efficient firm can be estimated from

observed data, either by (1) a piece-wise construction without assuming a functional form

of technology (non-parametric estimation), or by (2) assuming a priori the functional

form of the production function and fitting the data to it (parametric estimation).

Several efficiency-measure methods have emerged from Farrell’s work. Two of the most

known methods are the non-parametric Data Envelopment Analysis (DEA), and the

paramatric Stochastic Frontier Analysis (SFA)29

DEA method was operationalized by Charnes et al. (1978), and it “involves the use

of linear programming methods to construct a non-parametric piece-wise surface (or

frontier) over the data” (T. J. Coelli et al., 1998, p.140), meaning that the frontier is

constructed by ‘comparing’ each observation to all the others. The main advantage of

the DEA method is that it does not assume a particular production function, hence it

allows for heterogeneity in technology. However, as each observation is compared to all

the others, the construction of the frontier will be very sensitive to measurement errors

and outliers (Van Biesebroeck, 2007).

SFA was independently developed by Aigner et al. (1977), and Meeusen and Den

Broeck (1977). Deterministic parametric and non-parametric methods regard all the

deviation from the frontier as technical inefficiency. The authors of the SFA method

observed that in practice this was not the case, and part of the deviation from the frontier

could be ‘mere luck’ (for example, good or bad luck with rain), or measurement errors.

Hence, not all of the deviation should be associated with pure technical inefficiency.

They suggested that the frontier should be bounded by a stochastic term (all that

28Graphically, production frontiers represent feasible levels of output by given levels of inputs, whileisoquants represent different input combinations that give the same level of output.

29Other efficency measurement methods are OLS, Instrumental Variables (GMM), Olley and Pakes(OP), and Index Numbers. A review of each method can be found in Van Biesebroeck (2007), wherethe author compared how good each method perfomed under different problems (measurement errors,heterogeneous technology, lack of information, etc).

17

is not under the farmer’s control), which gave the name to the method (Coelli et

al., 1998).

Studies of technical efficiency in agriculture have used both methods. Helfand and

Levine (2004) used DEA to explore the determinants of technical efficiency of farms in

Brazil. One of their findings was that the relationship between efficiency and farm size

was non-linear, but that it followed a U-shaped relation. Specifically, they found an

inverse relationship between farm size and efficiency for farms with less than 2000 ha.,

but the relationship shifted for farms with more than 2000 ha. Coelli, T. J. and Battese,

G. E. (1996) used SFA to study the potential determinants of technical efficiency of

Indian farmers. They used farm-level data from the ICRISAT between 1975 and 1985.

In accordance with previous literature, they found that hired labour was less productive

than family labour. However, they found that technical efficiency increased with land,

contradicting the inverse size-productivity relationship hypothesis, possibly due to the

effect of irrigation.

The selection of an efficiency-measure method requires evaluating the advantages and

disadvantages they offer. According to T. J. Coelli et al. (1998, p.219), “Stochastic

frontiers are likely to be more appropriate than DEA in agricultural applications,

especially in developing countries, where the data are heavily influenced by measurement

error and the effects of weather, disease, etc.”. Based on the nature of the available data

for this study, the selected method is an output-oriented SFA. The following section

provides a more detailed review of the Stochastic Frontier Analysis.

18

4 Methodology and Theoretical Framework

Following Aigner et al. (1977), the stochastic frontier of a general production function

can be written as:

ln(yi) = f(xi , β) + εi (1)

εi = vi − ui, ui ≥ 0 (2)

vi ∼ N (0, σ2v) (3)

ui ∼ F (4)

Where yi is the observed output; xi is the vector of inputs; β is the vector of parameters

to be estimated; and εi is the composed error term that includes a stochastic term vi

(i.e. luck and measurement errors), and a technical inefficiency term ui (a one-sided

disturbance). Furthermore, it is assumed that the uis and vis are independent of each

other, and independent and identically distributed (i.i.d.) across observations30.

The assumption that vi is a two-sided disturbance means that it can take negative

or positive values. These values are added to the deterministic component of the

frontier, hence fully efficient outputs are bounded by the stochastic variable vi (i.e. ui =

f(xi, β) + vi − ln(yi))31, thus the name stochastic frontier (Coelli et al., 1998).

Figure 2 provides a graphic representation of the method (assuming diminishing returns

to scale). Pair (x1, y1) represents the case when vi is positive, for example due to luck

with rain. It is possible to see that if v1 is not added to the deterministic part of the

30The assumption that uis are identically distributed has been critized as being too restrictive andfar from reality. A brief discussion, and an alternative assumption is provided in the ‘Empirical Model’section.

31In a deterministic approach, technical inefficiency would be ui = f(xi, β)− ln(yi).

19

frontier, technical inefficiency would be underestimated. The opposite case is given

by the pair (x3, y3), where technical inefficiency would be overestimated if v3 is not

considered. The observed output can also lie above the deterministic component if

vi > ui, represented by (x2, y2). The assumption that ui is non-negative implies that

observed output, yi, cannot be larger than its corresponding stochastic output, yi∗.

Figure 2: Stochastic Frontier

Y

X

y = exp(xβ)Deterministiccomponent

x1 x2 x3

y1

y3

y2

noisevi

inefficiencyui

v2

u2

v3

u3

:Stochastic outputy∗ = exp(xβ + vi)

:Observed output

Adapted from Coelli et al. (1998)

Equation 1 can be estimated using Ordinary Least Squares (OLS), this method gives

unbiased estimators for the slope, except for the intercept, β0, which will be downward

biased (Kounetas, 2017). Winsten (1957) proposed to correct the intercept bias by

adding the maximum of residuals to the estimated intercept, this method is known as

Corrected Ordinary Least Squares, COLS (S. Kumbhakar et al., 2015). The advantage

of COLS is that it is a distribution-free approach, but it still regards all the deviation

from the frontier as technical inefficiency (S. Kumbhakar et al., 2015). To decompose the

error term as suggested in the SFA framework, Aigner et al. (1977) proposed to estimate

the parameters of the stochastic frontier using the method of Maximum Likelihood

(ML), and, as seen in figure 3, SFA lies in between COLS (deterministic frontier) and

OLS.

20

Figure 3: Production Frontier Estimators

COLS

SFA

OLS

ln(y)

xβ

Adapted from Kounetas (2017)

To estimate the stochastic frontier through ML, it is necessary to make an assumption

about the distributional form of the technical inefficiency component of the error 32.

The parameters to be estimated in the model are the vector β, σ2v and σ2

u. Aigner

et al. (1977) assumed a half-normal distribution (i.e. ui ∼ N+(0, σ2u)) and expressed

their log-likelihood function using the parameter lambda, λ = σu

σv:

ln(L) = −N2ln(π/2)− N

2ln(σ2

s) +N∑i=1

ln[1− Φ(εiλσ−1s )]− 1

2σ2s

N∑i=1

ε2i (5)

Where σ2s = σ2

u +σ2v , and Φ(.) is the standard normal distribution function. Battese and

Corra (1977) pointed out that the parameter lambda, λ, could take any non-negative

value, and instead proposed to use the following parameterization:

ln(L) = −N2ln(π/2)− N

2ln(σ2

s) +N∑i=1

ln[1− Φ(zi)]−1

2σ2s

N∑i=1

ε2i (6)

Where:

zi =εiσs

√γ

1− γ(7)

32The possible specifications include: half-normal (Aigner et al. 1977), exponential (Meeusen andVan den Broeck 1977), truncated-normal (Stevenson 1980) and the gamma distributions (Greene 2003).

21

γ =σ2u

σ2s

(8)

This expression is equivalent to that proposed by Aigner et al. (1977), but the parameter

gamma, γ, can only take values between 0 and 1. Values close to 0 would indicate that

the deviations from the frontier are mainly due to noise, and values close to 1 would

indicate that the deviations are mainly due to technical inefficieny33.

Once the estimation of the parameters is done, the main objective of the SFA is to

estimate the observation-specific technical efficiencies, TEi. The calculation of TEi

can be derived from the estimation of the ui′s. To see how this calculation is made,

it is convenient to express equation (1) in the alternative form (S. Kumbhakar et

al., 2015):

lnyi = lny∗i − ui (9)

Where lny∗i = f(xi , β) + vi, and y∗i is the stochastic frontier output.

Here it is possible to see that the condition that ui is non-negative implies that

the observed output can only be on or below the stochastic production frontier (i.e.

ui = lny∗i − lnyi ≥ 0).

Then TEi can be derived as the ratio between observed output and stochastic frontier

output :

TEi =yiy∗i

= exp(−ui) (10)

Studies about technical efficiency-measure are not only interested in the estimation of

the TEi’s, but also in the variables that might explain them. Several emprical papers

have used a two-stage regression approach. In the first stage, the parameters of the

33A calculation of γ is provided in the ‘Hypothesis Tests’ section.

22

stochastic frontier are calculated and the TEi’s are predicted. In the second stage, the

predicted TEi’s are regressed on a vector of possible determinants, such as farm size,

access to credit, education, etc.

The drawback with the two-stage procedure is that in the first stage, the model assumes

that inefficiency is independent and identically distributed (i.i.d) across observations,

but in the second stage it assumes that it is a linear combination of determinants, which

usually are not identically distributed across observations, hence there is no consistency

of assumptions between stages (Coelli et al., 1998). S. C. Kumbhakar et al. (1991)

proposed a single-stage ML procedure, where the assumption that ui is identically

distributed is relaxed.

The selection of the distributional form of ui has been regarded as rather arbitrary by

the critics of the method. To alleviate this problem, Coelli et al. (1998) recommend

to use the least restrictive distributional forms, such as the truncated-normal or the

gamma distributions. However, it is important to keep in mind that the results are

sensitive to the distributional assumption of ui. This study assumes a truncated-normal

distribution for ui, and a single-stage ML estimation procedure.

23

5 Data and Variables

This study uses cross-sectional data from the 3rd National Agricultural Census conducted

by the National Administrative Department of Statistics of Colombia (DANE, 2014)34.

The collection of information took place between November 2013 and July 2014. Ac-

cording to DANE’s presentation of results (2015), the Census covered 98.9% of the rural

areas that were delimited by the Geographical Institute Agustın Codazzi (IGAC)35.

Geographically, the census collected information from all 32 departments and 1,101

municipalities.

The Census had two levels of information: land register and producers. Land register

refers to a delimited extension of land in a given municipality that is registered under a

geographical code by the IGAC. One land register can either be divided into several

properties with different owners36 or entirely owned by one producer (person or company).

Producer refers to agricultural and non-agricultural producers. A producer’s property

can be a portion of a land register, an entire land register, or serveral land registers.

The unit of observation for this study is agricultural producers and their properties

in a given municipality (i.e. if the same agricultural producer owns two properties

in different municipalities, then it is counted as two separate observations), hereafter

called ‘farmers’.

The data offers disaggregated information about how farmers use their land. Figure 4

provides a (rough) diagram of farms’ areas. Sown land (A) refers to areas used for crop

production, and it can be used for more than one type of crop. Fallow land and other

agricultural uses (B) refers to areas with potential to be used for crop production, but

that are used for other activities, such as cattle ranching. Non-agricultural land (C)

refers to natural forest areas, and non-agricultural infraestructure (e.g. houses). For

this study, farm size will not consider non-agricultural land (C) due to possible legal or

physical restrictions of its use (i.e. farmsize = A+B).

34The 1st and 2nd Agricultural Census were conducted in 1960 and 1970. Microdata from the 3rd

Census is of open access in DANE’s website.35The delimitation was based on land registers (‘registro catastral’) and satellite maps.36In this context owner does not refer to ownership, but to who has the right to produce the land.

24

Figure 4: Diagram of a Farm’s Areas

A B

C

A: Sown Land

B: Fallow land & in other agricultural uses

C: Non-agricultural land

From the total data, 17,460 farmers reported to have grown oil palm, but some of those

used less than 1% of their sown land for oil palm. Considering that the information

about production inputs and possible determinants of technical inefficiency are not

dissagregated across the types of crops produced by the farmers, this study will only

consider farmers that reported using at least 75% of their sown land for oil palm. 4

outliers reported having a farm size of at least 10,000 hectares, and they were not

considered for the estimations. Then the sample size was 3,830 units of observation.

However, after accounting for missing values on relevant variables, the final sampling

frame consists of 3,113 units of observation. Figure 6 shows the geographical distribution

of the observations. An advantage of the data is that the information was collected and

reported in physical units, hence the estimations do not suffer from omitted price bias,

although they are still subject to meassurement error.

The dependent variable for this study is the yield of crude palm oil in tons per

hectare (t/ha)37. The aggregate values of the dependent variable were consistent

with information provided in the agricultural evaluation database, EVA (Ministry of

Agriculture, 2019), and consolidated data by Fedepalma (2020). Table 1 provides

summary statistics of the variables considered for this study. The variables Labour and

Land were considered as input variables for the estimation of the stochastic frontier; the

other variables were considered for the estimation of the mean of technical inefficiency.

The following sections provide a brief description of each variable.

37The percentage of crude palm oil extracted from a ton of fruit was about 21% in 2014 (Ceni-palma, 2017).

25

Table 1: Summary Statistics

Count Mean S.D. Min Max

Dependent VariableYield of crude palm oil in T/Ha 3113 2.782 0.24 0.42 3.72

FrontierLabour (workers) 3113 10.886 25.35 1.00 445.00Land (ha) 3113 25.086 71.79 0.01 879.18

Possible determinats of InefficiencyFarm size in hectares 3113 71.115 286.69 0.01 6570.25Farm size (0 - 2 hectares) 3113 0.109 0.31 0.00 1.00Farm size (3 - 5 hectares) 3113 0.166 0.37 0.00 1.00Farm size (6 - 10 hectares) 3113 0.201 0.40 0.00 1.00Farm size (11 - 50 hectares) 3113 0.313 0.46 0.00 1.00Farm size (51 - 500 hectares) 3113 0.183 0.39 0.00 1.00Farm size (> 500 hectares) 3113 0.029 0.17 0.00 1.00Region: Caribbean 3113 0.413 0.49 0.00 1.00Region: Orinoquia 3113 0.214 0.41 0.00 1.00Region: Andean 3113 0.251 0.43 0.00 1.00Region: Pacific 3113 0.117 0.32 0.00 1.00Region: Amazon 3113 0.005 0.07 0.00 1.00Territory:None 3113 0.906 0.29 0.00 1.00Territory:Indigenous 3113 0.019 0.14 0.00 1.00Territory:Afro 3113 0.075 0.26 0.00 1.00Use of machines 3113 0.373 0.48 0.00 1.00Owns cattle 3113 0.298 0.46 0.00 1.00Use of fertilizers 3113 0.619 0.49 0.00 1.00Irrigation system 3113 0.851 0.36 0.00 1.00Pest Control 3113 0.726 0.45 0.00 1.00Obtained credit 3113 0.117 0.32 0.00 1.00Assistance 3113 0.835 0.37 0.00 1.00Belongs to some association 3113 0.346 0.48 0.00 1.00HH Head Sex 1621 0.845 0.36 0.00 1.00HH Head Age 1621 49.289 15.09 13.00 100.00HH Head Education level 1591 2.272 1.16 1.00 6.00

Observations 3113

The variable ‘Land’ is sown land with oil palm trees (in hectares). Farm size is defined as A+B infigure 4. Use of machines, Owns cattle, Use of fertilizers, Irrigation system, Pest Contol, ObtainedCredit, and Assistance are dummy variables with 0=No and 1=Yes. ‘HH Head’ refers to HouseholdHead. HH Head Sex is a dummy with 0=Female, 1=Male. HH Head Education level is a categoricalvariable where 1 is the lowest level (none), and 6 is the highest level (university).

26

5.1 Input Variables in Frontier Estimation

• Labour (Li)

This variable is reported in number of workers, and it was calculated adding up

declared permanent labour and temporary labour. A possible shortcoming with

this variable is that the information reports number of permanent and temporary

workers at the day of the interview and not at the period when production took

place. Nevertheless, it will be considered as a proxy because oil palm trees are

not seasonal crops, hence the average number of required workers can be assumed

to be roughly constant.

• Land (Ti)

This variable refers only to the area planted with oil palm trees in hectares. In

other words, it is utilized land for oil palm trees. It was calculated dividing

reported information for production in tons and yield in t/ha. The calculation

was consistent with the reported “sown land with oil palm” at the day of the

interview.

5.2 Presumed determinants of Technical Inefficiency

• Farm size (fs1− fs6)

This variable is the main variable of interest in this study. As previously defined,

it includes all the available land the farmer can use for agricultural production.

It was calculated as the total area of the farm excluding natural forest areas,

non-agricultural infrastructure areas, and other non-agricultural areas. The reason

to exclude these areas is that their use might be physically or legally restricted,

hence including them could overestimate the actual area the farmer can use for

crop production.

As described in the Literature Review section, some empirical studies have found

a non-linear relationship between inefficiency and farm size. In the analysis of

the data, this study has also found signs of a non-linear relationship. A simple

quadratic term did not fully show the non-linear relationship because farm size

has a very wide range that goes from 0.01 to 6570.25 hectares. To address this

issue, the estimations were done over dummies for different farm size groups. The

delimitation of the groups was taken from Berry (1971)’s analysis of Colombian

agriculture.

Table 1 shows that approximately 79% of the farmers have less than 50 ha. This

27

is the group considered as small producers by Fedepalma38. Furthermore, about

31% are concentrated in the 10 to 50 ha. group.

• Geographical Regions (gr1− gr5)

Colombia can be divided in 5 natural regions: Caribbean (North), Orinoquia

(East), Andean (Center), Pacific (West), and Amazon (South). Figure 5 shows

the geographical location of these regions. According to aggregated data from

Fedepalma, the Caribbean and the Orinoquia regions have the highest yield of

crude palm oil, with 3.9 and 3.1 tons of oil per ha in 2013, respectively. Together,

they represent about 62% of the data for this study. To some extent, this can be

explained by weather conditions because yields of crude palm oil depend on high

temperatures and large amounts of water39. To control for the effect of weather

conditions, dummies for each region will be included in the estimation.

Figure 5: Natural Regions

Source: Hazzi et al. (2013)

Figure 6 provides the distribution of observations across the 32 departments of

Colombia. The observations are concentrated in Meta, Casanare, Santander, Cesar

and Magdalena, this is consistent with Fedepalma’s information (Rueda-Zarate

and Pacheco, 2015). Furthermore, it is important to remark that there are almost

no observations in the departments of the Amazon region.

38Standard literature defines small farmers as those with less than 2 hectares (Khalil et al., 2017)39The best climate conditions for oil palm grow are an average temperature of 28°C, annual rainfall

of 2000 mm or greater, and sunshine of 5 to 7 hours per day (Corley, R. H. V. and Tinker, P.B., 2008).

28

Figure 6: Distribution of observations by Departments

ANTIOQUIA

ATLANTICO

SANTAFE

BOLIVAR

BOYACA

CALDAS

CAQUETA

CAUCA

CESAR

CORDOBA

CUNDINAMARCA

CHOCO

HUILA

LA GUAJIRA

MAGDALENA

META

NARI?O

NORTE

QUINDIO

RISARALDA

SANTANDER

SUCRE

TOLIMAVALLE DEL CAUCA

ARAUCA

CASANARE

PUTUMAYO

AMAZONAS

GUAINIA

GUAVIARE

VAUPES

VICHADA

ARCHIPIELAGO

DE

DE

DE

BOGOTA

SANTANDER

SAN

D.C

ANDRESPROVIDENCIAYSANTACATALINA Observations(52,610](6,52](0,6][0,0]

1The observations are farmers that reported to use at least 75% oftheir sown land for oil palm trees.2 The distribution map was elaborated with Stata 16.1.

• Ethnical Territories (et1− et3)

The Colombian Constitution establishes the protection of ethnic minority groups,

such as indigenous and afro-descendant communities. The data included infor-

mation about the predominant ethnicity of the territory. Table 1 shows that

approximately 10% of the farmers’ land belong to either afro-descendent or in-

digenous territories, while 90% declared belonging to none. It is important to

remark that these variables do not represent the ethnicity of the producer, but if

whether the farm is located in a protected minority territory, such as indigenous

reservations or afro-descendant collective properties.

• Machinery use

The production and harvest of oil palm fruit requires the use of different types

of machines and implements. For example, tractors are a main source of power

29

to prepare the soil before planting the oil palm trees, and they can also be

used for the harvest process. Other implements that could positively affect the

techical efficiency of the farm are: scythes, polinization machines, brush cutters,

fumigators, etc.

Ideally, the production frontier should be estimated with information on all these

machines and implements, which was the original design for this study. However,

although the questionnaire for the census included questions on each of these

implements, approximately 87% were missing values. Therefore, this study will

use a dummy variable for whether the farmer used machines or not (which was

a separate question), as a proxy to capture the possible effects of machinery on

technical inefficiency. 37.3% farmers declared to have used machines for their

agricultural production.

• Cattle ownership

This is a dummy variable which includes oxen, horses, sheep and goats. Cattle

ownership can relate positively or negatively with technical inefficiency. As de-

scribed in previous sections, cattle ranching limits the land available for crop

production, meaning that farmers with extensive cattle ranching might be more

technically inefficient. On the other hand, oxen are a source of power for agricul-

tural production. In oil palm plantations, oxen are usually used as substitutes for

tractors because they are kinder with the soil (the weight of tractors can create

“pools” in clay soil, which leads to difficulties for irrigation). It would be appropiate

to treat ‘oxen’ as a variable, but, as with machines and implements, the data

was highly incomplete (about 95% missing values). Hence, it was not possible

to separate oxen from other cattle. The expected effect of cattle ownership on

technical inefficiency will depend on how much cattle is used for cattle ranching

and how much as source of power.

• Use of Fertilizers

It is a dummy variable for whether the farmer used some type of fertilizer or not,

it includes organic and chemical fertilizers. Approximately 62% declared to have

used fertilizers.

• Irrigation Systems

It is a dummy variable for whether the farm has an irrigation system or not. Access

to irrigation systems for the agricultural sector of developing economies is usually

30

constrained by physical and economical factors. Oil palm plantations require large

amounts of water to survive and produce fruits. Hence, the utilization of irrigation

systems is a relevant factor that can have an impact on technical inefficiency. 85%

of the observations declared to use some type of irrigation system. From those,

85% declared to use gravity irrigation.

• Pest Control

The lack of pest control can have a large impact on technical inefficiency because

some pests can spread diseases, such as lethal wilt. According to table 1 about

73% of observations apply pest controls.

• Obtained Credit

This is a dummy variable for whether the farmer obtained a credit or not. As

reported in table 1, only 11.7% of the observations obtained a credit. However,

only 14% of observations declared to have asked for it, meaning that about 84% of

those that asked for a credit, obtained it. Only 2.46% of the credits were reported

as obtained in the informal sector (i.e. particular money lenders).

• Technical Assistance

The yield of crude palm oil can be positively or negatively affected by the

management of the oil palm tree through its different phases. Therefore, technical

assistance is a relevant determinant for the level of technical inefficiency. Table 1

shows that approximately 85% of the observations received some type of technical

assistance. From the data it was possible to calculate that 80% received technical

assistance on good farming practices.

• Associations

This variable includes belonging to some type of association, such as unions,

cooperatives, research centers, councils, and producers associations. About 34%

of the farmers declared to belong to some type of association, and 57% of those

declared to participate in producers associations. There is no information in the

data about productive alliances, which is an outgrowing system with the goal to

work as a link between big farmers and small farmers.

• Demographic variables

Demographic information for the household head, such as age, sex and education

level is usually included as possible determinants of inefficiency in studies about

agricultural economy. For this study, regressions including demographic variables

31

showed a non-significant effect on inefficiency. Probably because the data for

these variables came from a separate module, and it focused on small and medium

size farms (i.e. the objective of this module was to be used to calculate multidi-

mensional poverty). Table 1 provides summary statistics for these variables, but

they will not be used for the empirical model because of the potential selection

bias as these variables have missing values for about half of the farmers (without

specifying the nature of the missing values).

5.3 Limitations

• Unspecified Variables

As previously described, the data does not provide enough information about

machines (tractors and tools), materials (fertilizers and pest controls) and oxen,

hence it is not possible to include them as continuous variables in the production

function. This is a potential source of omitted variable bias. The estimated

parameter of a model with omitted variables is (in matrix notation, adapted from

Verbeek (2012)):

β = β + (X ′X)−1X ′KΥ + (X ′X)−1E(X ′ε) (11)

Under common assumptions that the error has expectation zero and X is exoge-

nous, the last term goes away (i.e. E(X ′ε) = 0). Hence, the bias is defined by

the second term of the equation, X ′KΥ, where K is the unspecified variable

(machines, materials, and oxen) and Υ is its parameter. If Υ = 0, there would be

no bias, meaning that the effect of all the unspecified variables is zero. This does

not seem a plausible assumption as it is expected that the signs of the parameters

of machines, implements, and oxen are positive, and at least one of them should

be significant. If the correlation between specified and unspecified variables is

zero (i.e. X ′K = 0), the bias would also go away. However, in practice this is not

the case. Hence, the direction of the bias will depend on the correlation between

the specified variables (land and labour) and the omitted variables (machines,

materials, and oxen) (i.e. X ′K).

The relationship between labour and machines is expected to be negative because

they are usually used as substitutes, for example the use of tractors and autom-

atized implements reduce the required labour force to work the same quantity

32

of land. In a study about technical changes in Colombian agriculture, “it was

estimated that one man with an average-size tractor can plow and cultivate as

much land as six to 10 men with 12 to 20 oxen” (Atkinson, 1969, p.19). To a

lesser extent, the relationship between labour and oxen is also expected to be

negative. Hence, it is expected that the overall effect of unspecified variables gives

a downward bias in the parameter of labour.

In contrast, the relationship between land and machines, implements, and oxen is

expected to be positive because larger extensions of land would require the use of

more or better machines, implements and/or oxen. Therefore, it is expected that

the estimated parameter of land is upward biased.

The magnitude of both biases are unknown, but one of them would decrease

the estimated output, while the other one would increase the estimated output,

affecting the composed error term. To alleviate this problem, dummies for machine

use, fertilizers, and pest controls have been included as proxies in the estimation

of technical inefficieny. Cattle ownership was inititally considered as a possible

proxy for oxen, but as it includes other animals that are not a usual source of

power, it is not a good proxy. It is still included in the model to see the effect of

cattle on technical inefficiency. It is necessary to review the results when more

complete information about input variables is available.

• Output Variable

It is possible to see from table 1 that yield of CPO in t/ha has a mean of 2.782 with

a standard deviation of 0.24, meaning that there is a low variability of the output

variable. This suggests two possible scenarios: either yield does not vary much

across farmers, or there is some measurement problem with the output variable.

According to DANE (2016b), the information provided by the Census went

through a validation process, where imputation methods were used in variables

with empty or inconsistent values40. Analyzing kernel density estimations41, this

study found that the distribution of the dependent variable in small farms (i.e.

farmsize ≤ 50ha.) was concentrated in two peaks, suggesting that measurement

error is a likely scenario. Measurement error in the dependent variable affects the

40DANE has not provided detailed information about which imputation method was used for eachvariable. From the Census Methodological Guidelines it can be inferred either a Hot-Deck imputationor an imputation by median.

41Figure 7 in the ‘Preliminary Analysis’ section.

33

precision of the parameters of the frontier, but it does not affect their consistency42.

Nevertheless it could impact the calculation of technical efficiency if misreporting

was systematic in small farms. In theory, this is alleviated by the stochastic error

term, vi.

• Types of oil palm trees

The data consigned all oil palm trees under the category of african palm. Although

african palm is widely used in Colombia, a second type of palm known as hybrid

palm is also part of the industry. Hybrid palms are a genetically mixed seed of

american palm and african palm. The hybrid palm has a different cycle than the

african palm because it grows slower. Hybrid palms were developed in Colombia

in response to the Bud Rot disease (‘Pudricion de Cogollo’)43, meaning that they

were ‘designed’ to better withstand diseases than african palms. However, due to

their mixed nature (hybrid palms are hermaphrodite plants), its yield depends

on constant assisted pollination. It was not possible to tell african from hybrid

palms apart in the available data. Therefore, the analysis does not account for

this level of disaggregation.

• Technical Change

It is important to remark that this study focusses in measuring technical efficiency,

and not productivity. According to Coelli et al. (1998), although both terms are

often used indistinctly, they are not exactly the same. The term productivity

refers to identifying the optimal scale of production, meaning that a farmer can

be fully technically efficient in the short run, but still be able to achieve a higher

productivity in the long run through economies of scale. The calculation of

productivity in SFA is usually done by estimating technical change, which is not

possible to do with cross-sectional data. It would be an interesting extension to

address this limitation when panel data for this industry is available. Furthermore,

the inclusion of time in the analysis would lead to more consistent estimators of

technical inefficiency (Coelli et al., 1998).

42In a linear regression model, and under the usual assumption of exogeneity of the regressors,measurement error of the dependet variable does not lead to inconsistency of the parameters (Cameronand Trivedi, 2005).

43The Bud Rot disease is a lethal disease that spreads across Latin American oil palm plantations.In Colombia, it had a devastating impact in the municipality of Tumaco (Southwest) between 2007and 2008, when the percentage of sick palms jumped from 8.3% to 58% (Martınez et al., 2008).

34

6 Empirical Model

Assuming that technology follows a Cobb-Douglas form, the production function can

be expressed as:

F (L,K, T ) = Yi = Ai Lα1i Kα2

i Tα3i i = 1, ..., N (12)

Assuming Constant Returns to Scale (CRS):

3∑j=1

αj = 1 (13)

Where Yi is production of crude palm oil in tons; Ai is exogenous total factor productivity;

Li is labour in number of employees, which includes permanent and temporary hired

labour; Ki denotes all the capital inputs necessary for production, besides land, such as

tractors, oxen and materials (fertilizers, pest controls, etc.); and Ti is land planted with

oil palm trees in hectares.

Ideally, the inputs included in Ki would be included in the estimation of the frontier.

However, the available data does not have complete information about these input

factors44. Therefore, the model to be estimated will be reduced to:

F (L, T ) = Yi = Ai Lα1i Tα2

i i = 1, ..., N (14)

If the omitted variables in Ki are assumed to be independent from the specified variables

(i.e. Cov(K,L) = Cov(K,T ) = 0), the SFA method would recognize the unspecified

variables as measurement error, hence being absorbed by the noise, vi45.

44The literal question in the census was: “Today. Is there machinery for the development ofagricultural activities?”. This question is problematic because sometimes machinery is rented fromthird companies, meaning that quantities can vary from month to month. In the case of ‘tractors’ only418 observations reported to use at least one tractor, 609 reported zero tractors (across all farm sizegroups), and 2086 were missing values. Furthermore, it is possible that the length of the questionnaire(16 pages with approximately 200 questions, sometimes divided into more subquestions)‘tired’ thefarmers, and made them give incomplete answers. Hence, it is hard to know whether the zeroes arereal zeroes or not.

45This strong assumption will be kept for the illustration of this section, but the implications of theunspecified variables were discussed in the ‘Limitations’ section.

35

Dividing equation (14) by Ti and taking logarithms:

ln(yi) = β0 + β1ln(Li) + β2ln(Ti) + εi (15)

Where yi represents the yield of crude palm oil in t/ha; β0 + εi = ln(Ai); β1 is the factor

intensity of labour; β2 is the factor intensity of land minus 1 (i.e. α2 − 1); and εi is the

composed error term as in equation (2).

If CRS holds, β1 + β2 = 0

6.1 Estimation of inefficiency

This study assumes that technical inefficiency, ui, follows a truncated-normal (TN)

distribution. The TN distribution was first proposed by Stevenson (1980), and it is a

generalization of the half-normal distribution46. It allows the mean of ui to be different

from zero:

ui ∼ N+(µ, σ2u) (16)

Based on Stevenson (1980)’s model, S. C. Kumbhakar et al. (1991) developed an

approach where µ can vary across observations, meaning:

ui ∼ N+(µi, σ2u) (17)

µi = δ0 +∑k

δkZki (18)

Where Zi is the vector of exogenous variables that are pressumed to affect technical

inefficiency, δk are the corresponding parameters, and δ0 is the effect of unobserved

variables on technical inefficiency (e.g. experience).

46The half-normal distribution assumes ui ∼ N+(0, σ2u) (Aigner et al., 1977). A zero mean of the

inefficiency term, would imply that most of the observations are close to being fully efficient, which isa very restrictive assumption.

36

This means that the model assumes that the distribution of ui is a linear combination

of exogeneous variables, and these variables can be included in the estimation of

the stochastic frontier in a single-stage procedure. The model keeps the assumption

that technical inefficiency effects are independently distributed, but not identically

distributed (Coelli et al., 1998).

A comparison between a half-normal (HN) distribution and a truncated-normal (TN)

distribution is provided in the following section. For the comparison, the TN model

will only include farm size as a determinant of technical inefficiency. Later, different

sets of determinants, Zi, are analyzed for the TN distribution model.

6.2 Hypothesis Tests

Existence of a Stochastic Frontier

One of the underlying assumptions for the SFA method is that the error term is

composed of a two-sided normal error and a one-sided error. Assuming that the one-

sided error term follows a half-normal distribution, the composed error would be the

difference of a normal distribution and a half-normal distribution (εi = vi − ui). If this

is true, the error of estimating the frontier with an OLS should be skewed to the left

(or to the right when the analysis is of a cost-type frontier). This should hold for any

one-sided distributional form of ui. The statistic proposed is defined as (Schmidt and

Lin, 1984):

√b1 =

m3

m2√m2

(19)

Where m2 and m3 are the second and third moments of the OLS residuals, respec-

tively.

Ho : No skewness

H1 : Left skewness (negative skewness)

The test is performed following Kumbhakar et al.(2015). First, equation (15) is estimated

using OLS and the statistic√b1 is obtained from the summary statistics of the residuals.

The value of√b1 is equal to -8.6376, the negative sign indicates that the residuals are

skewed to the left. Second, the skewness test is applied to check if√b1 is statistically

37

significant. The test reported a p-value of 0.0000, hence the null hypothesis of no

skewness is rejected. This result gives support for the use of the stochastic frontier

method.

Existence of Technical Inefficiency

To complement the skewness test and find more support for the use of the SFA, Coelli

et al. (1998) proposed a One-sided Generalised Likelihood-Ratio Test. The intuition is

to compare the log-likelihood of the restricted model (H0 = OLS) and the unrestricted

model (H1=SFA).

The generalized likelihood-ratio test is calculated as:

LR = −2[L(H0)− L(H1)] (20)

Where L(.) is the log-likelihood value of the respective model. Coelli (1995) showed

that the LR statistic follows a mixture of chi-square distributions, hence the critical

values are not those of a standard chi-square distribution. The computed test statistics

will be compared to critical values of mixed distributions tabulated by Kodde and

Palm (1986).

The SFA model for this test assumes that ui follows a half-normal distribution, hence it

has 1 degrees of freedom because the only additional restriction is that σ2u is equal to

zero. The computed LR is 2036.0581, which is highly greater than the critical value of

5.412 at 1% of significance level. Hence, the null hypothesis of no technical inefficiency

is rejected.

For a half-normal distribution, the existence of technical inefficiency can be further

corroborated by the calculation of the gamma parameter as in equation (8). The

calculated gamma is equal to 0.978, which indicates that deviations from the frontier

are mainly due to technical inefficiency.

Functional form of Technology

The assumption that technology follows a Cobb-Douglas functional form has been

widely used in empirical studies. Its main advantages are that it is linear in parameters,

and it is easy to estimate and interpret. However, its simplicity can also be a drawback

because it imposes some restrictive properties, such as constant input elasticities for

all observations and that the substitution elasticities are equal to 1. An alternative

38

production function is the translog function. The translog function does not impose

restrictions on the substitution possibilities or returns to scale. However, it is harder to

interpret and it is susceptible to multicollinearity problems due to the use of several

interaction terms.

A generalized likelihood-ratio test was calculated to test which functional form is a

better representation of the data. First, it was necessary to estimate the following

Translog function:

ln(yi) = β0 + β1ln(Li) + β2ln(Ti) + 12β3(ln(Li))

2 + 12β4(ln(Ti))

2 + β5ln(Li)ln(Ti) + εi (21)

The LR value is calculated as in equation (20) to test whether:

Ho : Cobb-Douglas is an adequate representation of the data

H1 : Translog is a better representation of the data

The calculated LR is 9.0865 (both models were estimated assuming a half-normal

distribution for ui), and the critical value with 3 degrees of freedom at 5% of significance

level is 7.045, which would imply the rejection of H0. However, the critical value at

1% of significance level is 10.501, and the test would fail to reject the null hypothesis.

These results do not provide strong evidence to prefer the translog function over the

Cobb-Douglas function. Due to the simplicity of the latter, this study will use the

Cobb-Douglas form.

Distributional form of Technical Inefficiency

This study focuses on two types of distributional specifications for ui. The restricted

model with mean of the technical inefficiency effect equal to zero (HN), and the

unrestricted model with nonzero mean (TN). It means:

Ho : µ = 0

H1 : µ 6= 0

A generalized likelihood-ratio test was calculated to test which distributional assumption

is a better representation of the data. Table 2 shows the estimation of both models and

39

their respective log-likelihood values. With those values, the calculated LR is 1544.7079,

which is greater than the critical value with 6 degrees of freedom of 16.074 at 1% of

significance level. Therefore, the null hypothesis is rejected.

Table 2: Half-Normal vs Truncated-Normal

(1) (2)Ln yield HN TN

FrontierLn labour -0.00313∗∗ -0.00287∗∗∗

Ln land 0.00375∗∗∗ 0.00358∗∗∗

Constant 1.121∗∗∗ 1.090∗∗∗

UsigmaConstant -3.651∗∗∗ 0.909∗∗∗

VsigmaConstant -7.447∗∗∗ -6.863∗∗∗

InefficiencyFarm size (3 - 5 hectares) -4.982∗

Farm size (6 - 10 hectares) -2.932Farm size (11 - 50 hectares) -1.160Farm size (51 - 500 hectares) -13.44∗∗∗

Farm size (> 500 hectares) -30.34∗∗

Constant -28.77∗∗∗

Log Likelihood 3101.6 3873.9Observations 3113 3113∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

The comparison is done including only the effect of farm size in theestimation of technical inefficiency. Where HN refers to half-normal,TN refers to truncated-normal. The omitted category for farm sizeis 0 - 2 ha.

Additionally, the hypothesis of constant µ was tested, meaning if whether the estimated

parameters of equation (18) are simultaneously equal to zero or not:

Ho : δ1 = ... = δk = 0

This is done by applying the Wald test. The test gives a p-value of 0.0063, supporting

the rejection of the null hypothesis.

40

Returns to Scale

It is common to assume that the agricultural sector in developing economies present

constant returns to scale. In this study, it is equivalent to test if in equation (15):

Ho : β1 + β2 = 0

This is done by applying the Wald test to model (3) in table 6, which includes all

the possible determinants of technical inefficiency. The calculated chi-square with 1

degree of freedom is 8.51, this is slightly greater than the critical value of 6.64 at 1% of

significance level. The result might imply that this particular agricultural sector does

not present constant returns to scale. However, the result could be driven by the bias

of unspecified production inputs.

In summary:

Table 3: Hypotheses Tests

H0 Test Statistic Critical Valuea Decision

(1) No skewness√b1 = -8.6376 0.0000 Reject H0

(2) OLS LR = 2036.0581 5.412** Reject H0

(3) Cobb-Douglas LR = 9.0865 7.045* & 10.501** Fail to Reject H0

(4) Half-Normal LR = 1544.7079 16.074** Reject H0

(5) Constant Wald (χ2) = 16.19 12.59* Reject H0

(6) Constant Wald (χ2) = 8.51 6.64** Reject H0

*(p<0.05), **(p<0.01)

a For (1) it is p-value.b (1) Existence of Stochastic Frontier; (2) Existence of Technical Inefficiency; (3) Functional formof Technology; (4) Distributional form of ui; (5) Assumption over µ; and (6) Returns to Scale.

41

7 Preliminary Analysis

Tables 4 and 5 provide correlation coefficients for the variables included in the estimations.

It is important to have in mind that the interpretation of the correlation coefficient

between a continuous variable and a dummy variable is a comparison of means.

Table 4 shows the correlation of yield with the different groups of farm size, geographical

regions, and ethnical territories. It is possible to see that the average yield of farms

between 0 and 2 ha (fs1) is lower than the average yield of other farm sizes. The

same happens with groups up until 50 ha (fs4). The signs change for farms above 50

ha, meaning that their average yield is higher than that of other farm sizes. Figure 7

compares kernel density estimations of the distribution of yield between farms below

and above 50 hectares. It shows that the probability of having a yield above 3 tons

of CPO per hectare is higher for farms with more than 50 hectares. Furthermore,

it supports the assumption that the low variability of the output variable is due to

imputed values of the dependent variable in small farms47.

Figure 7: Kernel density of the distribution of yield

01

23

kdensity y

ield

0 1 2 3 4yield

Less equal than 50 More than 50

Farm size in ha.

Table 5 shows that farms with irrigation systems, and technical assistance have a higher

average yield than those without them. The relationship between yield and almost all

of the explanatory variables is statistically significant and with the expected direction,

except for labour. A possible explanation is that labour was reported in number of

47To some extent, the effect of this potential measurement error will be alleviated by the stochasticcomponent of the error term, vi.

42

workers, but not hours per worker. In addition, the data does not differentiate between

fieldwork labour and admistrative labour, which could be affecting the relationship

direction.

In general, most of the correlation coefficients are weak, but statistically significant.

This could be due to the low variability of the dependent variable (explained in

the ‘Limitations’ section). And, it could be intensified by the fact that most of the

explanatory variables are dummies. Information about quantities of fruit production,

machinery, oxen, fertilizers, pest control, etc., could lead to stronger results.

43

Tab

le4:

Cor

rela

tion

Mat

rix

I

yie

ldla

bou

rla

nd

fs1

fs2

fs3

fs4

fs5

fs6

gr1

gr2

gr3

gr4

gr5

et1

et2

et3

yie

ld1.

00la

bou

r-0

.01

1.00

land

0.11∗∗∗

0.14∗∗∗

1.00

fs1

-0.0

7∗∗∗

-0.0

4∗-0

.12∗∗∗

1.00

fs2

-0.0

4∗-0

.07∗∗∗

-0.1

4∗∗∗

-0.1

6∗∗∗

1.00

fs3

-0.0

5∗∗

-0.0

4∗-0

.14∗∗∗

-0.1

8∗∗∗

-0.2

2∗∗∗

1.00

fs4

-0.0

2-0

.01

-0.1

1∗∗∗

-0.2

4∗∗∗

-0.3

0∗∗∗

-0.3

4∗∗∗

1.00

fs5

0.14∗∗∗

0.11∗∗∗

0.31∗∗∗

-0.1

7∗∗∗

-0.2

1∗∗∗

-0.2

4∗∗∗

-0.3

2∗∗∗

1.00

fs6

0.07∗∗∗

0.12∗∗∗

0.44∗∗∗

-0.0

6∗∗∗

-0.0

8∗∗∗

-0.0

9∗∗∗

-0.1

2∗∗∗

-0.0

8∗∗∗

1.00

gr1

0.21∗∗∗

0.03

-0.0

8∗∗∗

-0.0

8∗∗∗

0.09∗∗∗

0.12∗∗∗

0.02

-0.1

1∗∗∗

-0.1

1∗∗∗

1.00

gr2

0.23∗∗∗

0.01

0.19∗∗∗

-0.0

3-0

.11∗∗∗

-0.1

5∗∗∗

-0.0

5∗∗

0.23∗∗∗

0.26∗∗∗

-0.4

4∗∗∗

1.00

gr3

-0.2

0∗∗∗

-0.0

1-0

.01

-0.0

4∗-0

.06∗∗∗

-0.0

20.

10∗∗∗

0.03

-0.0

7∗∗∗

-0.4

8∗∗∗

-0.3

0∗∗∗

1.00

gr4

-0.3

3∗∗∗

-0.0

5∗∗

-0.1

0∗∗∗

0.21∗∗∗

0.11∗∗∗

0.04∗

-0.1

0∗∗∗

-0.1

6∗∗∗

-0.0

6∗∗∗

-0.3

1∗∗∗

-0.1

9∗∗∗

-0.2

1∗∗∗

1.00

gr5

-0.0

6∗∗

0.01

0.01

0.03

-0.0

2-0

.01

0.02

-0.0

1-0

.01

-0.0

6∗∗∗

-0.0

4∗-0

.04∗

-0.0

31.

00et

10.

29∗∗∗

0.03

0.08∗∗∗

-0.0

7∗∗∗

-0.1

0∗∗∗

-0.0

6∗∗

0.07∗∗∗

0.11∗∗∗

0.06∗∗

0.18∗∗∗

0.14∗∗∗

0.17∗∗∗

-0.6

9∗∗∗

0.01

1.00

et2

-0.1

1∗∗∗

-0.0

1-0

.03

0.18∗∗∗

-0.0

1-0

.02

-0.0

6∗∗∗

-0.0

3-0

.02

-0.0

3-0

.03

-0.0

7∗∗∗

0.18∗∗∗

0.02

-0.4

3∗∗∗

1.00

et3

-0.2

7∗∗∗

-0.0

3-0

.07∗∗∗

-0.0

10.

11∗∗∗

0.07∗∗∗

-0.0

4∗-0

.10∗∗∗

-0.0

5∗∗

-0.1

9∗∗∗

-0.1

4∗∗∗

-0.1

5∗∗∗

0.68∗∗∗

-0.0

2-0

.88∗∗∗

-0.0

4∗1.

00∗p<

0.05

,∗∗p<

0.01

,∗∗

∗p<

0.0

01

Yie

ldre

fers

toyie

ldof

crude

pal

moi

lin

t/ha.

Fro

mfs

1to

fs6

are

dum

my

vari

able

sfo

rfa

rmsi

ze,

wher

e:fs

1is

0-

2ha,

fs2

is3

-5

ha,

fs3

is6

-10

ha,

fs4

is11

-50

ha,

fs5

is51

-50

0,an

dfs

6is>

500.

Fro

mgr1

togr5

are

du

mm

yva

riab

les

for

regio

ns,

wh

ere:

gr1

isC

ari

bb

ean

,gr2

isO

rin

oqu

ia,

gr3

isA

nd

ean

,gr4

isP

aci

fic,

an

dgr5

isA

mazo

n.

Fro

met

1to

et3

are

du

mm

yva

riab

les

for

eth

nic

al

terr

itor

y,w

her

e:et

1is

non

e,et

2is

indig

enous,

and

et3

isafr

o.

44

Tab

le5:

Cor

rela

tion

Mat

rix

II

yie

ldla

bou

rla

nd

hec

size

hec

size

2m

achin

ery

catt

lefe

rtiliz

erir

riga

tion

pes

tcon

trol

cred

itas

sist

ance

asoc

yie

ld1.

00la

bou

r-0

.01

1.00

land

0.11∗∗∗

0.14∗∗∗

1.00

hec

size

0.06∗∗

0.09∗∗∗

0.35∗∗∗

1.00

hec

size

2-0

.00

0.01

0.09∗∗∗

0.87∗∗∗

1.00

mac

hin

ery

0.12∗∗∗

0.09∗∗∗

0.09∗∗∗

0.15∗∗∗

0.05∗∗

1.00

catt

le0.

07∗∗∗

0.15∗∗∗

0.09∗∗∗

0.18∗∗∗

0.06∗∗∗

0.37∗∗∗

1.00

fert

iliz

er0.

06∗∗∗

0.04∗

0.06∗∗

-0.0

5∗∗

-0.0

20.

07∗∗∗

-0.0

21.

00ir

riga

tion

0.43∗∗∗

0.03

0.10∗∗∗

0.02

-0.0

20.

07∗∗∗

0.05∗∗

0.13∗∗∗

1.00

pes

tcon

trol

0.07∗∗∗

0.05∗∗

0.04∗

-0.0

0-0

.00

0.09∗∗∗

0.03

0.58∗∗∗

0.11∗∗∗

1.00

cred

it-0

.05∗

0.08∗∗∗

0.02

-0.0

2-0

.02

0.09∗∗∗

0.08∗∗∗

0.08∗∗∗

-0.0

20.

08∗∗∗

1.00

assi

stan

ce0.

44∗∗∗

-0.0

10.

05∗∗

0.07∗∗∗

0.03

0.13∗∗∗

0.11∗∗∗

0.12∗∗∗

0.43∗∗∗

0.11∗∗∗

0.01

1.00

asoc

-0.1

0∗∗∗

0.07∗∗∗

0.03

-0.0

2-0

.01

0.05∗∗

0.03

0.08∗∗∗

-0.0

9∗∗∗

0.11∗∗∗

0.11∗∗∗

0.02

1.00

∗p<

0.05

,∗∗p<

0.01

,∗∗

∗p<

0.0

01

Yie

ldre

fers

toyie

ldof

crude

palm

oil

int/

ha.

Hec

size

isa

conti

nuous

vari

able

for

farm

size

inhec

tare

s,and

hec

size

2ishecsize2

.M

ach

iner

y,ca

ttle

,fe

rtiliz

er,

irri

gati

on,

pes

tcon

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edit

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ance

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das

oc

(ass

oci

atio

n)

are

du

mm

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h0

=N

o&

1=

Yes

.

45

8 Results and Discussion

Table 6 provides the results of the stochastic frontier estimation and the possible

determinants of technical inefficiency. Model (1) was estimated considering only the

effect of farm size on inefficiency, Model (2) controls for geographical and territorial

ethnicity determinants, Model (3) includes economic and farm factors that are thought

to affect the level of technical inefficiency.

8.1 Frontier

For the three models the coefficient of labour is negative and significant. The elasticity

of labour in model (3) is -0.0019948. This implies that a 1% increase in the number

of workers, ceteris paribus, would reduce the yield of CPO in t/ha by approximately

0.2%. To explain this results, it is important to remark that oil palm trees need to be

grown and harvest in appropiate ways to enhance the extraction rate of palm oil from

the fruits. Mosquera and Garcıa (2005) found that among permanent crop plantations

in Colombia, oil palm plantations required the least number of workers per hectare (1

worker per 10 ha. against, for example, banana plantations that required 1 worker per 2

ha.). He concluded that apparently oil palm plantations in Colombia were not so labour

intensive as other agricultural production, suggesting that they might be intensive in

the use of machinery and oxen. This implies, to some extent, that using more workers

could reflect a lack of (enough) machines, implements and/or oxen.

The low (negative) labour productivity can also be explained by a shortage of skilled

workers, and measurment error. Oil palm plantations are usually located in places of

low population density, where they compete with the mining and oil sectors (which

usually offer better wages) for skilled workers, meaning that despite surplus of labour

at national level, there might be a shortage of workers with technical knowledge in the

oil palm industry49. Measurement error could also be affecting negatively the estimated

parameter of labour. In the census, production and yield are reported in quantities

48Luna (2012) studied the efficiency of the palm oil sector in the department of Magdalena (Caribbeanregion). He also found a negative elasticity of labour, and suggested that it could be due to endogeneitybias.

49This could also partially explain the higher average wage oil palm plantations offer to their workersin comparison to other agricultural production.

46

obtained in 2013, while number of workers is reported on the day of the interview, which

took place mainly in the first half of 2014. According to monthly data from Fedepalma,

the average harvested fruit in the first half of 2014 was about 93 000 tons more than

in 2013 (Fedepalma, 2020). This suggests that the reported number of workers in the

data could be higher than the real number of workers used in 2013, which could be

lowering the estimated productivity of labour. In summary, the results can be explained

by unmeasured differences in labour productivity (skills, hours worked, administrative

workers, etc.), accentuated by a downward bias due to measurement error, and omitted

variables (Cov(L,K) < 0).

The input elasticity of land is positive and significant at 0.1% of significance level for

the three models. In model (3) the value is 0.00443, meaning that a 1% increase in

planted land, ceteris paribus, would increase the yield of CPO in t/ha by approximately

0.4%. To some extent, the estimated parameter might be upward biased due to omitted

variables (i.e. Cov(T,K) > 0). Nevertheless, more utilized land for oil palm trees,

could translate in a higher focus on growing oil palm trees, which could lead to the

achievement of increasing returns to scale.

8.2 Technical Inefficiency

The second part of table 6 is the relationship between the mean of technical inefficiency,

µi, and its possible determinants. A negative (positive) sign implies a positive (negative)

effect on technical efficiency. In model (1) when the estimation only considers groups of

farm size, the relationship between farm size and technical inefficiency is negative, and

it ‘curves’ at 50 hectares. This suggests that the relationship between farm size and

technical efficiency is positive, meaning that big farmers are more efficient than small

farmers. However, the gain in efficiency from farm size is non-linear, and there seems to

be a threshold at 50 hectares. These results could be explained by geographical factors,

available resources big farmers have access to, and increasing returns to scale. Models

(2) and (3) include these possible determinants.

In model (2) it is possible to see that only with the inclusion of geographical and

territorial variables, the relationship between technical inefficiency and farm size already

47

Table 6: Regressions

(1) (2) (3)Ln yield Ln yield Ln yield

FrontierLn labour -0.00287∗∗∗ -0.00213∗∗ -0.00199∗∗

Ln land 0.00358∗∗∗ 0.00445∗∗∗ 0.00443∗∗∗

Constant 1.090∗∗∗ 1.074∗∗∗ 1.070∗∗∗

Technical InefficiencyFarm size (3 - 5 hectares) -4.982∗ -0.158 0.170Farm size (6 - 10 hectares) -2.932 1.099 0.988Farm size (11 - 50 hectares) -1.160 2.536∗∗ 1.235∗

Farm size (51 - 500 hectares) -13.44∗∗∗ 1.132 1.589∗

Farm size (> 500 hectares) -30.34∗∗ -0.130 0.195Region: Orinoquia -10.22∗∗∗ -8.989∗∗

Region: Andean 14.21∗∗∗ 7.050∗∗

Region: Pacific 14.60∗∗∗ 6.061∗∗

Region: Amazon 15.00∗∗∗ 7.639∗∗

Territory: Indigenous 5.043∗∗∗ 0.352Territory: Afro 2.917∗∗ -0.600Use machines -1.010∗

Owns cattle 0.0580Use fertilizers -0.0545Irrigation system -3.948∗∗∗

Pest Control -0.453Obtained credit 0.916∗

Assistance -4.254∗∗∗

Belongs to some association 1.150∗∗

Constant -28.77∗∗∗ -23.97∗∗∗ -9.185∗∗

UsigmaConstant 0.909∗∗∗ -0.177 -0.593∗

VsigmaConstant -6.863∗∗∗ -6.603∗∗∗ -6.558∗∗∗

Observations 3113 3113 3113∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

The omitted categories are farm size (0 - 2 hectares), Region: Caribbean, Territory:None. Usigma and Vsigma are the standard deviations of the technical inefficiencyerror term and the stochastic error term, respectively.

48

switches signs for all groups, except for the smallest (3 to 5 ha.) and the biggest (> 500

ha.) groups. In model (3), when all the presumed covariates of technical inefficiency are

included, the relationship between farm size and technical inefficiency is positive for all

groups, and the effect follows an inverted U-shape pattern (as the one found in Brazil

by Helfand and Levine (2004)). So far, it seems that, as described by Ray (1998), there

are two forces shaping the relationship between farm size and efficiency in opposite

directions. From one hand, location, and technology (use of machines, fertilizers,

irrigation, pest control, and technical assistance) are explaining the positive relationship

between farm size and efficiency found in model (1); after controlling for them in model

(3), the known inverse size-productivity50 relationship appears. However, the effect of

farm size is only statiscally significant for farms between 11 to 500 ha. This suggests

that for farms below 11 ha. and for very big farms above 500 ha., size is not a relevant

determinant of technical inefficiency.

Based on the literature, the negative relationship between farm size and technical

efficiency found in model (3) might be due to the lower productivity of hired labour

against family labour. To check if this could be the explanation, a variable for ‘hired

labour’ is calculated from the data51. Table 7 shows that there is a weak negative

correlation between hired labour and yield, while hired labour increases with farm size.

Nevertheless, the correlation is not statiscally significant, and although it gives some

support to the theory of low productivity of hired labour, it is not a conclusive result

for this study52.

The signs of the geographical regions are as expected. The base region for comparison

is the Caribbean region, which is one of the regions with the highest historical yield of

CPO. According to the estimations, producing in the Orinoquia region increases, on

average, the level of technical efficiency compared to producing in the Caribbean region

(or any other), and it is statistically significant at 0.1% of significance level. Producing

50It has been explained that productivity and efficiency are not the same, but in the short run itcan be assumed that more efficient farms are associated with higher productivity.

51The data offers information about the quantitiy of workers that belong to the household, whichwas used as ‘family labour’ for this study. Hired labour was calculated as total labour minus familylabour. It was not included in the estimations of the models because it has a very weak correlationwith yield, and the objective is to see the relationship of farm size and technical inefficiency.

52It would be necessary to extend the analysis with more disaggregated data about the labour marketof this industry. However, this was not available during the period of study.

49

Table 7: Correlation Matrix III

yield hiredlabour hecsize

yield 1.00hiredlabour -0.01 1.00hecsize 0.06∗∗ 0.09∗∗∗ 1.00∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Yield is in t/ha, hiredlabour was calculated as totallabour minus family labour, and hecsize refers to farmsize in hectares.

in any other region has, on average, a negative effect on the level of technical efficiency.

Figure 8 shows that the two regions with the highest average technical efficiency are the

Orinoquia and the Caribbean53. It also shows that the Pacific region had, on average,

the lowest technical efficiency. To some extent, this could be explained by the Bud Rot

disease that mainly impacted the Pacific Coast of the country in 2007. In 2013, the

affected plantations were still recovering form the effect of the disease54.

Figure 8: Mean of TEi by Regions

0 .2 .4 .6 .8 1Mean of TEi

Pacific

Amazon

Andean

Caribbean

Orinoquia

TEi calculated from Model (3) after Battese and Coelli.

According to the data, irrigation systems and technical assistance are significant deter-

minants of technical efficiency, and have the highest effect among technological variables.

Figure 9 shows that farmers with both, some type of irrigation system and technical

assistance, are the ones closest to being fully technical efficient. Nevertheless, the

53Technical Efficiency was predicted following equation 10.54In 2013, hybrid palms that replaced african palms were still in a young phase, meaning that they

had not reached their most productive age at the time of the census.

50

average technical efficiency seems to be rather ‘high’ for all groups, (possibly due to

data limitations previously described) but it does suggest that farmers that received

technical assistance and used some type of irrigation system have, on average, the

highest technical efficiency, while farms with none of these variables have, on average,

the lowest technical efficiency.

Figure 9: Mean TEi of Assistance by Irrigation0

.2.4

.6.8

1

No Yes No Yes

No Yes

Mean o

f T

Ei

Technical Assistance by Irrigation System

1 Effect of Technical Assistance by Irrigation.2 TEi calculated from Model (3) after Battese andCoelli.

This was expected because oil palm trees require large amounts of water to survive and

produce, meaning that counting with irrigation systems is essential for the extraction

rate of palm oil from the fruits. Furthermore, oil palm trees are a type of crop that

requires constant maintenance to keep them healthy and producing. For example, to

protect the trees from soil erosion and weed, it is recommended to plant vegetable covers,

which in itself also requires irrigation and fertilization. This is part of the guidelines of

good farming practices that are included in technical assistance (Cenipalma, 2017).

Cattle ownership has a negative relationship with technical efficiency, but it is not

statiscally significant. This was expected, as it was previously described, this result

might reflect two opposite forces of cattle on efficiency. From one hand, the positive

effect of the used of oxen as power source. On the other hand, other type of cattle that

limits the areas for crop production (extensive cattle ranching). Credit has a negative

effect on technical efficiency, and it is statistically significant at 5% of significance

51

level. This might be explained by a reverse causality bias (endogeneity), meaning that

farmers that asked for a credit could had been those with an already low technical

efficiency55.

In summary, as found in the preliminary analysis, the results suggest that big farms are

more efficient than small farms, and that it can be explained by technological factors.

Among the technological factors, technical assistance and irrigation systems are the

variables with the highest effect on technical efficiency. To some extent, the results

suggest that farms above 50 ha. have a more intensive use of technological variables,

which raises their level of technical efficiency. This is in line with empirical findings that

refer to a minimum farm size in order to benefit from the adoption of new technologies.

In other words, it is more economically viable for a big farm to invest in machinery,

irrigation systems, fertilizers, pest controls, oxen, etc. than for a small farm, making

it possible for big farms to expand their sown land and get more output with the

same amount of other inputs (increasing returns to scale) due to the adoption of new

technology. However, the higher technical efficiency of big farmers might also be a result

of market access problems that small farmers face. According to Ocampo (2015), rural

areas of Colombia are characterized by few local suppliers of fertilizers and agrochemicals,

meaning that there is some market power to set higher prices harming the efficiency of

small producers. Robust tests of the possible explanations would require panel data

with dissagregated information for each relevant input in order to analyze technical

changes of the industry, and the possible existence of economies of scale.

55To study the causal effect of credit on technical efficiency it would be necessary to solve theendogeneity issue. However, this effect is not the focus of this study, and the variable Credit is onlyincluded as a control variable.

52

9 Conclusions

Hypothesis tests confirmed that the SFA method was appropiate for the data, meaning

that part of the deviation from the frontier is due to factors outside the farmers’ control,

and not only due to technical inefficiency. Tests on the distributional form of technical

inefficiency validated that the truncated normal distribution was a better assumption

than a half normal distribution. Finally, it was decided that the Cobb-Douglas function

seemed to be a better fit for the data than a Translog function.

Model (1) shows that there is a positive relationship between farm size and technical

efficiency. Furthermore, farms above 50 hectares seem to be more efficient than farms

below 50 hectares. The inclusion of geographical and technological variables in model

(3), shifted the size-efficiency relationship for all farm size groups, implying that the

positive size-efficiency relationship found in model (1), could be explained by location

and technology. On one hand, this could mean that big farms have a better use of

technology, which allows them to have increasing returns to scale. On the other hand,

it could also reflect problems that small farms face to access these production inputs.

In particular, the use of machines, irrigation systems, and access to technical assistance

are the most important technological factors affecting the level of technical efficiency.

When it comes to geographical location, the Orinoquia region stands out as the most

efficient one to grow oil palm. This is due to the combination of weather conditions

and that this region is characterized by big farms.

In conclusion, based purely on the technical efficiency perspective, the first best alter-

native for the expansion of the sector is through farms above 50 hectares. However,

this alternative could meet political and social resistance by being regarded as harmful

to small farms. The second alternative is to stimulate the expansion of the industry

also through small farms, but this should go in hand with improving the access to

input markets for small farmers, such that they can implement irrigation systems, and

purchase implements, fertilizers, agrochemicals, etc. Moreover, the access needs to

be accompanied with training. In other words, with technical assistance about good

farming practices, such as appropiate use of implements, vegetable covers, pruning, soil

preparation, etc., thus improving the technical efficiency of small farmers.

53

To some extent, given the limitations of the data, these findings are affected by

measurement error and endogeneity. Hence, further research and robustness checks

are necessary to draw strong conclusions. Nevertheless, the results align with some

previous empirical findings that technology can offset the low productivity of hired

labour, making the size-efficiency relationship positive. Furthermore, the results are in

line with the conditions of rural markets and the characteristics of the oil palm sector

in Colombia.

54

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