Land Use and the Opportunity Cost of Forest Preservation in Bolivia

Land use and the opportunity cost of forest preservation in Bolivia

Felipe de Figueiredo Silva University of Nebraska-Lincoln [email protected]

Juan M. Murguia Inter-American Development Bank* [email protected]

Wanderley J. Ferreira Rumbol srl. [email protected]

Brisa Rejas Galindo Inter-American Development Bank* [email protected]

Boris Hinojosa Guzman Rumbol srl. [email protected]

Selected Paper prepared for presentation at the 2018 Agricultural & Applied Economics Association Annual Meeting, Washington, D.C., August 5-August 7

* The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the Inter-American Development Bank, its Board of Directors, or the countries they represent.

We thank the Bolivian Government, the Ministry of Rural Development and Land (Mdryt), the National Institute of Agrarian Reform (INRA) and the National Institute of Statistics (INE) for the assistance with data and relevant information for this paper

Copyright 2018 by Silva et al. (2018). All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies.

Land use and the opportunity cost of forest preservation in Bolivia

ABSTRACT

The objective of this paper is to estimate the opportunity cost of preserving one hectare of forest in Bolivia and identify potential areas for forest preservation and agriculture expansion using the agricultural census of 2013 and satellite image of land deforestation. In this paper we use an alternative method to what has been previously used in the literature. We estimate a stochastic frontier to represent the producer technology and obtain the shadow price of reducing deforestation in terms of value of production. Our results show that the opportunity cost varies significantly across municipalities and that, on average, to preserve one hectare of forest, US$

1,229 of annual value of agricultural production has to be foregone, which is equivalent to US$

20.50 per ton of sequestered CO2. These results indicate that it would be less costly to reduce deforestation in the northern departments of the country where agricultural production is less intensive, and to expand agriculture in other areas where agricultural expansion would be more productive.

Key words: Agriculture, Deforestation, Opportunity cost.

JEL: Q51, Q54, C61.

INTRODUCTION

In Bolivia, an area greater than 50 million hectares is covered by forest, which is approximately

50% of the country (Food and Agricultural Organization – FAO, 2017). The forest area contains an extensive and rich biodiversity (Andersen et al., 2016) spread throughout seven distinct types of forest (Müller et al., 2014a). Agricultural expansion in Bolivia has led to a conversion of forest to agricultural land, leading to high rates of deforestation in the country, which threatens forest’s biodiversity and other ecosystem services such as carbon sequestration. In this paper, we focus on identifying the tradeoff between agriculture and forest.

Bolivia has lost around 289,000 hectares of forest per year during the period of 2010-2015

(MacDicken et al., 2016) while around 400,000 hectares were deforested per year in 2007 and

2008 (Malky, Leguia and Ledezma, 2012), mainly to slash-and-burn agricultural production

(Andersen et al., 2016). From 1990 to 2010, Bolivia has lost 4.2 million hectares of forest

(Andersen et al., 2016). At the same time, agricultural expansion plays a critical role in both

Bolivia’s food sovereignty1 and in poverty reduction strategy2; mainly because poverty is concentrated in rural areas3, and it has been observed that agriculture is more efficient reducing poverty among the poorest of the poor (Christiaensen et al. 2011). It is arguable whether agricultural expansion is needed, as agricultural production could increase without expanding the production area, increasing productivity. Despite the rapid conversion of forest to grass and cropland, and considering the relevance of agricultural expansion for development in Bolivia, there is little information to guide policymakers about where this expansion should be taking place to maximize agricultural production growth and minimize forest preservation costs.

1 Economic and Social 2016-2020 Development Plan – Pillar 8 2 Economic and Social 2016-2020 Development Plan – Pillar 1 3 Extreme poverty was 38.8% in 2013 (UDAPE, 2018)

Agricultural production is indicated as the main driver of deforestation in Bolivia (Urioste,

2010), more specifically, mechanized agriculture, cattle ranching, and small-scale agriculture

(Müller et al., 2013). Cattle ranching was responsible for around 50% of the deforestation occurred in the period 2000-2010 (Müller et al., 2014b). Ferreira et al. (forthcoming) analyze and forecast the deforestation in 2025 in Santa Cruz, which comprises the Amazon and Chaco forests. They analyze different scenarios; the business scenario considers the current deforestation trends. Under this scenario they find that deforestation will increase by 148% with respect to 2013, 46% will be due to cattle ranching, while 23.4% will be due to agriculture.

In the literature, we find that the opportunity cost of sequestering one ton of CO2 in Bolivia lies on the range US$ 2.47 - US$ 5.77, which depends on the assumption made about discount rate, carbon content and period length (Stich, 2009; Malky, Leguia and Ledezma, 2012; Müller et al., 2013). Most of these studies used budget information on output revenue and input cost to obtain the foregone income stream and then obtain the opportunity cost estimate.

We estimate the producer technology to obtain the shadow price of reducing deforestation in terms of value of production using a dataset at municipality level from the Agricultural Census of 2013, the Encuesta Agropecuaria of 2015, and satellite images to obtain deforested area.

Rather than use an inductive strategy we use a deductive approach using municipality information on agricultural production of more than 115 thousand farms.

Our results show that the opportunity cost varies significantly across municipalities, from

US$100 to more than 3,000 per hectare per year; and that, on average, to preserve one hectare of forest, US$1,229.35 of annual agricultural production has to be foregone. This translates to a cost of US$ 20.50 per ton of sequestered CO2 using a social discount rate of 0.10 and a carbon content per hectare of forest of 163. These results contribute to the literature on the estimation of

4 opportunity cost of preserving the forest and sequestering CO2 using a deductive approach and readily available datasets, which may be useful to design forest preservation and agricultural expansion policies.

DEFORESTATION AND AGRICULTURE IN BOLIVIA

Agricultural activities have led to high rates of deforestation in Bolivia (Urioste, 2010; Malky,

Leguia and Ledezma, 2012). Around 80% of the CO2 emitted in the country comes from land use change (Programa Nacional de Cambio Climático – PNCC, 2009), mainly from slash-and-burn agriculture (Andersen et al., 2016). The department of Santa Cruz alone has emitted more than

100 million tons of CO2 during the period from 1990 to 2010, an equivalent to more than 70% of total emissions in the country (Andersen et al., 2016). This department alone contains 24.9 million hectares of forest (Servicio Nacional de Áreas Protegida – SERNAP, 2013). In 2015, around 40% of the bovine stock, 62% of the milk production, 57% of the land planted, and 95% of the oilseeds planted were located in Santa Cruz (Instituto Nacional de Estadistica – INE,

2017).

In this paper we use information on deforestation in the year 2013 from the National Protected

Areas Service (SERNAP, 2013), a variable which we explain later in more detail. Figure 1 display the geographical distribution of the forest cover in 2013 and the deforestation that occurred between 2010 and 2013. By the year 2013, Bolivia had a deforested an area equivalent of 8 million hectares (SERNAP, 2013). During this period, 1 million hectares of forest were logged, almost 70% of it clustered in the department of Santa Cruz (SERNAP, 2013). The top 10 municipalities with respect to deforestation cleared together an area equivalent to 44% of the total deforestation in the period from 2010 to 2013, nine of those are in Santa Cruz. The

5 municipalities of San Ignacio and Pailón cleared almost 200 thousand hectares during this period.

[Figure 1]

The geographical distribution of land deforested also corresponds to the agricultural production distribution. Figure 2 presents the value of production from the outputs considered in this paper, which are later described in more detail. We observe that municipalities with greater deforestation also show larger output revenue. For example, San Ignacio and Pailón are the municipalities with the greatest area deforested and there are also among the 5 largest producers of soy, corn and of cattle head sold in 2013.

[Figure 2]

Müller, Pacheco and Montero (2014a) suggest that mechanized agriculture, cattle ranching, and small-scale agriculture are the main drivers of deforestation in Bolivia. They point out that agricultural expansion into the lowlands was promoted by the Bolivian government in the late

1950s seeking to substitute food imports. In the 1980’s, another major expansion was prompted by the introduction of mechanized agriculture (Müller,Pacheco, and Montero, 2014a) which affected the preservation of forest biomes.

The production of soybean and sugarcane are clustered in areas with fertile soils in the northern portion of Santa Cruz while rice production is located in more humid areas of this department (Müller, Pacheco and Montero, 2014a). Sunflower, wheat, and sorghum are also produced in consortium with soybean in these regions (Müller et al., 2013). Soybean production, which happens mainly in Santa Cruz, is the most important crop production in Bolivia and targets the export markets (Müller et al., 2013). In the recent years, greater access to export

6 markets, a fertile soil, and intermediate rainfall levels have led to yet another expansion of mechanized agriculture (Müller et al., 2013).

In the period from 1992 to 2004, mechanized agriculture continued to be the main driver of deforestation (Müller et al., 2013), while cattle ranching was responsible for around 50% of the deforestation occurred from 2000 to 2010 (Müller et al., 2014b). Cattle ranching is practiced in most of the Bolivian lowlands but mainly in Chiquitania and northern Amazon (Müller et al.,

2014a). Müller et al. (2013) indicates that conversion of pasture to plantation is not common in

Bolivia while in Brazil is commonly observed the conversion of pasture to soybean plantation.

By 2025, deforestation is expected to reach up to 8.97 million hectares, 148% more than the observed land deforested land in 2013 (Ferreira et al., forthcoming).

Although the Bolivian government has been seeking to preserve the forest and the biodiversity, policies have led to broader institutional weaknesses and market failures that have strengthen the distributional problems and incentivized informal logging (Pacheco et al., 2010).

Müller, Pacheco and Montero (2014a) argue that the Bolivian government has opted to move away from the REDD guidelines to preserve the forest and from a market-driven alternative such as the CO2 international market. As stated in the “Conferencia Mundial de los Pueblos sobre el

Cambio Climático y Equilibrio con la Madre Tierra”, the Bolivian government condemns market mechanisms aiming at the reduction of deforestation emissions and forest degradation, and rejects mechanism that promote carbon markets (Pacheco, 2013). A summary of the Bolivian government position and of its policies can be find in Pacheco et al. (2010), Müller et al. (2013) and Pacheco (2017)4.

4 For a comprehensive analysis on Bolivian Government position on environment see Pacheco (2017):“Gestion de Sistemas de Vida”

There are several studies that have discussed forest preservation and the main drivers of deforestation in Bolivia. A few studies have calculated the opportunity cost of preserving one hectare of forest using information on output revenue and input cost to obtain the foregone income stream per hectare. Stich (2009) estimated the opportunity cost of a ton of carbon to be on average US$ 21.17 for the El Chore Forest Reserve in the department of Santa Cruz in

5 Bolivia . This is equivalent to an average price of US$5.77 for a ton of CO2. To obtain this estimate she first predicts the deforestation areas, agricultural yields, prices and production cost and then uses this information in a Net Present Value methodology with a discount rate of 8%. In this study, rice, corn, soybean and wheat are the outputs considered.

Malky, Leguia and Ledezma (2012) estimated the opportunity cost of preserving one hectare of forest in the Bolivian northwest region – in small portions of the La Paz and Beni departments6. Their opportunity cost is the difference between the benefits from the standing- forest and logging. They use a Net Present Value methodology on the farm production trajectory

(revenue and cost) over 30 years with a discount rate of 6%. They also considered several outputs such as corn, rice, cattle and its derivatives including dairy products (milk), timber sold, and agroforestry commodities such as orange, tangerine, banana, cocoa, sugarcane and cassava.

As benefits from the standing-forest they have considered jatata, a palm tree that can be used on construction and house utensils. They found an opportunity cost of US$ 113 per hectare per year.

After obtaining this estimate, Malky, Leguia and Ledezma (2012) performed a survey of local farmers seeking to identify farmers willing to accept the value proposed in exchange for preserving the forest. The survey results showed that these farmers were willing to accept a

5 By 2025, it is expected to observe a deforestation of 85% of the current forest in this region (Ferreira et al. Forthcoming). 6 Their estimates are based on 326 interviews done in these areas.

8 minimum of US$ 350 per hectare per year, which is a value three times higher than their estimate. To obtain carbon prices, they assume that each hectare of forest keeps 163 carbon7, based on Araujo-Murakami and Jorgensen (2008). They found prices of US$ 3.40 and US$ 2.47 per ton of CO2 for the one-product trajectory estimates of timber extraction and intensive cattle production, respectively.

Müller et al. (2013) estimate the opportunity cost of preserving one hectare of forest using a

30-year Net Present Value methodology with a discount rate of 8% for three main categories including mechanic agriculture, cattle ranching, and small agriculture. They find that the opportunity cost of preserving one hectare of forest is equal to US$ 1,956 for a scenario where only soybean is produced after logging8. They find a much smaller opportunity cost of US$ 270 per hectare in the surrounds of Santa Cruz in a scenario where cattle ranching takes place.

Assuming a carbon content of 163 carbon per hectare (ha) as in Malky, Leguia and Ledezma

(2012), this estimate translates to an average price of US$ 3.27 per ton of CO2 per year. A higher price, of US$ 3.75 per ton of CO2, is observed in a scenario where soybean (summer) and sunflower (winter) are jointly produced.

There have been studies that estimated the opportunity cost for other countries. Myers (2008) indicates that the shadow price for sequestering CO2 by reducing deforestation vary widely across the world. For Brazil, these estimates range from US$ 0.80 to US$ 21.02 depending on the assumptions made on discount rate, period length, carbon content per hectare of forest, and agricultural activity foregone (Margulis, 2004; Vera-Diaz and Schwartzman, 2005; Nepstad et

7 Following Palm et al. (2007), they only account for the released carbon from the forest in the estimation given that carbon release is production dependent. Therefore, on the opportunity cost estimation they have considered only the net carbon emissions opposed to 163 carbon per ha. 8 For this estimate, the initial investment includes a US$ 200.00 to clear the forest which is offset by timber sales of US$ 200.00 and soil preparation of US$ 97.50. Soybean production costs include crop inputs such as seeds and fertilizer and adds up to US$ 534.00 per hectare. Revenue is calculated using a soy yield of 1.83 tons per hectare and a price of US$ 200 per ton, which adds up to US$ 752.00 per hectare.

9 al., 2007; Börner and Wunder, 2008; Silva, Perrin and Fulginiti, 2017; Ickowitz, Sills and Sassi,

2017).

Silva, Perrin and Fulginiti (2017) estimate the opportunity cost of preserving one hectare of

Amazon forest using both nonparametric and parametric directional distance function. They find an annual opportunity cost of preserving one hectare of forest to be around US$ 800. To obtain an average CO2 shadow price they use a carbon content of 132.2 tons of carbon per hectare of forest biomass and a discount rate of 10%. At perpetuity, they estimated that the average shadow price of a ton of CO2 was US$ 14. Also, in Brazil, Ickowitz, Sills and Sassi (2017) estimate the opportunity cost of preserving one hectare of forest ranging from US$ 142.42 to US$ 1,522.00 for five villages in Brazil. The present value opportunity cost of a ton of carbon ranges from US$

10.63 to US$ 77.15 using a discount rate of 9%. This implies a price range of US$ 2.89 to US$

21.02 for a ton of CO2.

THE MODEL

In Bolivia, deforestation has been a recurring issue mostly to expand agricultural land. It has been used as an input on crop production and other agricultural commodities. Deforestation eliminates the ecosystem services that the forest provides such as carbon sequestration. Although the entire world benefits from forest preservation and carbon sequestration, the local Bolivian farms incur the opportunity cost of preserving the forest. Our objective is to estimate this opportunity cost for Bolivia using municipality dataset from the Agricultural Census of 2013, the

Encuesta Agropecuaria of 2015, and the analysis of official images of the land deforested from the Bolivian government satellite (SERNAP, 2013).

Farming technology is modeled using a production function and stochastic frontier approach.

Each farm 푖 = 1, … , 푁 uses a vector of inputs (푿풊) such as labor and capital, and land deforested

(푏푖) to obtain the value of production 푌푖 from soy, corn, sugarcane, wheat, livestock, and other commodities (described in the data section). This technology is represented in Equation (1).

(푣푖−푢푖) 푌푖 = 푓(푿풊, 퐵푖; 훽)푒 (1) where the error term is composed by the standard error term (푣푖) and a term that captures the deviation from the frontier (푢푖), also referred in the literature as inefficiency. We assume that the

2 distribution of the efficiency term, specifically 휎푢 , is a function of exogenous variables (푧푖) such as the percentage of farms that have access to rural extension. This error component captures factors associated with each municipality, beyond the inputs and outputs explicitly accounted for in the main structure of the production function. We presume that the set of variables 푧푖 capture some of this heterogeneity across municipalities. In the following sections we present the empirical specifications used to estimate Eq. 1.

This technology (in Eq. 1) allows us to estimate the production elasticities; e.g. percentage change on output due to a percentage change on input (see Equation 2 for the land deforestation elasticity).

휕푙푛(푌 ) 휕푌 퐵 푖 = 푖 푖 ≥ 0 (2) 휕푙푛(퐵푖) 휕퐵푖 푌푖 where it must be nonnegative due to monotonicity on inputs. The return to scale is estimated summing all the production elasticities; i.e. 푅푇푆 ⋚ 1 implies decreasing, constant and increasing return to scale.

To obtain the opportunity cost of preserving one hectare we assume that farmers maximize profit choosing the amount of input in the production of 푌푖. Farmers face exogenous output price

(푝) and the vector of input prices (풘풙). They also face an exogenous opportunity cost to land deforested (푤푏).

We assume profit-maximizing farmers that solve the following problem:

max풙풊,푏푖 휋푖 = 푝 푌푖 − 풘풙푿풊 − 푤푏퐵푖 (3) 푠푢푏푗푒푐푡 푡표 푌푖 = 푓(푿풊, 퐵; 훽)

The First Order Conditions of this problem imply

휕푌푖 (4) 푤푏 = 푝 휕퐵푖 where the opportunity cost of preserving the forest (푤푏) is the Marginal Value of Production added due to an additional unit of 퐵푖 (an additional hectare of land deforested).

DATASET

The dataset is composed of 339 observations of municipalities in Bolivia in the year 2013. To build the output and inputs variables we have used data from the Agricultural Census of 2013, the Encuesta Agropecuaria of 2015, and satellite images to obtain the area deforested (SERNAP,

2013). The outputs considered in this dataset were chosen based on the literature and information from the Ag. Census. Table 1 presents the descriptive statistics of the data. After dropping outliers9, we worked with a sample of 330 municipalities.

[Table 1]

In Bolivia, the department of Santa Cruz has the largest production of agriculture and area deforested. In 2013, around 2.6 million tons of soy and 7.6 million tons of sugarcane were

9 We have dropped observations at the bottom and top 1% percentile based on the log of the value of production. This procedure have generated a sample with 330 municipalities.

12 produced in this department (INE, 2017). These two commodities are among the most important agricultural products of the country. The municipalities that have shown deforestation during the period from 2010 to 2013 had an average deforestation of 2,638 hectares per year. The greatest area deforested in the department in 2013 was in San Ignacio, where nearly 29,758 hectares were logged. Table 2 and Figure 3 displays the top 10 municipalities with the highest level of deforestation and their main activities. Together, these municipalities deforested more than 150 thousand hectares of forest, an equivalent to 46% of the total deforestation in during this period.

Figure 1 displays the geographic distribution of the deforestation.

[Table 2]

[Figure 3]

The accumulated deforestation is estimated using official Bolivian government satellite images (SERNAP, 2013) for two periods, 2010 and 2013. To obtain the deforestation for 2013 we have subtracted the accumulated deforestation in 2013 by the accumulated deforestation in

2010 and divided by 3. Given that we do not observe an official measure of deforestation in 2013 we use this average as a proxy. It assumes that the deforestation pattern has been the same over this three years.

Cattle ranching and mechanized agriculture are the main drivers of deforestation (Müller et al., 2013; Müller et al., 2014b) and also the most relevant agricultural activities in this department. Given that we only observe aggregate dataset for the inputs we considered one output in the estimation which is value of production. In the calculation of this variable we have considered a large number of crops, which are obtained in the Agricultural Census of 2013 in quintals (QQ); they are: wheat, corn, rice, sorghum, soy, sugarcane, tobacco, passion fruit, amaranth, coffee, orange, grape, yuca, cacao, coca, tomato, papaya, onion, quinoa, lettuce, garlic,

13 barley, alfalfa, green bean, and sunflower. To obtain output quantities in tons we multiply output quantities by 46 and divided by 100010. This Census only provides the stock of cattle. To capture the relation cattle-deforestation discussed in the literature we assume that 80% of the bovine cattle with 3 years or more are sold, the other 20% are lost due to diseases and other factors

(Caputi and Murguia, 2003)11. It implies a similar pattern in all municipalities. Figure B1 and B2 in the Appendix displays the geographical distribution of the production of selected outputs.

While crop production is clustered in the center and northwestern portion of the department of

Santa Cruz livestock is almost uniformly distributed. Figure B1 and B2 in the Appendix B displays the value of production for the main outputs per municipality in Bolivia. It implies that municipalities at the center and northwestern portion of Santa Cruz focus on crop production while the eastern portion displays large livestock activity. Figure 2 displays the value of production from these activities. Although municipalities in the center-northwestern portion of the department are smaller in area, they face a similar or higher revenue from these activities.

These municipalities also have high rates of deforestation.

To obtain the value of production we used prices from the Encuesta Agropecuaria 2015 (INE,

2017). Although prices are not for 2013, as the Agricultural Census, this is the most reliable source of prices for all crops and cattle considered in this paper. This survey presents a weighted average price for each department in Bolivia for all crops. We have used12 the Encuesta microdata to obtain these prices for the following crops: wheat, corn, rice, sorghum, soy, sugarcane, tobacco, passion fruit, amaranth, coffee, orange, grape, yuca, cacao, coca, tomato,

10 The Agricultural Census uses a conversion measure of 1 QQ = 46 kilogram (Kg). 11 Table B2 displays the mean and sum of the cattle per age and sex. 12 푁 푁 These prices were calculated as ∑푖 푤푖 푝푖⁄∑푖 푤푖, where 푤푖 is the weighted given by the survey for the ith UPA and 푝푖 is the price of a specific crop for the same ith UPA. The summation is over the range of interested, thus we summed over all observations from a department and a production destiny (at the farm).

14 papaya, onion, quinoa, lettuce, garlic, barley, alfalfa, and green bean. The Encuesta presents prices for two crop seasons (summer and winter) and for three separate locations (at the farm, at the local market, and at the nearest city). We have used the price obtained at the farm for these products13. In addition to these prices, we obtained the price for cattle14 from this survey and the price of sunflower was obtained online15.

퐵표푙 These prices are presented in Bolivianos (Bs) per unit, such as 푝푚 = 퐵푠/푄푄. To convert to

U.S. dollars (US$) we assume that 1 Bs = 0.14 US$. Using the conversion 1 QQ = 46 Kg, we obtain price on US$ per ton

퐵표푙 푝푚 = (푝푚 푥 0.14) 푥 (1000⁄46)

퐵표푙 where 푝푚 is the price in US$ per ton, 푝푚 is the price in Bolivian per quintals (QQ).

We were able to observe 7 production inputs. In the literature, labor and capital are indicated as the most important inputs on agricultural production. We use number of workers in the farm as a proxy to labor. To measure capital, we have used and tested different proxies: number of trucks, length of fences, number of silos, and number of water pumps. Several models were estimated using different combinations of these proxies. In addition to these inputs we also observed total area of the farms (Unidade Productivas Agropecuaris – UPA) that have been used during the census year. Our model also allows to an error term that captures these municipalities’ heterogeneity, which might also reflect resource quality and account for other variables that not explicitly considered in the production function. We also have considered a few variables that are known to affect farm technical efficiency (see next section for details), such as the share of

13 Although this survey presents these different prices we only observe annual production without being able to differentiate whether it was a summer or a winter crop and if it was sold at the farm, in a local market or other place. 14 The Encuesta Agropecuaria consists of a survey rather than a census. For each observation there is a weight used to obtain information on the population. We use the price of cattle in Santa Cruz, which is displayed on page 529. It presents only one price for cattle sold (head sold), which was converted to dollar by multiplying it by 0.14. 15IBCE Instituto Boliviano de Comercio Exterior

15 farms that have accessed rural extension and credit, applied fertilizer16, hired labor and used female work force. Table 1 presents the descriptive statistics of these variables.

Bolivian farms still have low access to rural extension, on average, 18% of the farms in each municipality has had access to these services. Anderson and Feder (2003) states that rural extension can increase farm efficiency and productivity. Access to credit is also known to increase farm efficiency and productivity when combined with access to extension services and better inputs. However, on average, only 8% of the farms had access to credit in 2013. Around

40% of the farms hired labor and 36% of the workforce was female.

EMPIRICAL MODEL

In this section we present the empirical specification for the production function (Eq. 1) based on a Second Order Taylor expansion, also known as Translog, to be estimated using Maximum

Likelihood Estimation (MLE). However, we test several other functional forms as a robustness check such as Cobb-Douglas, and Ad-hoc modified Cobb-Douglas, and use other methods such as Ordinary Least Square (OLS). Each functional form has its set of assumptions, for instance, assuming a production function following a Cobb-Douglas imposes a constant production elasticity in addition to a zero input elasticity of substitution.

Equation (1), assuming a Translog and constant return to scale, is given by

퐽−1 퐽−1 퐽−1 퐽−1 1 1 2 푦 = 훽 + ∑ 훽 푥 + ∑ ∑ 훽 푥 푥 + 훼 푏 + 훼 (푏 ) + ∑ 훿 푥 푏 + 휀 (5) 푖 0 푗 푖,푗 2 푗푗 푖,푗 푖,푗 1 푖,1 11 2 푖,1 푗1 푖,푗 푖,1 푖 푗=1 푗=1 푗=1 푗=1

16 Although fertilizer is considered a production input, the Ag. Census does not provide the amount of fertilizer applied. The Census only provide whether the farmer applied fertilizer or not. This variable is capturing a measure of farm size and farm’s capitalization, which affect farm technical efficiency.

16 where all variables (푦푖, 푥푖,푗 and 푏푖,1) are divided by agricultural area other than deforestation area; 푦푖 is the logarithm of the value of production in US$ dollars for 2013; 푥푖,푗푠 are the following inputs in logs: labor, trucks, water pumps, length of fence, and agricultural area; 푏푖,1 is area deforested; 훽’s, 훼’s, and 훿’s are parameters to be estimated; and 휀푖 is the composite term, described later in this section. An estimation with the value of production per area is preferable if the data being analyzed are subject to heteroscedasticity. To estimate Eq. (5) we also impose symmetry, which implies, for instance, that 훽12 = 훽21. To recover the parameter associated with the agricultural area we use the homogeneity property

퐽 퐽 ∑푗=1 훽푗 = 1 and ∑푗=1 훽푗푘 = 0 (6)

The production elasticities (Eq. 2) can be found directly from Eq. (5) as

퐽−1 휕푙푛(푦푖) = 훽푗 + ∑ 훽푗푗푥푖푗 + 훿푗1푏푖,1 (7) 휕푙푛(푥푖,푗) 푗=1

퐽−1 휕푙푛(푦푖) = (훼1 + 훼11푏푖,1 + ∑ 훿푗1푥푖,푗) ∗ 푏푖,1 (8) 휕푙푛(푏푖,1) 푗=1

given that 푏푖,1 is not a logarithm. These elasticities vary across municipalities. The agricultural area elasticity can be found using the assumption of constant returns to scale

퐽−1 휕푙푛(푦 ) 휕ln (푦 ) 휕푙푛(푦 ) 푖 = 1 − ∑ 푖 − 푖 (9) 휕푙푛(푥푖,1) 휕ln (푥푖,푗) 휕푙푛(푏푖,1) 푗=1 where all production elasticities should be equal or greater than zero (at least at the mean of the variables).

The main goal of the paper is to estimate the shadow price of the deforested area, given by

Eq. (4). Using the parameters estimated on Eq. (5) the shadow price is found as

퐽−1

푤푏 = (훼1 + 훼11푏푖,1 + ∑ 훿푗1푥푖,푗) ∗ 푦푖 (10) 푗=1

17 18 given that 푏푖,1 is not in logarithm and 푦푖 is value of production (p = 1) . This value should be equal or greater than zero considering that the term in the brackets should be positive. It varies across all municipalities (including municipalities that do not have forest given that 훼1 ≠ 0 and

푥푖,푗 > 0 in these municipalities). We focus on the estimates of municipalities that have forest.

To estimate Eq. (5) we estimate a stochastic frontier approach using MLE. We estimate this equation with OLS and use the estimated parameters as initial values on the MLE procedure. In this approach the error term 휀푖 = 푣푖 − 푢푖 is composed by two components; 푣푖 represents the standard error and 푢푖 represents the deviation of each municipality from the frontier, also known as a measure of inefficiency. We assume that this component follows a half-normal distribution

+ 2 푢푖~푁 (0, 휎푢 ), as described in Kumbhakar, Wang, and Horncastle (2015). The distribution of

2 this term, specially 휎푢 , is a function of exogenous factors (풛풊) that affect farm efficiency. In the estimation we included variables such as the share of farms that have accessed rural extension and credit, applied fertilizer, hired labor and used female work force. We expect these factors to affect the distribution differently; for instance, a higher share of farms that have accessed rural extension is expected to decrease inefficiency19 (or increase efficiency).

Eq. (5) was also estimated in a Cobb-Douglas form, which implies that 훽푗푗 = 훼11 = 훿푗1 = 0, that production elasticities are the estimated parameters (훽푗 and 훼1 ∗ 푏푖,1), and that the

17 휕푙푛(푦푖) 1 휕푦푖 We observe = , so to obtain only the marginal product we have to multiply by 푦푖. 휕푏푖,1 푦푖 휕푏푖,1 18 The opportunity cost is being scaled by inefficient error component, 푒(−푢푖). It indicates that as municipalities become more inefficient (on agricultural production) the opportunity cost is scaled up (inefficiency ranges from 0 to 1). 19 The estimation was done using Stata 14 following the command sfmodel suggested by Kumbhakar, Wang, and Horncastle (2015) and sfcross suggested by Belotti et al. (2012).

18 opportunity cost (푤푏) is 훼1 ∗ 푦푖. We also estimated using a modified Cobb-Douglas (Ad-hoc model) where area deforested interacts with the other inputs. The production elasticities of inputs other than area deforested is now 훽푗 + 훿푗1푏푖,1 and the elasticity for area deforested and shadow price are calculated as in Eq. (8) and Eq. (10). In addition to these robustness checks, we also estimated these equations using a different set of inputs. Our interest was to test whether the opportunity cost and its distribution across the municipalities changed with these modifications.

RESULTS

In this section we present the results of the estimation of Eq. (5) and (7) to (10). We focus on the results of the Translog throughout this section but later we compare to other specifications. The results of the estimation using OLS and MLE are displayed in Table 3. The OLS estimation resulted in six statistically significant parameters out of 15, while there are eight significant MLE parameters (in addition to four statistically significant parameters out of six in the efficiency variable set). A Likelihood Ratio test of 39.07 indicates that MLE estimates with a half-normal distribution for the one-sided error term are superior to the OLS estimates at the 1% level of significance (critical value is 14.32). The analysis that follows is based on the MLE estimates20.

[Table 3]

Table 3 shows an estimation in which we considered two proxies for farm capital, trucks and water pumps. In the next section we present a few models that considered a different set of input variables and functional form specifications. Using the parameters from Eq. (5), in Table 3, we estimate the production elasticities using Eq. (7), (8) and (9). On average, labor production

20 In this estimation, most of the observations satisfied monotonicity (positive production elasticity). We observed nonpositive elasticities in 21% of the observations for labor, 0.6% for capital 1 (trucks), 21% for capital 2 (water pumps), 18% for area deforested, and 18% for agricultural land. On the average of the variables all production elasticities are positive.

19 elasticity was 0.16, trucks elasticity (proxy for capital) was 0.345, water pumps elasticity (proxy for capital) was 0.13, agricultural land elasticity was 0.257 and area deforested elasticity was

0.1121. These elasticities imply that, for instance, an increase of 10% on labor would lead, on average, to an increase of 1.6% on the value of production.

Even though the production elasticity of area deforested presented above considered the entire sample (330 observations), some observations have zero production elasticity (see Eq. 11)22.

This elasticity is 0.26 for the municipalities that have used area deforested in the production process. It implies that the productivity of old agricultural land, is the same as new agricultural land, i.e. deforested land. Additionally, it implies that an increase of 10% in deforestation (the use of area deforested in crop and cattle production) would lead, on average, to an increase of

2.6% on the value of production.

The MLE approach allows us to estimate the municipality technical efficiency and the factors affected it. It is important to notice that the efficiency estimate is capturing municipality heterogeneity and the inclusion of these factors helps to better estimate it. The average technical efficiency was 0.75, which implies that farmers could obtain the same value of production using

25% less inputs. Figure 4 displays the histogram of the estimated technical efficiencies. Our findings also suggest that the share of farms that have applied fertilizer, that had access to credit and had a female workforce affected technical efficiency23.

[Figure 4]

21 All these elasticities are statistically significant at 1%. 22 Some of the municipalities have shown 푏푖,1 = 0, and therefore they have a zero production elasticity for this input. 23 We found that an increase of 1% on the number of farmers that use fertilizer and had access to credit would lead to a decrease, on average, of 3% and 1% on the level of inefficiency. On the other hand, an increase of 1% on the number of female workers would lead to an increase, on average, of less than 0.9% on inefficiency.

The objective of this paper is to estimate the opportunity cost of preserving one hectare of forest. We use the parameter obtained from Eq. (5), displayed in Table 3, on Eq. (10) to obtain these estimates. Results are displayed in Table 4 and Figure 5. After dropping the bottom and the top 5% of the estimates distribution (to remove outliers) the median estimate is US$ 356.90 and the average estimate is US$ 1229.35. These results imply that to reduce one hectare of deforestation a farmer would have to forego, on average, US$ 1229.35 in value of production.

Note that these values are different in Table 4 given that we dropped the negative prices to build this table since a negative price is inconsistent with economic theory. In our estimates, less than

18% of the observations have shown a negative price.

[Table 4]

These estimates vary across municipalities. The municipalities in the department of Santa

Cruz were responsible for 67% of the Bolivian value of production considered in this paper, followed by Cochabamba and Tarija, each with 7% of the value of production. On the other hand, Santa Cruz was responsible for 57% of the deforestation during the period from 2010 to

2013 followed by Beni (18%) and Tarija (6%). The tradeoff between agriculture and forest is represented in this paper by the opportunity cost estimates. Santa Cruz, Tarija and Cochabamba have the highest opportunity cost estimates (see Table 4), which implies that decreasing deforestation in these departments will be much more costly than in others. Figure 5 displays the geographical variation on these estimates.

[Figure 5]

The comparison of Figure 1, 2 and 5 shows the clear tradeoff between agriculture and forest area. Areas where agricultural production have been established and it is in expansion have been observing high rates of deforestation, such as the Southwestern and Central-Western portions of

21 the country (Santa Cruz, Tarija and Cochabamba). Our findings suggest that municipalities in these regions have the highest opportunity cost of preserving one hectare of forest. On the other hand, the Northern portion of country (part of La Paz, Pando and Beni) which still have a large forest area (see Figure 1), have shown a lower opportunity cost compared to the Bolivian and

Santa Cruz averages (see Table 4).

After obtaining these estimates for each municipality we have replaced negative estimates by the median of the distribution to calculate how many hectares would have been preserved at a price of US$ 923.3724 per hectare (the 75th percentile of the opportunity cost distribution). In other words, how much area deforested is on municipalities that face a lower or equal opportunity cost to US$ 923.37. Around 65% of the deforestation that happened in 2013 would have been avoided at this opportunity cost estimate. This is equivalent to 220 thousand hectares of forest.

Carbon price estimate

There are several measures of carbon content per hectare of forest in Bolivia. This is in part due to the forest diversity and existence of seven different forest biomes. For instance, Malky,

Leguia, and Ledezma (2012) present measurements of carbon content that ranges from 58 to

348.3 carbon per hectare of forest biomass. We use a carbon content of 163 carbon per hectare of forest as in Malky, Leguia and Ledezma (2012). To reduce the emission of one ton of CO2 one would have to give up, on average, US$ 2.05 or, at the median, US$ 0.60 yearly. Our average opportunity cost translates to a median and an average present value of US$ 5.95 and US$ 20.50

24 We have chosen this estimate given its representative aspect: 75% of municipalities have shown an opportunity cost lower than this value. At the mean, 78% of the area deforested would have been avoided. This shows that the distribution of our opportunity cost estimates across municipalities is skewed, 75% of the municipalities face an estimate lower than the average.

22 to reduce one ton of CO2 emission in perpetuity. These prices depend on the assumptions made and would vary across municipality. A smaller carbon content and discount rate would lead to higher CO2 prices. Departments at the Northern portion of the country show a lower average of

CO2 price, for instance, in Pando the average present value would be US$ 4.55.

Our estimates are higher than what has been reported in the literature. Stich (2009) found a price for a ton of CO2 of US$5.77, Malky, Leguia, and Ledezma (2012) found a price of US$

3.40, while Müller et al. (2013) estimate it to be in the range of US$ 3.27 to US$ 3.75. Our estimates as well as theirs would be different if we change the assumptions. These values are not directly comparable given the agricultural commodities considered and assumptions made

(discount rate, period length, and carbon content).

Using these opportunity cost estimates from Figure 4, Table 4 and the data, we can also present the CO2 price information as a supply of carbon sequestration, in Figure 6. It indicates that at a price of US$ 5.00 (average reported in the literature) we would observe a decrease of around 120 thousand hectares while at US$ 20.50, we would achieve a decrease on deforestation of around 240 thousand hectares. It is worth mentioning that if we used the before mentioned

75th percentile estimate (US$ 15.42) we would achieve a decrease on deforestation of around

220 thousand hectares.

[Figure 6]

LIMITATIONS AND ROBUSTNESS CHECK

The specification of Eq. (5) using a Translog imposes theoretical properties on the technology that might affect the results. Unfortunately we do not observe an accurate measure of farm capital. In the previous section we have considered two proxies, trucks and water pumps. This

23 choice might also have led to different opportunity cost estimates. Therefore, we estimate the production using different functional forms and including a different set of inputs. Table 5 presents the estimation results and Table 6 presents the production elasticities and the opportunity cost estimates (median and mean).

[Table 5]

In Table 5, all Cobb-Douglas specifications satisfy monotonicity if the estimated parameters are positive (implies positive elasticity). We found all parameter to be positive for the four specifications displayed. The production elasticities are similar across specifications as well as the opportunity cost estimates. The latter has a higher median (around $490) when compared to the US$ 356 reported in the previous section and a lower mean (around $1100) if compared to

US$ 1229.35 from the previous section. The outcome from the Translog is quite similar to the others but the estimate from the Ad-hoc modified Cobb-Douglas specification is quite higher

(mean) than the others.

[Table 6]

We do not present the geographical distribution of these estimates except for two specifications (Cobb-Douglas A and alternative Translog), presented in Figure 7. They present the same pattern displayed in Figure 4. The outcome of these different specifications indicate that the estimation presented in the previous section is robust and preferred. In that estimation, we observed more statistically significant parameters and still found a similar opportunity cost estimate.

[Figure 7]

Another drawback of our opportunity cost estimate is that we did not include the cost of deforesting the land. In our previously calculations we assumed that in Bolivia we observe a

24 slash-and-burn behavior, as suggested by Andersen et al. (2016). However, we could incorporate the cost of deforesting by subtracting the cost from the opportunity cost estimate. Müller et al.

(2013) suggested that it cost $200 to clear the forested area and $97.50 to prepare the soil. This cost would be incurred only in the first year, which would not change the CO2 opportunity cost estimate dramatically given that we are analyzing in perpetuity.

CONCLUSIONS

Agricultural expansion has been in the center of the Bolivian development strategy, due to its implications in poverty reduction and food sovereignty, however it has led to high rates of deforestation in Bolivia. It posits a tradeoff between agricultural activities and forestland in this country. Farmers and local households bear the cost of preserving the forest when they are foregoing an income stream in order to preserve an extra hectare of land. In this paper, we add to the evidence on the opportunity cost of preserving the forest by obtaining an estimate using a deductive approach that requires only aggregate data. Our results are useful to determine which areas are more productive, indicating a direction for agricultural expansion, and which are the efficiency variables that are needed to maximize production minimizing the loss due to deforestation. We use the Agricultural Census of 2013, the Encuesta Agropecuaria of 2015 and satellite images on deforestation to estimate the farm technology represented by the production function.

Our results indicate that an average (median) of US$1,229.35 (US$ 356.90) in value of production must be foregone yearly for every hectare of deforestation reduced. The opportunity cost varies across municipalities, ranging from US$ 0 to almost US$ 17,000 per hectare. Using an average carbon content of 163 tons of carbon sequestered per hectare of forest and a 10%

25 discount rate, this implies that the average (median) present value of costs for permanent sequestration is US$ 20.50 (US$ 5.95) per ton of CO2.

These estimates vary widely across municipalities. While the cost to preserve one hectare of forest in Santa Cruz is, on average, US$ 2,646 per hectare, in Pando and Beni the cost is US$

272 and US$ 370 per hectare respectively. In 2013, Santa Cruz was responsible for around 44% of the forest area and 57% of deforestation occurred, while Pando and Beni together were responsible for 31% of the forest area and 23% of the deforestation in Bolivia. A less costly reduction in deforestation could be achieved in the latter two departments when compared to a policy that focus solely on Santa Cruz. This department produces more than 65% of the value of production in the country compared to less than 5% of the other two departments together. This conclusions are based on an uniform carbon content measure across the municipalities and they are not considering differences on the biodiversity kept by each forest type.

In this paper we have considered only the opportunity cost of preserving forest in terms of foregone value of agricultural production. It is not being included the other costs such as existence values. We are planning to include these costs in future research. Although we have performed several robustness checks to assure that our estimate is accurate, we believe that we would benefit from the availability of more micro-data.

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TABLE AND FIGURES

Figure 1 – Forest area (left) and deforestation in Bolivia, during the period 2010-2013.

Source: Agricultural Census of 2013.

Figure 2 – Value of production per municipality using prices from Encuesta Agropecuaria 2015 and quantities from the Agricultural Census of 2013, in Bolivia, 2013.

Table 1 – Descriptive statistics of the value of production, inputs, and efficiency variables for

330 municipalities, Bolivia, 2013.

Standard Units Average Min Max Deviation Outputs Value of US$ million 6.886 26.500 0.014 265.000 Production Inputs

Area thousand ha 103.078 219.331 0.108 2084.06 Area thousand ha 1.023 3.157 0.000 29.758 Deforested Labor sum (in thousand) 13.994 19.271 0.019 127.166

Trucks sum (in thousand) 0.208 0.284 0.000 2.364

Fence thousand ha 12.398 39.952 0.000 450.077

Silos sum (in thousand) 0.146 0.413 0.000 4.191

Water pump sum (in thousand) 0.170 0.266 0.000 1.644

Efficiency Variables Access to Technical share [0,1] 0.184 0.163 0.000 0.869 Assistance Access to Credit share [0,1] 0.075 0.074 0.000 0.375 Applied share [0,1] 0.249 0.254 0.000 0.929 Fertilizer Hired labor share [0,1] 0.402 0.182 0.039 0.964 Female share [0,1] 0.368 0.140 0.029 0.683 workforce share

Table 2 – Output quantity (in thousand tons – crops; in heads sold – cattle) and deforestation (in thousand hectares) for selected municipalities and outputs in Bolivia, 2013.

Municipio Deforest. Soy Corn Rice Sunflower Sugarcane Cattle

San Ignacio 29758.3 0.115 347.18 525.52 0.345 414.45 26957

Pailón 27974.2 384.92 30.29 0.013 72.48 0.040 21958

Charagua 19047.4 1.858 7.630 3.39 0.000 0.933 9450

San Julián 18897 529.28 142.93 5.96 86.50 69.54 3148

Concepción 10727.6 0 3899.09 1030.41 0 1791.68 5936

Santa Rosa 10514.6 85439.84 6530.18 60794.86 137.51 326430.4 1503 del Sara

San Matías 10450.9 0.020 915.13 31.17 0.000 439.6 9135

Villamontes 10378.8 261.26 1899.29 2.53 0.000 923.30 8100

Ascensión 9238.05 15288.70 10464.49 53440.82 2740.01 105.66 5111 de Guarayos

Yapacaní 8586.27 3689.97 3016.05 34723.74 1.92 96.35 3631

Figure 3 – Top 10 municipalities in annual deforestation in Bolivia during the period 2010-2013, also displayed in Table 2.

Note: Annual deforestation was built as the total deforestation in this period divided by 3.

Table 3 – OLS and MLE parameter estimates of the Translog production function in Bolivia,

2013.

Variables Coefficient MLE OLS -0.155 0.307*** 푥 훽 1 1 (0.197) (0.101) 0.037 -0.165 푥 훽 2 2 (0.189) (0.157) 0.139 -0.107 푥 훽 3 3 (0.132) (0.103) 57.275** 64.854** 푏 훼 1 1 (27.229) (30.734) 0.092** 0.041 푥 2 훽 1 11 (0.047) (0.038) -0.076** -0.099*** 푥 2 훽 2 22 (0.035) (0.033) -0.002 -0.031 푥 2 훽 3 33 (0.020) (0.020) 330.071 72.190 푏 2 훼 1 11 (267.959) (308.143) -0.007 0.030 푥 푥 훽 1 2 12 (0.029) (0.022) -11.600*** -12.925*** 푥 푏 훿 1 1 11 (2.757) (3.139) -0.082*** -0.041*** 푥 푥 훽 1 3 13 (0.021) (0.016) 0.027 0.006 푥 푥 훽 2 3 23 (0.021) (0.016) 7.679* 7.100 푥 푏 훿 2 1 12 (4.320) (4.910) 4.265*** 3.486 푥 푏 훿 3 1 13 (2.532) (2.869) 6.115*** 4.750*** Constant 훽 0 (0.605) (0.430)

Efficiency Variables (흈풖) 0.305 푧 휗 - 1 1 (1.363) -16.278** 푧 휗 - 2 2 (6.913) -5.955** 푧 휗 - 3 3 (2.464) 푧4 휗4 5.207** -

(2.453) 1.670 푧 휗 - 5 5 (1.200) -2.484* Constant 휗 - 0 (1.324) -0.569 흈 - 풗 (0.095) N 330 330 Note: Standard error in parenthesis; *** for p-value smaller than 0.01, ** smaller than 0.05, and * smaller than 0.1.

Figure 4 –Farm efficiency in Bolivia, 2013, obtained using the MLE approach (using Eq. 5) displayed in Table 3.

Table 4 – Opportunity cost of preserving one hectare of forest estimates (in US$ per ha) for

Bolivia in 2013

Standard Mean Minimum Maximum Deviation

Chuquisaca 451.22 358.16 81.14 1090.84

La Paz 813.46 959.88 86.13 2987.11

Cochabamba 1848.37 2251.52 339.75 7244.31

Tarija 1867.25 2011.88 226.37 4466.41

Santa Cruz 2646.10 4002.73 66.58 16594.55

Beni 370.13 272.68 47.58 1257.86

Pando 272.45 366.50 6.23 1185.75

Bolivia 1461.65 2755.27 6.23 16594.55 Note: To build this table we have excluded all negative prices, the bottom 5% and the top 5%, which lead us with

77% of the observations (98 out of 128 observations). The median and the average estimates for the full sample is

US$ 356.90 and US$ 5005.56. We have not calculated these estimates for the departments of Oruro and Potosi.

These departments have not shown any deforestation in the period analyzed and have small forest areas (41 and

2,297 hectares, respectively).

Figure 5 – Opportunity cost of preserving one hectare of forest in Bolivia, 2013, using parameters from the Translog production function (Eq. 5) on the Eq. (10).

Note: We have replaced the negative estimates with the median of the distribution to plot this map.

Figure 6 – Supply of carbon sequestration (in million tons): opportunity cost of carbon sequestered in forest that was deforested in 2004/2006 (in 1000 hectares).

Note: The opportunity cost displayed in the vertical axis is in 2013 dollars (Bs 1.00 = US$ ). It is the present value of the cost of sequestering CO2 using a discount rate of 10% and a carbon content of 163 tons of carbon/ha of forest.

To plot this supply curve, we have used the estimates from Figure 4, but we drop the top 5% of the sample to simplify the exposition.

Table 5 – MLE parameter estimates of the alternative Translog, Cobb-Douglas and Ad-hoc modified Cobb-Douglas production function specifications in Bolivia, 2013.

Variable CB.A CB.B CB.C CB.D ADCB Translog

푥1 0.209*** 0.197*** 0.190*** 0.199*** 0.293*** 0.284** (0.044) (0.044) (0.043) (0.044) (0.069) (0.114) 푥2 0.409*** 0.383*** 0.375*** 0.378*** 0.290*** -0.227 (0.049) (0.051) (0.051) (0.051) (0.055) (0.169)

푥3 0.053* 0.046 0.046 0.023 (0.031) (0.031) (0.031) (0.031) 푏1 12.954*** 13.865*** 13.972*** 13.586*** 88.807*** 27.512 (3.947) (3.947) (3.797) (3.824) (31.071) (26.011)

푥5 0.036 0.027 (0.026) (0.027)

푥6 0.018 (0.020) 2 푥1 0.025 (0.039) 2 푥2 -0.106*** (0.034) 2 푏1 377.898 27.322 (340.249) (215.089)

푥1푥2 -0.002 (0.024)

푥1푏1 -13.901*** -9.766*** (2.939) (2.654)

푥2푏1 10.044** 5.487 (4.439) (4.462)

푥3푏1 6.980*** (2.501) Constant 6.610*** 6.752*** 6.874*** 6.928*** 6.319*** 5.144*** (0.222) (0.236) (0.252) (0.258) (0.502) (0.427) Efficiency Variables (흈풖) 푧1 -0.573 -0.593 -0.626 -0.472 0.057 0.255 (2.090) (2.109) (2.075) (2.102) (2.626) (1.393) 푧2 -63.565 -63.720 -73.069 -72.845 -25.437 -16.178 (63.034) (61.432) (59.046) (61.006) (61.844) (8.096) 푧3 -62.861 -59.058 -70.393 -71.298 -13.142 -6.505*** (54.128) (50.501) (52.209) (54.205) (48.234) (3.350) 푧4 -3.832 -3.048 -3.630 -3.575 -1.007 0.537 (3.723) (3.661) (3.489) (3.518) (6.318) (2.213)

푧5 1.517 1.641 1.606 1.727 0.643 0.171 (1.699) (1.661) (1.627) (1.637) (1.642) (1.338) Constant 2.555 2.136 2.589 2.458 0.798 0.012 (2.193) (2.148) (2.059) (2.096) (3.951) (1.233)

흈풗 -0.294*** -0.302*** -0.309*** -0.309*** -0.428*** -0.460*** (0.085) (0.085) (0.083) (0.083) (0.233) (0.098) N 330 330 330 330 330 330 LR test 49.34 49.30 51.15 46.70 42.06 32.71 Note: Standard error in parenthesis; *** for p-value smaller than 0.01, ** smaller than 0.05, and * smaller than 0.1.

Table 6 – Production elasticities and opportunity cost estimates for the alternative Translog,

Cobb-Douglas and Ad-hoc modified Cobb-Douglas production function specifications in

Bolivia, 2013.

CB.A CB.B CB.C CB.D ADCB Translog

Production Elasticities

Labor 0.209 0.197 0.190 0.199 0.204 0.199

Trucks 0.409 0.383 0.375 0.378 0.354 0.383

Water pumps - 0.053 0.046 0.046 0.068 -

Area Deforested 0.215 0.230 0.232 0.225 0.356 0.233

Silos - - 0.036 0.027 0.000 -

Fences - - - - 0.000 -

Ag. land 0.299 0.278 0.263 0.244 0.235 0.327

Opportunity cost of

Forest: Median (US$/ha) 484.07 501.24 497.82 484.08 469.70 466.60

Forest: Mean (US$/ha) 1080.25 1102.80 1112.17 1080.25 1838.46 1093.83

CO2: Median (US$/ton) 8.09 8.38 8.32 8.09 8.55 8.49

CO2: Mean (US$/ton) 18.06 18.43 18.59 18.06 33.47 19.91

Mean Farm Efficiency 0.90 0.90 0.91 0.91 0.81 0.75 Note: The production elasticity for Area Deforested and Ag. Land are the average of observations that had deforested during the period 2010-13. Ag. Land elasticity for the observations that have not deforested is higher,

0.38, 0.37, 0.35 and 0.33 for the model with specification Cobb Douglas A, B, C and D. The model ADCB refers to the Ad-hoc Cobb-Douglas model specification. All elasticities are statistically significant at 1%.

Figure 7 – Opportunity cost of preserving one hectare of forest in Bolivia, 2013, using parameters from the Cobb-Douglas A and Alternative Translog presented in Table 5 and 6.

Note: We have replaced the negative estimates with the median of the distribution to plot this map.

APPENDIX B

Figure B1. Outputs value of production (soy, sugarcane, soy and rice) for Bolivia in 2013 using prices from the Encuesta Agropecuaria of 2015.

Figure B2. Outputs value of production (Quinua, cattle, wheat, sorghum and coca) for Bolivia in 2013 using prices from the Encuesta Agropecuaria of 2015.

Table B1. Cattle distribution per age class and sex in Bolivia, 2013.

Age Mean Sum

< 1 year 2295.57 778198 [1,2] years 2145.79 727423 Male Cattle [2,3] years 1717.16 582116 > 3 years 1588.96 538658 < 1 year 2618.32 887612 [1,2] years 2635.14 893313 Female Cattle [2,3] years 2847.12 965173 > 3 years 8192.18 2777148 Note: In addition to these categories, the census also presents bueyes o chiñuelero. We did not include it in this table because it accounts for less than 2% of the total cattle in Bolivia. To build our variable value of production we used the age class “> 3 years” and the sex “male”.