Journal of Development Economics 158 (2022) 102934
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Journal of Development Economics
journal homepage: www.elsevier.com/locate/devec
Regular articleAgricultural composition and labor productivityCesar Blanco a,1, Xavier Raurich b,∗,1
a Central Bank of Paraguay, Federacion Rusa 1767, Asuncion, Paraguayb University of Barcelona, Department of Economics, Av. Diagonal 696, 08034 Barcelona, Spain
A R T I C L E I N F O
JEL classification:O11, O13, O41.
Keywords:Structural changeAgricultural compositionLabor productivityCapital intensityCross-country
A B S T R A C T
Labor productivity differences between developing and developed countries are much larger in agriculture thanin non-agriculture. We show that differences in agricultural composition across countries explain a substantialpart of these labor productivity differences. To this end, we group agricultural products into two sectors:capital-intensive and labor-intensive agriculture. As the economy develops and capital accumulates, the priceof labor-intensive agricultural goods relative to capital-intensive agricultural goods increases. This price changedrives a process of structural change that moves land and farmers to the capital-intensive sector, increasinglabor productivity in agriculture. We illustrate this mechanism using a multisector growth model that generatestransitional dynamics consistent with patterns of structural change observed in Brazil and also differences inagricultural composition and labor productivity consistent with cross-country data.1. Introduction
A recent branch of the growth literature claims that a substantialpart of cross-country income differences can be explained by differ-ences in agricultural labor productivity across countries.2 This claimis based on two observations. First, employment in agriculture is largein developing countries. Second, labor productivity differences betweendeveloped and developing countries are much larger in agriculture thanin non-agriculture. In particular, Caselli (2005) finds that agriculturallabor productivity in countries in the 90th percentile of the worldincome distribution is 45 times larger than that of countries in the10th percentile of the distribution. In contrast, non-agricultural laborproductivity is only 4 times larger in advanced countries. This impliesthat agricultural labor productivity relative to non-agricultural laborproductivity increases along the development process.A central issue to understand economic growth is, therefore, toexplain the increase of relative productivity between agriculture andnon-agriculture along the development path. In this paper, we iden-tify a process of substitution of crops associated with development,which we denote as structural change within agriculture, and showthat this process explains a significant fraction of the rise in relativeproductivity. Consequently, we show that crop diversity is a key ele-ment to consider in explaining the relationship between agriculturalproductivity and development.
∗ Corresponding author.E-mail addresses: cblancoa@bcp.gov.py (C. Blanco), xavier.raurich@ub.edu (X. Raurich).1 The two authors have the same contributions and roles in the elaboration of this paper.2 See Cao and Birchenall (2013), Chanda and Dalgaard (2008), Caselli (2005), Gollin et al. (2002, 2014a,b), Restuccia et al. (2008) and Vollrath (2009).3 The increase of capital intensity in agriculture relative to non-agriculture, along the process of economic development, is consistent with evidence provided byChen (2020) and Alvarez-Cuadrado et al. (2017). In particular, Chen (2020) indicates that the capital–output ratio in agriculture is 2.9 times larger in developedcountries than in developing countries, whereas it is only 2.1 times larger in non-agriculture.
We use data from the US Census of Agriculture and the Foodand Agriculture Organization (FAO) to group crops into two differentsectors: a capital-intensive and a labor-intensive agricultural sector.Using this classification of crops, we document two novel facts. First,countries with a high share of land in capital-intensive agriculturehave higher relative productivity. Second, developed countries havemore land allocated to capital-intensive agriculture. These facts sug-gest a relationship between economic development, changes in thecomposition of agriculture and agricultural productivity. We proposethe following mechanism to explain this relationship. As the economydevelops, capital becomes more abundant and less expensive, whichreduces the production cost in the capital-intensive agricultural sec-tor more than in the labor-intensive agricultural sector. As a result,the price of labor-intensive crops relative to capital-intensive cropsincreases. If the two crops are imperfect substitutes in preferences,the consumption and, hence, the production of labor-intensive cropsrelative to capital-intensive crops declines. As a consequence, the com-position of agriculture shifts towards the capital-intensive sector, whichincreases capital intensity in agriculture and, therefore, capital intensityin agriculture increases relative to non-agriculture.3 This contributesto explain the increase in labor productivity in agriculture relativeto labor productivity in non-agriculture. Therefore, according to ourvailable online 13 July 2022
304-3878/© 2022 The Author(s). Published by Elsevier B.V. This is an open access ar
c-nd/4.0/).
https://doi.org/10.1016/j.jdeveco.2022.102934Received 24 March 2020; Received in revised form 29 June 2022; Accepted 4 July
ticle under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-
2022
Journal of Development Economics 158 (2022) 102934C. Blanco and X. Raurich
mechanism, relative labor productivity increases due to changes inthe composition of the agricultural sector that occur along economicdevelopment.We introduce this mechanism in a multisector overlapping gener-ations model, in which a continuum of individuals is born in eachperiod. These individuals have heterogeneous agricultural abilities andhomogeneous ability for non-agricultural work. As in Lucas (1978),individuals with low abilities choose to become workers, whereas in-dividuals with high abilities become entrepreneurs. In our framework,workers are employed in non-agriculture, while entrepreneurs are farm-ers specialized in the production of either labor or capital-intensivecrops. Since technologies exhibit complementarity between ability andcapital, only farmers endowed with high abilities choose to producecapital-intensive crops. Individuals consume both an agricultural anda non-agricultural good. To introduce substitution in consumption be-tween agricultural sectors, we define the agricultural good as a constantelasticity of substitution aggregate of the goods produced in the twoagricultural sectors.In the model, exogenous technological progress causes economicdevelopment and drives two different processes of structural change:between sectors and within agriculture. Structural change betweensectors depends on a minimum consumption requirement in the agri-cultural good. This minimum consumption introduces an income effectthat reduces the number of farmers as the economy grows. The remain-ing farmers have larger farms and higher abilities. This is consistentwith evidence provided by Adamopoulos and Restuccia (2014), whoreport that the average farm size in the poorest 20% of countriesis 34 times smaller than in the richest 20% of countries. It is alsoconsistent with Lagakos and Waugh (2013), who argue that selectionamplifies labor productivity differences between sectors. On the otherhand, structural change within agriculture depends on the elasticityof substitution between the two types of agricultural goods. When itis larger than one, the two types of agricultural goods are imperfectsubstitutes. In this case, as the economy develops and capital becomesmore abundant, the price of labor-intensive crops relative to capital-intensive crops increases, which causes a process of structural changethat turns aggregate agriculture more capital intensive. This increaseslabor productivity in the agricultural sector. This second process ofstructural change and its relation with labor productivity in agricultureare the main contributions of this paper.The model is calibrated to match data from Brazil and we simulatethe dynamic transition. Along the transition, which is driven by ex-ogenous sector-specific technological progress, the economy develops,capital accumulates and this results in the following patterns: (i) areduction in the number of farmers; (ii) an increase in the average farmsize; (iii) a reduction in the fraction of harvested land in the labor-intensive sector; (iv) an increase in the capital intensity of agriculturerelative to non-agriculture; and (v) an increase in the productivity ofagriculture relative to non-agriculture. We show that these develop-ment patterns are consistent with patterns observed in Brazil duringthe period 1960–2018. Moreover, we show that the model accounts for66.2% of the increase in the relative productivity of Brazil, measuredat constant prices, observed during this period.Relative productivity increases due to different mechanisms: (i)sector-specific technological progress that can be faster in agriculture,(ii) the reduction in the number of farmers that increases average farmsize and increases the ability of the average farmer, and (iii) structuralchange within agriculture that increases capital intensity in agriculturerelative to non-agriculture. This third mechanism is the focus of thispaper and to determine its significance we measure the fraction of theincrease in relative productivity that is explained by structural changewithin agriculture. To this end, we simulate a counterfactual economyin which the elasticity of substitution between crops is set equal toone and, hence, there is no structural change within the agriculturalsector and capital intensity in agriculture relative to non-agriculture re-2
mains constant even though the relative price between labor-intensiveagriculture and capital-intensive agriculture increases. From the com-parison between the benchmark and the counterfactual economies, weconclude that structural change within agriculture explains 24.8% ofthe increase in relative productivity observed in Brazil.We also provide cross-country evidence, for a large sample includingdeveloping and developed countries, that supports the patterns ofdevelopment implied by our model. The cross-country data shows apositive correlation between (i) GDP per worker and the fraction ofharvested land in capital-intensive agriculture, and (ii) between thisfraction and relative productivity. We calibrate the model to match thecross-country correlation between GDP per worker and the fraction ofharvested land in capital-intensive agriculture. More precisely, we usethe calibration of Brazil and adjust sectoral TFPs to match cross-countrydifferences in income, land in the capital-intensive sector and alsoemployment in agriculture. We show that the model can generate thesedifferences and can also explain the positive correlation between GDPper worker and relative productivity. In particular, the data shows thatrelative productivity between agriculture and non-agriculture of coun-tries in the top quartile of the world income distribution is 7.05 timeslarger than relative productivity of countries in the bottom quartile. Weshow that the model generates a 6.36-fold gap in relative productivitybetween rich and poor countries and that structural change withinagriculture accounts for 27.5% of this gap.This paper is related to three branches of the literature. First, it isrelated to the structural change literature that introduces income andprice effects to explain changes in the sectoral composition of an econ-omy (see Kongsamut et al., 2001; Ngai and Pissarides, 2007; Acemogluand Guerrieri, 2008). We consider price and income effects to accountfor structural change among broad sectors and within agriculture.Second, it is related to the literature on agricultural productivitydifferences across countries. This literature has considered misallo-cations of production factors (Chen, 2017; Gottlieb and Grobovsek,2019; Hayashi and Prescott, 2008; Restuccia et al., 2008; Restuccia andSantaeulalia-Llopis, 2017), differences in farm sizes (Adamopoulos andRestuccia, 2014), differences in technology (Chen, 2020; Gollin et al.,2007; Manuelli and Seshadri, 2014; Yang and Zhu, 2013), selection(Lagakos and Waugh, 2013), uninsurable risk and incomplete capitalmarkets (Donovan, 2020), and differences in the quality of capital(Caunedo and Keller, 2021). This literature considers an aggregateagricultural sector producing a single commodity. However, agricul-tural products are in fact diverse, they can be produced with differenttechnologies and the consumption composition of these products canchange along economic development. Recent papers examine agricul-tural product diversity. For example, Sotelo (2020) considers a modelof regional specialization, Adamopoulos and Restuccia (2020) studyhow land reforms affect farmers’ decisions between producing cash orfood crops, and Rivera-Padilla (2020) shows that the crop choice isaffected by subsistence requirements and trade costs. We contributeto this literature by studying how crop diversity affects agriculturalproductivity.Third, it is also related to the literature that studies the increase inthe capital intensity of agriculture relative to non-agriculture driven bytechnological change (see Gollin et al., 2007; Alvarez-Cuadrado et al.,2017). In particular, it is closely related to Chen (2020), who links theincrease in both capital intensity and average farm size in agricultureto technology adoption. In Chen (2020), there is a single agriculturalproduct and, as the cost to adopt technology declines, farmers switchto a more capital-intensive technology. This explains the increase ofcapital per worker in agriculture. As in our paper, the increase ofagricultural capital-intensity is behind the increase in relative produc-tivity. Our paper provides a different, but complementary, explanationfor the increase in capital intensity. In our framework, agriculturalcapital-intensity increases, not as consequence of technology adoptionbut because of substitution between different crops. Capital-intensityof agriculture grows because the share of agriculture produced in themore capital-intensive sector expands. This is an important difference
Journal of Development Economics 158 (2022) 102934C. Blanco and X. Raurich
Table 1Capital intensity for main crop categories.Capital/Value added 1978 1982 1992 1997 2002 2012
Oilseed and grain 1.52 1.62 1.62 1.53 1.73 1.43Other crop 1.28 1.19 1.10 1.21 3.92 2.55Vegetable and melon 0.50 0.47 0.48 0.44 0.53 0.58Fruit and tree nut 0.55 0.59 0.49 0.44 0.53 0.44
Note:[1] We use data from the US Census of Agriculture for the following years: 1978, 1982, 1992, 1997, 2002, and 2012. The last three censusesclassify crops according to the North American Industry Classification System (NAICS). The first 3 censuses use the Standard IndustrialClassification System (SIC), however, we reclassify crops in these censuses according to categories in NAICS. We exclude hay, greenhouseand floriculture production, which are not considered in the FAO dataset.[2] Capital intensity is defined as capital over value added. We compute the value added as the market value of crops excluding governmentpayments and expenditures in fertilizers, chemicals, seeds, gasoline, utilities, supplies, maintenance and all other production expenses. Capitalis defined as the value of equipment and machinery.aii
aTable 2Capital intensity by crop.Oilseed and grain farming 0.93 Vegetable and melon farming 0.35Soybean 1.16 Potato 0.41Oilseed (ex soybean) 1.15 Other vegetable and melon 0.34Dry pea and bean 0.95 Fruit and tree nut farming 0.29Wheat 1.16 Orange groves 0.23Corn 0.86 Citrus (ex. orange) groves 0.25Rice 0.66 Noncitrus fruit and tree nut 0.44Other grain 0.93 Apple orchards 0.29Other crop farming 1.44 Grape vineyards 0.24Tobacco 0.73 Strawberry 0.11Cotton 0.89 Berry (except strawberry) 0.53Sugarcane 0.40 Tree nut 0.32All other crop 1.33 Other non-citrus fruit farming 0.44
Note: Data is from the 2012 US Census of Agriculture. This census provides data onproduction and capital at crop-level. For this reason, we compare the ratio betweencapital and production, instead of capital and value added.
that affects not only the model, but also the calibration targets. Inthe technological change literature, the model is calibrated to match atechnological adoption curve or a measure of capital intensity. Instead,we calibrate the model to account for the change in the sectoralcomposition of agriculture observed in the data and documented inthis paper. We see both explanations as complementary, since we couldconsider a single model including substitution between agriculturalgoods and technological adoption within each agricultural sector toaccount for the increase in agricultural capital-intensity.The rest of the paper is organized as follows. Section 2 shows theempirical strategy followed to construct the two agricultural subsectorsand introduces the main facts. Section 3 introduces the model. Section 4characterizes the equilibrium. Section 5 describes the quantitative anal-ysis and shows that the model explains a sizable part of the increase inrelative productivity observed in Brazil and that it also accounts for alarge part of cross-country differences in relative productivity observedin the data. Finally, Section 6 concludes.
2. Agricultural sectors
In this section, we classify crops according to capital intensity. Usingthis classification, we first show that, in a cross-section of countries,using more land in capital-intensive agriculture correlates with capitalintensity in agriculture relative to non-agriculture and with relativeproductivity. We then focus on development patterns of Brazil duringthe period 1960–2018 and show that both the fraction of land incapital-intensive agriculture and relative productivity increase in thiscountry.We use the US Census of Agriculture to obtain the ratio betweencapital and value added by crop, which is a standard measure of capitalintensity. Table 1 shows the value of this ratio for different years inwhich the census is available and for the main crop categories under theNorth American Industry Classification System (NAICS). Although there
3
are some important changes in capital intensity among censuses, a clear cpattern emerges: the first two categories, Oilseed and grain farming andOther crop farming, have a capital intensity, on average, larger than1.5, whereas the last two categories, Vegetable and melon farming andFruit and tree nut farming, have an average capital intensity of 0.5.Therefore, there is a large and persistent gap in the capital intensitiesacross different categories of crops.This gap remains if we consider crops within categories. Table 2shows that capital intensity, defined as the ratio between capital andproduction, of crops in the first two categories is in general largerthan capital intensity of any crop in the last two categories.4 Giventhese findings, we distinguish between two agricultural sectors. Wegroup crops in the first two categories of Table 1 in the capital-intensive agricultural sector, whereas crops in the other two categoriesare grouped in the labor-intensive agricultural sector.5 We assume thatthis classification remains stable through time and across countries.Next, we use the Food and Agriculture Organization (FAO) dataset,that provides crop-level data on production, prices and area harvestedfor a large number of countries. We consider the period 1961–2018.Using the classification of crops obtained from the US Census of Agri-culture, we classify all crops in the FAO dataset in order to constructthe two agricultural sectors. This gives us the value of production, theprice index and the fraction of total harvested land in both capitaland labor-intensive agriculture, for each country and time period. Theclassification of all crops is shown in detail in the supplementaryappendix.In Fig. 1 we show cross-country evidence that supports the mecha-nism in our model. In particular, Panel (a) of Fig. 1 shows a positivecorrelation between the fraction of harvested land in capital-intensiveagriculture and relative capital intensity between agriculture and non-agriculture. Relative capital intensity is defined as capital per workerin agriculture divided by capital per worker in non-agriculture. Wecombine data on capital by sector from Larson et al. (2000) with dataon employment by sector from the Groningen Growth and DevelopmentCentre (GGDC) 10-Sector Database. This results in a sample of 25countries. Although data is limited, we obtain a positive correlation thatis statistically significant. This positive correlation provides supportto our classification of crops: economies with more land in capital-intensive agriculture, according to our classification, are also the oneswith higher capital intensity in agriculture relative to non-agriculture.The mechanism in our model implies that the fraction of har-vested land in capital-intensive agriculture increases as the economydevelops. It also implies that agricultural productivity relative to non-agricultural productivity increases as the fraction of harvested land
4 The US Census of Agriculture provides crop-level data on productionnd capital. Therefore, we compare the ratio between capital and production,nstead of capital and value added, which is the standard measure of capitalntensity.5 Using Table 1, we distinguish between a more capital-intensive sectornd a less capital-intensive sector. In the model of Section 3, the lessapital-intensive sector is also the labor-intensive sector.
Journal of Development Economics 158 (2022) 102934C. Blanco and X. Raurich
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iilbwFig. 1. Cross-country comparisons. Note: [1] This figure shows correlations between: (a) Relative capital intensity between agriculture and non-agriculture and the fraction of landn capital-intensive agriculture (𝐿𝑘∕𝐿), (b) Relative productivity between agriculture and non-agriculture and 𝐿𝑘∕𝐿, (c) GDP per worker and 𝐿𝑘∕𝐿, and (d) Relative productivitybetween agriculture and non-agriculture and GDP per worker. Relative productivity and GDP per worker are PPP-adjusted. [2] Data for relative productivity between agricultureand non-agriculture and GDP per worker is obtained from Restuccia et al. (2008). Relative capital intensity between agriculture and non-agriculture is from Larson et al. (2000)and the GGDC 10-Sector Database. The fraction of land in capital-intensive agriculture is computed from FAO. All data is for year 1985.Fig. 2. Development patterns. Note: [1] Panel (a) shows the increase in the fraction of land in capital-intensive agriculture (𝐿𝑘∕𝐿) and Panel (b) shows the increase in relativeproductivity between agriculture and non-agriculture (𝑌𝑎∕𝑁𝑎)∕(𝑌𝑚∕𝑁𝑚) in 6 developing countries. [2] Data for 𝐿𝑘∕𝐿 is computed from FAO and relative productivity at 2005onstant prices is obtained from the GGDC 10-Sector Database. We include all developing countries for which we have relative productivity data from GGDC 10-Sector Databaseince the 1960s and for which both 𝐿𝑘∕𝐿 and (𝑌𝑎∕𝑁𝑎)∕(𝑌𝑚∕𝑁𝑚) increase. Countries included are: Argentina, Bolivia, Kenya, Brazil, Tanzania, Senegal.
ip(in capital-intensive agriculture increases. Therefore, this mechanismnvolves a positive correlation between: (i) the fraction of harvestedand in capital-intensive agriculture and relative labor productivity; (ii)etween this fraction and GDP per worker; and (iii) between GDP perorker and relative labor productivity. Panels (b), (c) and (d) of Fig. 1
4
pllustrate these three positive correlations, using the cross-country com-arable measure of relative productivity provided by Restuccia et al.2008). These authors provide GDP per worker and labor productivityn each sector, measured at Purchasing Power Parity (PPP) adjustedrices, for a large sample of countries for the year 1985. Using this
Journal of Development Economics 158 (2022) 102934C. Blanco and X. Raurich
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tTable 3Relative productivity across countries.Dependent variable: Relative productivity (1) (2) (3)
Constant −0.0589
(0.0675)
−0.6733
(0.1170)
*** 0.0264
(0.0414)Fraction of land in capital-intensive agriculture 0.2791
(0.0931)
*** – 0.2305
(0.0490)
***Log real GDP per worker – 0.0920
(0.0131)
*** –
Country fixed effects – – YesTime fixed effects – – YesCountries 80 80 37Observations 80 80 1802R2 0.103 0.385 0.388
Note:[1] Standard errors in parenthesis.[2] This table shows that relative productivity (𝑌𝑎∕𝑁𝑎∕𝑌𝑚∕𝑁𝑚) is correlated with thefraction of land in capital-intensive agriculture (𝐿𝑘∕𝐿) and with real GDP per worker(𝑌 ∕𝑁). Regressions in columns (1) and (2) use cross-section data, while the regressionin column (3) uses a panel of 37 countries. Data on relative productivity and real GDPper worker in columns (1) and (2) is from Restuccia et al. (2008) and is PPP-adjusted,the fraction of land in capital-intensive agriculture is constructed from FAO data, andrelative productivity at constant prices in column (3) is from GGDC 10-Sector Database.***Indicates 𝑝-value < 0.01.
Table 4Agricultural composition across countries.Dependent variable: Land in capital-intensive agriculture(1) (2)
Constant 0.3575
(0.1673)
** 0.5170
(0.0216)
***Log real GDP per worker 0.0392
(0.0188)
** 0.0181
(0.0024)
***
Countries 80 82Observations 80 4897R2 0.053 0.012
Note:[1] Standard errors in parenthesis[2] This table shows that the fraction of land in capital-intensive agriculture (𝐿𝑘∕𝐿)s correlated with real GDP per worker (𝑌 ∕𝑁). The regression in column (1) usesross-section data and the one in column (2) uses panel data from 82 countries. Datan the fraction of land in capital-intensive agriculture is constructed from FAO. RealDP per worker in column (1) is from Restuccia et al. (2008) and is PPP-adjusted.eal GDP per capita in columns (2) is from Penn World Table 10.0.*Indicates 𝑝-value < 0.05.**Indicates 𝑝-value < 0.01.
ata, in the first two columns of Table 3 and in the first column ofable 4 we show that the three positive correlations in Panels (b), (c)nd (d) of Fig. 1 are statistically significant.We complement the previous cross-country analysis with two addi-ional linear regressions using panel data. First, we run a regressionetween relative productivity and the fraction of harvested land inapital-intensive crops, using a panel of 37 countries during the period961–2011. Data on relative productivity is from the GGDC 10-Sectoratabase and is not PPP-adjusted; therefore, it is not directly compa-able across countries.6 This justifies the introduction of country andtime fixed effects in the regression. The results from this regression arein the third column of Table 3 and show a positive and statisticallysignificant correlation. Second, in the second column of Table 4, we runa regression between the fraction of land in capital-intensive agricultureand real GDP per capita. This regression includes 82 countries duringthe period 1960–2020. The results from this regression also show apositive and statistically significant correlation.From this evidence, it can be argued that as countries move tohigher income levels, land shifts towards capital-intensive crops, andthis shift involves an increase in relative productivity. Therefore, wefind evidence that supports the mechanism proposed in this paper.
6 We exclude the following 5 countries for which data is unavailable duringhe entire period: Germany, Hong-Kong, Ethiopia, Mauritius and Singapore.5In Fig. 2, we provide time series evidence for selected developingcountries. This figure shows countries that exhibit a process of develop-ment in which both the fraction of land in capital-intensive agricultureand relative productivity increase over time. Among these countries, weselect Brazil to calibrate the model and perform numerical simulations.We choose Brazil because it is a large country with a diversifiedagricultural sector that exhibits the classical patterns of development,including structural change and a large increase in relative productiv-ity. These patterns are documented in Fig. 3 for the period 1960–2018.Panels (a) and (b) of this figure show that Brazil has experiencedtwo important patterns of structural change. First, there is structuralchange across broad sectors, which is measured by the fraction of totalemployment in agriculture. This fraction, obtained from the GGDC 10-Sector Database for 1960–2011 and the GGDC/UNU-WIDER EconomicTransformation Database for 2012–2018, exhibits a major decline dur-ing this period, from 59% to 12%. Second, there is structural changewithin agriculture, which is measured by the fraction of total landin the labor-intensive sector. This fraction also exhibits a pronounceddecline, from 30% to 8.2%.In Panel (c), we report a steep increase in relative capital intensitybetween agriculture and non-agriculture. Data on relative capital inten-sity for Brazil is obtained from the 2012 World Input–Output Databaseand it is available for the period 1995–2009.Panel (d) shows the increase of agricultural productivity relative tonon-agricultural productivity in Brazil from 7.9% in 1960 to 53.8% in2018. This is a considerable increase of 45.9 percentage points. Relativeproductivity is measured at 2015 constant prices and is obtained fromthe GGDC 10-Sector Database for the period 1960–2011 and from theGGDC-UNU/WIDER Economic Transformation database for the period2012–2018. In Section 5.2, we study how much of the increase ob-served in this variable is due to the process of structural change withinagriculture reported in Panel (b).In Fig. 4, we calculate the price index and the value of produc-tion for both agricultural sectors using data from FAO and show thatthe relative price between labor and capital-intensive agriculture ex-hibits a rising trend (despite large fluctuations), whereas the relativevalue of production between these two sectors declines. This evidencesuggests imperfect substitution in consumption between agriculturalgoods, which is a feature implied by the mechanism in our paper. Atthis point, we clarify that production is not measured in value addedterms, hence, it cannot be used to calibrate the model.In the analysis that follows, we assume that the driver of struc-tural change within agriculture is domestic consumption demand. Thesubstitution of consumption from labor to capital-intensive agriculturalproducts changes the composition of agriculture. Cockx et al. (2018),Huang and David (1993), Kearney (2019) and Rae (1998) provideevidence on this substitution. They document that, as economies de-velop, diets shift from traditional staples such as cassava, potatoes,bananas and other starchy foods to consumption of rice, bread, pasta,cereals and prepared foods. This is consistent with our classificationof crops, in which the first group is considered labor-intensive andthe second is considered capital-intensive. In the supplementary ap-pendix, we provide further evidence on this substitution based onfindings in the literature and on data from FAO. An alternative potentialdriver of structural change within agriculture, not considered in ouranalysis, could be exports of agricultural products. However, in thesupplementary appendix, we show that exports are not the main driverof structural change within agriculture in Brazil. Therefore, in thefollowing sections we present a multisector growth model of a closedeconomy and analyze the effect of structural change within agricultureon relative productivity in Brazil.
Journal of Development Economics 158 (2022) 102934C. Blanco and X. Raurich
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𝑁tapFig. 3. Development patterns of Brazil. Note: Panel (a) shows the fraction of employment in agriculture using data from GGDC 10-Sector Database (1960–2011) and GGDC/UNU-WIDER Economic Transformation Database (2012–2018). Panel (b) shows the fraction of land in labor-intensive agriculture during 1961–2018, using data from FAO. Panel (c) showscapital intensity in agriculture relative to non-agriculture using data from the World Input–Output Database 2012, available for 1995–2009. Panel (d) shows agricultural productivityrelative to non-agricultural productivity at 2015 constant prices using data from GGDC 10-Sector Database (1960–2011) and GGDC/UNU-WIDER Economic Transformation Database(2012–2018). All data is for Brazil.Fig. 4. Relative price and value of production in Brazil. Note: [1] This figure shows evidence on crop substitution. Panel (a) shows an increase in the linear trend of the relativeprice. Panel (b) shows a decline in the linear trend of the relative value of production. [2] Data for the relative price of labor-intensive agriculture to capital-intensive agriculture(𝑃𝑛∕𝑃𝑘) and for the relative value of production in labor-intensive agriculture to capital-intensive agriculture (𝑃𝑛𝑌𝑛∕𝑃𝑘𝑌𝑘) are computed from FAO.
sc. The model.1. Individuals
The economy is populated by a continuum of individuals of mass
𝑡. Individuals live for two periods. In the first period, they are young,hey choose the sector of activity, they work and save buying capitalnd land. Therefore, young individuals supply the capital that will be6
roductive next period. We assume that capital and land are perfectubstitute assets and, therefore, the return of land equals the return ofapital, 𝑅𝑡+1. In the second period of life, individuals are old, they donot work and consume the accumulated savings. As in Laitner (2000),individuals consume only when they are old. As a result, young indi-viduals save all their income and, therefore, consumption expendituresof old individuals in period 𝑡 + 1 are given by 𝐸𝑖𝑡+1 = 𝑅𝑡+1𝐼 𝑖𝑡 , where
𝑅𝑡+1 is the return of savings and 𝐼 𝑖𝑡 is the income obtained by youngindividual 𝑖 at period 𝑡.
Journal of Development Economics 158 (2022) 102934C. Blanco and X. Raurich
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𝑎Young individuals are differentiated by their ability in agriculture,which we denote by 𝑎𝑖. In every generation, these abilities follow thesame Pareto distribution with density function 𝑓 (𝑎𝑖) = 𝜆𝜂𝜆 (𝑎𝑖)−(1+𝜆)and cumulative function 𝐹 (𝑎𝑖) = 1−(𝜂∕𝑎𝑖)𝜆, with 𝜂 > 0 and 𝜆 > 1. Thearameter 𝜂 is the minimum ability and 𝜆 determines the shape of theistribution. We assume that all individuals have the same ability foron-farm work.An individual 𝑖 born at period 𝑡 derives utility from consumption inhe second period of his life according to the following non-homothetictility function:
𝑖
𝑡 = 𝜔 ln
(
𝑐𝑖𝑎,𝑡+1 − 𝑐
)
+ (1 − 𝜔) ln 𝑐𝑖𝑚,𝑡+1, (1)
where 𝑐𝑖𝑎,𝑡+1 is the consumption of agricultural goods, 𝑐𝑖𝑚,𝑡+1 is theconsumption of non-agricultural goods, 𝑐 is a subsistence level ofagricultural consumption, and 𝜔 ∈ (0, 1) is the weight of agricul-tural consumption in the utility function. The agricultural good isdefined as the following aggregate of goods produced in the capitaland labor-intensive sectors:
𝑐𝑖𝑎,𝑡+1 =
[
𝜇
(
𝑐𝑖𝑛,𝑡+1
) 𝜀−1
𝜀 + (1 − 𝜇)
(
𝑐𝑖𝑘,𝑡+1
) 𝜀−1
𝜀
] 𝜀
𝜀−1
, (2)
here 𝜇 ∈ (0, 1) is the weight of labor-intensive goods, and 𝜀 > 0 is thelasticity of substitution between the consumption of labor-intensivegricultural goods, 𝑐𝑖𝑛, and capital-intensive agricultural goods, 𝑐𝑖𝑘.Let total consumption expenditure be defined as
𝑖
𝑡+1 = 𝑃𝑛,𝑡+1𝑐
𝑖
𝑛,𝑡+1 + 𝑃𝑘,𝑡+1𝑐
𝑖
𝑘,𝑡+1 + 𝑃𝑚,𝑡+1𝑐
𝑖
𝑚,𝑡+1, (3)here 𝑃𝑛,𝑡+1 is the price of the labor-intensive goods, 𝑃𝑘,𝑡+1 is therice of the capital-intensive goods and 𝑃𝑚,𝑡+1 = 1 for all 𝑡, since theutput of the non-agricultural sector is assumed to be the numeraire.n Appendix A, we obtain the individuals’ consumption demands fromaximizing utility subject to (3).
.2. Technology
We distinguish between three production sectors: two agriculturalectors that produce consumption goods and one non-agricultural sec-or that produces both a consumption good and productive capital.irms in the non-agricultural sector produce combining capital andabor according to the following constant returns to scale productionunction:
𝑚,𝑡 = 𝐴𝑚,𝑡𝐾
𝛼𝑚
𝑚,𝑡𝑁
1−𝛼𝑚
𝑚,𝑡 , (4)here 𝑌𝑚,𝑡 is output in non-agriculture, 𝐴𝑚,𝑡 is total factor productivityTFP) in the non-agricultural sector, 𝐾𝑚,𝑡 is the capital stock employedn this sector, 𝑁𝑚,𝑡 is the total amount of workers employed in thisector and 𝛼𝑚 ∈ (0, 1) is the capital–output elasticity. We assume thatapital completely depreciates after one period. We also assume perfectompetition and, hence, the wage and the rental price of capital satisfy
𝑡 =
(
1 − 𝛼𝑚
)
𝐴𝑚,𝑡𝐾
𝛼𝑚
𝑚,𝑡𝑁
−𝛼𝑚
𝑚,𝑡 , (5)nd
𝑡 = 𝛼𝑚𝐴𝑚,𝑡𝐾
𝛼𝑚−1
𝑚,𝑡 𝑁
1−𝛼𝑚
𝑚,𝑡 . (6)Individuals working in agriculture are the owners of farms. Farmersan produce either labor or capital-intensive crops using the followingechnology:
𝑖
𝑠,𝑡 = 𝐴𝑠,𝑡𝑎
𝑖
(
𝐿𝑖𝑠,𝑡
)𝛽𝑠 (
𝐾 𝑖𝑠,𝑡
)𝛼𝑠
, 𝑠 = {𝑘, 𝑛} ,
here 𝑦𝑖𝑠,𝑡 is the output produced in the agricultural sector 𝑠 by a farmerith ability 𝑎𝑖, 𝐴𝑠,𝑡 is the TFP in sector 𝑠, 𝐿𝑖𝑠,𝑡 and 𝐾 𝑖𝑠,𝑡 are the amount ofand and capital that a farmer with ability 𝑎𝑖 rents, 𝛽𝑠 ∈ (0, 1) measureshe land output elasticity and 𝛼 ∈ 0, 1 measures the capital–output
7
𝑠 ( )lasticity. The subindex 𝑠 equals 𝑛 for labor-intensive agriculture and 𝑘or capital-intensive agriculture. We assume that 𝛼𝑘 > 𝛼𝑛, 𝛽𝑠+𝛼𝑠 < 1 forll 𝑠 and 𝛽𝑘 + 𝛼𝑘 > 𝛽𝑛 + 𝛼𝑛. The first inequality is consistent with sectorbeing capital intensive. The second one implies that both productionunctions exhibit decreasing returns to scale. In what follows, we showhat the third inequality implies that sector 𝑛 is labor intensive.Since the production functions exhibit decreasing returns to scale,armers make positive profits that can be interpreted as the laborncome of the farmer. Profit is given by
𝑖
𝑠,𝑡 = (1 − 𝜏)𝑃𝑠,𝑡𝑦
𝑖
𝑠,𝑡 − 𝑥𝑡𝐿
𝑖
𝑠,𝑡 − 𝑅𝑡𝐾
𝑖
𝑠,𝑡, (7)here 𝑥𝑡 is the rental cost of land and 𝜏 ∈ (0, 1) is a tax on agriculturalroduction. This tax introduces a wedge between the marginal productf capital in agriculture and in non-agriculture, that we use in thealibration to match the level of relative capital intensity between agri-ulture and non-agriculture in Brazil. The farmers’ optimal demands ofand and capital are
𝐿𝑖𝑠,𝑡 =
[(
𝛼𝑠
𝑅𝑡
)𝛼𝑠 ( 𝛽𝑠
𝑥𝑡
)1−𝛼𝑠
(1 − 𝜏)𝑃𝑠,𝑡𝐴𝑠,𝑡𝑎𝑖
] 1
1−𝛽𝑠−𝛼𝑠
, (8)
𝐾 𝑖𝑠,𝑡 =
[(
𝛼𝑠
𝑅𝑡
)1−𝛽𝑠 ( 𝛽𝑠
𝑥𝑡
)𝛽𝑠
(1 − 𝜏)𝑃𝑠,𝑡𝐴𝑠,𝑡𝑎𝑖
] 1
1−𝛽𝑠−𝛼𝑠
, (9)
and the amount produced is
𝑦𝑖𝑠,𝑡 = 𝐴𝑠,𝑡𝑎
𝑖
[(
𝛼𝑠
𝑅𝑡
)𝛼𝑠 ( 𝛽𝑠
𝑥𝑡
)𝛽𝑠 [
(1 − 𝜏)𝑃𝑠,𝑡𝐴𝑠,𝑡𝑎𝑖
]𝛼𝑠+𝛽𝑠] 11−𝛽𝑠−𝛼𝑠 . (10)
Note that the size of a farm, measured by 𝐿𝑖𝑠,𝑡, increases witharmer’s ability, but decreases with the rental cost of land and capital.inally, we replace (8), (9) and (10) in the profit function to obtain
𝑖
𝑠,𝑡
(
𝑎𝑖
)
=
(
1 − 𝛽𝑠 − 𝛼𝑠
)[( 𝛼𝑠
𝑅𝑡
)𝛼𝑠 ( 𝛽𝑠
𝑥𝑡
)𝛽𝑠
(1 − 𝜏)𝑃𝑠,𝑡𝐴𝑠,𝑡𝑎𝑖
] 1
1−𝛽𝑠−𝛼𝑠
. (11)
Using (11), we observe that profits are an increasing function of abil-ities. Using the same equation, it is immediate to show that the as-sumption 𝛽𝑘 + 𝛼𝑘 > 𝛽𝑛 + 𝛼𝑛 implies that the fraction of the after taxalue of production that the farmer obtains as labor income is larger inabor-intensive agriculture.
.3. Individuals’ decisions
Young individuals’ decision regarding the sector of activity dependsn their abilities. To understand this decision, we first obtain the abilityf the two marginal individuals that are indifferent between two sectorsf activity. We denote by 𝑎𝑡 the ability of the first marginal individual,who is indifferent between working in non-agriculture and in labor-intensive agriculture. Therefore, this ability is obtained from solvingthe following equation: 𝜋𝑖𝑛,𝑡 (𝑎𝑡) = (1 − 𝜙)𝑤𝑡, where 𝜙 ∈ (0, 1) is aabor income tax that workers in the non-agricultural sector must pay.his tax introduces a wedge between agricultural and non-agriculturalabor income that we use in the calibration to match the difference inabor productivity between agriculture and non-agriculture, when laborroductivity is measured at current prices. We find that
𝑡 =
(
1
(1 − 𝜏)𝑃𝑛,𝑡𝐴𝑛,𝑡
)(
(1 − 𝜙)𝑤𝑡
1 − 𝛽𝑛 − 𝛼𝑛
)1−𝛽𝑛−𝛼𝑛 ( 𝑥𝑡
𝛽𝑛
)𝛽𝑛 (𝑅𝑡
𝛼𝑛
)𝛼𝑛
. (12)
We denote by 𝑎𝑡 the ability of the second marginal individual,who is indifferent between being a farmer in labor and in capital-intensive agriculture. Therefore, this ability is obtained from solvingthe following equation: 𝜋𝑖𝑛,𝑡 (𝑎𝑡) = 𝜋𝑖𝑘,𝑡 (𝑎𝑡). We obtain
𝑎𝑡 = 𝛹
[(
𝛼𝑛
𝑅𝑡
)𝛼𝑛 ( 𝛽𝑛
𝑥𝑡
)𝛽𝑛
(1 − 𝜏)𝑃𝑛,𝑡𝐴𝑛,𝑡
] 1−𝛽𝑘−𝛼𝑘
𝛽𝑘+𝛼𝑘−𝛽𝑛−𝛼𝑛
[(
𝛼𝑘
)𝛼𝑘 ( 𝛽𝑘 )𝛽𝑘 (1 − 𝜏)𝑃𝑘,𝑡𝐴𝑘,𝑡]
1−𝛽𝑛−𝛼𝑛
𝛽𝑘+𝛼𝑘−𝛽𝑛−𝛼𝑛
, (13)
𝑅𝑡 𝑥𝑡
Journal of Development Economics 158 (2022) 102934C. Blanco and X. Raurich
if
I
odmsdn
sci
itletofatm
4
ea
d
𝐿
wwhere 𝛹 = [(1 − 𝛽𝑛 − 𝛼𝑛) ∕ (1 − 𝛽𝑘 − 𝛼𝑘)](1−𝛽𝑛−𝛼𝑛)(1−𝛽𝑘−𝛼𝑘)∕(𝛽𝑘+𝛼𝑘−𝛽𝑛−𝛼𝑛).The assumption 𝛽𝑛 + 𝛼𝑛 < 𝛽𝑘 + 𝛼𝑘 implies that the profit of capital-ntensive farms as a function of abilities is steeper than the profitunction of labor-intensive farms at 𝑎𝑖 = 𝑎𝑡. Given that individualschoose the sector to maximize their labor income, it follows that wecan only have both types of farms if 𝑎𝑡 > 𝑎𝑡. Therefore, as shownin Fig. 5, individuals with 𝑎𝑖 ∈ [𝜂, 𝑎𝑡] will be workers in the non-agricultural sector, individuals with 𝑎𝑖 ∈ [𝑎𝑡, 𝑎𝑡] will be farmers inthe labor-intensive sector and individuals with 𝑎𝑖 ∈ [𝑎𝑡,∞] will befarmers in the capital-intensive sector. Note that since the distributionof abilities is unbounded, there are always capital-intensive farmers. Incontrast, if 𝑎𝑡 < 𝑎𝑡 then all farmers will produce capital-intensive crops.n our simulations, the condition 𝑎𝑡 > 𝑎𝑡 will always be satisfied alongthe dynamic equilibrium.The abilities of the marginal farmers determine structural changealong economic development. Eq. (12) sets the value of 𝑎𝑡, which deter-mines the number of non-agricultural workers. This number increaseswith the wage and decreases with profits of the labor-intensive sector.In fact, Eq. (12) shows that the number of non-agricultural workersincreases (𝑎𝑡 increases) when the rental cost of land or capital increases,r when either the price or the TFP of the labor-intensive agricultureecline. These changes reduce profits in labor-intensive agriculture,aking it more attractive to become a worker in the non-agriculturalector. Finally, the wage and rental cost of land increase with economicevelopment, which explains the shift of workers from agriculture toon-agriculture.Eq. (13) sets the value of 𝑎𝑡, which determines the fraction of agri-cultural workers in the labor-intensive sector. This fraction increaseswhen profits in labor-intensive agriculture increase and decreases whenprofits in capital-intensive agriculture increase. Eq. (13) shows that thisfraction increases (𝑎𝑡 increases) if the price or the TFP of the labor-intensive sector increase and declines if the price or the TFP of thecapital-intensive sector increase. The fraction also increases with therental cost of capital, 𝑅𝑡. When 𝑅𝑡 increases, profits in capital-intensiveagriculture suffer a larger reduction than in labor-intensive agricultureand, as a result, more individuals prefer to be labor-intensive farmers.The effect of an increase in the rental cost of land, 𝑥𝑡, depends on therelationship between 𝛽𝑘 and 𝛽𝑛. If 𝛽𝑘 > 𝛽𝑛 then the capital-intensiveector is also land-intensive and, as a result, an increase in the rentalost of land reduces to a larger extend profits of this sector, whichncreases the number of labor-intensive farmers.Finally, the assumption 𝛽𝑛 + 𝛼𝑛 < 𝛽𝑘 + 𝛼𝑘 implies that the marginalndividual with ability 𝑎𝑡 satisfies 𝑃𝑛,𝑡𝑦𝑖𝑛,𝑡 (𝑎𝑡) < 𝑃𝑘,𝑡𝑦𝑖𝑘,𝑡 (𝑎𝑡). Thus,here is a productivity gain when the marginal farmer moves from theabor to the capital-intensive sector. This productivity gain is mainlyxplained by the increase in the stock of capital that occurs whenhe farmer chooses to produce capital-intensive crops. The existencef a productivity gain implies that the sectoral composition that resultsrom individuals decisions is not the one that maximizes the value ofgricultural production. In fact, given that 𝛽𝑛 + 𝛼𝑛 < 𝛽𝑘 + 𝛼𝑘, the size ofhe labor-intensive agricultural sector is larger than the size that wouldaximize the value of agricultural production.
. Equilibrium
In this section, we characterize the equilibrium of the model. To thisnd, we first obtain aggregate factor demands, aggregate productionnd aggregate consumption demands for each sector.Using (8) and (9), in Appendix B we obtain the following aggregateemands of land and capital in each agricultural sector:
𝑠,𝑡 = 𝑁𝑡
[(
𝛼𝑠
𝑅𝑡
)𝛼𝑠 ( 𝛽𝑠
𝑥𝑡
)1−𝛼𝑠
(1 − 𝜏)𝑃𝑠,𝑡𝐴𝑠,𝑡
] 1
1−𝛽𝑠−𝛼𝑠
𝛥𝑠,𝑡, (14)
and
𝐾𝑠,𝑡 = 𝑁𝑡
[(
𝛼𝑠
)1−𝛽𝑠 ( 𝛽𝑠)𝛽𝑠 (1 − 𝜏)𝑃𝑠,𝑡𝐴𝑠,𝑡]
1
1−𝛽𝑠−𝛼𝑠
𝛥𝑠,𝑡, (15)
8
𝑅𝑡 𝑥𝑡for 𝑠 = {𝑛, 𝑘}, where 𝛥𝑛,𝑡 and 𝛥𝑘,𝑡, defined in Appendix B, are bothpositive when 𝜆 > 1∕ (1 − 𝛽𝑘 − 𝛼𝑘). This condition is satisfied in thenumerical exercises of Section 5.We use (6) to obtain the demand of capital in the non-agriculturalsector
𝐾𝑚,𝑡 =
(𝛼𝑚𝐴𝑚,𝑡
𝑅𝑡
) 1
1−𝛼𝑚
𝑁𝑚,𝑡, (16)
here the amount of workers in this sector is given by 𝑁𝑚,𝑡 = 𝐹 (𝑎𝑡)
𝑁𝑡 =
(
1 − 𝜂𝜆𝑎−𝜆𝑡
)
𝑁𝑡.In equilibrium, the total amount of agricultural land, 𝐿𝑡, equals thesum of the aggregate demands of land of each sector. Therefore, thefollowing equation is satisfied: 𝐿𝑘,𝑡 + 𝐿𝑛,𝑡 = 𝐿𝑡. Regarding the marketfor capital, young individuals supply the capital that will be productivenext period. In equilibrium, the aggregate supply of capital, 𝐾𝑡, equalsthe sum of the aggregate demands of capital of each sector. Therefore,the following equation is satisfied:
𝐾𝑡 = 𝐾𝑛,𝑡 +𝐾𝑘,𝑡 +𝐾𝑚,𝑡. (17)Next, using (10), in Appendix B we obtain that the aggregateproduction of agricultural goods in each sector is
𝑌𝑠,𝑡 = 𝐴𝑠,𝑡𝑁𝑡
[(
𝛼𝑠
𝑅𝑡
)𝛼𝑠 ( 𝛽𝑠
𝑥𝑡
)𝛽𝑠 [
(1 − 𝜏)𝑃𝑠,𝑡𝐴𝑠,𝑡
]𝛽𝑠+𝛼𝑠] 11−𝛽𝑠−𝛼𝑠 𝛥𝑠,𝑡. (18)
Finally, we obtain aggregate consumption demands, which dependon consumption expenditure. As noted above, young individuals do notconsume and save all their income. Therefore, consumption expendi-ture of an old individual is 𝐸𝑖𝑡+1 = 𝑅𝑡+1𝐼 𝑖𝑡 , where 𝐼 𝑖𝑡 is the incomeobtained by young individual 𝑖 in period 𝑡 that depends on abilityand the sector of activity. Consequently, the consumption expenditureof an old individual that was a non-agricultural worker in period
𝑡 is 𝐸𝑚,𝑖𝑡+1 = 𝑅𝑡+1 [(1 − 𝜙)𝑤𝑡 + 𝑇 𝑖𝑡 ], where 𝑇 𝑖𝑡 is a transfer from thegovernment. The consumption expenditure of an old individual thatwas a labor-intensive farmer is 𝐸𝑛,𝑖𝑡+1 = 𝑅𝑡+1 [𝜋𝑖𝑛,𝑡 (𝑎𝑖) + 𝑇 𝑖𝑡 ]. Similarly,the consumption expenditure of an old individual that was a capital-intensive farmer is 𝐸𝑘,𝑖𝑡+1 = 𝑅𝑡+1 [𝜋𝑖𝑘,𝑡 (𝑎𝑖) + 𝑇 𝑖𝑡 ]. Aggregate consumptionexpenditure is then given by
𝐸𝑡+1 = 𝑁𝑡
(
∫
𝑎𝑡
𝜂
𝐸𝑚,𝑖𝑡+1𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖 + ∫
𝑎𝑡
𝑎𝑡
𝐸𝑛,𝑖𝑡+1𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖
+ ∫
∞
𝑎𝑡
𝐸𝑘,𝑖𝑡+1𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖
)
. (19)
We assume that tax revenues are returned to individuals as atransfer and that the government budget constraint is balanced ineach period. Using the balanced government budget constraint and(19), in Appendix C we obtain the following equation for aggregateconsumption expenditure:
𝐸𝑡+1 = 𝑅𝑡+1
{(
1 − 𝛼𝑚
)
𝑌𝑚,𝑡 +
[
1 − (1 − 𝜏)
(
𝛼𝑛 + 𝛽𝑛
)]
𝑃𝑛,𝑡𝑌𝑛,𝑡
+
[
1 − (1 − 𝜏)
(
𝛼𝑘 + 𝛽𝑘
)]
𝑃𝑘,𝑡𝑌𝑘,𝑡
}
. (20)
Given that the utility function in the model belongs to the classof Gorman preferences, the aggregate demand of the different con-sumption goods does not depend on the distribution of consumptionexpenditures, but on aggregate consumption expenditure only. Usingthe individuals’ consumption demands obtained in Appendix A, we ob-tain the aggregate consumption demands of labor and capital-intensiveagricultural goods and of non-agricultural goods that, respectively, aregiven by
𝐶𝑛,𝑡+1 = 𝜔𝜇𝜀
(𝑃𝑛,𝑡+1
𝑃𝑎,𝑡+1
)1−𝜀 𝐸𝑡+1
𝑃𝑛,𝑡+1
+ (1 − 𝜔)𝜇𝜀
(𝑃𝑎,𝑡+1
𝑃𝑛,𝑡+1
)𝜀
𝑐𝑁𝑡, (21)
𝐶𝑘,𝑡+1 = 𝜔 (1 − 𝜇)𝜀
(𝑃𝑘,𝑡+1
𝑃𝑎,𝑡+1
)1−𝜀 𝐸𝑡+1
𝑃𝑘,𝑡+1
+ (1 − 𝜔) (1 − 𝜇)𝜀
(𝑃𝑎,𝑡+1
𝑃𝑘,𝑡+1
)𝜀
𝑐𝑁𝑡,(22)
Journal of Development Economics 158 (2022) 102934C. Blanco and X. RaurichFig. 5. Income profile of individuals. Note: This figure shows that the profits of farmersare increasing in abilities. It also shows that for farmers with 𝑎𝑖 ∈ [𝜂, a𝑡] the non-agricultural wage is larger than profits in agriculture, for 𝑎𝑖 ∈ [a𝑡 , a𝑡] profits are largerin labor-intensive agriculture, and for 𝑎𝑖 ∈ [a𝑡 ,∞] profits are larger in capital-intensiveagriculture.
𝐶𝑚,𝑡+1 = (1 − 𝜔)𝐸𝑡+1 − (1 − 𝜔)𝑃𝑎,𝑡+1𝑐𝑁𝑡, (23)where 𝑃𝑎,𝑡+1 is the price of the agricultural good. In Appendix A, it isshown to be equal to
𝑃𝑎,𝑡+1 =
[
𝜇𝜀𝑃 1−𝜀𝑛,𝑡+1 + (1 − 𝜇)
𝜀 𝑃 1−𝜀𝑘,𝑡+1
] 1
1−𝜀 . (24)
Definition 1. Given an initial level of capital, 𝐾0, and a path of{
𝐴𝑚,𝑡, 𝐴𝑘,𝑡, 𝐴𝑛,𝑡, 𝑁𝑡, 𝐿𝑡
}∞
𝑡=0, an equilibrium in this economy is a pathof ability thresholds {𝑎𝑡, 𝑎𝑡}∞𝑡=0 that satisfies (12) and (13), a path ofaggregate demands of land {𝐿𝑛,𝑡, 𝐿𝑘,𝑡}∞𝑡=0 that satisfies (14), a path ofaggregate demands of capital {𝐾𝑛,𝑡, 𝐾𝑘,𝑡, 𝐾𝑚,𝑡}∞𝑡=0 that satisfies (15) and(16), a path of aggregate consumption demands {𝐶𝑛,𝑡, 𝐶𝑘,𝑡, 𝐶𝑚,𝑡}∞𝑡=0 thatsatisfies (21), (22) and (23), a path of sectoral outputs {𝑌𝑛,𝑡, 𝑌𝑘,𝑡, 𝑌𝑚,𝑡}∞𝑡=0that satisfies (4) and (18), a path of aggregate consumption expenditureand capital {𝐸𝑡, 𝐾𝑡}∞𝑡=0 that satisfies (17) and (20), and a path of prices{
𝑃𝑎,𝑡, 𝑅𝑡, 𝑃𝑛,𝑡, 𝑃𝑘,𝑡, 𝑥𝑡
}∞
𝑡=0 that satisfies (24), and market clearing condi-tions for labor-intensive agriculture, 𝐶𝑛,𝑡 = 𝑌𝑛,𝑡, for capital-intensiveagriculture, 𝐶𝑘,𝑡 = 𝑌𝑘,𝑡, for non-agricultural products, 𝑌𝑚,𝑡 = 𝐶𝑚,𝑡 +𝐾𝑡+1,and for land holdings 𝐿𝑡 = 𝐿𝑛,𝑡 + 𝐿𝑘,𝑡.At this point, we discuss some remarks on the equilibrium. First,capital is obtained from the market clearing condition in the non-agricultural sector and, since capital fully depreciates after one period,it is equal to 𝐾𝑡+1 = 𝑌𝑚,𝑡 − 𝐶𝑚,𝑡.Second, since capital and land are perfectly substitute assets, theprice of land is not required in the definition of equilibrium. In fact,this price is obtained from arbitrage. To see this, we define the price ofland as 𝑃𝑡. Since the income of young individuals is used to purchaseland and capital, aggregate income of the young is equal to 𝑃𝑡𝐿𝑡+𝐾𝑡+1.The old consume the return from these assets. Therefore, aggregateconsumption expenditures can be written as 𝐸𝑡+1 = (𝑃𝑡+1 + 𝑥𝑡+1)𝐿𝑡 +
𝑅𝑡+1𝐾𝑡+1. Non-arbitrage between the two assets implies equal return inperiod 𝑡 + 1, that is 𝑅𝑡+1 = (𝑃𝑡+1 + 𝑥𝑡+1) ∕𝑃𝑡. Using this condition andthe aggregate consumption expenditure equation, we obtain the priceof land as 𝑃𝑡 = (𝐸𝑡+1∕𝑅𝑡+1 −𝐾𝑡+1)∕𝐿𝑡.Third, the novelty in this paper is the process of structural changewithin agriculture. Therefore, it is important to clarify what drives thisprocess in equilibrium. To this end, we combine Eqs. (21) and (22) withthe market clearing conditions for labor and capital-intensive agricul-ture to obtain the sectoral composition of agricultural production
𝑃𝑛,𝑡𝑌𝑛,𝑡 =
(
𝜇
)𝜀 (𝑃𝑛,𝑡 )1−𝜀 .
9
𝑃𝑘,𝑡𝑌𝑘,𝑡 1 − 𝜇 𝑃𝑘,𝑡Combining the equation above with expressions (14), (15) and (18), weobtain the sectoral composition of both land and capital in agriculture,which are, respectively:
𝐿𝑛,𝑡
𝐿𝑘,𝑡
=
𝛽𝑛
𝛽𝑘
(
𝜇
1 − 𝜇
)𝜀 (𝑃𝑛,𝑡
𝑃𝑘,𝑡
)1−𝜀
, (25)
𝐾𝑛,𝑡
𝐾𝑘,𝑡
=
𝛼𝑛
𝛼𝑘
(
𝜇
1 − 𝜇
)𝜀 (𝑃𝑛,𝑡
𝑃𝑘,𝑡
)1−𝜀
.
Finally, in the supplementary appendix, we obtain that the fraction offarmers in capital-intensive agriculture, 𝑛𝑘, is
𝑛𝑘 =
[
1 +
(
𝜇
1 − 𝜇
)𝜀 (𝑃𝑛,𝑡
𝑃𝑘,𝑡
)1−𝜀( 𝜆 (1 − 𝛽𝑛 − 𝛼𝑛) − 1
𝜆
(
1 − 𝛽𝑘 − 𝛼𝑘
)
− 1
)] 𝜆(1−𝛽𝑛−𝛼𝑛)
1−𝜆(1−𝛽𝑛−𝛼𝑛)
.
These equations show that the sectoral composition of agriculturedepends on the term (𝑃𝑛,𝑡∕𝑃𝑘,𝑡)1−𝜀. If this term decreases, then thevalue of production, capital and land shift towards the capital-intensiveagricultural sector and the fraction of farmers in capital-intensive agri-culture increases. The value of the elasticity of substitution betweenthe agricultural goods, 𝜀, is crucial. In fact, when 𝜀 = 1, sectoralcomposition within agriculture remains constant even under the pres-ence of biased technological progress. Therefore, if 𝜀 = 1, there is noreallocation of production factors towards capital-intensive agriculture.Finally, when population, land and the sectoral TFPs converge to aconstant value, the long run equilibrium is a steady state in which thesectoral composition and the variables characterizing the equilibriumare constant. In the numerical analysis of the following section, westudy the process of structural change along the transition to this steadystate.
5. Quantitative analysis
The goal of this section is to quantify the effect of structural changewithin agriculture on relative productivity. We perform two differentanalyzes. First, we quantify this effect for Brazil during the period1960–2018. In Section 5.1, we calibrate the model assuming that theequilibrium is in a transition driven by permanent shocks in sectoralTFPs, and by the increase in the amount of land and in the total numberof workers in the economy. In Section 5.2, we show that along thistransition the productivity of agriculture relative to non-agricultureincreases. We quantify the effect of structural change within agricultureby comparing the calibrated economy with a counterfactual economy inwhich the elasticity of substitution between the two agricultural goodsis unitary and, as a consequence, there is no structural change withinagriculture.Second, in Section 5.3 we quantify the effect of agricultural com-position on relative productivity in a cross-section of economies. In thesimulation, we assume that these economies are in the steady state.We also assume that all cross-country differences are generated bydifferences in sectoral TFPs, which are calibrated to match observeddifferences in GDP per worker, in the fraction of workers in agriculture,and in the fraction of land used in capital-intensive agriculture. Weshow that the model generates cross-country differences in sectoralproductivities that are consistent with observed data. Finally, we com-pare these results with those of a counterfactual economy in whichthe elasticity of substitution between agricultural goods equals one toquantify the effect of differences in agricultural composition on relativeproductivity.
5.1. Calibration
We distinguish between two sets of parameters. The first set consistsof capital and land–output elasticities in each sector that are calibratedusing data for the US. The remaining parameters are calibrated usingdata for Brazil. In particular, we match the process of structural change,both between broad sectors and within agriculture, observed in this
Journal of Development Economics 158 (2022) 102934C. Blanco and X. Raurich
afi(
auTable 5Calibration.Parameter Value Target Data
Technology
𝛼𝑚 0.33 Capital income share in non-agriculturea 0.33
𝛽𝑛 0.03 Relative land–output ratio between the two agricultural sectorsb 0.15
𝛽𝑘 0.22 Land income share in agriculturea 0.18
𝛼𝑘 0.42 Relative capital–output ratio between the two agricultural sectorsb 0.313
𝛼𝑛 0.13 Capital income share in agriculturea 0.36Preferences
𝑐 0.04682 Employment share in agriculture in Brazil in 1960c 59%
𝜔 0.0146 Employment share in agriculture in Brazil in 2018d 12%
𝜇 0.5255 Fraction of land in labor-intensive agriculture in Brazil in 1961e 30%
𝜀 12.9 Fraction of land in labor-intensive agriculture in Brazil in 2018e 8.2%Abilities
𝜆 8.3 Fraction of farms smaller than 10 ha. in Brazil in 1960f 44.8%
𝜂 1 Normalization -.-Taxes
𝜏 0.32 Relative cap. intensity btw. agr. and non-agr. in Brazil, avg. 1995–2009g 0.545
𝜙 0.832 Relative nom. prod. btw. agr. and non-agr. in Brazil, avg. 2000–2018d 35.2%Exogenous processes
𝐴𝑚,1960 1 Normalization. -.-
𝐴𝑛,1960 0.1912 Price of agriculture relative to non-agriculture in 1965 1
𝐴𝑘,1960 0.2734 Relative real. prod. btw. agr. and non-agr. in Brazil in 1960 c 7.9%
𝐴𝑚,2020 1.38 Annual growth of GDP per worker between 1960–2018h 1.7%
𝐴𝑛,2020 0.6883 Relative price of agriculture relative to non-agriculture in 2019i 0.327
𝐴𝑘,2020 1.5855 Fraction of farms smaller than 10 ha. in Brazil in 2017f 50.1%
𝑁1960 1 Normalization -.-
𝑁2020 4.01 Increase in the number of workers in Brazil between 1960 and 2018h 4.01
𝐿1960 5.074 Average farm size in Brazil in 1960 (hectares)f 8.6
𝐿2020 5.9 Average farm size in Brazil in 2017 (hectares)f 12.5Note:[1] The model is calibrated to fit the values in the data exactly.[2] Relative productivity in agriculture and non-agriculture is measured at 2015 constant prices. Relative land–output (capital–output) between the two agricultural sectors island–output (capital–output) ratio in labor-intensive agriculture divided by the same ratio in capital-intensive agriculture. Relative capital intensity is the ratio between capitalintensity in agriculture and in non-agriculture.[3] All exogenous processes increase gradually from 1960 to 2020 and remain constant after year 2020.Source:aValentinyi and Herrendorf (2008).b2012 US Census of Agriculture.cGGDC 10-Sector Database.dGGDC/UNU-WIDER Economic Transformation Database.eCalculated from FAO.fIBGE, Agricultural Census of Brazil for 1960 and 2017.gWorld Input–Output Database 2012.hPenn World Table 10.0.iCalculated from World Development Indicators.ow
iwtcountry during the period 1960–2018. We also match the change inthe distribution of farm sizes, the growth of real GDP per worker, andthe decline of prices in agriculture observed during this period. Thecalibration matches all the targets in the data, specified below, exactly.The parameter values and the targets of the calibration are summarizedin Table 5. The calibration strategy is as follows.First, we assume that capital and land–output elasticities for Brazilre the same as for the US and, hence, we set their values using dataor the US. The value of 𝛼𝑚 is obtained from the capital income sharen the non-agricultural sector as reported by Valentinyi and Herrendorf2008). The technological parameters of the agricultural sector, 𝛼𝑛, 𝛼𝑘,
𝛽𝑛 and 𝛽𝑘, are set jointly to match the following four targets of the USeconomy: (i) capital–output ratio of labor-intensive agriculture relativeto capital–output ratio of capital-intensive agriculture, which gives us
𝛼𝑛∕𝛼𝑘 = 0.313; (ii) land–output ratio of labor-intensive agriculture rel-tive to land–output ratio of capital-intensive agriculture, which givess 𝛽𝑛∕𝛽𝑘 = 0.15; (iii) capital income share in agriculture, which givesus (𝛼𝑛𝑃𝑛𝑌𝑛 + 𝛼𝑘𝑃𝑘𝑌𝑘) ∕ (𝑃𝑘𝑌𝑘 + 𝑃𝑛𝑌𝑛) = 0.36; and (iv) land income sharein agriculture, which gives us (𝛽𝑛𝑃𝑛𝑌𝑛 + 𝛽𝑘𝑃𝑘𝑌𝑘) ∕ (𝑃𝑘𝑌𝑘 + 𝑃𝑛𝑌𝑛) = 0.18.The capital–output ratio and the land–output ratio of the two agricul-tural sectors are obtained from the US Census of Agriculture in 2012,while capital and land income shares in agriculture are obtained from10
Valentinyi and Herrendorf (2008).Second, preference parameters 𝜇 and 𝜀 are set to match the fractionf harvested land in labor-intensive agriculture in 1961 and 2018,hile preference parameters 𝑐 and 𝜔 are set to match the values ofthe share of employment in agriculture in 1960 and 2018. Therefore,preference parameters are jointly calibrated to explain the process ofstructural change in Brazil. Note that the calibrated value of 𝜀 is largerthan one, which implies that the two agricultural sectors are imperfectsubstitutes.Third, sectoral TFPs are assumed to grow at a constant rate duringthe period 1960–2020 and remain at a constant value after that. Table 5reports the values of sectoral TFPs in 1960 and 2020. The initial valueof TFP in labor-intensive agriculture, 𝐴𝑛,𝑡, is set to match the value ofthe agricultural price index in 1965, whereas the initial value of TFPin capital-intensive agriculture, 𝐴𝑘,𝑡, is set such that productivity inagriculture relative to non-agriculture in 1960, measured at constantprices, is 7.9%.7 The initial value of the sectoral TFP in non-agriculture,
𝐴𝑚,𝑡, is normalized to 1. We set the path of 𝐴𝑛,𝑡 to match the declinen the price index of agriculture observed in Brazil during 1965–2019,hich is obtained from the World Development Indicators database ofhe World Bank. The path of 𝐴𝑚,𝑡 is set to match the growth rate of real
7 The base year in the data is 2015 and in the simulation is 2020.
Journal of Development Economics 158 (2022) 102934C. Blanco and X. Raurich
t
i1
in
inbtariio
frac
ei
5
tap
bddaip
ll1 tGDP per worker observed in Brazil during 1960–2018 of 1.7%, obtainedusing data from the Penn World Table 10.0. As explained below, we setthe path of 𝐴𝑘,𝑡 to match the farm size distribution in Brazil.Fourth, we set jointly the parameter 𝜆 of the Pareto distribution,he path of 𝐴𝑘,𝑡, and the path of agricultural land, 𝐿𝑡, to match thechange in the distribution of farm sizes observed in Brazil between1960 and 2017. More specifically, we match (i) the 1.45-fold increasein average farm size from 8.6 hectares in 1960 to 12.5 hectares in2017, and (ii) the percentage of small farms in agriculture in both1960 and 2017 which are, respectively, 44.8% and 50.1%. We computeaverage farm sizes using data from the IBGE Agricultural Census ofBrazil for years 1960, 1970, 1975, 1980, 1985, 1996, 2006, and 2017.A small farm is defined as a farm with less than 10 hectares. Tocalculate averages, we consider only cultivated land, which includesland in permanent and temporal crops. We exclude land used for otherpurposes or non-cultivated land.8Fifth, the number of workers, 𝑁𝑡, is set to match the 4.01-foldncrease in the number of persons engaged in Brazil during the period960–2018, as reported in the Penn World Table 10.0.Sixth, the tax 𝜏 is set to match, jointly with the sectoral factorncome shares, the relative capital intensity between agriculture andon-agriculture, which is given by
𝑅𝑡
(
𝐾𝑘,𝑡 +𝐾𝑛,𝑡
)
𝑃𝑘,𝑡𝑌𝑘,𝑡 + 𝑃𝑛,𝑡𝑌𝑛,𝑡
⟋𝑅𝑡𝐾𝑚,𝑡
𝑌𝑚,𝑡
= (1 − 𝜏)
(
𝛼𝑘
𝛼𝑚
𝑃𝑘,𝑡𝑌𝑘,𝑡
𝑃𝑘,𝑡𝑌𝑘,𝑡 + 𝑃𝑛,𝑡𝑌𝑛,𝑡
+
𝛼𝑛
𝛼𝑚
𝑃𝑛,𝑡𝑌𝑛,𝑡
𝑃𝑘,𝑡𝑌𝑘,𝑡 + 𝑃𝑛,𝑡𝑌𝑛,𝑡
)
. (26)
Since the sectoral factor income shares are set using data for the US,we must set 𝜏 = 0.32 to match the average value of relative capitalintensity in Brazil during the period 1995–2009. Note that 𝜏, calibratedn this way, reduces relative capital intensity between agriculture andon-agriculture. If 𝜏 = 0, the value of relative capital intensity woulde close to the US level, which is much larger than in Brazil. However,his parameter has no effect on relative capital intensity between labornd capital-intensive agriculture, which is determined by 𝛼𝑛∕𝛼𝑘. Thiselative capital intensity remains constant at the level of the US. Thiss a caveat of our calibration, since the value of this relative capitalntensity influences the effect of structural change within agriculturen relative productivity.Finally, using data from the GGDC/UNU-WIDER Economic Trans-ormation Database, we obtain that the average value during the pe-iod 2000–2018 of relative productivity between agriculture and non-griculture in Brazil is 35%, when productivities are measured aturrent prices. We set the tax 𝜙 to match this value.In the following subsection, we use this calibration to measure theffect of structural change within agriculture on relative productivityn Brazil.
.2. Structural change and labor productivity
Fig. 6 compares the time path of the main variables implied byhe simulation of the calibrated economy with actual data. Taking intoccount that each period is 20 years, the simulation is reported for theeriod 1960–2020 and matches the data for Brazil during 1960–2018.The first two panels in Fig. 6 show the process of structural changeetween broad sectors and within agriculture. Panel (a) shows theecline in the fraction of employment in agriculture. In the model, thisecline is mainly driven by income growth and an income effect due tominimum requirement of agricultural consumption. The model is cal-brated to match the fall in agricultural employment of 47 percentageoints.
8 In Brazil, there are large differences between cultivated and totaland. The latter also includes forestry, pastures and other land such asakes, degraded land, idle land, and land unsuitable for exploitation. During960–2018, cultivated land grew faster than total land.11
eIn Panel (b), we show the process of structural change withinagriculture in terms of land shares.9 Although the simulation is unableto explain the large drop of the fraction of land in labor-intensiveagriculture during the sixties and early seventies, it matches the re-duction of 21.8 percentage points observed during the entire period.This process of structural change is driven by the change in the rela-tive price between the two agricultural sectors. The accumulation ofcapital, associated with economic development, benefits the capital-intensive agricultural sector more and, as a consequence, the price oflabor-intensive crops relative to capital-intensive crops increases. Thisrelative price increase generates a process of structural change fromlabor to capital-intensive agriculture when these sectors are imperfectsubstitutes; that is, when the elasticity of substitution is larger than one.In fact, to match the observed change in land shares, the calibratedvalue of the elasticity is greater than one.As shown in Panel (c), data on capital intensity in agriculturerelative to non-agriculture is available for the period 1995–2009. Al-though the data spans for only 14 years, it shows a clearly increasingpath. In the simulation, while the average value of relative capitalintensity is targeted, the increase in relative capital intensity is not.This increase is entirely driven by structural change within agriculture.Too see this, we can use Eq. (26), where relative capital intensitybetween agriculture and non-agriculture is expressed as the weightedaverage of relative capital intensities between each agricultural sectorand non-agriculture, with weights being the fraction of value addedin each agricultural sector. Given that technologies are Cobb–Douglas,the relative capital intensity between each agricultural sector and non-agriculture are constant and equal to 𝛼𝑘∕𝛼𝑚 and 𝛼𝑛∕𝛼𝑚. Therefore, theincrease in the capital intensity of aggregate agriculture relative tonon-agriculture is driven entirely by the increase in the fraction ofagricultural value added generated in the capital-intensive sector.Notice that the novelty of our calibration is to use 𝜇 and 𝜀 tomatch changes in the sectoral composition in agriculture. Instead, thetechnological change literature, and Chen (2020) in particular, utilizestechnological parameters to match a technological adoption curve. InChen (2020), there is a single agricultural product and the share offarmers producing with the more capital-intensive technology increasesas the technology becomes less expensive. Our contribution to thisliterature is to relate the rise in capital intensity to observed changesin the composition of the agricultural sector.The average farm size increases as a result of the reduction inagricultural employment and the increase in cultivated land. This isshown in Panel (d), where we decompose the average farm size inaverage size of small and large farms. As we can observe, the rise inaverage farm size is driven by the rise in average size of large farms.As before, small farms are defined as those with less than 10 hectares.In the data, the average size of small farms slightly declines, while theaverage size of large farms shows a 1.86-fold increase between 1960and 2017. The simulation matches these very different patterns and,in particular, explains the considerable increase in the average sizeof large farms. Notice that we target the average farm size, not theaverage farm size of small and large farms. In the simulation of thecalibrated economy, the average size of large farms increases becausethis segment of farms includes all capital-intensive farms, which are theones benefiting the most from economic development in Brazil.In panel (e), we show the relative price of agriculture, whichis a target of our calibration. The data shows a clearly decreasingtrend, despite large initial fluctuations. The simulation matches thereduction in this relative price. In the calibrated economy, this declineresults from an increase in the productivity of agriculture relative tonon-agriculture.
9 The process of structural change within agriculture could also be illus-rated in terms of the fraction of farmers or the fraction of value added inach agricultural sector. We use land shares due to data availability.
Journal of Development Economics 158 (2022) 102934C. Blanco and X. Raurich
m[TD1pp
di7dtoiftiaaiFig. 6. Quantitative results. Note: [1] This figure compares the results of the benchmark simulation with the data for Brazil. Continuous lines indicate data, dashed lines indicateodel simulation. In Panel (d) lines with crosses show average size of large farms, triangles show average farm size of all farms, and circles show average size of small farms.2] The fraction of employment in agriculture is obtained from GGDC 10-Sector Database (1960–2011) and GGDC/UNU-WIDER Economic Transformation Database (2012–2018).he fraction of land in labor-intensive agriculture is computed from FAO. Capital intensity in agriculture relative to non-agriculture is obtained from the World Input–Outputatabase 2012. The average farm size and the average size of small and large farms is elaborated from the IBGE Agricultural Census of Brazil for years 1960, 1970, 1975, 1980,985, 1996, 2006, and 2017. To compute averages we consider only cultivated farmland, which includes land in permanent and temporal crops. We exclude land used for otherurposes or non-cultivated. The price of agriculture relative to non-agriculture is calculated from World Development Indicators. Agricultural productivity relative to non-agriculturalroductivity at 2015 constant prices is obtained from GGDC 10-Sector Database (1960–2011) and GGDC/UNU-WIDER Economic Transformation Database (2012–2018).
Panel (f) in Fig. 6 shows the increase of agricultural labor pro-uctivity relative to non-agricultural labor productivity. Note that thencrease of this ratio is not a target of the calibration. It increases from.9% to 53.8% in the data and from 7.9% to 38.3% in the simulation,uring the period 1960–2018. Therefore, our model explains 66.2% ofhe observed increase in relative productivity. This increase is the resultf the combination of different mechanisms: an increase in TFP thats larger in the agricultural sectors, selection, the increase in averagearm size and the increase of agricultural capital intensity relativeo non-agricultural capital intensity. On the one hand, the reductionn the number of farmers implies that the farmers who remain ingriculture have higher abilities and manage more land. As in Lagakosnd Waugh (2013) and Adamopoulos and Restuccia (2014) both effectsncrease productivity in agriculture. On the other hand, the increase in12productivity is also explained by the increase in capital intensity that, inour model, results entirely from the process of structural change withinagriculture. In the following subsection, we measure the importance ofthis mechanism.
5.2.1. The role of structural change within agricultureTo measure the effect of structural change within agriculture onrelative productivity, in Fig. 7 we compare the calibrated economy witha counterfactual economy in which the elasticity of substitution is setto one. In the counterfactual, we set 𝑐 = 0.0533 and 𝜇 = 0.761 to matchthe initial sectoral composition, given by the fraction of employmentin agriculture (59%) and by the fraction of harvested land in labor-
𝑐 and 𝜇 are set sointensive agriculture (30%). Therefore, the parameters
Journal of Development Economics 158 (2022) 102934C. Blanco and X. RaurichFig. 7. Counterfactual simulation. Note: This figure compares the results of the counterfactual simulation with the benchmark simulation and the data for Brazil. Continuous linesindicate data, dashed lines indicate model simulation, and dotted lines indicate counterfactual simulation. In Panel (d) lines with crosses show average size of large farms, trianglesshow average farm size of all farms, and circles show average size of small farms. Data sources are the same as in Fig. 6.
that the two economies are initially identical, with the same initial sec-toral composition, relative capital intensity and farm size distribution,and all differences along the transition are due to different processes ofstructural change that result from different elasticities of substitution.More precisely, in both economies, the price of labor-intensive cropsrelative to capital-intensive crops increases. However, as shown in (25),while the relative price increase reduces the fraction of harvested landin labor-intensive agriculture under imperfect substitution, it has noeffect on sectoral composition when the elasticity of substitution isequal to one. These different patterns are illustrated in Panel (b) ofFig. 7.The process of structural change within agriculture determines thedynamics of relative capital intensity in Panel (c). It remains constantin the absence of structural change within agriculture and it increasesin the benchmark economy as farmers move to the capital-intensivesector. Obviously, these different dynamics of capital intensity affectagricultural labor productivity negatively in the counterfactual econ-13
omy. As a consequence, the reduction in the number of farmers andthe increase in the average farm size are limited in the counterfactualeconomy, as shown in Panels (a) and (d) of Fig. 7. Note also thatthe counterfactual economy generates only a small increase in theaverage size of large farms and does not explain the reduction in theaverage size of small farms. The failure of the counterfactual economyto explain the change in the distribution of farms is a consequence ofthe absence of structural change within agriculture.Since average farm size and relative capital intensity are negativelyaffected by the absence of structural change in the counterfactualeconomy, the increase in relative productivity is smaller than in thebenchmark economy. In fact, relative productivity in the counterfactualeconomy increases from 7.9% to 26.9% only. This counterfactual econ-omy without structural change explains only 41.4% of the observedincrease in relative productivity in the data. Since the benchmarkeconomy explains 66.2%, we conclude that structural change in theagricultural sector accounts for 24.8% of the observed increase inrelative productivity of Brazil during the period 1960–2018.
Journal of Development Economics 158 (2022) 102934C. Blanco and X. Raurich
arii
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uTable 6Cross-country quantitative results.Targeted moments Non-targeted moments
𝑌 ∕𝑁 𝐿𝑘∕𝐿 𝑁𝑎∕𝑁 𝑌𝑎∕𝑁𝑎 𝑌𝑚∕𝑁𝑚
𝑌𝑎∕𝑁𝑎
𝑌𝑚∕𝑁𝑚Data 16.0 0.83/0.67 0.06/0.82 27.3 3.87 7.05Benchmark 16.0 0.83/0.67 0.06/0.82 22.9 3.61 6.36Counterfactual 13.1 0.67/0.67 0.26/0.82 15.9 3.59 4.42
Note:[1] Data on GDP per worker (𝑌 ∕𝑁), labor productivity in agriculture (𝑌𝑎∕𝑁𝑎), laborproductivity in non-agriculture (𝑌𝑚∕𝑁𝑚) and agricultural productivity relative to non-agricultural productivity (𝑌𝑎∕𝑁𝑎∕𝑌𝑚∕𝑁𝑚) is obtained from Restuccia et al. (2008) andis PPP-adjusted. Data on agricultural employment (𝑁𝑎∕𝑁) is obtained from Restucciaet al. (2008) and the fraction of land in capital-intensive agriculture (𝐿𝑘∕𝐿) is calculatedfrom FAO. All data refers to the year 1985. In the simulation, we use prices of thehigh-income country to value the sectoral outputs of each country.[2] For 𝑌 ∕𝑁 , 𝑌𝑎∕𝑁𝑎, 𝑌𝑚∕𝑁𝑚 and 𝑌𝑎∕𝑁𝑎∕𝑌𝑚∕𝑁𝑚 we compute the ratio between themedian value of the 25% richest countries and the median value of the 25% poorestcountries of the world income distribution. For 𝐿𝑘∕𝐿 and 𝑁𝑎∕𝑁 we report both richand poor country median values. Median values are computed to minimize the effectof outliers.
5.2.2. Nominal labor productivityIn the previous subsection, we have analyzed relative productivitymeasured at constant prices. More precisely, relative productivity isdefined as the ratio between agricultural labor productivity and non-agricultural labor productivity when these productivities are valued atconstant prices.10 Alternatively, other authors have studied the agricul-tural productivity gap, as defined by Gollin et al. (2014a). This gap isdefined as the ratio of nominal productivity in agriculture relative tonominal productivity in non-agriculture. That is, output is measured atcurrent prices.Structural change within agriculture also contributes to explain thechange in the ratio of productivities when valued at current prices. Tosee this, we use data from the GGDC/UNU-WIDER Economic Trans-formation Database and find that the ratio of nominal productivitiesbetween agriculture and non-agriculture increases by 31 percentagepoints in Brazil during the period 1990–2018, for which data is avail-able. In the calibrated economy, this ratio increases by 8 percentagepoints during the same period. In contrast, in the counterfactual econ-omy with an elasticity equal to one, this ratio is constant. Therefore,the increase in nominal relative productivity of 8 percentage pointsgenerated in the simulation is explained entirely by structural changewithin the agricultural sector. We conclude that structural changewithin agriculture contributes to explain the increase in both nominaland real relative productivity.
5.3. Cross-country labor productivity differences
In this section, we ask how much of the difference in relative pro-ductivity observed across countries can be explained by differences inagricultural composition. The cross-country data is summarized in thefirst row of Table 6.11 As shown in the table, the difference in real GDPper worker between countries in the top and bottom quartiles of theworld income distribution is 16-fold. While employment in agricultureis only 6% of total employment in advanced countries, it is 82% in low-income countries. Regarding productivity, Table 6 shows that countriesin the top quartile are 27.3 times more productive in agriculture than
10 We make comparisons of real output, that is, we value sectoral productionlong the transition using constant prices. Other authors have also usedeal sectoral output to compare sectoral productivity across countries. Fornstance, Restuccia et al. (2008) and Lagakos and Waugh (2013) use the samenternational prices to value the sectoral outputs of each country.11 For each variable, we report the ratio between the median country in theop quartile of the world income distribution and the median country in theottom quartile. Results hold if instead we compare top and bottom quintiles14
r deciles.countries in the bottom quartile. In non-agriculture, the difference inproductivity between high and low-income countries is only 3.87-fold.As a result, there is a 7.05-fold difference in the agricultural produc-tivity relative to non-agricultural productivity ratio between high andlow-income countries. These facts have been documented by Caselli(2005) and Restuccia et al. (2008). The novelty reported here is thatcountries in the top quartile of the world income distribution allocatemore land to capital-intensive agriculture compared to countries inthe bottom. That is, while 83% of total harvested land is allocatedto capital-intensive agriculture in high-income countries, only 67% ofharvested land is allocated to this sector in low-income countries.The second row in Table 6 shows how much of the difference inrelative productivity across countries can be explained by the model. Todo this, we assume countries are in the steady state and we set sectoralTFPs, 𝐴𝑚, 𝐴𝑘 and 𝐴𝑛, to match differences in real GDP per worker,gricultural employment and land in capital-intensive agriculture be-ween countries in the top and bottom quartile of the world incomeistribution.12 All other parameters are set as in the benchmark calibra-tion for Brazil and the exogenous variables 𝐿𝑡 and 𝑁𝑡 are set at their1960 values for Brazil. That is, we calibrate cross-country momentsusing only the sectoral TFPs. For the country in the top quartile, weset 𝐴𝑚, 𝐴𝑘 and 𝐴𝑛 so that GDP per worker equals the median value ofcountries in the top quartile, employment in agriculture is 6% of totalemployment and land in capital-intensive agriculture is 83%, as in thedata. Then, for the country in the bottom quartile, we reduce 𝐴𝑚, 𝐴𝑘and 𝐴𝑛 to match that real GDP per worker is one-sixteenth of that inhigh-income countries, employment in agriculture is 82% and land incapital-intensive agriculture is 67%. More specifically, for countries inthe top quartile we set 𝐴𝑚 = 1.487, 𝐴𝑘 = 1.6485 and 𝐴𝑛 = 1.7189 andfor countries in the bottom quartile we set 𝐴𝑚 = 0.6320, 𝐴𝑘 = 0.2885and 𝐴𝑛 = 0.1591. Notice that we match 100% of the difference in realDP per worker, agricultural employment and land in capital-intensivegriculture between rich and poor countries observed in the data. Withhis calibration, we can analyze moments not directly targeted such aselative productivity.The benchmark model generates a 6.36-fold difference betweenich and poor countries in agricultural productivity relative to non-gricultural productivity, compared to a 7.05-fold difference in theata. That is, it accounts for 90.2% of differences observed in theata, which gives a sense of the good fit of the model. The modelenerates roughly the same non-agricultural productivity differenceetween rich and poor countries, 3.61 in the model and 3.87 in theata. It also accounts for a large fraction of the difference in agriculturalroductivity between rich and poor countries, 22.9 in the model and7.3 in the data.How much of the cross-country difference in agricultural productiv-ty relative to non-agricultural productivity is explained by agriculturalomposition? To answer this, we compare the results of the benchmarkodel with a counterfactual simulation with unitary elasticity of sub-titution between capital and labor-intensive agricultural products. Inhe counterfactual simulation, we set 𝜀 = 1 to keep the compositionof agriculture constant and we set 𝑐 = 0.06492 and 𝜇 = 0.778 so thathe fraction of land in capital-intensive agriculture is fixed at 67%, asn the bottom quartile, and the fraction of employment in agriculturen poor countries is 82%. To keep comparability, the differences inectoral TFPs across countries are the same in both the benchmark andhe counterfactual simulation. Results are shown in the third row ofable 6.The main result of this exercise is that, in the counterfactual sim-lation, cross-country differences in sectoral TFPs have no effect on
12 Data on sectoral productivities and GDP per worker is from Restucciaet al. (2008). In these data, the same international prices are used to valuethe sectoral outputs of each country. To compare the result from the modelwith these data, we use prices of the high-income country to value the sectoraloutputs of each country.
Journal of Development Economics 158 (2022) 102934C. Blanco and X. Raurich
f
ioMtcfc1t
tftptae
mwsbpwfalrcaoTsbspd
6
cSdeitad
aiaoispcihiaitbwc
twsttt1Table 7Quantitative results by quartiles.Quartiles Targeted moments
𝑌 ∕𝑁 𝐿𝑘∕𝐿 𝑁𝑎∕𝑁Data Model 𝜀 = 1 Data Model 𝜀 = 1 Data Model 𝜀 = 1
4 16.0 16.0 13.1 0.83 0.83 0.67 0.06 0.06 0.263 6.6 6.6 5.0 0.75 0.75 0.67 0.28 0.28 0.462 3.0 3.0 2.2 0.70 0.70 0.67 0.53 0.53 0.671 1.00 1.00 1.00 0.67 0.67 0.67 0.82 0.82 0.82
Quartiles Non-targeted moments
𝑌𝑎∕𝑁𝑎 𝑌𝑚∕𝑁𝑚
(
𝑌𝑎∕𝑁𝑎
)
∕
(
𝑌𝑚∕𝑁𝑚
)
Data Model 𝜀 = 1 Data Model 𝜀 = 1 Data Model 𝜀 = 1
4 27.3 22.9 15.9 3.87 3.61 3.59 7.05 6.36 4.423 5.41 3.25 2.86 2.06 1.89 1.89 2.62 1.72 1.522 2.68 1.60 1.52 1.51 1.26 1.26 1.78 1.27 1.211 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Note: This table shows cross-country quantitative results by quartile of the worldincome distribution. For 𝑌 ∕𝑁 , 𝑌𝑎∕𝑁𝑎, 𝑌𝑚∕𝑁𝑚 and 𝑌𝑎∕𝑁𝑎∕𝑌𝑚∕𝑁𝑚 we compute the ratiobetween the median value of countries in each quartile relative to the median value ofcountries in the first quartile. For 𝐿𝑘∕𝐿 and 𝑁𝑎∕𝑁 we report median values for eachquartile. Median values are computed to minimize the effect of outliers. Data sourcesare the same as in Table 6.
agricultural composition and, consequently, the counterfactual econ-omy is less effective than the benchmark economy in explaining relativeproductivity differences. Table 6 shows that the counterfactual simula-tion, which excludes changes in the sectoral composition of agriculture,generates a 4.42-fold gap in agricultural productivity relative to non-agricultural productivity between rich and poor countries. Since thebenchmark model explains 90.2% (6.36/7.05) of the relative produc-tivity differences observed in the data and the counterfactual modelexplains 62.7% (4.42/7.05), we conclude that agricultural compositionaccounts for 27.5% of cross-country differences in relative productivity.Table 6 also shows cross-country differences in agricultural andnon-agricultural productivity. The counterfactual simulation generatesa 3.59-fold difference in non-agricultural productivity between rich andpoor countries, a value similar to that of the benchmark simulation.However, the counterfactual model generates a much lower gap inagricultural productivity between rich and poor countries. While thebenchmark model generates a 22.9-fold productivity gap in agriculture,in the model with 𝜀 = 1 this gap is only 15.9-fold. This shows that themechanism in this model is driving agricultural productivity differencesbetween the rich and the poor.The results in Table 6 hold for other quartiles of the world incomedistribution, as shown in Table 7. The data shows that, as expected,employment in agriculture declines with income in each quartile. Moreinterestingly, in the data, the fraction of land in capital-intensive agri-culture increases with income, with countries in the first, second, thirdand fourth quartile allocating, respectively, 67%, 70%, 75% and 83%of land to this sector. To simulate the benchmark model, as before, weset sectoral TFPs to match real GDP per worker, employment and landcomposition in each quartile. More precisely, in the third quartile weset 𝐴𝑚 = 0.974, 𝐴𝑘 = 0.5121 and 𝐴𝑛 = 0.3767, and in the second quartilewe set 𝐴𝑚 = 0.745, 𝐴𝑘 = 0.3631 and 𝐴𝑛 = 0.2249 (for quartiles one andour, sectoral TFPs are the same as before).Table 7 shows that the benchmark model explains the increasen agricultural productivity relative to non-agricultural productivitybserved in the data, as countries move to higher income quartiles.oreover, for each quartile, the benchmark model explains more ofhe relative productivity gap between rich and poor countries than theounterfactual model with fixed agricultural composition. For example,or countries in the third quartile, the gap in relative productivityompared to countries in the bottom quartile is 2.62-fold in the data,.72-fold in the benchmark simulation and only 1.52-fold in the coun-
15
erfactual. For countries in the second quartile, the gap is 1.78-fold in the data, 1.27 in the benchmark model and 1.21-fold in the counter-actual. Clearly, differences in 𝐿𝑘∕𝐿 are larger across countries whenhey are further apart in the distribution of income. For this reason, theerformance of our mechanism is better for countries further apart inhe distribution. However, we can conclude that our mechanism is stillble to explain part of the relative productivity differences observed inach quartile.Finally, in this section, we generate cross-country differences in theodel by introducing differences in sectoral TFPs only. Alternatively,e could introduce differences in the parameter 𝜆 that governs thehape of the distribution function. This parameter affects the distri-ution of abilities and, hence, affects the farm size distribution. Inarticular, a higher value of 𝜆 increases the fraction of individualsith low agricultural abilities, which increases the number of smallarms. As a consequence, employment in agriculture increases, theverage farm size declines and agricultural composition shifts towardsabor-intensive agriculture. The shift towards the labor-intensive sectoreduces capital intensity of agriculture relative to non-agriculture. Thehange in the distribution of abilities combined with the reduction inverage farm size and in relative capital intensity results in a reductionf agricultural productivity relative to non-agricultural productivity.he effect of an increase in 𝜆 is, therefore, similar to that of lowerectoral productivities, both of them impoverish the economy. By com-ining differences in 𝜆 and in sectoral TFPs, we could carry out morepecific cross-country analysis such as the comparison of the relativeroductivity among economies with similar level of development butifferent distribution of farm sizes.
. Concluding remarks
Differences in labor productivity between developed and developingountries are substantially larger in agriculture than in non-agriculture.ince agricultural employment is large in developing countries, theevelopment literature has concluded that explaining these large differ-nces in agricultural productivity is central to understand cross-countryncome differences. We contribute to this literature by showing thathe composition of agriculture can explain a significant part of lowgricultural productivity relative to non-agricultural productivity ineveloping countries.We use data from the US Census of Agriculture and FAO to groupgricultural products into two agricultural sectors that differ in cap-tal intensity. Using this data, we calibrate a model and show that,s the economy develops and capital becomes abundant, the pricef labor-intensive agriculture relative to capital-intensive agriculturencreases. When the agricultural goods produced in both agriculturalectors are imperfect substitutes in preferences, this change in relativerices, along with economic development, drives a process of structuralhange that implies: (i) a reduction in the number of farmers; (ii) anncrease in the average farm size; (iii) a decrease in the fraction ofarvested land used in the labor-intensive sector; and (iv) an increasen the capital intensity of the agricultural sector relative to the non-gricultural sector. Since farms are larger and the agricultural sectors more capital intensive, productivity in agriculture increases relativeo non-agriculture. We show that these development patterns, impliedy our model, are consistent with time series evidence for Brazil, andith a cross-country sample that includes developing and developedountries.In order to quantify how much of the increase in relative produc-ivity is explained by structural change within the agricultural sector,e conducted counterfactual simulations in which the elasticity ofubstitution between the two agricultural goods is unitary and, hence,here is no structural change in the agricultural sector. We concludehat changes in the sectoral composition of agriculture explain 24.8% ofhe observed increase in the relative productivity of Brazil in the period960–2018 and 27.5% of the observed differences in relative produc-ivity across countries. Therefore, structural change within agriculture
Journal of Development Economics 158 (2022) 102934C. Blanco and X. Raurich
ac
𝐸
wt
𝑐
w
𝑃
N
𝑃
𝐸
M
𝑐
𝑃
S
𝑁
𝐾
a
𝛥
N
Texplains roughly a quarter of the increase in relative productivity bothacross countries and over time.We conclude this paper by discussing two avenues for future work.First, this model can be used to study how misallocation associatedto taxes or regulations affect relative labor productivity. From thedevelopment literature, we know that taxes that produce a direct wedgebetween income in agriculture and non-agriculture affect relative laborproductivity. In this model, taxes could also affect relative labor pro-ductivity by altering the composition of agriculture, even if they do notgenerate a wedge between income in agriculture and non-agriculture.Regarding regulations, a policy that limits the mobility of individ-uals out of agriculture could shift agricultural composition towardsthe labor-intensive sector and reduce the relative labor productivity.Therefore, this model offers a benchmark to study how misallocationsof factors across agricultural sectors could have a negative impact onrelative labor productivity. Second, throughout this paper, we maintainthat the force that drives the process of structural change within agri-culture is the change in domestic consumption of agricultural goods.However, we acknowledge that exports of agricultural products couldbe another potential source of structural change in some countries.This suggests that the introduction of trade could be an interestingextension.
Declaration of competing interest
The authors declare that they have no known competing finan-cial interests or personal relationships that could have appeared toinfluence the work reported in this paper.
Data availability
Data will be made available on request.
Acknowledgments
We thank seminar participants at the University of Vienna, theUniversity of Guanajuato, the 43rd Symposium of the Spanish Eco-nomic Association, the 2018 Society for Economic Dynamics meeting,and the XI Workshop on Public Policy Design in Girona. Financialsupport from the Government of Spain and the European Union throughgrants RTI2018-093543-B-I00 and PID2021-126549NB-I00, and fromthe Central Bank of Paraguay is gratefully acknowledged.
Appendix A. Consumers’ problem
The consumer chooses 𝑐𝑖𝑛, 𝑐𝑖𝑘 and 𝑐𝑖𝑚 to maximize (1) subject to (2)nd (3). We break down this problem into two steps. First, consumershoose 𝑐𝑖𝑛 and 𝑐𝑖𝑘 to maximize (2) subject to
𝑖
𝑎,𝑡+1 = 𝑃𝑛,𝑡+1𝑐
𝑖
𝑛,𝑡+1 + 𝑃𝑘,𝑡+1𝑐
𝑖
𝑘,𝑡+1,here 𝐸𝑖𝑎,𝑡+1 is the agricultural expenditure of individual 𝑖. Maximiza-ion implies
𝑖
𝑛,𝑡+1 = 𝜇
𝜀
(𝑃𝑛,𝑡+1
𝑃𝑎,𝑡+1
)1−𝜀 𝐸𝑖𝑎,𝑡+1
𝑃𝑛,𝑡+1
, (27)
𝑐𝑖𝑘,𝑡+1 = (1 − 𝜇)
𝜀
(𝑃𝑘,𝑡+1
𝑃𝑎,𝑡+1
)1−𝜀 𝐸𝑖𝑎,𝑡+1
𝑃𝑘,𝑡+1
, (28)
here 𝑃𝑎,𝑡+1 is the price of the agricultural good and is equal to
𝑎,𝑡+1 =
[
𝜇𝜀𝑃 1−𝜀𝑛,𝑡+1 + (1 − 𝜇)
𝜀 𝑃 1−𝜀𝑘,𝑡+1
] 1
1−𝜀 .
ote that this price satisfies
𝑐𝑖 ≡ 𝐸𝑖 = 𝑃 𝑐𝑖 + 𝑃 𝑐𝑖 .16
𝑎,𝑡+1 𝑎,𝑡+1 𝑎,𝑡+1 𝑛,𝑡+1 𝑛,𝑡+1 𝑘,𝑡+1 𝑘,𝑡+1Second, consumers choose 𝑐𝑖𝑎 and 𝑐𝑖𝑚 by maximizing (1) subject to
𝑖
𝑡+1 = 𝑐
𝑖
𝑚,𝑡+1 + 𝑃𝑎,𝑡+1𝑐
𝑖
𝑎,𝑡+1.aximization implies
𝑖
𝑚,𝑡+1 = (1 − 𝜔)𝐸
𝑖
𝑡+1 − (1 − 𝜔)𝑃𝑎,𝑡+1𝑐, (29)and
𝑎,𝑡+1𝑐
𝑖
𝑎,𝑡+1 = 𝜔𝐸
𝑖
𝑡+1 + (1 − 𝜔)𝑃𝑎,𝑡+1𝑐.Combining this last equation with (27) and (28), we obtain
𝑐𝑖𝑛,𝑡+1 = 𝜔𝜇
𝜀
(𝑃𝑛,𝑡+1
𝑃𝑎,𝑡+1
)1−𝜀 𝐸𝑖𝑡+1
𝑃𝑛,𝑡+1
+ (1 − 𝜔)𝜇𝜀
(𝑃𝑛,𝑡+1
𝑃𝑎,𝑡+1
)−𝜀
𝑐, (30)
𝑐𝑖𝑘,𝑡+1 = 𝜔 (1 − 𝜇)
𝜀
(𝑃𝑘,𝑡+1
𝑃𝑎,𝑡+1
)1−𝜀 𝐸𝑖𝑡+1
𝑃𝑘,𝑡+1
+ (1 − 𝜔) (1 − 𝜇)𝜀
(𝑃𝑘,𝑡+1
𝑃𝑎,𝑡+1
)−𝜀
𝑐.
(31)Eqs. (29)–(31) determine the individuals’ consumption demands.
Appendix B. Factors’ demands and aggregate production
To obtain Eqs. (14) and (15), we take into account that land inlabor-intensive agriculture is given by 𝐿𝑛,𝑡 = 𝑁𝑡 ∫ 𝑎𝑡𝑎𝑡 𝐿𝑖𝑛,𝑡𝑓 (𝑎𝑖) 𝑑𝑎𝑖 and incapital-intensive agriculture it is given by 𝐿𝑘,𝑡 = 𝑁𝑡 ∫ ∞𝑎𝑡 𝐿𝑖𝑘,𝑡𝑓 (𝑎𝑖) 𝑑𝑎𝑖.imilarly, capital in labor-intensive agriculture is given by 𝐾𝑛,𝑡 =
𝑡 ∫ 𝑎𝑡𝑎𝑡 𝐾 𝑖𝑛,𝑡𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖 and in capital-intensive agriculture it is given by
𝐾𝑘,𝑡 = 𝑁𝑡 ∫ ∞𝑎𝑡 𝐾 𝑖𝑘,𝑡𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖. Using these equations, (8), (9) and thedistribution of abilities, we obtain
𝐿𝑠,𝑡 = 𝑁𝑡
[(
𝛼𝑠
𝑅𝑡
)𝛼𝑠 ( 𝛽𝑠
𝑥𝑡
)1−𝛼𝑠
(1 − 𝜏)𝑃𝑠,𝑡𝐴𝑠,𝑡
] 1
1−𝛽𝑠−𝛼𝑠
𝛥𝑠,𝑡
𝑠,𝑡 = 𝑁𝑡
[(
𝛼𝑠
𝑅𝑡
)1−𝛽𝑠 ( 𝛽𝑠
𝑥𝑡
)𝛽𝑠
(1 − 𝜏)𝑃𝑠,𝑡𝐴𝑠,𝑡
] 1
1−𝛽𝑠−𝛼𝑠
𝛥𝑠,𝑡
for 𝑠 = {𝑘, 𝑛}, where
𝛥𝑛,𝑡 = ∫
𝑎𝑡
𝑎𝑡
(
𝑎𝑖
) 1
1−𝛽𝑛−𝛼𝑛 𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖 = 𝜆𝜂𝜆
⎛⎜⎜⎝
(
𝑎𝑡
) 1
1−𝛽𝑛−𝛼𝑛
−𝜆 −
(
?̄?𝑡
) 1
1−𝛽𝑛−𝛼𝑛
−𝜆
𝜆 − 11−𝛽𝑛−𝛼𝑛
⎞⎟⎟⎠ ,nd
𝑘,𝑡 = ∫
∞
𝑎𝑡
(
𝑎𝑖
) 1
1−𝛽𝑘−𝛼𝑘 𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖 = ∫
∞
𝑎𝑡
𝜆𝜂𝜆
(
𝑎𝑖
) 1
1−𝛽𝑘−𝛼𝑘
−(1+𝜆)
𝑑𝑎𝑖.
ote that only if 𝜆 > 11−𝛽𝑘−𝛼𝑘 then 𝛥𝑘,𝑡 is finite and equal to
𝛥𝑘,𝑡 = 𝜆𝜂𝜆
⎛⎜⎜⎝
(
?̄?𝑡
) 1
1−𝛽𝑘−𝛼𝑘
−𝜆
𝜆 − 11−𝛽𝑘−𝛼𝑘
⎞⎟⎟⎠ .
he inequality 𝜆 > 11−𝛽𝑘−𝛼𝑘 implies that 𝛥𝑘,𝑡 > 0. It also implies that
𝜆 > 11−𝛽𝑛−𝛼𝑛
and, hence, 𝛥𝑛,𝑡 is also positive when ?̄?𝑡 > 𝑎𝑡. Therefore, weassume that 𝜆 > 11−𝛽𝑘−𝛼𝑘 .To obtain Eq. (18), we take into account that output in labor-intensive agriculture is given by 𝑌𝑛,𝑡 = 𝑁𝑡 ∫ 𝑎𝑡𝑎𝑡 𝑌 𝑖𝑛,𝑡𝑓 (𝑎𝑖) 𝑑𝑎𝑖, whereas out-put in capital-intensive agriculture is given by 𝑌𝑘,𝑡 =
𝑁𝑡 ∫ ∞𝑎𝑡 𝑌 𝑖𝑘,𝑡𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖. Using these equations and (10), we obtain (18).
Appendix C. Aggregate consumption expenditures
We use (7) and (19) to obtain aggregate consumption expenditureas
𝐸𝑡+1 = 𝑅𝑡+1𝑁𝑡
⎧⎪⎪⎨⎪⎪
∫ 𝑎𝑡𝜂 (1 − 𝜙)𝑤𝑡𝑓 (𝑎𝑖) 𝑑𝑎𝑖
+ ∫ 𝑎𝑡𝑎𝑡
[
(1 − 𝜏)𝑃𝑛,𝑡𝑦𝑖𝑛,𝑡 − 𝑥𝑡𝐿
𝑖
𝑛,𝑡 − 𝑅𝑡𝐾
𝑖
𝑛,𝑡
]
𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖
+ ∫ ∞𝑎𝑡
[
(1 − 𝜏)𝑃𝑘,𝑡𝑦𝑖𝑘,𝑡 − 𝑥𝑡𝐿
𝑖
𝑘,𝑡 − 𝑅𝑡𝐾
𝑖
𝑘,𝑡
]
𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖
∞ 𝑖 ( 𝑖) 𝑖
⎫⎪⎪⎬⎪⎪
.⎩ + ∫𝜂 𝑇𝑡 𝑓 𝑎 𝑑𝑎 ⎭
Journal of Development Economics 158 (2022) 102934C. Blanco and X. Raurich
W
𝐸
a
𝐸
U
𝑌(
A
a
R
A
A
A
A
C
C
C
CWe assume that tax revenues are returned to individuals as a trans-fer and the government budget constraint is balanced in each period,hence,
∫
∞
𝜂
𝑁𝑡𝑇
𝑖
𝑡 𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖 =
(
∫
𝑎𝑡
𝜂
𝜙𝑤𝑡𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖 + ∫
𝑎𝑡
𝑎𝑡
𝜏𝑃𝑛,𝑡𝑦
𝑖
𝑛,𝑡𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖
+∫
∞
𝑎𝑡
𝜏𝑃𝑘,𝑡𝑦
𝑖
𝑘,𝑡𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖
)
𝑁𝑡.
e use the government budget constraint to obtain
𝑡+1 = 𝑅𝑡+1𝑁𝑡
⎧⎪⎪⎨⎪⎪⎩
∫ 𝑎𝑡𝜂 𝑤𝑡𝑓 (𝑎𝑖) 𝑑𝑎𝑖 + ∫ 𝑎𝑡𝑎𝑡 [𝑃𝑛,𝑡𝑦𝑖𝑛,𝑡 − 𝑥𝑡𝐿𝑖𝑛,𝑡
−𝑅𝑡𝐾 𝑖𝑛,𝑡
]
𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖
+ ∫ ∞𝑎𝑡
[
𝑃𝑘,𝑡𝑦𝑖𝑘,𝑡 − 𝑥𝑡𝐿
𝑖
𝑘,𝑡 − 𝑅𝑡𝐾
𝑖
𝑘,𝑡
]
𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖
⎫⎪⎪⎬⎪⎪⎭
,
nd using (8)–(10) we get
𝑡+1 = 𝑅𝑡+1𝑁𝑡
⎧⎪⎪⎨⎪⎪⎩
𝑤𝑡 ∫ 𝑎𝑡𝜂 𝑓 (𝑎𝑖) 𝑑𝑎𝑖 + [1 − (1 − 𝜏) 𝛽𝑛 − (1 − 𝜏) 𝛼𝑛]𝑃𝑛,𝑡
× ∫ 𝑎𝑡𝑎𝑡 𝑦𝑖𝑛,𝑡𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖
+
[
1 − (1 − 𝜏) 𝛽𝑘 − (1 − 𝜏) 𝛼𝑘
]
𝑃𝑘,𝑡
× ∫ ∞𝑎𝑡 𝑦𝑖𝑘,𝑡𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖
⎫⎪⎪⎬⎪⎪⎭
.
sing the definition of aggregate output for each agricultural sector,
𝑛,𝑡 = 𝑁𝑡 ∫ 𝑎𝑡𝑎𝑡 𝑦𝑖𝑛,𝑡𝑓
(
𝑎𝑖
)
𝑑𝑎𝑖 and 𝑌𝑘,𝑡 = 𝑁𝑡 ∫ ∞𝑎𝑡 𝑦𝑖𝑘,𝑡𝑓 (𝑎𝑖) 𝑑𝑎𝑖, Eqs. (4) and5) and 𝑁𝑚,𝑡 = 𝑁𝑡 ∫ 𝑎𝑡𝜂 𝑓 (𝑎𝑖) 𝑑𝑎𝑖, we obtain Eq. (20).
ppendix D. Supplementary data
Supplementary material related to this article can be found onlinet https://doi.org/10.1016/j.jdeveco.2022.102934.
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