Capital Deepening, Technology Diffusion, and Agricultural Productivity Chaoran Chen∗

Abstract The cross-country differences of capital intensity are larger in the agricultural sector than in the non-agricultural sector. To study this stylized fact, I build a two-sector general equilibrium model with technology diffusion that can account for the capital deepening process in agriculture observed in the U.S. data. As the economy develops, farmers gradually adopt a modern technology with higher capital intensity. Using this model, I find that economy-wide productivity, land endowment, and barriers to investment affect technology diffusion and that differences in these aggregate factors can explain two thirds of the differences in the agricultural capital intensity. Moreover, the model can explain three fourths of the agricultural productivity differences across countries. Besides those aggregate factors, land misallocation in agriculture also impedes technology diffusion and magnifies the productivity differences. Keywords: Capital Intensity, Technology Diffusion, Agricultural Productivity, Misallocation. JEL classification: E13, O41, Q12, Q16.

∗

Department of Economics, University of Toronto, 150 St. George Street, Toronto, On-

tario, Canada, M5S 3G7. Email: [email protected]. I thank Diego Restuccia for his encouragement and supervision. I also benefit from discussions with Stephen Ayerst, Margarida Duarte, Peter Morrow, Joseph Steinberg, and Xiaodong Zhu. All errors are my own.

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1

Introduction

The international labour productivity differences are larger in the agricultural sector than in the non-agricultural sector. Moreover, poor countries allocate larger percentages of employment in agriculture due to their low agricultural productivity together with the subsistence requirements of agricultural goods (Restuccia et al., 2008). Therefore, it is crucial to understand why poor countries are so unproductive in agriculture. Considerate literature has focused on explaining this agricultural productivity differences, but a portion remains unexplained. In this paper, I show that the capital intensity of agricultural production is much lower in poor countries because of their low development levels as well as various distortions. Their low capital intensity contributes substantially to their low agricultural productivity. I measure the capital intensity using the capital-output ratio and the capital-labour ratio. Rich and poor countries differ in their capital intensity, but the differences are much larger in the agricultural sector than in the non-agricultural sector. This pattern coincides with that of the international labour productivity differences. Therefore, it is important to explore why the capital intensity differs more in the agricultural sector, and how these differences contribute to the international agricultural productivity differences. To answer these two questions, I build a two-sector general equilibrium model with technology diffusion in agriculture, motivated by the following fact in the U.S. data: in the twentieth century, the capital-output ratio is roughly constant in the non-agricultural sector, while it increases over time in the agricultural sector. This increase coincides with the mechanization of the U.S. agriculture, especially in the post-war periods.1 Therefore, the low capital 1

Please see Sunding and Zilberman (2001) for an excellent discussion on the technology

2

intensity of agriculture in poor countries may reflect a lack of mechanization. I model this mechanization as a process of technology diffusion in agriculture. In the model, farmers choose from two technologies: a traditional technology with a lower capital share and a modern technology with a higher capital share. I also model the investment-specific technology as Greenwood et al. (1997) to match the observed phenomenon that capital becomes relatively cheaper over time, compared to consumption goods and labour. Therefore, as the economy develops, modern technology becomes more profitable and gradually replaces the traditional technology. Along with this technology diffusion process, the capital intensity increases in agriculture, and labour is substituted by capital, resulting in an increased labour productivity over time. I calibrate the model to the historical data of the U.S. for more than a century (1900-2007). My model is able to replicate the time series of agricultural employment share, capital intensity, and the technology diffusion curve reasonably well. Then I change the aggregate factors, including the endowments, economy-wide total factor productivity (TFP), and the barrier to investment to match those of the poor countries. These aggregate factors can explain two thirds of the observed differences in capital intensity across countries and three fourths of the differences in agricultural productivity. Furthermore, I find that the channel of technology diffusion is key to explaining these observed differences: without this channel, the aggregate factors can only explain less than half of the observed differences in capital intensity. Then I show that land market frictions can be good candidates to explain the remaining portion of the observed differences. Recent literature suggests that land market misallocation is especially severe in the agricultural sector of diffusion in agriculture.

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poor countries.2 I explicitly model the problem of untitled land, where farmers are allocated equal amounts of land and land transactions among farmers are prohibited. This land misallocation further reduces the capital intensity and agricultural productivity. With untitled land on top of the aggregate factors of poor countries, the model is able to explain almost all the observed differences in capital intensity and around 90% of the agricultural productivity differences. My paper is related to the revival macroeconomic literature on the international agricultural productivity differences.3 My paper differs from this existing literature by focusing on a new stylized fact, the differences of capital intensity in agriculture across countries, and exploring its impact on agricultural productivity. My paper also introduces the technology diffusion in agriculture to capture the phenomenon of agricultural mechanization, which has not been studied before. My paper is also related to the literature studying long-run economic growth, in particular, the transition to the modern balanced growth.4 The two most related papers are Gollin et al. (2007) and Yang and Zhu (2013). They both model the choice between a traditional technology and a modern technology, and study how the economy converges to the modern long-run growth. My paper differs from them in two ways. First, I use explore the technology diffusion to study the international agricultural productivity differences, instead of the long-run growth. Second, I model heterogeneous farmers and study the technology diffusion at the farm level. This setup allows me to 2

See, for example, Adamopoulos and Restuccia (2014a) and Chen (2015), among others. See, for example, Gollin et al. (2002), Gollin et al. (2004), Gollin et al. (2007), Restuccia et al. (2008), Adamopoulos (2011), Lagakos and Waugh (2013), Gollin and Rogerson (2014), Donovan (2014), Gollin et al. (2014), Adamopoulos and Restuccia (2014b), Chen (2015), and Adamopoulos and Restuccia (2014a), among others. 4 See, for example, Hansen and Prescott (2002), Ngai (2004), Gollin et al. (2007), and Yang and Zhu (2013), among others. 3

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empirically match the diffusional curve of modern technology and also study the role of misallocation across heterogeneous farmers. My paper examines the role of misallocation on capital deepening and technology diffusion; therefore, it also contributes to the literature studying misallocation in agriculture.5 My paper is also related to the literature on structural transformation and capital deepening.6 I show that capital deepening happens within agriculture along with economic development. Higher capital intensity increases labour productivity in agriculture, and therefore reduces the agricultural employment share. The paper proceeds as follows. Section 2 shows the basic facts about the capital intensity in agriculture, both across countries and in the U.S. history. Section 3 describes the model. Section 4 discusses the calibration and shows my results of the quantitative analysis. Section 5 concludes the paper.

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Evidence on Capital Intensity

In this section, I document two stylized facts of agricultural capital intensity. The first fact is about the agricultural capital intensity across countries; the second one is about the that intensity over time in the U.S. history.

2.1

Agricultural Capital Intensity across Countries

It is well-known that poor countries have lower capital-output ratios and capital-labour ratios than rich countries, as summarized in Hsieh and Klenow (2007). Perhaps what is less well-known is that these differences are larger 5

See, for example, Restuccia and Santaeulalia-Llopis (2014) and Adamopoulos and Restuccia (2014a). 6 See, for example, Acemoglu and Guerrieri (2008) and Alvarez-Cuadrado et al. (2015).

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Real Capital−Output Ratio (US=1) .1 .5 1 2

Figure 1: The Capital Intensity across Countries

Non−Agriculture Agriculture .02

.1 .25 GDP Per Capita (US=1)

.5

1

Real Capital−Labour Ratio (US=1) .001 .01 .1 1

(a) Capital-Output Ratio

Non−Agriculture Agriculture .02

.1 .25 GDP Per Capita (US=1)

.5

1

(b) Capital-Labour Ratio

Note: [1] The capital-output ratio, capital-labour ratio and GDP per capita are normalized relative to their levels of the U.S. and are in log scale for illustration purpose. [2] Capital and output are real measures with common prices across countries. [3] The data of the sectoral capital stocks are from the World Bank (see Larson et al. (2000)); the agricultural output and employment are from the FAO; the aggregate GDP and employment are from the Penn World Table 8.0.

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Nominal Capital−Output Ratio (US=1) .1 .5 1 2

Figure 2: Nominal Capital-Output Ratio

Non−Agriculture Agriculture .02

.1 .25 GDP Per Capita (US=1)

.5

1

Note: [1] The capital-output ratio and GDP per capita are normalized relative to their level of the U.S. and are in log scale for illustration purpose. [2] Capital and output are nominal measures with local prices. [3] The data of the sectoral capital stocks are from the World Bank (see Larson et al. (2000)); the agricultural output and employment are from the FAO; the aggregate GDP and employment are from the Penn World Table 8.0.

in the agricultural sector than in the non-agricultural sector. Figure 1 shows the real capital-output ratio and the real capital-labour ratio across countries, both in the agricultural sector and in the non-agricultural sector. Capital stock and output are measured using international prices. It is obvious that richer countries have higher capital-output ratio and capital-labour ratio in both sectors, but the differences in agriculture are much larger. For example, in the non-agricultural sector, the capital-labour ratio differs for around 15 fold between the U.S. and the poorest countries in my sample, while it differs for more than 100 folds in the agricultural sector. It is also illustrative to compare the nominal capital-output ratio across countries. As Figure 2 shows, the nominal capital-output ratio in the non-

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Table 1: Capital-output Ratio across Countries Measurement Nominal Nom. Real of ∆K/Y Log GDP 0.66** 0.31** 0.43** (0.03) (0.09) (0.03) Dummies: Time X Country X Observations 426 426 426 Data Source World Bank

Real

Nom.

Nom.

0.56** (0.07)

0.41** (0.03)

0.19 (0.14)

X X 426

X X 504 504 WIOD

Note: [1] The data are from the World Bank (Larson et al., 2000) and the World Input-Output Database (Timmer et al., 2015). a n [2] I regress ∆ K (log( K ) − log( K )) on countries’ log GDP per capita (PPP), Y Ya Yn country dummies and time dummies. Standard errors are in bracket. [3] Nominal measure means capital and output are measured using local price; real measure uses international comparable prices. agricultural sector is roughly the same across countries, while it differs substantially in the agricultural sector. This fact provides evidence that the aggregate production function of the agricultural sector cannot be summarized by a single Cobb-Douglas production function with constant capital share. I will explain this result in detail later in this section. I further consider the following regression form. Let ∆ K denotes the difY a n ference of capital-output ratios between sectors (log( K ) − log( K )). I have Ya Yn

measures of the capital-output ratios in both the nominal and real terms. I regress this variable on countries’ real GDP per capita, time dummies, and country dummies. The results are in Table 1. The basic result is that the capital-output ratio of agriculture increases with GDP per capita relative to that of the non-agricultural sector, under both nominal and real measures. This result is consistent with Figure 1 and Figure 2. I further note that this

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result holds using data from two different sources. Therefore, it is a robust fact that the international differences of capital intensity are larger in the agricultural sector than in the non-agricultural sector.

2.2

U.S. Agricultural Capital Intensity over Time

The second stylized fact is that in the U.S. the capital intensity of the agricultural sector has been increasing faster than the non-agricultural sector. The upper panel of Figure 3 shows the nominal capital-output ratio in the U.S. of both agricultural and non-agricultural sectors. We can see that the nominal capital-output ratio is stable in the non-agricultural sector, which is consistent with the Kaldor facts, while it is increasing over time in the agricultural sector. The lower panel shows the real capital-labour ratio in both sectors. It is increasing in both sectors, but it increases faster in agriculture. The period of increasing capital intensity coincides with the postwar period of mechanization in the U.S. agriculture. Figure 4 shows the percentage of farms with tractors in the U.S. agricultural sector starting from 1920. The tractor usage increases rapidly between 1940 and 1980, which is also the period that agricultural capital intensity increases relative to the non-agricultural sector.7 Other agricultural machines, such as threshers or harvesters, also share the similar adoption pattern as tractors.

2.3

The Nominal Capital-Output Ratio

The increasing nominal capital-output ratio is of particular importance, as it provides evidence that the agricultural sectoral production cannot be summa7 Manuelli and Seshadri (2014) provide an excellent discussion on how tractors replace horses and human powers in the agricultural production, as a response to the relative price of tractors versus other inputs.

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Figure 3: The Capital Intensity of U.S. Historically

Nominal Capital-Output Ratio

5 Agriculture Non-Agriculture 4 3 2 1 0 1930 1940 1950 1960 1970 1980 1990 2000 2010

Year

Capital-Labour Ratio, Year 1930 = 1

(a) Capital-Output Ratio 25

Agriculture Non-Agriculture

20 15 10 5 0 1920

1940

1960

1980

2000

2020

Year

(b) Capital-Labour Ratio

Note: The capital-output ratio is measured using nominal capital and output, while the capital-labour ratio is measured using real capital stock, or the chain-type quantity of capital provided by BEA. Please see the data appendix for the source of the data.

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Percentage of Farms with Tractors

Figure 4: U.S. Farms with Tractors, 1920-2007 1 0.8 0.6 0.4 0.2 0

1920

1940

1960 Year

1980

2000

Note: The tractor data are from the U.S. Census of Agriculture (USCA hereafter). Please see the data appendix for a detailed description of the data.

rized by a single Cobb-Douglas technology with constant capital share. To see this, consider the following example. Suppose the agricultural and nonagricultural technologies are given by Ya = AKaαa Na1−αa

and Yn = AKnαn Nn1−αn ,

where Y , K, N , and α are the sectoral output, capital, land, and capital share, and a and n denote the agricultural and non-agricultural sectors, respectively. Here we assume the agricultural sectoral production has a Cobb-Douglas technology with a constant capital share. I will show how this assumption contradicts with our stylized facts. If we denote the prices of the agricultural good, the non-agricultural good, and capital as Pa , Pn , and PK , respectively, then profit-maximization requires the following relationships: αa PK Ka = Pa Ya r

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(1)

and P K Kn αn = , Pn Yn r

(2)

where r is the rental rate of capital. These two equation show that the nominal capital-output ratio is a function of the sectoral capital share and the rate of return only. We first focus on the historical fact. As one of the Kaldor facts, the rate of return r should be stable over time. Then Equation (1) and Equation (2) suggest that the nominal capital-output ratio should be stable over time, in both sectors. This prediction contradicts with our second fact that the nominal capital-output ratio is increasing in the agricultural sector. We can also focus on the cross-country fact. By rearranging Equation (1) and Equation (2) we can get PK Ka αa PK Kn = . Pa Y a αn Pn Yn

(3)

Equation (3) suggests that the nominal capital-output ratios of the two sectors are proportional to each other, contradicting with our first fact that crosscountry differences of the nominal capital-output ratio are larger in the agricultural sector than in the non-agricultural sector. The above analysis suggests that the assumption of a constant capital share in agriculture, which is often made in the literature, is inconsistent with the data. Therefore, in the following section I introduce a model which allows for technology diffusion and capital deepening in agriculture. My model predicts an increasing capital share in agriculture, consistent with the stylized facts.8 8

Another explanation, instead of allowing for multiple technologies, is to assume the aggregate production function in agriculture has the feature that the elasticity of substitution between capital and labour greater than unity (Alvarez-Cuadrado et al., 2015). In the appendix, I show that my conjecture does not conflict with this view: the agricultural pro-

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3

A Model with Technology Diffusion

Time is discrete. There are two sectors in this economy: an agricultural sector and a non-agricultural sector. The non-agricultural good is treated as the numeraire, while the price of the agricultural good at period t is pt . The agricultural good is for consumption only, while the non-agricultural good can also be transformed into capital good using an investment-specific technology. The price of the capital good is pkt . There is a measure one of infinitely-lived representative household in this economy, who allocates its members to be a farmer in the agricultural sector or a worker in the non-agricultural sector. The population size of this household is Nt at period t, and grows at a rate of n. Workers are homogeneous and earn the the wage wt at period t, while farmers are heterogeneous in their farming ability s. Farmers operate farms using span-of-control technologies like Lucas (1978), so there is a non-degenerate farm size distribution in the equilibrium.

3.1

Technologies in the Agricultural Sector

The agricultural good can be produced from two technologies: a traditional technology and a modern technology. The traditional technology is relatively less capital intensive, while the modern technology is more capital intensive. Farmers are heterogeneous in their farming ability s ∈ S, where F (s) describes the cumulative distribution of s. Consider a farmer with ability s. duction in my model also aggregates to a technology with the elasticity greater than unity, consistent with Alvarez-Cuadrado et al. (2015). My conjecture of mechanization actually provides a micro foundation for Alvarez-Cuadrado et al. (2015) why the elasticity is greater than unity in the aggregate production function.

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She can operate a farm with the modern technology given by yt = At κt s1−αm −γm ktαm ltγm , where yt is the farm’s output, At is the economy-wide productivity, κt is the agricultural-specific productivity, kt and lt are the capital and land inputs of the farm, and αm and γm are the capital and land shares of the modern technology. Following the literature, I assume the labour input of a farm is inelastic and therefore normalized to 1.9 Her profit is given by πtm (s) = arg max

{kt ,lt }

At κt s1−αm −γm ktαm ltγm − pkt rt kt − qt lt ,

where rt and qt are the rental rates of capital and land. She can also choose to operate a farm with the traditional technology given by yt = At Bt κt s1−αr −γr ktαr ltγr , where αr and γr are the capital and land shares of the traditional technology, and Bt measures the relative productivity difference between the traditional and the modern technologies. Her profit of operating the traditional farm is πtr (s) = arg max

{kt ,lt }

At Bt κt s1−αr −γr ktαr ltγr − pkt rt kt − qt lt .

Choosing the modern technology incurs a fixed cost of f units of capital, or pkt rt f units of the non-agricultural good in period t. This fixed cost may be interpreted as indivisible equipments, up-front investment in learning, or the 9

Please see Adamopoulos and Restuccia (2014b) and Chen (2015) for a detailed discussion on this assumption.

14

Figure 5: Technology Choice

π

Modern Traditional

0 −pk rf

sˆ

s

required structures of the modern technology.10 A farmer with s will choose the modern technology if and only if πtm (s) − pkt rt f > πtr (s). The difference of profits between the two technologies is linear in this farmer’s ability s: ∆πt (s) = πtm (s) − πtr (s) = sΩ(At , Bt , κt , pt , qt , rt , pkt ), where Ω is a collection of terms independent of s. Therefore, as shown in Figure 5, there is a cut-off level sˆt =

pkt rt f , Ω(At ,Bt ,κt ,pt ,qt ,rt ,pkt )

such that farmers with ability s > sˆt adopt

the modern technology, while farmers with ability s < sˆt use the traditional technology. Denote πt (s) = max{πtm (s) − pkt rt f, πtr (s)} as the profit function after choosing the technology. 10

See Sunding and Zilberman (2001) for examples of this fixed cost.

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3.2

Technologies in the Non-Agricultural Sector

The non-agricultural sector has a representative firm which combines capital ˜ nt and labour N ˜nt to produce the non-agricultural good Ynt : K ˜ αn N ˜ 1−αn , Ynt = At K t nt where αn is the capital share in the non-agricultural sector. The non-agricultural good can be used for consumption or transformed into capital good through a linear technology. Let υt denote this investmentspecific technology: 1 unit of non-agricultural good can be transformed into υt units of capital good. Therefore, the price of capital good is given by pkt =

3.3

1 . υt

The Household’s Problem

The representative household has a population size of Nt at period t and chooses a portion of its members Nat to be farmers in agriculture, with the remaining Nnt = Nt −Nat being workers working in the non-agricultural sector. All workers earn the wage rate wt , while farmers are heterogeneous in their farming profit πt (s). The total labour income of this household is given by ∫ Nnt wt + Nat

πt (s)F (ds). s∈S

I follow Adamopoulos and Restuccia (2014b) by assuming there is no selection among household members in the occupational choice. In other words, the household only determines the fraction of population working in agriculture without selecting its members based on their ability. This assumption keeps the distribution of farmers’ ability the same across time and across country. The selection channel has been well studied in Lagakos and Waugh (2013), who 16

find that selection amplifies the agricultural productivity differences across countries. Since this selection channel is well understood in the literature, I abstract from it in this paper to keep my analysis stylized. The household makes its intertemporal choice by solving the following utility maximization problem

max

{cat ,cnt ,xt ,Nat }∞ t=0

∞ ∑

β t log

{[ 1 } ε−1 1 ε−1 ] ε ϕ ε (cat − c¯) ε + (1 − ϕ) ε cntε ε−1 Nt ,

t=0

∫ s.t.

(pt cat +cnt )Nt +pkt xt

= wt (Nt −Nat )+

πt (s)F (ds)Nat +qt L+rt pkt kt , s∈S

kt+1 = (1 − δ)kt +

xt . π

Here L is the endowment of land owned by this household, and π is the barrier to investment: one unit of investment increases capital good by

1 π

units.11

The household’s problem can be broken down into two subproblems: a static one and a dynamic one. I describe the static one first. Suppose the household has a budget ct for consumption for each of its members at period t. The Marshallian demands of both goods are given by cat = ϕ

ct − pt c¯ + c¯, ϕpt + (1 − ϕ)pεt

cnt = (1 − ϕ)pεt

ct − pt c¯ . ϕpt + (1 − ϕ)pεt

(4)

The indirect utility function is given by u˜(ct , pt ) = log(ct − pt c¯) −

1 log(ϕp1−ε + (1 − ϕ)). t 1−ε

The household also chooses Nat to maximize its labour income Nat 11

A similar setup is also used in Ngai (2004) and Restuccia (2004).

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∫ s∈S

πt (s)F (ds)+

(Nt − Nat )wt . The first order condition implies ∫ wt =

πt (s)F (ds).

(5)

s∈S

Now consider the dynamic part of the household’s problem. The household ∫ divides its total income Nat s∈S πt (s)F (ds)+(Nt −Nat )wt +rt pkt kt +qt L between consumption Nt ct and investment pkt xt by solving the following problem in each period t: max ct ,xt

s.t. Nt ct +

pkt xt

∞ ∑

β t Nt u˜(ct , pt ),

t=0

∫

= wt (Nt − Nat ) +

πt (s)F (ds)Nat + qt L + rt pkt kt , s∈S

kt+1 = (1 − δ)kt +

xt . π

It is easy to show that the optimal consumption sequence should satisfy the following Euler equation: 1 u˜c (ct , pt ) rt+1 ] 1 ct+1 − pt+1 c¯ pkt+1 [ = = k (1 − δ) + . β u˜c (ct+1 , pt+1 ) β ct − pt c¯ π pt

(6)

It implies the interest rate at period t + 1 to be rt+1

[g g ] c v =π − (1 − δ) , β

(7)

where gc is the growth rate of disposable consumption budget, i.e., the consumption expenditure net of the subsistence part (ct − pt c¯), and gυ is the growth rate of the investment-specific technology υt .

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3.4

The Competitive Equilibrium

I focus on the competitive equilibrium of this economy defined as follows. Definition 1. The competitive equilibrium consists sequences of consumption ∞ bundles {cat , cnt }∞ t=0 , investments {xt }t=0 , farm inputs and outputs {kt (s), lt (s), k ∞ yt (s), ∀s ∈ S}∞ t=0 , prices of agricultural goods and capital goods {pt , pt }t=0 , ∞ wage {wt }∞ t=0 , interest rate {rt }t=0 , factor demands and outputs of the repre-

˜ nt , N ˜nt , Ynt }∞ , aggregate capisentative firm in the non-agricultural sector {K t=0 ∞ tal stock in the economy {Kt }∞ t=0 , and agricultural employments {Nat }t=0 , such

that • Given the prices, interest rates and wages, the representative household maximize its utility by choosing the optimal level of consumption and investment given by Equation (4) and Equation (6). The interest rate is given by (7). The representative household also choose the optimal employment in agriculture, which requires the no-arbitrage condition given by Equation (5). • Given the prices, interest rates and wages, the representative firm in the ˜ nt , N ˜nt }∞ . non-agricultural sector maximizes its profit by choosing {K t=0 • Given the prices and interest rates, farms choose the optimal level of inputs and outputs {kt (s), lt (s), yt (s), ∀s ∈ S}∞ t=0 . • All markets clear: – Agricultural good: ∫ cat Nt = Nat

yt (s)F (ds). s

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– Non-agricultural goods: cnt Nt +

xt = Y˜nt . υt

– Capital market: ∫ ˜ nt = Kt = kt . kt (s)F (ds) + K

Nat s

– Labour market:

∫ ˜nt = Nt . F (ds) + N

Nat s

– Land market:

∫ Nat

lt (s)F (ds) = Lt . s

In general, the balanced growth path does not exist in this type of structural transformation models with non-homothetic preferences and different growth rates of technology between sectors.12 I will come back to this point in the calibration section.

4

Quantitative Analysis

4.1

Calibration

I calibrate the model to the U.S. economy after 1900. The historical data of the U.S. economy give us information on how technology diffusion happens in a relatively undistorted economy. Therefore, I use the U.S. agricultural sector as a benchmark of technology diffusion. The calibration comes in three steps. First I determine the parameters that are fixed over time and the parameters 12

See Herrendorf et al. (2014) for a detailed discussion on this issue.

20

governing the endowments Nt and Lt . Given those fixed parameters, I then choose the sequence of At and υt to match the model’s prediction with the historical time series data in the non-agricultural sector. Finally I choose the fixed cost f to match the technology diffusion curve. The factor shares of the technologies are chosen to be consistent with the literature. The modern technology has a capital share of 0.42, a labour share of 0.42, and a land share of 0.16. In the literature, Valentinyi and Herrendorf (2008) estimate a capital share of 0.36, while Herrendorf et al. (forthcoming) estimate a capital share of 0.54. I choose a point in the range. The traditional technology has capital, labour, and land shares of 0.15, 0.6, and 0.25. In the literature, Hayami and Ruttan (1985) and Gollin et al. (2007) estimate the capital share to be 0.1, while Caselli and Coleman (2001) use a capital share of 0.21. My value is also in the rage. My results are not qualitatively affected by using different factor shares, as long as the assumption that the modern technology has a higher capital share is satisfied. The farmer’s ability distribution is calibrated to match the farm size distribution in 2007. I assume the ability s ∈ S follows a lognormal distribution with mean 0 and standard deviation σs , which is set to minimize the difference of farm size distribution between the equilibrium results of the model and the data. I set the preference parameter ϕ = 0.005 such that the long-run employment share in agriculture is 0.5%. The subsistence level of consumption c¯ is set to match the employment share of 2.45% in the year 2007. The depreciation rate is set to 0.08. The preference parameter β is set to match a capital-output ratio of 2 in the non-agricultural sector. The productivity specific to traditional technology κ is set such that in the year 1900, the employment share in agriculture in the U.S. is 38.7%. The endowment parameters Nt and Lt are 21

Figure 6: Relative Price of Capital Goods

Relative Price, 1929 = 100

1.2 1 0.8 0.6 0.4 0.2

1940

1960

1980

2000

Year

Note: This graph shows the relative price of investment and durable goods over consumption non-durable goods and services. The data of price series are from the Bureau of Economic Analysis (BEA) tables. Please see the data appendix for a detailed description of the data.

calibrated to the series of population and total farm size in the U.S. historical data. I assume the economy differs between 1900 and 2007 by two other parameters: the economy-wide productivity At and the investment-specific productivity υt . υt is chosen to match the relative price of investment and durable goods over consumption non-durable goods and services, as in Greenwood et al. (1997). This relative price series is shown in Figure 6. I assume the investment-specific productivity is constant before 1950, and then grows at a constant rate of 1.55% thereafter, roughly consistent with the data. The series of At is chosen to match a difference of output per capita in the nonagricultural sector of 8.5-fold between 1900 and 2007. Then I choose the fixed cost of adopting the modern technology f to match the diffusion curve. In the data, I measure the percentage of output produced

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Figure 7: Technology Diffusion Curve

Technology Adoption Rate

1 0.8

Data Model

0.6 0.4 0.2 0 1900

1920

1940

1960 Year

1980

2000

Note: [1] The technology adoption rate of the model is the percentage of output produced using modern technology; the rate in the data is the percentage of output produced by farms with tractors. [2] The data are from the historical versions of U.S. Census of Agriculture with author’s computation.

by farms with tractors from historical versions of the U.S. Census of Agriculture. I assume farms with tractors are modern farms. Then I also measure the percentage of output produced by modern technology at each time period. I then choose f to minimize the difference between the model’s prediction and the data. The result is in Figure 7. Table 2 summarizes the values of parameters that are constant over time. Note that some parameters are set to exogenous values, such as {αr , γr , αm , γm , δ, ϕ, π}. The remaining parameters, {κ, c¯, β, σs , f }, are jointly determined by comparing the equilibrium moments with the data. I simulate the model from 1900 to 2007. Before 1950, I assume the economywide TFP (At ) is growing at a constant rate. After 1950, I assume both At and the investment-specific technology (υt ) are growing at constant rates. Then I 23

Table 2: Calibration Summary Category Parameter Value Technology αr 0.15 γr 0.25 αm 0.42 γm 0.16 κ 0.45 δ 0.08 αn 0.33 Preference c¯ 0.1204 ϕ 0.005 β 0.85 Ability σs 1.273 Production f 0.459 π 1

Moment Capital share (traditional technology) Land share (traditional technology) Capital share (modern technology) Land share (modern technology) Agricultural employment share in 1900 Depreciation rate Capital share (non-agricultural sector) Agricultural employment share in 2007 Long-run agricultural employment share K/Y ratio (non-agricultural sector) Farm size distribution in 2007 Technology diffusion over time Normalization

Note: The table shows a list of parameters that are constant over time. {αr , γr , αm , γm , δ, αn , ϕ, π} are directly set to exogenous values, while {κ, c¯, β, σs , f } are jointly determined by comparing the equilibrium moments with the data. compare the model’s prediction on the agricultural employment share, capitallabour ratio, and capital-output ratio with data. Figure 8 compares the agricultural employment share between the model and the data over time. Note that the employment shares at the year 1900 and 2007 are targeted in the calibration. The figure shows that the model fits the agricultural employment share well, not only in the targeted years, but also the overall trend. Figure 9 shows the model fit of the capital-labour ratio and the capital-output ratio. The model captures the trends of the capital-labour ratio and the capital-output ratio in both sectors well, although they are not targeted in the calibration. The above comparison shows that my model replicates the capital deepening process of agriculture in the U.S. reasonably well. I use this calibrated

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Figure 8: The Employment Share in Agriculture

Agricultural Employment Share

0.4 Data Model 0.3

0.2

0.1

0 1900

1920

1940

1960 Year

1980

2000

Note: The this figure compares the agricultural employment share in the data and in the model’s simulation. The employment shares at the year 1900 and 2007 are targeted in the calibration.

model to do quantitative analysis on the capital deepening differences across countries.

4.2

The Importance of Aggregate Factors

This experiment seeks to answer how differences in aggregate factors across countries can explain their differences of agricultural capital intensity. In other words, this experiment gives information on whether the low capital intensity in agriculture in poor countries is a natural phenomenon given their low development levels, or it is due to some other frictions. I also use this experiment to illustrate how the technology diffusion channel works in my model. I compare the U.S. with the poorest 20% countries in my sample. The first difference in aggregate factors is that poor countries on average have only 47% ˙ top of these differences of land endowment per capita compared to the U.S.On in endowments, I also compare their non-agricultural sectors: I treat the differ-

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Table 3: Aggregate Factors U.S. - Poor Model’s Differences Prediction Agriculture: Capital-Labour Ratio Capital-Output Ratio Labour Productivity Non-Agriculture: Capital-Labour Ratio Whole Economy: GDP per Capita

Explained Portion

156 4.3 42

26 3.2 16

65% 79% 75%

11.96

11.85

-

13.96

6.17

-

Note: [1] The second column shows the differences between the U.S. and the poorest 20% countries in my sample. For example, the capital-labour ratio in the U.S. in agriculture is 156-fold of that of poor countries. [2] The third column shows the model’s prediction when the three parameters governing aggregate factors {A, π, L} are set to the levels of poor countries. [3] The explained portion is computed in the following way: suppose the difference is x-fold in the data and the model explains y-fold, then the explained log y portion is log . x ences of the non-agricultural sectors as exogenous. In particular, there are two important differences in the non-agricultural sector: the real capital-output ratio in the U.S. is 2.36-fold of that ratio in poor countries; output per capita in the non-agricultural sector differs for 5.02-fold. I vary three parameters of the model: the economy-wide TFP (A), the land endowment (L), and the barrier to investment (π), to jointly match those three moments of differences in aggregate factors mentioned above. With all the differences in aggregate factors, the model can explain about two-third of the differences in agricultural capital intensity across countries. The results are in Table 3. The differences in capital-labour ratio between the U.S. and the poorest countries is 156-fold, and the model explains for 2626

fold with the differences in aggregate factors. Therefore, the aggregate factors explain

log 26 log 156

= 65% of the observed differences of capital-labour ratio in

the data. The aggregate factors also explains 3.2-fold of capital-output ratio, which is 79% of the observed differences in the data. The model can also explain a large portion of the observed difference in agricultural productivity with differences in aggregate factors. The key to these explanation power is from the channel of technology diffusion. To see this, I also perform this experiment in a model with the modern technology only, which is commonly used in this literature. Table 4 compares the predictions of both models. For example, without the technology diffusion channel, the model predicted difference in capital-output ratio reduces from 3.2-fold to 1.9-fold, much further away compared to the data (4.3-fold). The predicted agricultural productivity difference also reduces from 16-fold to 11-fold. Therefore, the technology diffusion channel amplifies the importance of aggregate factors in explaining the international differences in agricultural capital intensity and productivity. The technology diffusion channel has an impact on the labour productivity differences for the following reason. The international differences in agricultural productivity are typically measured in labour productivity, i.e.,

Ya Na

in

my model. Modern technology has a higher capital share than the traditional technology, thus using capital to substitute labour given the same output level. As labour is substituted by capital, the measured labour productivity

Ya Na

will

increase. The technology diffusion channel also casts doubts on the methodology of growth accounting that attributes the differences of output per capital into the differences of capital-output ratio and TFP. For example, consider the most

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Table 4: The Importance of the Technology Diffusion Channel U.S. - Poor Differences Agriculture: Capital-Labour Ratio Capital-Output Ratio Labour Productivity

Model’s Modern Prediction Tech Only

156 4.3 42

26 3.2 16

10 1.9 11

Note: [1] The second column shows the differences between the U.S. and the poorest 20% countries in my sample. For example, the capital-labour ratio in the U.S. in agriculture is 156-fold of that of poor countries. [2] The third column shows the model’s prediction when the three parameters governing aggregate factors {A, π, L} are set to the levels of poor countries. [3] The fourth column replicates the results in the third column in a model with modern technology only. standard growth accounting equation used in Hall and Jones (1999): α ( K ) 1−α 1 Ya a = Aa1−α . Na Ya

This equation decomposes the labour productivity into the contributions of capital-output ratio and TFP. The key to this accounting is to sign a correct capital share α. However, under my setup with technology diffusion, the capital share in agriculture is endogenous, depending on the aggregate factors, and different across countries. Therefore, using this equation to do the growth accounting cannot properly identify the contributions from both parts.13 13 An important exception is Hulten (1992), who takes into consideration the case when technical change is embeded in capital.

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4.3

Land Misallocation

As the previous experiment shows, aggregate factors cannot account for all the differences in the agricultural capital intensity and productivity. In this experiment, I show that land misallocation can be a good candidate to explain the remaining portion. Recent literature shows that resource allocation matters for the aggregate productivity. Literature also identifies land misallocation as one of the main obstacles in agricultural development. For example, Adamopoulos and Restuccia (2014b) show that the differences of farm size distributions across countries have important impacts on their agricultural productivity. Chen (2015) further considers a specific form of land misallocation: the prevalence of untitled land in poor countries. In many poor countries, land is not allowed to trade or rent among farmers due to a lack of proper title. Local leaders grant this untitled land to farmers based on criteria that are more or less egalitarian. In this experiment, I show how this form of untitled land can affect the capital intensity in agriculture as well as the agricultural productivity. Assume every farmer is allocated an equal amount of land and there is no land market. This setup means the farm size distribution is a degenerated one. I still keep the parameters governing the aggregate factors at the levels of poor countries. Table 5 shows the results when the model is enriched with untitled land. We can see that the explained portion further increases. The model is now able to generate 60-fold difference in capital-labour ratio and 4.4-fold in capital-output ratio, which are much closer to the data. Untitled land further lowers the agricultural productivity of poor countries from 1/16 of the U.S. to 1/26. Untitled land is a friction in land market; however, it does have an impact

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Table 5: The Impact of Untitled Land U.S. - Poor Differences Agriculture: Capital-Labour Ratio Capital-Output Ratio Labour Productivity

156 4.3 42

Model’s Prediction AF Only +Untitled Land 26 3.2 16

60 4.4 26

Explained Portion 81% 103% 87%

Note: [1] The second column shows the differences between the U.S. and the poorest 20% countries in my sample. For example, the capital-labour ratio in the U.S. in agriculture is 156-fold of that of poor countries. [2] The third column shows the model’s prediction when the three parameters governing aggregate factors {A, π, L} are set to the levels of poor countries. [3] The fourth column shows the results when the model includes untitled land. [4] The fifth column shows the percentages explained by the model with untitled land. on the capital intensity. The intuition is as follows. In order for the modern technology to be profitable, the optimal farm size should be large enough so that the extra profit from the modern technology is sufficient to pay the fixed cost. In this setup with untitled land, however, the egalitarian allocation of land prevents those more talented farmers from operating larger farms. Therefore, untitled land may hinder the diffusion of the modern technology. Various land market frictions can affect the technology diffusion in a similar way as untitled land. For example, another common form of land market frictions is ceilings on farm size. Adamopoulos and Restuccia (2014a) describe a land reform in Philippines that imposed a ceiling on farm size (5 hectares) and restricted the farm land transaction. This type of land friction also affects the technology diffusion through the channel that talented farmers cannot operate farms large enough to pay the fixed cost of the modern technology.

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5

Conclusion

The differences of capital intensity between rich and poor countries are larger in agriculture than in the non-agricultural sector. Meanwhile, the capital intensity of the U.S. agricultural sector has been increasing in the 20th century. I study these phenomena using a model with technology diffusion, which can explain the increasing capital intensity in the U.S. agricultural sector. Then I find that the aggregate factors across countries can explain about two thirds of their differences in capital intensity and the channel of technology diffusion is very important. Land market frictions that are prevalent in poor countries can also lower their capital intensity in agriculture. Moreover, these differences in capital intensity substantially contribute to the international agricultural productivity differences.

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Capital-Labour Ratio, Year 1925 = 1

Figure 9: The Capital-Labour Ratio in Agriculture

Agri. (Data) Non-Agri. (Data) Agri. (Model) Non-Agri. (Model)

10 1

10 0 1920

Capital-Output Ratio

4

1940

1960 Year

1980

2000

1980

2000

Agri. (Data) Non-Agri. (Data) Agri. (Model) Non-Agri. (Model)

3

2

1 1920

1940

1960 Year

Note: The this figure compares the capital-labour ratios and the nominal capitaloutput ratios of both sectors in the data and in the model’s simulation. Both ratios are not targeted in the calibration.

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