Agriculture and Aggregate Productivity: A Quantitative Cross-Country Analysis

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1 Agriculture and Aggregate Productivity: A Quantitative Cross-Country Analysis Diego Restuccia University of Toronto Dennis Tao Yang Virginia Polytechnic Institute Xiaodong Zhu University of Toronto March 2003 Abstract A decomposition of aggregate productivity across countries reveals that low agricultural productivity and high agricultural labor share can largely account for poor countries current position in the world income distribution. We show that there is a systematic positive relationship between agricultural labor productivity and the intensity of non-agricultural intermediate input use in agriculture. In an otherwise standard two-sector growth model with agriculture and non-agriculture and minimum consumption requirements of agricultural goods, exogenous differences in non-agricultural productivity and intermediate input to output ratios alone can account for 60% of the observed agricultural labor productivity differences, 78% of the labor share differences in agriculture, and 93% of the aggregate productivity differences across countries. We investigate the role of barriers to intermediate input use and labor mobility and TFP differences in agriculture in generating the observed differences in intermediate input to output ratios across countries. While barriers are successful at accounting for 77% of the intermediate input to output ratios, TFP differences in agriculture imply larger intermediate input to output ratios in poor than in rich countries, an implication that is inconsistent with the evidence. We show that the model with barriers and non-agricultural productivity differences across countries closely matches the data. Our analysis thus implies an emphasis on the importance of removing blocks to the use of efficient technologies in non-agriculture and reducing the barriers that impede the more intensive use of intermediate inputs in agriculture and therefore the movement of labor away from agriculture. Keywords: Subsistence, Intermediate Input, Land, Barriers, Agriculture, Productivity. JEL Classification: O1. Preliminary. Department of Economics, University of Toronto, 150 St. George Street, Toronto, Ontario, M5S 3G7, Canada. 1

2 1 Introduction A remarkable feature of modern economies is the large disparity observed in the average labor productivity across countries. GDP per worker in the richest countries is about 30 times that of the poorest countries. Understanding the source of these productivity differences across countries remains to be a formidable task. (See McGrattan and Schmitz, 1999 for a recent survey.) Using a recently expanded data set of agricultural production across countries, we decompose aggregate labor productivity into agricultural and non-agricultural productivity. This simple disaggregation of aggregate production reveals a striking pattern: labor productivity differences in agriculture are several order of magnitude larger than those for non-agriculture. While the GDP per worker of the richest countries is roughly 30 times the GDP per worker of the poorest countries, non-agricultural labor productivity differences are only a factor of 8 and agricultural productivity differences a factor of more than 100. (For a more detailed documentation of these observations see Table 1 and Figure 1.) 1 Because the poorest countries allocate almost 90% of their labor to agriculture (compared to only 5% in the richest countries), aggregate productivity is mostly determined by the labor productivity in agriculture in these countries. From this perspective, understanding current 1 The data is from the Food and Agriculture Organization of the United Nations (FAO). To our knowledge, this is the best data available to study agricultural productivity. This data is relevant for our purpose of studying agricultural productivity because the methodology to aggregate agricultural goods follows a procedure similar to the methodology used in the Penn World Tables for the comparison of aggregate income across countries. The idea is to price a representative and common basket of goods across countries and convert output valued at domestic prices into a measure of output valued at a common set of prices (international prices), rendering comparable measures of output across countries that is less subject to price distortions across countries. Moreover, the data is relevant for international comparisons of agricultural output because it uses producer agricultural prices, that is, prices received by farmers at the farm gate that exclude charges related to transportation, distribution, and marketing of products to the consumers. These activities belong to the service sector and should not affect agricultural measures of output. This is particularly relevant as service prices vary systematically with development (see Summers and Heston 1991, Table 1, page 338). 2

3 income differences across countries requires understanding both productivity and labor share differences in agriculture. Table 1: Labor Productivity and Labor Shares Across Countries GDP/N GDP n /L n GDP a /L a L a /N Top 5% 30,497 33,711 19, Bot 5% 941 4, Ratio std(log) L a =labor force in agriculture, L n =labor force in non-agriculture, N = L a + L n. Understanding low productivity and high labor shares in agriculture across countries requires a movement away from simple two-sector growth models. The reason is that in these models, low productivity in agriculture implies less labor allocated to that sector. We consider an extension of a two-sector growth model with minimum consumption requirements of agricultural goods, a standard feature in the traditional development literature. (For empirical evidence supporting minimum consumption requirements on food see Atkeson and Ogaki, 1996, 1997 and Rosenzweig and Wolpin, 1993.) With subsistence constraints on agricultural goods, low productivity in agriculture translates into more labor allocated there. Our aim in this paper is to understand the current differences in agricultural labor productivity and agricultural labor shares. We focus in this paper on the role of non-agricultural intermediate inputs (such as pesticides, chemical fertilizers, fuel and energy, among others) in accounting for labor productivity differences in agriculture across countries. Figure 2 documents the ratio of non-agricultural intermediate input expenditures relative to final agricultural output, both measured at common (international) prices. 2 There is a system- 2 We use two measures of agricultural output in this study: agricultural final output and agricultural 3

4 atic positive relationship between the intermediate input to output ratio and agricultural labor productivity, with a correlation coefficient of 62%. Intermediate inputs represent 10% of final output in agriculture in poor countries and 50% in rich countries. 3 Notice that the factor differences in the intermediate input to output ratio across rich and poor countries compare in magnitude to the differences observed in the physical capital investment to output ratio between poor and rich countries. (See for example Restuccia and Urrutia 2001, table 7 page 114.) To illustrate quantitatively how differences in intermediate input use can account for differences in agricultural labor productivity across countries, we do a simple accounting exercise based on a standard Cobb-Douglas production technology in agriculture and subsistence consumption demand for agricultural goods. We find that exogenous differences in non-agricultural labor productivity and differences in intermediate input to output ratios alone can account for 60% of the differences in agricultural labor productivity, 78% of the differences in the share of labor in agriculture, and 93% of the differences in aggregate income differences across countries. These results show that understanding differences in intermediate input use is crucial for understanding the differences in agricultural labor productivity and aggregate income across countries. Why do poor countries use non-agricultural intermediate inputs in agricultural production less intensively than rich countries? In this paper we focus on three potential reasons: (1) low productivity in the non-agricultural sector, (2) barriers to uses of intermediate inputs, gross domestic product. The difference between these two measures is expenditures on non-agricultural intermediate inputs. 3 Even larger differences are observed when comparing intermediate inputs relative to agricultural GDP (10% in poor countries and up to 100% in rich countries). 4

5 and (3) barriers to labor mobility. Low productivity in the non-agricultural sector implies that non-agricultural intermediate inputs are costly relative to labor in agricultural production. Distortions in the intermediate input market may further increase the costs of these inputs. Finally, barriers to labor mobility between the agricultural and non-agricultural sectors suppress wages in the agricultural sector, giving farmers greater incentives to substitute labor for intermediate inputs in production. To investigate quantitatively these factors in accounting for cross-country differences in intermediate input use in agriculture, we consider an otherwise standard two-sector growth model with agricultural and non-agricultural goods and non-homothetic preferences. We take differences in non-agricultural labor productivity directly from the data and treat them as exogenous. We also assume that TFP differences in the agricultural sector are proportional to the differences in non-agricultural productivity. Finally, we measure barriers to intermediate input use as the relative price of intermediate input to non-agricultural output, and the barriers to labor mobility by the average wage differential between the agricultural and non-agricultural sectors. Taking these measure exogenously, we use our model to generate implications for intermediate input to output ratios, agricultural labor productivity, share of labor in agriculture, and aggregate output per worker for all the countries in our sample. We find that the quantities implied by the model closely match those observed in the data. Relative to the standard one-sector growth model, our model with agriculture and barriers amplifies aggregate productivity differences across countries by a factor of 3. Another interesting finding of our paper is the potential difficulties of using agricultural TFP differences in accounting for labor productivity differences in agriculture and in ag- 5

6 gregate. Holding the productivity in the non-agricultural sector as given, lower TFP in agriculture implies a higher relative price of the agricultural output and therefore a stronger incentive for farmers to use intermediate inputs. If labor productivity differences in agriculture are mainly driven by TFP differences, it would imply that the intermediate input to output ratio is negatively correlated with agricultural labor productivity, which is the opposite of what we observe in the data. Although our approach is closely related to the literature that focuses on understanding aggregate labor productivity differences, most notably Mankiw, Romer, and Weil (1992) and Chari, Kehoe, and McGrattan (1996), the novelty of our analysis is in its focus on agricultural production. As we emphasized above, accounting for these differences can take us a lot closer to understanding aggregate labor productivity differences. Our paper is also related to a large literature in development economics that emphasizes the importance of agriculture in development. See, among others, Johnston and Mellor (1961), Fei and Ranis (1964), Schultz (1964), Jonston and Kilby (1975), Hayami and Ruttan (1985), Mellor (1986), Timmer (1988), and Syrquin (1988). Recently, there have been several papers that use two (or three) sector general equilibrium models to study long-term economic development. See, for example, Matsuyama (1992), Hansen and Prescott (1998), Laitner (1998), Eswaran and Kotwal (2001), Ngai (2001), Stokey (2001), and Yang and Zhu (2001). Most of these papers focus on the process of industrialization and the role of agriculture in that process. The focus of our paper, similar to Gollin, Parente and Rogerson (2001), is in understanding the disparities in agricultural productivity across countries in the postwar data. Our paper is also related to a recent literature that focuses on the timing of 6

7 the transition to modern economic growth as fundamental determinant of current income differences. (See for example Lucas 2000, Hansen and Prescott 2002, Ngai 2000, and Gollin, Parente, and Rogerson 2002.) Our theory complements this literature by accounting for a large portion of the agricultural productivity differences without relying on the timing of start of modern growth. This feature can be embedded in our framework by considering a traditional technology and a modern technology in agriculture. Finally, Coleman and Caselli (2001) study the role that a reduction of barriers to labor mobility between agricultural and non-agricultural sectors played in accounting for the income convergence between Southern and Northern states in the U.S. The paper is organized as follows. In the next section we use a simple framework to illustrate the quantitative importance of the differences in intermediate input uses and the potential factors that may cause these differences. In section 3 we present the model that we use for our quantitative exercises. We describe how we calibrate the model and our quantitative results in section 4. Finally, we provide some discussions and conclusions in section 5. 2 A Simple Illustrative Framework To understand the importance of non-agricultural intermediate inputs in accounting for cross-country differences in agricultural labor productivity and labor share, we posit the following agricultural production function Y a = ( A a Z 1 σ L σ a) 1 α X α, 0 < σ < 1, 0 < α < 1. 7

8 Here, Z, L a, and X are land, labor, and intermediate input, respectively. Under this production technology, we can decompose the output per worker in agriculture as ( )1 σ ( ) Y a Z X α ( ) 1 α L σ 1 a = A a, (1) L a N Y a N where N is the population size. To simplify the exposition, we also assume that the supply of agricultural output is determined by the population s subsistence consumption demand for agricultural goods. That is, Y a = Nā, where ā is the per capita subsistence consumption of the agricultural good. 2.1 The Role of Intermediate Inputs in Agriculture Our simplifying assumption implies that L a N = Y a L a = ( A Z a N ( A Z a N ā ) 1 σ ( ) α X 1 α Ya ) 1 σ ( X Ya ) α 1 α ā 1 σ 1/σ 1/σ,. So, along with the subsistence constraint on agricultural consumption, a standard agricultural production technology with an intermediate input, labor, and land implies that the intermediate input to output ratio, X/Y a, is positively correlated with agricultural labor productivity and negatively correlated with the share of labor in agriculture. Notice that the direct effect of the intermediate input to output ratio on labor productivity is (X/Y a ) α 1 α. However, low productivity implies that more labor is allocated to produce agricultural output 8

9 to satisfy the subsistence demand. This reduces productivity further because of diminishing returns to labor (since land is a fixed factor of production). As a result, the impact of the the intermediate input to output ratio is magnified by a factor of 1/σ (in logarithmic scale). Using the equations above and parameter values that are justified later in the calibration section, Table 2 illustrates the importance of intermediate inputs and productivity differences in non-agriculture in determining labor shares in agriculture and productivity differences. Our assumption is that TFP differences in agriculture A a are proportional to TFP differences in non-agriculture. The range considered for intermediate inputs and non-agricultural productivity are reasonable given our discussion of the data above. Labor shares in agriculture can be quite high. Also, differences in labor productivity in agriculture and aggregate productivity can be very large. Of course, our simplifying assumptions so far exaggerate these results, but we hope it provides a motivation for the quantitative experiments we pursue in section Barriers to Intermediate Input Use What determines farmers choice of intermediate input in agricultural production? To answer this question, we look at a representative farm s profit maximization problem: { ( ) } max p a Aa Z 1 σ L σ 1 α a X α p x X w a L a, X,L a 9

10 Table 2: Quantitative Example X/Y a A n /A us n (L a /N) i / / / / (Y a /L a ) us /(Y a /L a ) i / / / / (Y/N) us /(Y/N) i / / / / L a /N =labor share in agriculture, Y a /L a =output per worker in agriculture, and Y/N =aggregate output per worker. The parameters used are given in Table 3. where p a is the price of agricultural good, p x the price of intermediate input, and w a the wage in the agricultural sector. The first order condition with respect to X implies that X = ( αpa p x ) 1 (1 α) Aa Z 1 σ L σ a. Substituting it into the production function we have Y a = ( αpa p x ) α (1 α) Aa Z 1 σ L σ a. 10

11 So, taking prices as given, the optimal intermediate input to output ratio for the farmer is given by X Y a = α p a p x. That is, the intermediate input to output ratio is determined by the price of the agricultural good relative to the price of the intermediate input. Again, if we assume that the agricultural output is used to simply satisfy the subsistence consumption, then, we can solve for the equilibrium level of agricultural price, p a that clears the market for agricultural good (see appendix). Substituting the equilibrium price into the equation above, we have X Y a = µw a ( ) 1 σ p x A Z a N (1 α) 1 (1 α)(1 σ), (2) where µ is a constant given by ( ) σ µ = ā 1 σ α. σ(1 α) Equation (2) shows two potential reasons for low intermediate input to output ratio in poor countries: high intermediate input prices and low agricultural wage. The price of intermediate input may be high because either the cost of producing it is high, or there are barriers to use intermediate inputs. If labor is completely mobile between the two sectors, then the agricultural wage equals the wage rate in the non-agricultural sector, which equals the marginal product of labor in 11

12 that sector. Therefore, low labor productivity in the non-agricultural sector could contribute to the low intermediate input to output ratio in the agricultural sector. In addition, the agricultural wage may be depressed down further if it is costly to for workers to move from the agricultural sector. Therefore, barriers to labor mobility may also imply a low intermediate input to output ratio. Finally, notice that the agricultural TFP also affects the intermediate input/output ratio, but in a different direction: low agricultural TFP implies high intermediate input/output ratio. This implication of the theory points to a potential limitation of using low agricultural TFP as an explanation for low labor productivity in agriculture. 3 Economic Environment We consider a two-sector growth model with agriculture and non-agriculture that features non-homothetic preferences. A detailed description of the environment follows. 3.1 Household Consumption The economy is populated by a large and constant number (mass N) of homogeneous households. Households derive utility from consumption of an agricultural good and a nonagricultural good. The representative household s preferences over consumption goods are summarized by the following utility function U = a ln(c a ā) + (1 a) ln(c n ), 12

13 where c a is the individual s consumption of the agricultural good, ā is the subsistence level of agricultural good consumption, and c n is the consumption of the non-agricultural good. Let the non-agricultural good be the numeraire and p a be the price of the agricultural good. The utility function implies that the individual will allocate the first ā amount of income on consumption of the agricultural good, and then allocate the rest of the income proportionally to the agricultural and non-agricultural goods. More specifically, c a = ā + ap 1 (y pā), (3) c n = (1 a)(y t pā). (4) 3.2 Agricultural and Non-Agricultural Production The agricultural production technology is the same as that specified in the previous section. The non-agricultural good is produced with a constant returns to scale technology using labor only: Y n = A n L n, and the stand-in firm s profit maximization problem is max L n {Y n w n L n }, (5) where w n is the wage in the non-agricultural sector. 13

14 3.3 Barriers to Labor Mobility We assume there are barriers to labor mobility. In our environment we represent the barriers as a cost to labor reallocation, which is proportional to the wage in the non-agricultural sector, θw n. No-arbitrage condition in the labor market implies that w a = (1 θ)w n. (6) 3.4 Goods Market Clearing Conditions N = L a + L n, (7) Y a = Nc a, (8) Y n = Nc n + p x X. (9) 3.5 Definition of Equilibrium A competitive equilibrium is a set of allocations {L a, L n, c a, c n, X} and prices {p a, p x, w a, w n } such that: (i) Given prices, c a, c n solve the household s problem; (ii) Given prices, L a, X, and L n solve firms problems in each sector, (iii) Condition (6) holds so that households are indifferent between working in the two sectors, and (iv) All markets clear. 14

15 4 Quantitative Results In this section we assess the quantitative role of productivity differences in non-agriculture and intermediate input use in generating the observed cross-country patterns in agricultural labor share and agricultural and aggregate productivity. We find that the model can account for a large portion of these differences across countries. 4.1 Calibration We calibrate the benchmark economy to U.S. data. The following 7 parameters values need to be determined: a, ā, α, σ, Z/N, A n, and A a. The land to population ratio Z/N is taken directly from U.S. data in The ratio of arable land (in hectares) per working age person in the U.S. economy is 1.8. The TFP parameters are computed from sectoral Solow residual calculations for the U.S. economy using the production functions specified in the previous section, which results in A n = 34, 254 and A a = 17, 659 (a ratio of 1.9). The labor income share in agriculture σ is set at 0.7, consistent with the estimates of agricultural production functions reported by Hayami and Ruttan (1985) and Mundlak (2001). The elasticity parameter of intermediate inputs in agricultural output α is chosen to match the intermediate input to output ratio in the U.S. economy. This implies α = 0.4. Finally, the values of a and ā are selected two targets for the agricultural labor share. Roughly speaking, a is selected to match an agricultural labor share of in the longrun, and ā is chosen to match an agricultural labor share of as observed for the U.S. 15

16 economy in These targets imply a = and ā = 839. A summary of the calibrated parameter values and targets is provided in Table 3. Table 3: Calibration to U.S. Data Parameter Value Target Z/N 1.8 Land to population ratio A n 34,254 Labor prod. in non-ag. A a 17,659 Labor prod. in ag. σ 0.7 Hayami and Ruttan 1985 α 0.4 Intermediate Input Ratio a Long-run ag. labor share ā 839 Labor share in ag Quantitative Role of Intermediate Inputs We consider a set of closed economies that differ in non-agricultural productivity and intermediate input use as described in Figures 1 and 2. We assume that the ratio of total factor productivity between non-agriculture and agriculture is constant and equal to the U.S. ratio across countries. 4 Countries also differ in the observed land to population ratios, although these differences are not quantitatively important since they are not systematically related to development. We compute the equilibrium labor share in agriculture implied by these exogenous differences in productivity and intermediate input to output ratios. The results of this experiment are displayed in Figure 3. In this Figure, the first panel reports the agricultural labor share 4 In this paper, we focus on agricultural productivity differences, taking non-agricultural productivity differences as given. There is a large literature dealing with aggregate productivity differences, with emphasis on capital accumulation and total factor productivity. (See for example, McGrattan and Schmitz 1999 and Parente and Prescott 2000.) 16

17 in the model and the data. The model implies labor shares that are close to the data. The second panel displays the intermediate input to output ratio in the model and the data. Since these are taken exogenously in this experiment, the points lie in the 45 degree line. The third panel displays the relative aggregate GDP differences in the model and the data. The model does reasonably well in accounting for aggregate productivity differences. To understand the relative contribution of each exogenous factor (productivity in nonagriculture and intermediate input to output ratio) in accounting for the labor shares and agricultural and aggregate productivity, we calculate the percentage of the variance in each variable accounted for by the model with exogenous productivity differences and intermediate input to output ratios. Table 4 summarizes the results of these calculations. The model accounts for 78% of the differences in the agricultural labor share, 60% of the differences in agricultural productivity, and 93% of the differences in aggregate productivity. The model without intermediate input differences (assuming all countries have X/Y a equal to the U.S. level) accounts for 48% of the labor share differences, 40% of the agricultural productivity differences, and 58% of the aggregate productivity differences. These results strongly suggests the importance of understanding both the low labor productivity in non-agriculture and the low intermediate input intensity in agriculture in poor countries. The model implies aggregate relative productivity differences of factors of 22, while a standard one-sector growth model with the same non-agricultural labor productivity differences would imply productivity differences of a factor of 8, that is, the model with agricultural production and subsistence amplifies the role of non-agricultural productivity by a factor of 3. 17

18 Table 4: % of Variation Accounted for by the Model Model with: (A n, X/Y a ) (A n only) Variable L a /N X/Y a Y a /L a Y/N (% of Y a /L a ) (X/Y a ) α (1 α) (Z/N) 1 σ (L a /N) σ A n What Accounts for the Intermediate Input Ratio? Barriers to Intermediate Input Use The FAO data provides information on the prices paid by farmers (at the farm-gate) for non-agricultural intermediate inputs used in agricultural production (such as pesticides, fertilizers, electricity, and other miscellaneous items). Roughly speaking these purchase power parity prices are the ratio of expenditures in these items relative to the international priced quantity of intermediate inputs. We use the price of non-agricultural output as the numeraire (following the set up in our model) and compute the relative price of intermediate inputs relative to the non-agricultural output for each country. These prices are reported in Figure 4. There are important differences in relative intermediate input prices and the differences are systematically related to development. For instance, Ethiopia, Nepal, and Mali report relative prices of intermediate inputs that are factors of 6 and 7 of the U.S. relative price. We interpret these relative price differences as barriers to intermediate input 18

19 use. We denote these barriers by p x = π. Jones (1994) and Restuccia and Urrutia (2001) use the price of investment relative to consumption as a measure of barriers to investment in one-sector growth models. Figure 5 illustrates the implications of the model when we allow barriers to intermediate input use π for the agricultural labor share (first panel), the intermediate input to output ratio (second panel) and aggregate productivity (third panel). Table 5 summarizes the implications of the model. The first column reports the implications of the model for this case. The model with barriers to intermediate input use π accounts for 23% of the differences in X/Y a across countries. Table 5: % of Variation Accounted for by the Model (1 θ) Model with: p x (1 θ) p x Model with (A n, X/Y a ) Variable L a /N X/Y a Y a /L a Y/N (% of Y a /L a ) (X/Y a ) α (1 α) (Z/N) 1 σ (L a /N) σ A n Barriers to Labor Mobility In an environment with perfect labor mobility, wages must be equalized across sectors. As we suggested in section 2, low wages in the agricultural sector relative to the non-agricultural sector may account for the low intensity with which farmers utilize non-agricultural inter- 19

20 mediate inputs in poor countries. We investigate this possibility by constructing measures of sectoral wages across countries using the no-arbitrage condition for relative wages (1 θ) = w a w n. Under constant returns to scale production functions, the average labor product is proportional to the wage in each sector. As long as the labor income shares are constant across countries, as suggested by the evidence in Gollin (2002), relative barriers should not be affected by this proportionality factor. 5 We find large and systematic differences in barriers to labor mobility across countries. These are illustrated in Figure 6. Figure 7 illustrates the results of the model when (1 θ) is allowed to vary as suggested by the wage differences emphasized above. In Table 4, the second column reports the results for this version of the model. The model with barriers to labor mobility accounts for 31% of the differences in X/Y a across countries Both Barriers When both kinds of barriers are considered together, the model is able to account for almost 77% of the differences in X/Y a across countries. Through intermediate input use, these barriers have a large impact on labor allocations and labor productivity in agriculture. Figure 8 reports the results when both (1 θ) and p x are allowed to vary as in the data. The results 5 We use data from FAO and Summers and Heston (1991) to construct measures of relative prices and relative labor products to obtain the measure of barriers. Similar quantitative barriers are obtained if instead, a direct measure of labor products in domestic prices are used. Also, the same quantitative implications are derived when wages are measured directly as suggested by the evidence in Hayami and Ruttan (1985). 20

21 are striking. See third column in Table 5. 5 Discussion To be written. 6 Conclusions Low agricultural labor productivity and high agricultural labor shares are at the core of low aggregate productivity in poor countries. In this paper we show that labor productivity in non-agriculture and intermediate input use in agriculture can account for the agricultural labor share and agricultural productivity across countries in an otherwise two-sector growth model with minimum consumption requirements of agricultural goods. We show that with barriers to intermediate input use and labor mobility as measured in the data, the model can largely account for the differences in intermediate input ratios. By accounting for an important portion of the agricultural productivity differences and agricultural labor share differences across countries, this paper provides both a better understanding of aggregate productivity differences across countries. 21

22 A Data for Agriculture In this appendix we summarize the construction of agricultural output statistics. A complete description of these procedures is in Prasada Rao (1993). The main source of data is the Food and Agricultural Organization of the United Nations (FAO). Due to data limitations, agricultural activities include agriculture and hunting and exclude forestry and fishing. Also, within agricultural activities, only crops and livestock production is included, due to limitations of reasonable cross-country data for agricultural services. Output is comprised of a large and representative set of commodities and aggregation is done using prices. A key aspect of the exercise is the extent and quality of prices used. An important advantage of the FAO data set is that agricultural production is valued at producer prices, that is, using farm-gate prices that exclude expenses such as transportation costs, distribution and marketing. Using data of N commodities, indexed by i, and M countries, indexed by j, total agricultural output in country j is defined as, N T j = p i,j q i,j, i=1 where q i,j and p i,j are the quantity and price of commodity i in country j. Hence, this is a measure of total output in country j prices (currency). In order to obtain comparable measures of agricultural total production across countries, a common set of prices must be used. Let π i be the international price of commodity i measured in a reference currency (dollars), therefore, total agricultural output in country j at international prices is defined 22

23 as, N Tj = π i q i,j. i=1 There are two important measures of agricultural output considered: final output and GDP. Final output comprises total output as defined above minus any intermediate agricultural inputs used in production such as feed and seed. GDP consists of final output minus any intermediate non-agricultural input such as fertilizer, pesticide, fuel and energy, etc. Therefore, agricultural final output, F j, is defined as, N N N F j = p i,j q i,j p s i,js i,j p f i,jf i,j, i=1 i=1 i=1 where s i,j is the quantity of commodity i used as seed and f i,j is the quantity of commodity i used as feed. Notice that the prices of these inputs are allowed to differ from the producer price, that is, the general principle is that all prices are valued at the farm-gate, and therefore, prices for inputs are the purchase price paid by farmers at the farm gate including any distribution charges, such as transportation costs, and any taxes, subsidies and/or bulk discounts. Agricultural GDP is defined as, K Y j = F j w k,j x k,j, k=1 where x k,j and w k,j are the quantity and price of non-agricultural commodity k in country j. Again, the general pricing principle is that w k,j is the farm-gate purchase price paid by the farmer. 23

24 Both final output and GDP are converted in comparable units across countries using standard methods. These are extensively described in Prasada Rao (1993) and the references therein. A general principle of these aggregation methods is the property of country invariance and transitivity, that is the results of these methods are independent of the political subdivision of the world and the comparison of two countries in not affected by the comparison through a third alternative country. We present the basic aggregation procedure used, the Geary-Khamis (GK) method. This methods involves finding the fixed point of the following system of equations: π i = P P P j = ( M pi,j j=1 P P P j ) Ni=1 p i,j q i,j Ni=1 π i q i,j, γ i,j, where γ i,j = q i,j M j=1 q i,j are quantity weights. The first N equations correspond to the determination of international prices for every commodity i, as a weighted average of prices in the world, and the second set of M equation correspond to the determination of agricultural purchase power parities for every country j, as the ratio of output in domestic prices relative to output valued at international prices. A slightly different method is used to compute a comparable measure of agricultural GDP taking non-agricultural input prices into account. The data is contained in the FAO Interlinked Computerized Storage and Purchasing System of Food and Agricultural commodities (ICS). The output data includes 185 commodities at a fairly detailed level (although it is not adjusted for quality differences), 58 commodities used as seed, and 146 commodities used as feed. Data on quantities and prices is collected 24

25 for all benchmark years, 1970, 1975, 1980, 1985 and There are 103 countries in the sample, representing 99% of total world agricultural production and 98% of the world population. The sample of countries is fairly well distributed along the cross-country income distribution. B Solution of Equilibrium To be written. C Productivity Accounting in Agriculture To formally investigate the importance of the land to labor ratio and intermediate input use in accounting for agricultural labor productivity we posit the following agricultural production function ( ) Y a X α ( 1 α Z = L a Y a N ) 1 σ ( ) σ 1 La A a, (10) N where Y a is final output in agriculture, X/Y a is the intermediate input ratio, Z is land, L a /N is the labor share in agriculture, and A a is the residual. Because we abstract from physical capital in our model (due to data constraints on sectoral allocation of capital), and physical capital is produced in the non-agricultural sector, we assume the following relationship between A a and the productivity in the non-agricultural sector A n, A a ξa n  a ; ξ = ( ) Aa A n us, 25

26 where Âa is the residual and ξ is a fixed proportion factor. The implicit assumption here is that the capital income share is constant between the agricultural and non-agricultural sector. The available evidence suggests this might be a conservative strategy. Using data on intermediate input ratio X/Y a, land to population ratios Z/N, agricultural labor shares L a /N and non-agricultural TFP as labor productivity in non-agriculture A n = Y n /L n and this equation we perform an accounting exercise and ask: how much of the labor productivity differences can be accounted for by intermediate inputs and the land to labor ratio across countries. The results of this exercise are reported in Table 6. About 34% of the differences in agricultural productivity is accounted for by differences in the intermediate input ratio, land to population ratio, and the agricultural labor share. Together with differences in non-agricultural productivity (as a proxy of the capital to output ratio differences) account for 61% of all labor productivity differences in agriculture across countries. Table 6: Variance Decomposition of Agricultural Productivity Variable W Y a ) α cov[log(y a /L a ),log(w )] var[log(y a /L a )] W = ( X 1 α 0.15 W = ( ) 1 σ Z 0.02 N W = ( ) σ 1 L a 0.17 N W = A n 0.27 W = Âa

27 References [1] Dahan, Momi, and Daniel Tsiddon Demographic Transition, Income Distribution, and Economic Growth. Journal of Economic Growth 3(1): [2] Echevarria, Cristina Changes in Sectoral Composition Associated with Economic Growth. International Economic Review 38(2): [3] Goh, Aiting Trade, Employment, and Fertility Transition. Journal of International Trade and Economic Development 8(2): [4] Gollin, Douglas, Stephen Parente, and Richard Rogerson Farm Work, Home Work, and International Productivity Differences. Manuscript. University of Pennsylvania. [5] Hansen, Gary, and E. C. Prescott Maltus to Solow. Staff Report 257. Federal Reserve Bank of Minneapolis. [6] Johnson, Gale D Population, Food, and Knowledge. American Economic Review 90(1): [7] Kuznets, S The Pattern of Shift of Labor Force from Agriculture. in Economic Development, Family and Income Distribution. [8] Kuznets, S Mordern Economic Growth: Rate, Structure, and Spread. New Heaven, CT: Yale University Press. 27

28 [9] Mundlak, Y., Production and Supply, in B. Gardner and G. Rausser, eds., Handbook of Agricultural Economics, Volume 1A, Chapter 1, (New York: North-Holland Elsevier, 2001), [10] Prasada Rao, D.S Intercountry Comparisons of Agricultural Output and Productivity. FAO Economic and Social Development Paper 112. Food and Agriculture Organization of the United Nations. [11] Summers, Robert and Alan Heston The Penn World Table: An Expanded Set of International Comparisons, Quarterly Journal of Economics: [12] World Bank. World Development Indicators. Various issues. To be completed. 28

29 Figure 1: Labor Productivity across Countries 1985 YnLn (U.S./Country i) MOZ ETH TZA SOM GHA TCD AGO HTI NGA MWI UGA MDG SDN BFA BDI CIV SLV GIN KEN IND PHL NER MLI PAK HND SWZ CMR BGD IDN BOL NIC PRYDOM RWA NPL SEN ZWE PNG THALKAMAR TUR EGY GTMPERCRI COL ECU CHL ZAF URY KOR MYS HUN BRA PRT YUG DZA IRN ARGIRQ GRC MEX SYR VEN JPN IRL ESPISR GBR FIN AUT DNK NZLFRA ITA DEU BELSAU NLD NOR AUSCHE CAN USA YaLa (U.S./Country i) YnLn/YaLa (relative to U.S.) MOZ BFA NER ETH AGO NPL BDI TZA MWI RWA CHN SEN GIN NGA ZAR TCDKEN BGD UGA MLI HTI IND LAO MDG BUR SOM GHAZWE CMR IDN SDN THA PAK LKA PNG CIV PHL HNDSLV BOLMAR DOM EGY GTM KOR NIC TURPER MNG ROMSWZPRY POLCRI COL ECUMYS BGR CHL ZAF BRA PRT YUG DZA IRN SUN IRQ MEX GRCSYR VEN JPN 0 CSK URY HUN ARG DDR IRL ESPISR GBR FIN AUT DNK NZL SWE FRA ITA DEU BELSAU NLD NOR AUSCHE CAN NPL BFA NER RWA BDI GIN SEN BGD MWI MLI AGO KEN ETH CMR TCD IND THA TZA UGA MDG HTINGA ZWE PNG IDN LKA DZA GHA CIV BOL EGY GTM KOR MOZ PAK IRN HND MAR PER IRQ MEX SOMSDN TUR PHL SLV NIC DOM CRI COL ECUMYS CHL BRA PRT YUG SYR JPN SWZPRY ZAF GRC VEN IRL ESPISR FIN AUT ITA 0 URY HUN ARG GBRDNK NZLFRA DEU BEL NLD AUS CAN Relative Per Worker GDP SAU NORCHE USA USA 29

30 Figure 2: Intermediate Inputs and Labor Productivity in Agriculture 250 MOZ NER BFA 200 Y a /L a (U.S. relative to country) ETH NPL AGO BDI MWI SEN RWA NGA TZA GIN BGD KEN ZAR TCD MLI UGA IND HTI MDG GHA SOM SDN PHL SLV ZWE IDN CMR THA LKA PAK PNG HND CIV KOR GTM PER MAR BOL EGY TUR NIC DZA DOM MEX IRQ IRN ECU COLMYS YUGSWZ PRT PRY BRA VENCHL ZAF ITA HUN IRL URY ARG AUS CRI GRC ESP AUT CHE FIN FRA JPN SYR NOR GBR SWE DEU ISRBEL 0 NZL NLD USA DNKCAN SAU X/Y a 30

31 Figure 3: Model with Non-Ag. Productivity and Intermediate Inputs Model MOZ ZAF URY JPN HUNCHL PRT GBR BELDEU ARG AUS DNK FRA AUT ITA IRL ISR NLD CHE NZLVEN IRQ USA NORFIN ESP NGA PHL GHA HTI SOM TZAETH TCD SLV AGO KEN UGA MWI IND BDI IDN SDN MDG MLI GIN BFA BGD DOM HND LKA NER KOR PAK EGY CIV NPL NIC MEX BOL PNG RWA ZWE SEN SWZ PER PRY COL MAR CRI ECU GTM THA CMR BRA MYS YUG GRC DZA TUR SAU IRN SYR 0 CAN Ag. Labor Share Data 1 Model Model 0.5 BEL CANDEU JPN ISR DNK SWE NOR ARG AUS AUT CRIFINFRA GRC NLD BRA CHL DZA COL IRN HUN AGO BGDBOL CIV GTM DOM CMR ECU EGY IRQ IRL KOR MYS MAR NZL PRT SAUESP CHEUSA SYR GBR ETH TCD BDI GHA BFA SLV GINHTI HND IND IDN ITA MDG NIC MEX MLI NER MWI NPL MOZ KEN NGA PNG PAK PER PRY ZAF LKA THA YUG SWZ URY TUR VEN PHL RWASEN ZWE SOM TZA UGA SDN ZAR SAU X/Ya Data TUR YUG BRA CMR GTM ECU MYSPRT RWA NPL PNG THA MAR PERCRI COL CHL ZAF HUN SEN BGD BOL EGY URY KOR BFA GIN ZWE PRY NER MLI CIV PAK HND DOM BDI MDG TCD MWI AGO KEN IND IDN SWZ LKA NIC SDN UGA SLV SYR FIN AUT DNK IRN ESP GRC ISR GBR DZA IRQ VENIRL JPN ARG MEX CAN NOR AUS FRA CHE ITA DEU BEL NLD NZL 0 ETH TZA MOZ SOM HTI GHA NGA PHL Relative Income Data USA 31

32 Figure 4: Barriers to Intermediate Input Use ETH Relative Price of Intermediate Input NPL MLI RWA BGD PNG TCD SDN MOZ TZA NIC MDG SLV EGY BFA PRY MAR HTI PHL LKA BDI MWI GIN CIV IND PER CHL KEN THA NER PAK CRI ECU ZWE COL BRA AGO DOM URY YUG GHA TUR MYS CMR IDN HND KOR SEN UGA GTM HUN PRT BOL NGA ZAF SYR IRQ JPN IRL MEX ARG GRC DZA VEN IRN ESPISR AUT GBR FIN DNK ITA NZL AUS FRA CHE DEU BEL NLD NOR CAN SAU USA Relative Per Worker GDP Price of non-agricultural intermediate inputs relative to the price of non-agricultural output. Relative to the U.S. price. 32

33 Figure 5: Model s Implications with p x 1 MOZ SOM ETH TZA Model 0.5 URY CHL BELDEU ARG AUS DNK FRA AUT JPN ZAF HUN PRT GBRISR NLD CHE NORFIN ITA NZL ESP IRL IRQ USA VEN NIC SLV DOM SWZ KOR PRY CRI BRA COL PER MEX MYS YUGECU GRC SAU DZA SYR IRN GHA NGA PHL EGY LKA PAK CIV HND IDN MAR BOL GTMTUR HTI IND SDN MDG AGO BGD KEN ZWE PNG THA CMR SEN TCD MWI UGA MLI NPL BDI GINER BFA RWA 0 CAN Ag. Labor Share Data 1 Model 0.5 MEX NGA KOR JPN BEL GHA IDN VEN NLD DEU AGOBOLGTM DOM DZA AUT DNK BDI EGY SLV GIN HTI IRN SAU CHE GBR ISR UGA KEN ZAF NOR TZA PHLHND IND COL HUN GRC MWI MOZ SEN BFA ARG CRIFINFRA BGD CIV MDG CMR ECUIRQ IRL NZL PRT PAK MYS NER ITA BRA MAR NIC CHL CAN ETH TCD MLINPL PNG ZWE LKA PER THA ESP USA YUG URY RWA PRY SWZ TUR SDN AUS SOM SYR Model SAU X/Ya Data RWA NPL TUR YUG GTM ECUMYS BRA PNG CMRTHA PRT GIN SEN BGD EGY CRI COLKOR BFA BDI BOLMAR PER CHL ZAFHUN NER MLI ZWE KEN CIV PAK HND DOM MWI SLV TCD AGOIND IDN LKA URY PRY UGA NIC MDG SDN PHLSWZ HTI GHA NGA ETH TZA SYR FIN AUT DNK IRN MEX ESP GRC ISR GBR DZA IRQ VENIRL JPN ARG CAN NOR AUSCHE FRA ITA DEU NLD BEL NZL 0 MOZ SOM Relative Income Data USA 33

34 Figure 6: Barriers to Labor Mobility NER 14 BDI SEN AGO BFA 12 MWI RWA (1 θ) us /(1 θ) i 10 8 CMR THA KEN ZWE NPL PER GIN MLI 6 HND GTM MEX 4 2 MDGIND BGD BOL TCD CIV TUR NGA PAK IDN LKA UGA GHA PHL MAR SDN EGY TZA MOZ SLV HTI PNG NIC ETH PRY DOM SOM SWZ KORYUG COL BRA ZAF MYSPRT ECU CHL CRI HUN URY DZA IRN IRQ VEN NOR JPN GRC ESP FIN AUT ARG DEU IRL CHE CAN SYR ISR GBRDNK FRA ITA AUS USA NZL BEL NLD Relative Per Worker GDP 34

35 Figure 7: Model s Implications with (1 θ) 1 MOZ Model Model Model 0.5 SOM BEL ARG AUS AUT JPN ZAF DEU CHL PRT GBRISR DNK FRA FIN IRL HUN IRQ NLD CHE NOR VEN USA ITA NZL ESP URY PER KOR SLV DOM SAUMEX NIC COL BRA CRI DZA SWZ MYS YUGECU PRY GRC IRN SYR AGO MWI NGA GHA KEN TZA BDI NER IND MDG ETH BFA PHL HND HTI ZWE SEN TCD UGA LKA PAK IDN CIV THA GIN BOL BGD CMR MLI SDN NPL RWA EGY MARGTM SOM TUR PNG CAN Ag. Labor Share Data BEL URY NZL NLD GBR ISR MOZ DOM ETHTZAHTI SWZ ITA HUN CHE JPN PNG CRI SLV EGY FRA DNK DEU GHA ECU CHL AUT BGD COLARG GRC IND IDN IRL KOR PHL NIC NGA PRY LKAMEX UGA SDN MYS FIN TCD CIV MDG PAK MAR ZAF PRT USA SYR BRA AUS BOL IRQ VEN ESP CAN NOR MLI GIN NPL KEN YUG HND GTMDZA IRN BDI BFA MWI RWA PER TUR NER AGO ZWE SEN CMR THA SAU X/Ya Data 1 SAU 0.5 RWA NPL PNG TUR ECUMYS YUG GTM BRA CMR BGD EGY CRI COL CHLHUN PRT GIN THA MAR KOR MLI BOL DOM BFA CIV SLV BDI NER PAK HND TCD MDG KEN HTI IND IDN PRY PER ZAF URY SEN LKA NIC SOM SDN ZWE SWZ UGA PHL ETH TZA MWI AGO GHA NGA SYR FIN ESP AUT DNK IRN ISR GBR GRC MEX IRL DZA IRQ VEN JPN ARG CAN ITA AUS FRA DEU NLD NORCHE BEL NZL 0 MOZ Relative Income Data USA 35

36 Figure 8: Model s Implications with (1 θ)/p x Model MOZ AGO TZA MWI ETH BDI GHA KEN MDG TCD BFA SOM NER IND MLI NGA PHL HTI ZWE NPL RWA CIV BGD SDN SEN PER GIN SLV HND LKA PAK IDN THA UGA NIC KOR EGY MAR CMR DOM COL PRY BOL PNG GTM JPN CHL BRA CRI MEX ZAF SWZ PRT SAU MYS YUGECU TUR ARG DZA BELDEU CAN AUS DNK FRA AUT HUN IRQ GBRISR NLD CHE NORFIN ITA VEN URY NZL ESP IRL GRC SYR IRN USA Ag. Labor Share Data 1 Model Model 0.5 BEL NLD NZL GBR ISR URY HUN CHE DNK DOM FRA DEU JPN SOM HTINGA SWZ ITA ARG AUT CRI GHA MEX IRL KOR VEN USA TZA GRC FIN UGA SLV IDN ZAF MOZ BOL DZA AUS CAN ECU EGY IRN ETH COL MYSPRT NOR PHL PNGPRY CHL BRA TCDGINBGD HND IND NIC ESP LKA IRQ KEN CIV PAK MDG GTM MAR SYR SDN YUG TUR MLI NER BDI BFA MWI NPL AGO CMR PER RWA SEN ZWE THA SAU X/Ya Data 1 SAU 0.5 TUR ECUMYS YUG BRA PNG GTM CRI COL HUN PRT CMR CHL BGD BOLMAR EGY ZAF URY KOR RWA GINNPL THA DOM SEN CIV PAK IDN HND SWZ SLV LKA PRY PER NIC BFA NER UGA MLISDN ZWE BDI TCD MDG KEN HTI IND GHA NGA PHL SOM SYR FIN AUT DNK IRN ESP ISR GBR GRC MEX VENIRL DZA IRQ JPN ARG CAN AUS FRA ITA DEU NLD NORCHE BEL NZL 0 ETH TZA MWI MOZ AGO Relative Income Data USA 36

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