Agricultural Risk, Intermediate Inputs, and Cross-Country Productivity Differences

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1 Agricultural Rik, Intermediate Input, and Cro-Country Productivity Difference Kevin Donovan Univerity of Notre Dame February 2016 Abtract Agricultural productivity i crucial for undertanding aggregate cro-country income difference. Thi paper conider the impact of low intermediate input intenity in developing countrie. In a dynamic general equilibrium model with idioyncratic hock, incomplete market, and ubitence requirement, farmer in developing countrie rationally ue fewer intermediate input becaue it limit their expoure to uninurable hock. The calibrated model account for nearly half of the difference in intermediate hare between the U.S. and India and amplifie difference in per capita GDP by twenty percent relative to an identical model with perfect inurance. JEL Claification Code: O11, O41 Keyword: Agriculture, intermediate input, miallocation, productivity, rik Thi i a ubtantially revied verion of a chapter from my diertation, o I thank to Berthold Herrendorf, David Lagako, Ed Precott, and Todd Schoellman for detailed dicuion and guidance on thi project. Thi paper ha alo benefited from comment and inight by participant at Arizona State, ITAM, Notre Dame, Rocheter, the St. Loui Fed, Virginia, The World Bank, the SED Annual Meeting, the CASEE Macro Reunion Conference, and the Econometric Society NASM, epecially thoe from Alex Bick, Chri Herrington, Joe Kaboki, B. Ravikumar, and Richard Rogeron. The uual diclaimer apply. Contact Info: 434 Flanner Hall, Notre Dame, IN kdonova6@nd.edu

2 1 Introduction Difference in agricultural labor productivity between the richet and pooret countrie are twice a large a difference in aggregate labor productivity. In pite of thi, the leat developed countrie in the world employ over eighty percent of their population in the agricultural ector. Since thee countrie employ uch a large fraction of their population in a particularly unproductive ector, development accounting ugget that undertanding agricultural productivity difference are crucial for undertanding aggregate difference. 1 One poible caue of agricultural productivity difference i that farmer in developing countrie ue fewer intermediate input. For example, a a hare of harvet value, the value of intermediate input ued on farm range from 4 percent in Uganda to 40 percent in the United State. Moreover, I document in Section 2 that thi poitive cro-country correlation doe not exit in other ector, uggeting that it may be an important margin for undertanding why the agricultural ector exhibit ignificantly lower labor productivity than the nonagricultural ector in developing countrie. The goal of thi paper i to provide a theory to undertand the cro-country correlation between the agricultural intermediate input hare and per capita income, and in turn, quantitatively ae it role for cro-country productivity difference. In thi paper, low intermediate input intenity i generated endogenouly a a repone to low total factor productivity (TFP). Becaue intermediate deciion are made before the realization of productivity hock, the abence of inurance market require farmer to internalize the impact thi choice will have on ex pot conumption. In particular, purchaing more intermediate input lead to lower conumption in the event of a low hock realization. The extent to which thi conideration impact the ex ante intermediate choice depend critically on the income level of farmer. Low hock realization are 1 Thi argument ha been made in variou form tarting with Retuccia et al. (2008), and alo Caelli (2005), Vollrath (2009), and Gollin et al. (2014), among other. 1

3 particularly diatrou for farmer in extremely poor countrie, ince conumption move cloe to ubitence. Thee farmer are le willing to take on the rik aociated with intermediate input uage, thu driving down labor productivity in developing countrie. I formalize and quantify thi idea with a dynamic general equilibrium model in which both aggregate and ector-pecific difference can potentially influence farmer repone to hock. Farmer produce agricultural output utilizing intermediate input, and are ubject to incomplete market and random fluctuation in farm productivity. In thi ene, the model i imilar to thoe ued to focu on capital miallocation with elf-inurance (e.g. Buera et al., 2011; Midrigan and Xu, 2014; Moll, 2014, among other). Here, however, deviation from uncontrained profit maximization are driven not by explicit input market friction, but intead by the inability to inure ex pot conumption. The timing of input choice implie that each hock realization i weighted it rik neutral probability which include a normalized meaure of marginal utility. A TFP decreae in poor countrie, income move cloer to ubitence and marginal utility at low hock realization increae, o that farmer in poor countrie put relatively more weight on bad potential outcome. From the perpective of miallocation (e.g. Retuccia and Rogeron, 2008; Hieh and Klenow, 2009), thi implie a wedge between the expected profit-maximizing marginal value and price of intermediate input, and i in fact iomorphic to a tax wedge in a model with no rik. The reult depend critically on the incluion of a ubitence requirement when the equilibrium price of agricultural output varie acro countrie. I how that without ubitence, uninurable hock play no role in undertanding difference in the agricultural input mix nor aggregate productivity acro countrie. That i, the agricultural productivity gap between any two economie i identical regardle of inurance againt farm-level hock. The 2

4 addition of the ubitence requirement then ha two important implication. Firt, I how theoretically that it generate a poitive correlation between the intermediate hare and aggregate income conitent with the empirical evidence in Section 2. Second, identical ditortion have differential impact in rich and poor countrie when combined with thi rik channel. In thi ene, the model with ubitence provide an otherwie abent complementary amplification channel for ditortion conidered within a complete market framework, including tranportation cot (Adamopoulo, 2011; Gollin and Rogeron, 2014), the link from ditortion to farm ize (Adamopoulo and Retuccia, 2014) or technology choice (Yang and Zhu, 2013), or more general ditortion that affect input market (Gollin et al., 2004; Retuccia et al., 2008). I then turn to quantify the cro-country impact of thi theory. I calibrate the model uing a mix of aggregate and micro-level data from India, where the nominal intermediate input hare in agriculture i 11 percent. I jointly match conumption and production volatility to allow for ome conumption moothing in the model, and I alo include relevant ector-neutral and agriculture-pecific feature to iolate the importance of each. I then vary exogenou ector-neutral productivity and the cot of intermediate input to U.S. level. Since thee difference exogenouly increae labor productivity, I iolate the impact of the theory developed here by aking how much larger productivity difference are relative to an identical model in which hock are perfectly inured. The quantitative reult imply that the eemingly ub-optimal intermediate input choice in agriculture can be partially explained a a rational repone by farmer to rik, and through that ditortion, affect aggregate labor productivity acro countrie. The calibrated model predict that the Indian economy ha an intermediate input hare of 0.26, compared to the U.S. intermediate hare of Thi i 48 percent of the difference found in the data. Thi rik- 3

5 driven ditortion then amplifie cro-country productivity difference relative to a model with perfectly inured hock. Agricultural productivity difference increae by 30 percent from a factor of 34.5 to 45.0, while GDP per capita difference increae from a factor of 6.4 to 7.8 for an amplification of 22 percent. Rik, therefore, play an important role in undertanding both agricultural input mix and productivity acro countrie. Thi paper contribute to a recent macroeconomic literature on the role of agriculture in undertanding cro-country income difference, including Gollin et al. (2004), Lagako and Waugh (2013), Adamopoulo and Retuccia (2014), Herrendorf and Schoellman (2015), and Tombe (2015). Motly cloely related i the work of Retuccia et al. (2008), who alo focu on the role of intermediate input. Building off their work, thi paper contribute a micro-founded rationale for ditortion in the intermediate input market by focuing on the rik aociated with intermediate input choice. Moreover, I how that the ditortion emphaized in their work have a larger impact when combined with rik, and can help explain reource miallocation in agriculture. In thi ene, the paper more broadly relate to the literature relating etablihment-level ditortion to aggregate productivity (Retuccia and Rogeron, 2008; Hieh and Klenow, 2009). While recent work ha focued on the role of financial development to explain pervaive deviation from unditorted profit maximizing behavior (e.g. Buera et al., 2011; Midrigan and Xu, 2014; Moll, 2014), uninurable rik ha the potential to imilarly ditort input choice when combined with a ubitence requirement. The paper i therefore alo imilar to Angeleto (2007), who how that the increae in aving relative to a complete market benchmark in Aiyagari (1994)-tyle model i revered when one conidered capital income intead of labor income. 4

6 2 Motivating Evidence Define the real intermediate input hare a X j := p xx j /p ay j a, where X j i intermediate input conumption in agriculture of country j, Y j a i agricultural output, and p x and p a are international price of intermediate and output. The nominal intermediate hare i given by X j := p j xx j /p j ay j a, where the only difference i that intermediate and output are valued at nominal countrypecific price p j x and p j a. A dicued in the introduction, the influential work of Retuccia et al. (2008) find that real intermediate hare differ ubtantially acro countrie. Uing data from Praada Rao (1993), which i contructed from Food and Agricultural Organization (FAO) tatitic and underlie the Retuccia et al. (2008) analyi, Figure 1a reproduce their finding of a trong poitive correlation between GDP per capita and the real intermediate hare. In addition to the correlation, the level difference are alo large compared to other input. Merging thi data with FAO etimate on capital tock in agriculture I find that the cro-country ratio of intermediate per worker i more than double that of capital per worker in agriculture (Table 1). then compute a imple variance decompoition in the tyle of Caelli (2005). Relative to capital per worker difference, variation in real intermediate per worker account for three time more of the variance in agricultural gro output per worker. While difference in real hare drive productivity difference, difference in the nominal hare identify ditortion. and plot the nominal hare. Figure 1b ue the ame data Again, there i a trong poitive correlation of The tenth percentile country, a ranked by GDP per capita, ha a nominal intermediate hare that i one-fourth of the intermediate hare in the United State. 2 The poitive correlation with per capita GDP in both 2 If rich countrie are producing different crop than developing countrie, one might upect that the reult i driven by different production technique for thee different type of output. While I cannot directly tet thi, I do group countrie by latitude to control for the type of agricultural production, and compare within-group variation. The ame correlation hold within group. I 5

7 real and nominally priced hare implie that the price ratio p x /p a doe not ytematically vary with development, though there i ubtantial variation in the price ratio, a Figure 1c how. 2.1 Evidence from Micro Data I next turn to evidence from micro data. I ue the Living Standard Meaurement Studie (LSMS) releaed by the World Bank in cooperation with local government. I include all countrie with urvey after 2000, taying a cloe to 2010 a poible. There are 14 countrie with ufficient data that, combined with weight in the data, provide nationally repreentative ample in each country. I firt compute the nominal expenditure hare of fertilizer and peticide to corroborate aggregate tatitic. 3 I ue the median ale price to value harvet quantitie in countrie where the nominal expenditure are not directly available. Since the data i nationally repreentative when combined with available weight, aggregating give the national expenditure hare. Figure 2 combine thi data with Penn World Table GDP per capita, and confirm the poitive relationhip The Role of Rik I there a relationhip between input ue and agricultural rik in the data? I examine thi uing available data on rainfall variability, an exogenou ource of agricultural rik acro region within an available et of ub-saharan African countrie for which I have LSMS data. 4 3 Other intermediate input, uch a fuel, are only available in ome countrie o I exclude them here. Alo, note that thee are not conumption hare. Fertilizer and peticide conumption i only available in 6 of the countrie. Since I focu on inorganic fertilizer and peticide (i.e. not manure) nominal expenditure and conumption valued at market price hould be imilar. 4 Comparable cro-country data on agricultural input and output combined with tandard meaure of houehold rik uch a conumption volatility do not exit. Conumption volatility i nonethele an endogenou meaure, reflecting both inherent rik and rik coping meaure uch a intermediate choice. Moreover, the within country variation I ue ha the added advantage of keeping other relevant economic variable, uch a the price of intermediate, relatively contant. 6

8 Rainfall data come from the Tropical Rainfall Meauring Miion (TRMM), available from the Goddard Earth Science Data and Information Service Center adminitered by the U.S. National Aeronautic and Space Adminitration (NASA), and i a U.S.-Japan collaboration on atellite monitoring of world-wide precipitation. It provide monthly rainfall etimate ( ) for the entire non-arctic world ([ 50, 50] [ 180, 180] latitude-longitude) on degree cell, for a total of 576,000 cell. I ue thi data to create hitorical rainfall variation (weather rik) for each cell during the countrypecific main cropping eaon defined in the LSMS documentation. I then merge thi information with houehold GPS coordinate available in ome of the LSMS countrie. Since the rainfall data begin in January 1998, I retrict attention to the ubet of countrie with data after The retriction of (1) pot-2005 data and (2) GPS coordinate leave four of the original fourteen countrie: Malawi, Niger, Tanzania, and Uganda. The degree grid i fine enough to enough to allow ubtantial variation within each country. The Malawi LSMS ha houehold contained in 144 unique TRMM cell, Niger ha 129, Tanzania ha 223, and Uganda ha 171. To ae the impact of rik on intermediate expenditure, I run the regreion y ir = α + βσ rain ir + γsave ir + θ(σ rain ir Save ir ) + ηx ir + ε ir (2.1) where i i houehold and r i region. The dependent variable y ir take two form. Firt i expenditure on fertilizer and peticide (plu one to allow for zero) and the econd i the expenditure hare relative to harvet value. Both are normalized by regional mean. On the right hand ide, σ rain ir hitorical tandard deviation of rainfall from 1998 to the year before the urvey, Save ir i the value of livetock holding one year earlier normalized by regional i 7

9 mean, and X ir i a et of control. 5 I ue livetock holding for two reaon. Firt, they are an important part of aving ued to mooth conumption (e.g. Roenzweig and Wolpin, 1993). Second, the LSMS ak about livetock holding one year prior to the urvey, which idetep concern about conflating pre-harvet aving and pot-harvet repone. Livetock i the only aving vehicle with thi quetion, hence it ue in lieu of a broader notion of aving. Table 2 and 3 preent the reult for log expenditure and expenditure hare repectively. In all cae, etimated coefficient i le than zero and i ignificant for all countrie except Uganda. 6 Houehold who face larger weather rik acro all four countrie pend le on fertilizer and peticide and have lower expenditure hare of harvet value, conitent with the idea of rik playing an important role determining intermediate hare. The interaction term i poitive acro all pecification, conitent with the idea that rik i le of a problem for richer houehold, but i impreciely etimated. Thi i driven by the fact that relatively little variation in livetock holding. In Malawi and Uganda for example, the median value of livetock i zero. In Niger, where the twenty-fifth percentile of livetock value i poitive, the interaction term i poitive and ignificant. Thee reult complement a growing micro literature on the importance of rik for agricultural invetment acro a large et of developing countrie. Dercon and Chritiaenen (2011) how downide conumption rik depree fertilizer ue in Ethiopia by recontructing potential conumption realization from panel data. Emerick et al. (2015) provide experimental evidence that decreaed downide rik through the introduction of new flood tolerance rice increae fertilizer invetment in India. Further experimental evidence from the introduction of rainfall inurance how that inurance can incentivize farmer 5 Control include number of adult men, adult women, and children in the houehold, houehold head gender, education, age, quared age, hitorical average rainy eaon rainfall, and quared and cubed term of Save ir 6 The (unweighted) total expenditure hare of harvet value in Uganda i and only 360 of 2139 obervation have poitive expenditure, which explain why the etimate are le precie. 8

10 to take more rik acro a variety of countrie (Mobarak and Roenzweig, 2012; Cole et al., 2013b; Cai et al., 2014; Karlan et al., 2014). 7 Taken together, the reult ugget rik i an important contraint to intermediate input ue acro the developing world. 2.2 Comparion to Manufacturing and Service A a lat tep, I turn back to aggregate data to compare intermediate input hare acro ector uing the United Nation Sytem of National Account (SNA). The U.N. data include 87 countrie in which data i ufficiently complete to contruct nominal intermediate hare acro the broadly defined ector of agriculture, manufacturing, and ervice. Thee nominal intermediate hare are plotted for in Figure 3, along with the nonagricultural ector meaured a the total economy net of agriculture. Figure 3a confirm the relationhip between the agricultural intermediate input hare and per capita GDP. Figure 3c and 3d, however, how the intermediate input hare in manufacturing and ervice exhibit no uch relationhip. The figure alo include the etimated coefficient from the imple linear regreion of the ectoral intermediate hare on log PPP GDP per capita. Only agriculture ha a lope ignificantly different from zero, implying that the poitive relationhip between the intermediate input hare and per capita income i unique to the agricultural ector. The ret of thi paper i devoted to developing and quantifying a model to undertand the caue of the correlation in agriculture and ae it impact on cro-country productivity difference. 7 There i alo a growing literature on the difficulty in deigning the proper inurance contract in thee etting, including iue of trut, bai rik, and limited undertanding. See for example Mobarak and Roenzweig (2012), Cole et al. (2013a), and Karlan et al. (2014). 9

11 3 Model Time i dicrete, and a model period i one year. There are two ector, ector a for agriculture and ector m for manufacturing, which include all nonagriculture. The manufacturing good i the numeraire, o it output price i normalized to p mt = 1 for all t. Within an economy, deciion are made by a meaure one of infinitely-lived houehold. 3.1 Technology Manufacturing The manufacturing output good can be ued a either conumption or a intermediate input in agricultural production. Production i characterized by a tand-in firm which ue only labor ervice N mt to produce output according to the contant return to cale production function Y mt = AN mt where A i a ector neutral TFP parameter. The parameter A i country-pecific, and i a meaure of the overall productivity of the economy. The firm maximize profit at each date t, o that N mt i the olution to max AN mt w t N mt (3.1) N mt 0 where w t i the wage paid per unit of N mt. In a competitive equilibrium w t = A for all t. Agriculture Each houehold i endowed with one farm that require intermediate input x and labor n a. Production occur according to the decreaing return to cale production function y at = z t Ax ψ t n η at, where ψ +η < 1 and A i, again, ector neutral TFP. 8 The hock z t i a houehold-pecific productivity hock drawn from a time-invariant ditribution with cumulative ditribution 8 Alternatively, one could aume land i normalized to l = 1 and inelatically upplied. In principal, thi eliminate land a margin for adjutment. Ex pot adjutment of land i unlikely given the non-exitent or limited land market in poor countrie. 10

12 function Q(z) and upport on [z, z]. 9,10 The realization of z t i i.i.d. with repect to both houehold and time. I aume the law of large number hold, o that the ditribution of hock acro houehold i certain. Intermediate input are purchaed from the manufacturing ector, at the price p x 1, which varie acro countrie. Note that the implicit aumption made i that there exit a technology to turn one unit of manufacturing output into 1/p x unit of intermediate input. Thi i a imple way to capture the fact that intermediate input are more expenive in developing countrie. 3.2 Houehold Utility and Deciion A houehold value conumption from both ector a and m, and maximize expected utility E 0 [ t=0 βt u(c at, c mt )] with dicount factor β (0, 1). The period t utility flow take the form u(c at, c mt ) = α log(c at ā) + (1 α) log(c mt ), where c jt i conumption from ector j {a, m} and ā > 0 i the ubitence requirement of agricultural conumption. The utility function i conitent with the tructural tranformation path when houehold conume gro output (Herrendorf et al., 2013). Houehold do not have acce to inurance market, o that the hock can only be inured againt through elf-inurance. To thi end, they ave by toring agricultural output. Thi torage depreciate at a country-pecific rate δ to capture difference in agricultural aving technologie acro countrie Deciion Timing At time t 1, houehold ave b t unit of the agricultural good. A fraction δ depreciate, and the houehold enter time t with (1 δ)b t unit of aving. 9 Throughout, it i aumed z i high enough to guarantee ubitence can be atified for all economie with TFP A in ome et A R +. The reult hould be interpreted a holding for economie with TFP in the et A. 10 Note that increaed intermediate intenity doe not decreae the variance of hock. Thi i upported by micro evidence in both developed and developing countrie (Jut and Pope, 1979; Traxler et al., 1995). 11

13 The period t deciion problem i broken down into two tage denoted ordering and production, which are eparated by the realization of the hock z. In the ordering tage, each houehold chooe intermediate x t to ue in their farm. After ordering, z t i realized. All production and conumption occur in the production tage. Firt, a houehold chooe how to allocate labor between the agricultural ector, where they can work on the houehold farm, and in the manufacturing ector, where they can work for wage w t which i taxed at rate τ 0. Note that thi allow labor to be ued to mooth conumption acro hock realization. A fraction ν of the tax revenue i rebated back to houehold a a lump-um tranfer T (b, z), while the fraction 1 ν i ued to purchae manufacturing output and dicarded. After labor i decided, all production take place. There i a centralized market for buying and elling good, implying a unique equilibrium price p a. Profit are made, all factor of production are paid, and conumption and aving choice (c at, c mt, b t+1 ) take place Recurive Problem The timing decribed above implie that the houehold tate variable i aving b, and the aggregate tate i the ditribution of aving acro all houehold, denoted µ(b). Since I will be primarily tudying the tationary equilibrium, I uppre the dependence of the deciion problem on the aggregate tate µ(b). At the production tage, once the choice of x i made and z realized, the value of entering time t with (1 δ)b aving i v p (x, b, z) = max α log(c a ā) + (1 α) log(c m ) + βv o (b ) (3.2) c a,c m,n a,b 11 I abtract from manufacturing rik here becaue manufacturing houehold are ignificantly richer. A I how in Section 6, the impact of rik i mall at ufficiently high level of aving. 12

14 ubject to contraint et p a c a + c m + p a b = p a zax ψ n η a p x x + (1 τ)w(1 n a ) + p a (1 δ)b + T (b, z) b 0, c a ā, c m 0 where v o i the value of entering the ordering tage at t + 1 with b unit of aving in the tationary equilibrium. The production problem in (3.2) define deciion rule a a function of the intermediate choice. Working backward, the ordering tage value of entering time t with b aving i v o (b) = max x 0 z v p (x, b, z)dq(z). (3.3) Thi define the deciion rule for intermediate input x(b) and therefore the production tage deciion rule c a (b, z), c m (b, z), n a (b, z), and b (b, z). 3.4 Stationary Equilibrium The tationary competitive equilibrium of thi economy i defined by an invariant ditribution µ = µ, a value function v o, deciion rule x, n a, b, c a, c m, labor choice N m, price p a and w, and a tranfer function T (b, z) uch that (1) the value function v o olve the houehold problem given by (3.2) and (3.3) with the aociated deciion rule, (2) N m olve the ector m firm problem (3.1), (3) the tate contingent tranfer balance for all (b, z): ντa(1 n a (b, z)) = T (b, z), (4) the law of motion for µ, denoted Λ(µ), i uch that Λ(µ ) = µ, and µ i conitent with Q(z) and deciion rule, and (5) market clear: (a) Manufacturing labor market: N m = 1 n a (b, z)dµdq(z) z b 13

15 (b) Agricultural conumption market: b z c a (b, z)dq(z)dµ + δ bdµ = zax(b) ψ n a (b, z) η dq(z)dµ b b z (c) Manufacturing conumption market: b z c m (b, z)dq(z)dµ+p x b x(b)dµ+(1 ν)τ A (1 n a (b, z))dq(z)dµ = AN m b 4 Characterization and Analytic Reult To clarify the mechanic of the model, thi ection analytically characterize ome of the main model prediction. In particular, I how that the interaction of uninured hock and ubitence requirement generate a poitive correlation between TFP and the nominal intermediate hare. To highlight TFP pecifically, I aume throughout thi ection that p x = 1 and τ = 0 in all economie, though none of the reult rely on thi aumption. I further conider the tatic verion of the model (identically, δ = 1 for all economie). All proof are relegated to Appendix D. Given total conumption expenditure C := p a c a +c m, the optimal allocation between agricultural and manufacturing conumption i given by c a (C) = ā + (α/p a )(C p a ā) and c m (C) = (1 α)(c p a ā). Uing thee deciion rule, the utility flow can be rewritten a a function of total expenditure C, ũ(c) = Ω α log(p a ) + log(c p a ā), where Ω i a contant. Thi reduce the problem to olving jut the input choice x and n a (z). A variance decompoition of the intermediate input firt order condition yield ψ Z z1/(1 η) Ap 1/(1 η) a F (x)dq(z) ( 1 = cov ũ (C(x, z)) E z [ũ (C(x, z))], z1/(1 η) Ap 1/(1 η) a F (x) (4.1) where F (x) i the production function after olving for optimal labor n a (z). The lefthand ide of (4.1) i the percentage change in the nominal intermediate ) 14

16 hare by moving from incomplete to complete market. Thi immediately implie that the nominal intermediate hare in all countrie will be le that ψ, a the covariance between the rik neutral weight and the marginal return to intermediate i negative when hock are uninurable. Morduch (1995) refer to thi reult a income moothing, a houehold hift away from riky input choice to mooth conumption acro tate of the world, and i the broad motivation behind the agricultural inurance initiative cited in Section 2.1. However, Propoition 1 how that the appeal to rik averion and incomplete market alone i not ufficient to generate exce income moothing in poor economie when the price of agriculture varie acro economie. Propoition 1. If ā = 0, (1) the nominal intermediate hare i independent of TFP, (2) the hare of labor in agriculture i independent of TFP, and (3) for two economie with TFP level A 1 and A 2, the agricultural output per worker difference between the two economie i the ame regardle of whether or not market are complete. That i, denoting Y ij a and N ij a a agricultural output and employment in economy i {1, 2} with market tructure j {C, I} (complete and incomplete), Y 1C a Y 2C a /N 1C a /N 2C a = Y a 1I Ya 2I /N 1I a /N 2I a Depite the fact that conumption rik lower the nominal intermediate hare relative to it profit-maximizing level, it remain contant acro countrie when ā = 0. The key here i relative rik averion. Since the utility function ũ i defined over aggregate conumption expenditure C, relative rik averion can alo be defined over C, and i given by C/(C p a ā). When ā = 0, houehold exhibit contant relative rik averion. The equilibrium price therefore adjut in repone to low TFP and offet the cot of conumption rik. Propoition 2 how that the incluion of ubitence requirement and therefore the change from contant to decreaing relative rik averion break thi reult, and can qualitatively replicate the empirical correlation between the. 15

17 nominal intermediate hare and income from Section 2. Propoition 2. In the competitive equilibrium, the nominal intermediate hare i increaing in A if and only if ā > 0. The ame non-homothenticity that generate income effect in tructural tranformation (and therefore the negative relationhip between agricultural labor and TFP in the model) alo implie a poitive relationhip between the intermediate hare and aggregate income. I how in the appendix that the rik-baed wedge between the marginal value and price of intermediate input i iomorphic to a reduced form tax wedge on intermediate input in the correponding model that abtract from riky production. 5 Calibration and Teting Model Prediction Since the model predict that uninured hock both depre intermediate intenity and act a a ditortion in developing countrie, I turn to quantifying the impact on cro-country productivity difference. I begin by calibrating the model to India uing a combination of micro and aggregate tatitic. I then vary agriculture-pecific ditortion (p x, τ, δ) and ector-neutral TFP A to create a U.S. model economy to ae the impact of agricultural rik on intermediate hare and labor productivity acro countrie. The exogenou difference fed into the model generate labor productivity difference acro the two countrie, o I iolate the impact of rik by comparing the model prediction againt an identical model with complete inurance againt hock. I calibrate the model with the ICRISAT Village Level Studie (VLS2) data from India. The ICRISAT VLS2 i a houehold-level urvey on in India tarting in 2001 and running through 2013, and i a continuation of earlier ICRISAT data from The VLS2 include information houehold compoition, conumption, farm input, and harvet value, and include both 16

18 a cro-ectional and panel component. Conumption data i not collected in 2007, o I focu on the panel. Since rainfall i a key component of rik in the developing world, I firt compute the coefficient of variation of annual rainfall to ee whether the ICRISAT village are a reaonable approximation for India. I do o uing the ame rainfall data in Section 2.1 for each of about 13,500 cell in India, from The map of rainfall c.v. i in Figure 4a, while the denity acro cell i plotted in Figure 4b. The ix ICRISAT village are all very cloe to the mean, a 5 of 6 village fall within 5 percent of the mean cell. The ixth, Shirapur, i omewhat higher at 25 percent above the mean cell. The model include ten parameter, ix of which are common acro the two economie, and four that determine the ditortion facing India that do not exit in the United State. They are dicued in turn. 5.1 Common Parameter The ix common parameter are the production exponent ψ and η, the hock ditribution, the rebate on taxe ν, and preference parameter ā, α, and β. I et α = following Retuccia et al. (2008) and Lagako and Waugh (2013) and β = I et ā = 0.03, o that the Indian model economy ha 50 percent of the population engaged in agriculture in the tationary equilibrium, conitent with ectoral employment in India (World Bank, 2015). That leave the production parameter, hock ditribution, and tax rebate. The production parameter cannot be et to match nominal factor hare in the Indian economy, a the realized hare combine both the technological parameter and the ditortion I eek to invetigate. Intead, I aume the technologie are the ame acro U.S. and India and chooe η = 0.40 and ψ = 0.40 to be conitent with U.S. etimate. Note however that the model predict that the nominal labor hare hould equal η = 0.40 in both the U.S. 17

19 and India. Thi i conitent with the ICRISAT data. ICRISAT include both hired and houehold labor, valued at gender-pecific market wage, which i the counterpart to the model definition. For each houehold (363 in 2006) I compute the value of labor ervice a a hare of harvet value, and the average i The ame procedure for the nominal intermediate hare implie a value of 0.11, much lower than the U.S. level, and conitent with ubtantial ditortion in intermediate ue in India. The lat two parameter are the variance of the hock ditribution and tax rebate hare ν. I chooe thee parameter to match the average tandard deviation of growth rate in houehold-level harvet value and total conumption expenditure. For thi, I ue the ix year panel of of houehold from , of which there are 236 acro ix village with conumption, harvet, and houehold characteritic data available. However, the data include variation in harvet and conumption due to heterogeneity in houehold ize, education, and village-level variation that are not modeled here. To the extent that thee are predictable, directly uing variance in the data would attribute them to unanticipated hock. Intead I follow Kaboki and Townend (2011) and other and purge the data of thee factor with the regreion log(y ivt ) = α Y + β Y X ivt + θ Y vt + ε Y ivt log(c ivt ) = α C + β C X ivt + θ C vt + ε C ivt where θ vt i a village-time fixed effect, and X ivt i a et of control for houehold i at time t that include number of men, women, and children, and age, gender, and education of the houehold head. Y and C are the houehold value of harvet and conumption, deflated by the Indian conumer price index. The R 2 on thee regreion are 0.33 and 0.74 repectively, o that thee feature account for a large part of the variation, epecially for conumption. I then compute the ample average for the vector X ivt, denoted X ivt, and compute 18

20 the new data a log(y ivt ) = α Y + β Y X ivt + ε Y ivt (5.1) log(c ivt ) = α C + β C X ivt + ε C ivt. (5.2) My meaure of the growth of harvet and conumption are then the difference Y ivt = log(y ivt ) log(y ivt 1 ) and C ivt = log(c ivt ) log(c ivt 1 ). The etimated harvet growth rate are more volatile than conumption, conitent with the ability of houehold to partially mooth income hock. The average tandard deviation of harvet growth acro houehold i σ Y = 1.00 compared to σ C = 0.49 for conumption. Matching thee two tandard deviation imply a tandard deviation of the hock ditribution of σ z = 0.48 and ν = That i, 8.5 percent of tax revenue i rebated to houehold. While the average are targeted, Figure 5a and 5b plot the denity of harvet and conumption growth rate volatility in both the model and the data to ae whether the ditribution match with the data. I compute the implied volatility in the model by imulating 100,000 individual for ix year each, conitent with the ICRISAT panel length. Both implied ditribution fit the data well depite not being targeted directly. 5.2 Economy Specific Parameter There are four dimenion along which India will differ from the U.S. economy: TFP A, the depreciation rate δ, the tax rate τ, and the intermediate input price p x. I ue TFP and p x number from Retuccia et al. (2008). Thi implie (A India, p India x ) = (0.22, 2.77) and normalized value (A US, p US x ) = (1, 1). The lat two parameter, τ and δ, control the relevance of the two moothing channel in the model. Firt, τ i the eae by which houehold can mooth conumption by moving labor acro ector in repone to hock. I et τ US = 0, and calibrate τ India from the ICRISAT data. ICRISAT in- 19

21 clude houehold hour and earning at wage job in both the agricultural and nonagricultural ector. I compute the wage in ector a w = i e i i h i for {a, m} where e i i earning in ector for houehold i, and h i i total hour worked in ector. The ditortion i τ = 1 w a /w m. The ICRISAT data in 2006 imply τ India = The depreciation rate of aving δ determine the availability of moothing through toring agricultural output. Udry (1995), Fafchamp et al. (1998), and Kazianga and Udry (2006) all point to the importance of crop torage for moothing conumption in the developing world. There i alo evidence that livetock i ued to mooth conumption, particularly in India (e.g. Roenzweig and Wolpin, 1993). I therefore ue the total value of livetock holding and crop torage a the meaure of aving, both of which are available in ICRISAT. In 2006, 54 percent of aving in the average ICRISAT houehold i livetock, while the other 46 percent come from tored crop, uggeting both are important. 12 The total market value of livetock and tored crop i 96 percent of total harvet value in the average houehold, and I et δ India = 0.15 to match thi fact. Thi i conitent with large cot to torage in developing countrie. Depite targeting only the average, Figure 5c how that the aving ditribution in the model matche the data well. I et δ US = 0, but thi ha no impact on the reult a the U.S. model economy i ufficiently rich that the aving ditribution at any negative interet rate i nearly degenerate at zero. 12 ICRISAT alo include the peticide and fertilizer torage. Conitent with the model ued here, there i almot no torage of either. Including thee intermediate in aving, only 0.6 percent of aving in the average houehold i made up of peticide and fertilizer. Only 8 percent of houehold tore any fertilizer or peticide. 20

22 5.3 Saving, Conumption, and Intermediate Ue: Model v. Data With the calibrated model in hand, I latly ae model prediction for the relationhip between conumption volatility, aving, and intermediate intenity by comparing the Indian model prediction to ICRISAT data. Thee are out-of-ample tet deigned to ae whether the key model prediction are operational in the data. To compute the regreion in the model, I imulate 100,000 houehold in the Indian tationary equilibrium. I then compute tandard error uing a boottrap procedure to create 1000 ample of 205 houehold, conitent with the number of houehold in ICRISAT with the full ix year panel and the requiite data. 13 The reult are broken into two ection. The firt relate to the relationhip between aving and intermediate ue. The model predict that the ex ante intermediate choice and farm yield are poitively related to aving, a houehold can better inure low hock realization. The econd cover the relationhip between conumption volatility and intermediate ue. Here, the model predict a poitive relationhip between intermediate input and the coefficient of variation of conumption. I tet both et of of prediction, and find that the ame relationhip hold in the data Saving and Intermediate Intenity I conider the relationhip between aving and intermediate ue with the regreion x 2006 = α + βb ε (5.3) ( ) px x = α + βb ε (5.4) p a y a 2006 yield 2006 = α + βb ε (5.5) houehold are miing data on fertilizer ue, hence the decreae in ample ize from the the 236 ued in Section 5.1. Redoing the analyi excluively with thi maller ample doe not change the reult. 21

23 where aving i lagged to prevent endogeneity concern. In all regreion, both dependent and independent variable are normalized by their repective mean. Reult are preented in Table 4. Firt, regreion (5.3) how that the model and data match well when conidering the ex ante intermediate choice, where β data = 0.37 and β model = Both are ignificant at one percent. In contrat, the ex pot nominal hare are partially driven by unexpected volatility in output. Correpondingly, the R 2 in model regreion (5.4) decreae from 0.53 to 0.02 in the model and from 0.17 to 0.00 in the data. Moreover, the etimate of β data = 0.01 i mall and tatitically inignificant. The model prediction i omewhat tronger, with β model = Thi etimate i ignificant at ten percent, but no tricter, depite the trong relationhip between the ex ante choice and aving. Latly, regreion (5.5) conider the relationhip between farm yield, meaured a harvet value per acre, and lagged aving. Both the model and the data predict a trong poitive relationhip. The model etimate i β model = 0.26, omewhat larger than the data etimate β data = 0.11, but both are ignificant at one percent. Thee poitive etimate occur depite the fact that uing yield a the dependent variable uffer from the ame ex pot iue a uing the realized intermediate hare, evidenced by the relatively low R 2 etimate in both the model and the data regreion. To rationalize the different prediction of thee two regreion, note that the ex pot nominal intermediate hare and farm yield in the model are p x x p a y a (x, z) ( = p x z 1 1 η ψ 1 η x 1 η (p a A) 1 1 η η ) η 1 η w p a y a (x, z) = z 1 1 η x ψ 1 η (pa A) 1 1 η ( η w ) η 1 η. The calibrated model implie (1 η ψ)/(1 η) = 0.33 and ψ/(1 η) = The increaed relevance of variation in x when conidering yield, which regre- 22

24 ion (5.3) how i tightly related to variation in b, allow for a tatitically ignificant etimate of aving on yield Conumption Volatility and Intermediate Intenity I next turn to the relationhip between conumption volatility and intermediate ue. In both the model and the data, I ak the relationhip between the coefficient of variation of conumption and average intermediate ue during the ix year panel. That i, denoting x it a the realized nominal intermediate hare of houehold i at time t, I run the regreion t=2006 t=2001 x it 6 ( ) σ C = α + β + ε i, (5.6) The preferred comparion i the conumption etimate from regreion (5.2), in which C it = exp( log(c ivt )), for the reaon dicued in Section 5.1. For completene, I alo report reult the houehold conumption directly from ICRISAT (deflated by the Indian CPI). The reult are in Table 5. The model i conitent with the poitive relationhip between the conumption coefficient of variation and the average intermediate hare found in the data, in which the model predict β model = 0.09, compared to β et data = 0.15 uing the etimated conumption data. The key intuition for thi reult i the poitive correlation between the tandard deviation and mean of conumption acro houehold, in which the model alo matche the data. The model predict a correlation of 0.88, compared to 0.85 uing the conumption data etimated from (5.2) and 0.90 uing the direct ICRISAT conumption data. Given the trong poitive correlation in the model, the reult from regreion (5.6) imply that an increae in mean conumption mut be met with a le than one-for-one increae in the tandard µ C i 23

25 deviation of conumption. That i, the regreion µ C i = α + βσ C i + ε i (5.7) implie an etimate of β model (0, 1) in the model. Table 6 how the reult of thi regreion in the model and compare it to the data. The model matche the etimated data well with β model = 0.22 and β et data = 0.28, though the unmodified conumption data predict a higher etimate β data = The model prediction are conitent with the empirical houehold-level relationhip between intermediate input uage, aving, and conumption volatility. In the next ection I therefore proceed to ae the quantitative crocountry implication of the model teted here. 6 Quantitative Cro-Country Reult The main cro-country reult on productivity and input mix are in Table 7. Firt, note that the U.S. model economy i ufficiently rich that the move from complete to incomplete market ha little impact. The nominal intermediate hare and employment hare remain nearly identical. Thi i not the cae in India. The elimination of complete market caue the nominal intermediate hare in India to drop from 0.40 to The model therefore capture 48 percent of the nominal intermediate hare difference between the U.S. and India. 14 Thi caue agriculture to become more labor intenive in India, a the employment hare in agriculture increae by 47 percent relative to it complete market counterpart. The change in input mix i driven by an increae in houehold-level miallocation. Figure 6a plot the ratio φ rik (b) := ψ/e z [ x(b)], where E z [ x(b)] i the expected nominal intermediate 14 An alternative exercie i to lower exogenou agricultural productivity until the predicted real intermediate hare difference matched the data. Targeting thi moment directly implie a productivity too low to atify ubitence among the houehold who receive the lowet hock realization while holding no aving. 24

26 hare for a houehold with aving b, in both the U.S. and Indian economie. 15 The implied houehold-level ditortion i higher in the Indian economy, particularly among the pooret. Thu, rik ditort the efficient ditribution of intermediate input acro production unit, in the tyle of Retuccia and Rogeron (2008) or Hieh and Klenow (2009). The increaed labor intenity in Indian agriculture then impact productivity in both agriculture (meaured a the U.S. India ratio of agricultural gro output per worker) and in the aggregate (U.S. priced GDP per capita). The agricultural productivity gap the two countrie increae by 32 percent from 34.2 to 45.3, while the aggregate gap increae by 22 percent from 6.4 to 7.8. Thu, the introduction of rik provide a ubtantial amplification of cro-country productivity difference at both the agricultural and aggregate level. I next turn to undertanding the underlying force generating the amplification. There are two: a direct decreae in the real intermediate hare driven by an unwillingne to take rik, and a general equilibrium effect a the price p a adjut in repone. I decompoe the importance of thee two effect in Table 8. Firt, the complete market model require p x to increae from p x = 2.77 to p x = 3.70 (34 percent) to match the real intermediate hare predicted in the incomplete market Indian economy. Thi i the direct effect of rik relative to a complete market model uch a Retuccia et al. (2008). Thi direct effect implie a 15 percent increae in agricultural employment and a 14 percent decreae in agricultural productivity. Depite the identical real intermediate hare, the model developed here predict a larger change in agricultural employment (N a = 0.40 to N a = 0.50), which i driven by the larger increae in the agricultural price (p a = 3.14 to p a = 3.52). Thi exce increae i the additional general equilibrium effect of 15 Thi ratio i the rik-generated houehold-level wedge required in a model in which the intermediate choice i made after the realization of the hock, and thu meaure intermediate input miallocation in the model. See Appendix A for the complete formulation of thi reult. 25

27 incomplete market. Comparing row two and three of the table, 58 percent of the change in agricultural productivity in the Indian model economy come from the direct effect of a drop in the real intermediate hare. The other 42 percent come from the fact that generating the drop in the real intermediate hare require a higher price, and thu a larger hift of employment toward agriculture. Fifty-five percent of the increae in p a i due to thi direct effect, while the other 45 percent i the larger general equilibrium repone of the incomplete market model. (p India x How reaonable i thi general equilibrium effect? /p India a )/(p USA x The model predict /p USA a ) = The tatitic in Retuccia et al. (2008) derived from Praada Rao (1993) imply a value of 0.55, o the model actually omewhat underpredict the gap. Looking back on Figure 1c, which plot the relationhip between the price ratio p x /p a relative to the U.S., the relatively trict 90 percent confidence interval around regreion line include the value 0.66 for India. The amplification predicted by the model i therefore well within reaon of variation in the data Heterogenou Impact of Agricultural Ditortion A can be een in Figure 6a, the model predict ubtantial variation in the implied houehold-level ditortion. I next turn to aeing how variation in agricultural ditortion change thi underlying houehold-level miallocation. I do o by varying p x from p x = 2.77 to p x = 1 in both the Indian and U.S. model economie. Thi price play an important role in a number of recent theorie of agricultural productivity, including thoe that rely on agriculture-pecific input market ditortion (Gollin et al., 2004; Retuccia et al., 2008), internal trade and tranportation cot (Adamopoulo, 2011; Gollin and Rogeron, 2014), 16 Thi general equilibrium effect alo implie that the aggregate increae in income from a large-cale inurance program i larger than would be expected from a partial equilibrium reult. Thi i in contrat to Buera et al. (2014), who find that the general equilibrium effect of microfinance dampen the partial equilibrium effect on income. 26

28 and thoe that link intermediate price to technology choice (Yang and Zhu, 2013). The main reult are in Table 9. The reult how that the impact on productivity depend critically on the level of overall initial productivity in the economy, which i contrat to theorie uch a Retuccia and Rogeron (2008) and Hieh and Klenow (2009). Agricultural productivity increae by 98 percent in India compared to 65 percent in the United State (Table 9). Thi i driven by differential repone to the underlying houehold ditortion. A can be ee in Figure 6b, it drop by a much a 60 percent among the pooret houehold in India compared to negligible change in the U.S.. Table 10 decompoe the productivity change into the two effect dicued in Section 6. Change in the real intermediate hare play only a mall role. A highlighted in Retuccia et al. (2008), the decreae in p x caue both countrie to increae their real intermediate hare. However, while there i a lightly larger increae in India, the impact i imilar acro countrie. The real intermediate hare increae by 70 percent in the U.S. and 74 percent in India. The change in ectoral labor i more tark. While agricultural employment drop by 34 percent in the U.S., it drop by 52 percent in India. 17 To further undertand the impact of a change in the ditortion p x, Figure 7 how the dynamic of the repone of the baeline Indian economy to a urprie decreae in p x from 2.77 to The model reache it new teady tate relatively quickly. In doing o, the agricultural aggregate all overhoot their teady tate level. Initially when p x = 1, houehold are aving too much and thu are willing to take on more rik, a evidenced by the harp increae in the nominal intermediate hare. Saving i a cotly activity here, o there i a balance between aving and conumption. A uch, aving 17 The lack of variation in cro-country real intermediate hare change i due the ame equilibrium force that generate the large change in ectoral employment. Intuitively, when p x decreae, Indian houehold are willing to take more rik ceteri paribu. However, the large drop in p a 94 percent in India lower the return to intermediate, and therefore dampen the effect. I detail thi argument and provide a decompoition of thi reult in Appendix B.2. 27