The role of agriculture in aggregate business cycles

Review of Economic Dynamics 9 (2006) 455–482 www.elsevier.com/locate/red

The role of agriculture in aggregate business cycles ✩ José M. Da-Rocha a , Diego Restuccia b,c,∗ a Universidade de Vigo b Federal Reserve Bank of Richmond c University of Toronto, Department of Economics, 150 St. George Street, Toronto, ON, Canada M5S 3G7

Received 18 October 2002; revised 28 November 2005 Available online 18 April 2006

Abstract There are substantial differences in business cycle fluctuations across countries. These differences are systematically related to the share of agriculture in the economy: Countries with a high share of employment in agriculture feature high fluctuations in aggregate output, low relative volatility of aggregate employment, and low correlation of aggregate output and employment. In addition, agriculture has certain distinctive features over the business cycle: Output and employment in agriculture are more volatile than and not positively correlated with output and employment in the rest of the economy and output and employment are less correlated in agriculture than in non-agriculture. Because of these features, agriculture may play a role in accounting for aggregate business cycles across countries. We calibrate an otherwise standard twosector indivisible-labor business cycle model with agriculture and non-agriculture to aggregate and sectoral data for the United States. We find that an increase in the employment to population ratio in agriculture from 2 to 30 percent in our model increases fluctuations in aggregate output by almost 40 percent. This is about 2/3 of the difference in aggregate fluctuations between countries such as Turkey and the United States. © 2006 Elsevier Inc. All rights reserved. JEL classification: E32 Keywords: Business cycles; Agriculture; Two-sector model

✩

The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Richmond or the Federal Reserve System. * Corresponding author. Fax: +1 416 978 5519. E-mail addresses: [email protected] (J.M. Da-Rocha), [email protected] (D. Restuccia). 1094-2025/$ – see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.red.2005.12.002

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1. Introduction There are substantial differences in aggregate output and employment fluctuations across countries. In particular, countries with high fluctuations in output tend to present low relative volatility of employment and low correlation of aggregate output and employment. In this paper, we document that these business cycle observations across countries are systematically related to the share of agriculture in the economy. We calibrate a two-sector indivisible-labor business cycle model with agriculture and non-agriculture to aggregate and sectoral data for the United States. We find that an increase in the employment to population ratio in agriculture from 2 to 30 percent in our model increases fluctuations in aggregate output by almost 40 percent. This is about 2/3 of the difference in aggregate fluctuations between countries such as Turkey and the United States. Agriculture may be important in understanding aggregate business cycles across countries because agriculture features singular properties during business cycles. We document these business-cycle properties using cross-country data. First, output and employment in agriculture are more volatile than and not positively correlated with output and employment in nonagriculture. Second, output and employment are less correlated in agriculture than in the rest of the economy. Third, agriculture fluctuates more in countries where the share of employment in agriculture is small relative to countries where the share of employment in agriculture is large. The opposite occurs for fluctuations in non-agriculture. In addition, the strength of the correlation between employment in agriculture and non-agriculture changes with the share of agriculture in economic activity. Whereas employment across sectors are not correlated in the United States, the correlation of employment across sectors is negative in Greece, Turkey, and Portugal where the share of employment in agriculture is large. These observations suggest two possible channels through which the size of agriculture in the economy affects aggregate business cycles. The first channel is the direct result of a composition effect of two sectors with different business-cycle properties. The second channel is an indirect result of the size of agriculture affecting businesscycle properties across sectors in the economy. Our analysis suggests that for an empirically plausible range of shares of output in agriculture, the composition effect accounts for none of the differences in aggregate business cycles across countries. We introduce agriculture into an otherwise standard indivisible-labor real business cycle model and show that agriculture can account for some of the observed differences in business cycle patterns across countries. This simple extension of the real business cycle model has important implications for aggregate business cycles across countries. In the one-sector model, shocks to technology are propagated by the inter-temporal substitution of consumption over time. In a two-sector model, there is an extra margin of substitution: intra-temporal substitution of consumption across sectors. The amount of intra-temporal substitution hinges on the importance of agriculture in the economy. For a given stochastic process of technology shocks, as the share of agriculture in the economy declines to zero, the economy only substitutes consumption intertemporally and, therefore, converges to the behavior of a one-sector economy. When the share of agriculture increases, the importance of agriculture in the economy increases and the amount of intra-temporal substitution of consumption alters the sectoral properties of business cycles. Our quantitative results indicate that economies with a large share of output and employment in agriculture present high fluctuations in aggregate output, low relative volatility of employment, low correlation of aggregate employment and output, and reallocate factor inputs across sectors more intensively. These results suggest caution in comparing business cycles across countries if the countries have different economic structures.

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There is a literature on sectoral business cycles emphasizing the importance of factor allocation across sectors for aggregate business cycles (e.g. Long and Plosser, 1983; Huffman and Wynne, 1999; and Horvath, 2000). This literature focuses on the US economy and on sectors that co-move during the cycle such as consumption and investment and industries within the manufacturing sector. Our paper focuses on the role of agriculture in aggregate business cycles across countries. In this respect, our paper relates to a literature assessing the role of different factors in accounting for business cycle patterns across countries. For instance Conesa et al. (2002) emphasize the role of home production in output fluctuations across countries and Maffezzoli (2001) emphasizes the role of labor market frictions in employment fluctuations across countries. Our paper differs from this literature in that we assess the role of agriculture in accounting for the cyclical properties of output and employment across countries. Our paper also relates to Danthine and Donaldson (1993) and Kollintzas and Fiorito (1994) in documenting business cycle observations across countries but our paper focuses on sectoral observations. The paper proceeds as follows. In the next section, we document the main properties of business cycles across countries and show that these properties are related to the share of agriculture in the economy. We also document sectoral business cycle properties for OECD countries. In Section 3, we describe a two-sector real business cycle model with agriculture and non-agriculture. Section 4 presents the calibration and results of the benchmark economy. Sections 5 and 6 report quantitative experiments aimed at illustrating the role of agriculture in accounting for the business cycle observations across countries. In the last section we conclude. 2. Business cycle observations In this section we document three sets of observations. First, we document substantial differences in the properties of aggregate business cycles across countries and show that these properties are related to the share of agriculture in the economy. Second, we document business cycle regularities of agriculture using a panel of OECD countries. We argue that the properties of business cycles in agriculture may be important in understanding the observed differences in aggregate business cycles across countries. Third, we document systematic differences of sectoral business cycles across countries that differ in the share of agriculture in the economy. We construct a panel data composed of OECD countries using the National Accounts and Labor Force Statistic data published by the OECD (see OECD, various issues (b), various issues (a)). Due to sectoral data availability, we restrict our sample to annual frequencies and for most countries from 1966 to 1997. The data are de-trended using the Hodrick-Prescott filter with smoothing parameter λ = 100. In Appendix A we include a complete description of variables, data sources, sample periods, and summary tables. 2.1. Aggregate business cycles There are substantial differences in business cycle fluctuations across countries. These differences in business cycles are summarized in Figs. 1, 2, and 3. In particular, fluctuations in aggregate GDP and employment differ by a factor of 2 among the group of OECD countries. The fluctuation of GDP, measured as the standard deviation of the log of GDP, is as high as 3.25 in Turkey and 3.22 in Portugal, and as low as 1.80 in Belgium and 1.81 in Denmark. The fluctuation of employment relative to GDP is as high as 0.63 in the United States and as low as 0.23 in Turkey. These business cycle differences are systematic in the sense that countries with low relative volatility of employment tend to present high fluctuations in aggregate GDP. Moreover,

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Note. σY is the standard deviation of the log of aggregate GDP, de-trended using the Hodrick–Prescott filter with λ = 100. Fig. 1. GDP fluctuations and agriculture across countries.

the correlation of aggregate employment and GDP is as high as 0.82 in the United States and as low as 0.13 in Turkey and −0.36 in Greece. There is an extensive literature documenting and analyzing business-cycle differences across countries (e.g. Danthine and Donaldson, 1993 and Kollintzas and Fiorito, 1994). An important portion of this literature has focused on the role of labor market institutions as an explanation for the observed differences in the relative volatility of aggregate employment across countries, in particular, between Europe and the United States. Our focus in this paper is on the sectoral composition of GDP in aggregate fluctuations and in particular on the role of agriculture. Indeed, a closer look at the business cycle statistics across countries reveals a link between these observations and the share of agriculture in the economy. Figures 1, 2, and 3 document that countries with a large employment to population ratio in agriculture tend to present high fluctuations in aggregate GDP, low relative volatility of aggregate employment, and a low correlation between aggregate employment and GDP. Our conjecture is that agriculture may be important in understanding aggregate business cycles across countries. This conjecture is motivated by the singular properties of agriculture during business cycles, properties that we document in the following subsection. 2.2. Business cycles in agriculture There are three salient features of agriculture in business cycles that we emphasize in Table 1 for an un-weighted average of OECD countries and the United States:

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Note. σL /σY is the standard deviation of the log of aggregate employment relative to the standard deviation of the log of aggregate GDP, both variables de-trended using the Hodrick–Prescott filter with λ = 100. Fig. 2. Relative volatility of employment and agriculture across countries.

(1) Agriculture fluctuates more than the rest of the economy: For the average of OECD countries, GDP in agriculture fluctuates two times more than GDP in non-agriculture. (Although not reported in the table, employment in agriculture fluctuates more than one and a half times than employment in non-agriculture.) (2) Agriculture is not positively correlated with the rest of the economy: For the average of OECD countries the correlation of GDP in agriculture and non-agriculture is not positive, −0.03. Employment in agriculture is not positively related to GDP in nonagriculture. (3) GDP and employment in agriculture are not highly correlated: For the average of OECD countries, the correlation of GDP and employment in agriculture is 0.06 while the correlation of GDP and employment in non-agriculture is 0.60.

2.3. Sectoral business cycles across countries We emphasize two features of sectoral business cycles across countries: First, agriculture fluctuates more in countries where the share of agriculture is small relative to countries where the share of agriculture is large. The opposite occurs for fluctuations in non-agriculture. Second, the strength of the correlation between employment in agriculture and non-agriculture changes with

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Note. ρ(L, Y ) is the correlation of log aggregate employment and GDP, both variables de-trended using the Hodrick– Prescott filter with λ = 100. Fig. 3. Correlation of aggregate employment and GDP across countries.

Table 1 Business cycles in agriculture OECD average Observation I: σYn σYa Observation II: ρ(Ya , Yn ) ρ(La , Yn ) Observation III: ρ(Yn , Ln ) ρ(Ya , La )

US

2.45 4.94

2.16 5.48

−0.03 −0.18

−0.01 −0.14

0.60 0.06

0.83 0.09

Notes. σx is the standard deviation of the log of variable x, Y is aggregate GDP, Yn is GDP in non-agriculture, Ya is GDP in agriculture, Ln is employment in non-agriculture, La is employment in agriculture, and ρ(x, z) is the correlation of variables x and z. All variables are de-trended using Hodrick–Prescott filter with λ = 100.

the share of agriculture in economic activity. Whereas employment across sectors are not correlated in the United States, the correlation of employment across sectors is negative in Greece,

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Note. σYi is the standard deviation of the log of GDP in sector i, de-trended using the Hodrick–Prescott filter with λ = 100. Fig. 4. Fluctuations of GDP in non-agriculture relative to agriculture across countries.

Turkey, and Portugal where the share of employment in agriculture is large.1 Figures 4 and 5 document these features of sectoral fluctuations across countries. 2.4. Composition effect in aggregate business cycles Given that agriculture fluctuates much more than non-agriculture, an intuitive explanation for the fact that countries with a large agricultural sector fluctuate more than countries with a small agricultural sector is simply that of aggregation. The cross-country differences in sectoral fluctuations documented in the previous sub-section suggest that the aggregate properties of business cycles across countries are not driven by a pure composition effect in economies with different shares of activity across sectors. Nonetheless, in order to investigate the magnitude of this possible channel in explaining the differences in aggregate business cycles across countries, we calculate fluctuations in aggregate output for hypotheticaleconomies with different shares of output in agriculture using sectoral data for the United States. 1 There is some evidence of employment reallocation between agriculture and non-agriculture being important in developing countries, see for instance Rozelle et al. (2001) for evidence in rural China and Lee (1980) for evidence in Korea.

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Note. ρ(La , Ln ) is the correlation of log employment in agriculture and non-agriculture, both variables de-trended using the Hodrick–Prescott filter with λ = 100. Fig. 5. Correlation of sectoral employment across countries.

In particular, we first transform the time series of output for the United States in each sector by dividing each series by the average share of output in that sector (i.e., we define Y¯a,t = Ya,t /sa and Y¯n,t = Yn,t /(1 − sa ) where Yi,t is the time series data on output for each sector and sa is the average share of output in agriculture in the US data). We use this transformed data to construct hypothetical economies that differ in the share of output in agriculture. We define Y¯t (¯sa ) ≡ s¯a Y¯a,t + (1 − s¯a )Y¯n,t , for any s¯a ∈ [0, 1]. Notice that aggregate output in the hypothetical economy corresponds exactly to the US data if s¯a = sa . Also, the standard deviation of the log of Y¯t is equal to the standard deviation of the log of Ya,t when s¯a = 1 and to the standard deviation of the log of Yn,t when s¯a = 0. More importantly, using the sectoral US data for this counterfactual is helpful since in all hypothetical economies the statistical properties of sectoral business cycles are identical to the US data.2 The aggregate output of each hypothetical economy is then logged, de-trended, and the standard deviation is computed.

2 The statistical properties of the sectoral time series for the United States (log(Y ), log(Y )) are identical to the a,t n,t properties of the time series for each hypothetical economy (log(Y¯a,t ), log(Y¯n,t )), in particular, these two sets of time series share the same variance–covariance matrix.

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Note. σY is the standard deviation of the log of aggregate GDP, de-trended using the Hodrick–Prescott filter with λ = 100. The solid line represents a counterfactual situation where aggregate output is constructed using sectoral data for the United States for different shares of output in agriculture. As with the data, aggregate output is de-trended and the standard deviation of the log is computed using the de-trended series. Fig. 6. Aggregation in output fluctuations.

The results of this experiment are reported by the solid line in Fig. 6 along with data on aggregate GDP fluctuations across countries. Notice that in Fig. 6 the standard deviation of aggregate output for a hypothetical economy with a share of output in agriculture of one corresponds to the volatility of the agricultural sector in the US data, while the hypothetical economy with a share of output in agriculture of zero corresponds to the volatility of output in non-agriculture in the US data. From this figure we conclude that a large share of output in agriculture (about 60%) would be required for aggregation alone to account for the difference in aggregate GDP fluctuations between countries such as the United States and Turkey. For a reasonable range of shares of output in agriculture across countries (between 0 and 30 percent), aggregation alone accounts for almost none of the differences in aggregate fluctuations across countries. Following a similar reasoning as above, a composition effect could be explaining the lower correlation of aggregate output and employment in economies intensive in agriculture given that output and employment in agriculture are less correlated than in non-agriculture. Figure 7 reports the results of a similar counterfactual as described above but for the correlation of aggregate

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Note. ρ(L, Y ) is the correlation of log aggregate employment and GDP, both variables de-trended using the Hodrick– Prescott filter with λ = 100. The solid line represents a counterfactual situation where aggregate output and employment are constructed using sectoral data for the United States for different shares of agriculture (a common share of output and employment in agriculture is used for these calculations). As with the data, aggregate output is de-trended and the standard deviation of the log is computed using the de-trended series. Fig. 7. Aggregation in the correlation of output and employment.

output and employment along with the data across countries.3 We find that a large share of agriculture would be required in order for aggregation alone to account for the differences in the correlation in aggregate output and employment observed between countries such as the United States and Turkey. We conclude that the share of agriculture in the economy may be affecting aggregate fluctuations through an additional channel. Our conjecture is that sector-level fluctuations are influenced by the size of agriculture in the economy. 3. The economic environment We consider a two-sector real business cycle model. A different good is produced in each sector and we denote them as agriculture (a) and non-agriculture (n). Output in each sector is produced with a constant returns to scale production function. The technology in non-agriculture 3 Sectoral employment for the US is first transformed by dividing by the average share of employment in each sector and then aggregated using different shares of employment in agriculture. The results assume the same share of employment and output in agriculture.

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requires physical capital and labor services as inputs while the technology in agriculture requires the inputs of physical capital, labor, and land services. Fluctuations are driven by shocks to total factor productivity in each sector. The production function for non-agriculture is given by, θ 1−θ Yn,t = γnt λn ezn,t Kn,t Hn,t ,

and the production function for agriculture is described by, μ

φ

Ya,t = γat λa eνt eza,t Ka,t Ha,t T 1−μ−φ , where for each sector i ∈ {a, n}, γi  1 is an exogenous growth rate of productivity, Ki is the physical capital input, Hi is the labor input, T is the input of land services that are in fixed supply, and λi is a time invariant technology parameter. The shocks to technology are divided in two components. First, z = [zn , za ] follows a vector auto-regressive process described by zt+1 = ρzt + εt+1 ,

(1)

where ε is normally distributed with zero mean and variance-covariance matrix Ω. As is standard in real business cycle theory, these shocks are known before any decisions take place. Second, the shock ν affecting output in agriculture is known after economic decisions take place. We assume that νt is i.i.d. over time and is normally distributed with mean zero and variance σν2 . We introduce this second shock to agriculture in our environment for two reasons. First, we think this shock is empirically relevant in agriculture since weather shocks may affect agricultural output after some decisions have been made regarding factor inputs. Second, we find that this shock is critical in accounting for the quantitative properties of business cycles in agriculture. We discuss in detail the appropriateness of these assumptions in the calibration section. Output in non-agriculture Yn can be allocated to consumption of non-agriculture Cn and investment in physical capital X, Cn,t + Xt  Yn,t ,

(2)

and output in agriculture Ya can only be consumed Ca , Ca,t  Ya,t .

(3)

The physical capital stock follows a standard accumulation equation and can be allocated to either sector, Kt+1 = (1 − δ)Kt + Xt ,

Kn,t + Ka,t  Kt .

The economy is populated by a measure of identical households that grows over time at an exogenous gross rate η. We normalize the initial population measure to one. The representative household has preferences over sequences of per-capita consumption Ct /Lt and leisure (1 − ht ) for each member of the household described by   ∞  Ct t βu , 1 − ht Lt , Lt t=0

where β is the time discount factor. The per-period utility function is defined as     Ct Ct + (1 − b) log(1 − ht ), , l − ht = b log u Lt Lt

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and aggregate consumption as 1  e e e Ct = aCn,t + (1 − a)Ca,t . Every member of the household is endowed with one unit of productive time in each period. Since our data is restricted to the level of employment in each sector we assume that labor hours are indivisible: the household works a given number of hours in either sector or does not work. This assumption is not too restrictive since in the data changes in employment account for large portion of the aggregate fluctuations in the labor input. Since the commodity space is not convex when labor is indivisible we allow households to trade lotteries as in Rogerson (1988). Hansen (1985) introduces Rogerson’s lotteries in a dynamic real business cycle model. We assume that with probability πn the household works h¯ n hours in non-agriculture, with probability πa the household works h¯ a hours in agriculture, and with probability 1 − πa − πn the household does not work. The solution to this model implies that these labor probabilities are equal to the employment to population ratio in each sector and the non-employment to population ratio. It is convenient to write the problem in terms of efficiency units of labor. To this end, we divide variables that are growing by the population size and the exogenous productivity level at each date. We denote variables in efficiency units of labor with lower case letters. Because there are no externalities or distortions in our model and the choice set with lotteries is convex, we use the welfare theorems to characterize the equilibrium solution of our model by the solution to the associated planner’s problem. To describe the planner’s problem and its solution, it is convenient to adopt a recursive structure. At the beginning of the period, the state variables for the planner are the productivity shock in each sector and the aggregate capital stock. The planner makes decisions about consumption of non-agriculture, investment in physical capital, and capital and labor allocation across sectors based on the expected value for the realization of the i.i.d. agricultural shock. The decision for consumption of agriculture is contingent on the realization of the i.i.d. agriculture shock.4 Formally, the state variables at the beginning of the period are za , zn , and k, and the Bellman equation for the planner is as follows:   

 Ez ,z v za , zn , k  , v(za , zn , k) = max Eν max u(ca , cn , πa πn ) + β (4) a n {cn ,k  ,kn ,πa ,πn }

ca

subject to the feasibility constraints in (2) and (3), the stochastic process for the shocks in (1), and the i.i.d. process for ν, where u(ca , cn , πa , πn )

 e  

 b e ¯ ¯ log acn + (1 − a)ca + (1 − b) πn log 1 − hn + πa log 1 − ha , = e 4 We assume that the investment decision is not contingent on the realization of the shock ν to output in agriculture. We think this is not a severe restriction given that ν is i.i.d. over time. An alternative specification would allow investment (and therefore consumption in non-agriculture) to be contingent on the realization of ν. We argue that this alternative specification would affect the relative volatility of investment depending on the elasticity of substitution between consumption of agriculture and non-agriculture. In particular, this alternative specification may lead to lower fluctuations in investment and larger fluctuations of consumption relative to the model without this shock, making these implications of the model closer to the data. For a discussion on this issue see Benhabib et al. (1991). Since we do not focus on investment fluctuations we abstract from this complication in the environment in our analysis.

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 = βη. This problem generates policy rules: g cn (za , zn , k) for consumption of nonand β  agriculture, g k (za , zn , k) for the capital stock next period, g kn (za , zn , k) for capital allocated in non-agriculture, g πn (za , zn , k) and g πa (za , zn , k) for the employment ratio in non-agriculture and agriculture, and g ca (za , zn , k; ν) for consumption of agriculture. The solution to this optimal stochastic growth problem is defined by a set of functions: value function v(za , zn , k) and policy functions g such that v(za , zn , k) solves (4) and functions g are feasible optimal policy functions. When za , zn , and ν are constant over time and are set to their mean values (¯za , z¯ n , 0), the economy converges to a stationary state which is defined by a fixed point of the policy rule for  the capital stock g k (¯za , z¯ n , ks ) = ks and constant values for all other variables defined by the decision rules at (za , zn , ks ) and ν = 0. 4. The benchmark economy We calibrate our benchmark economy (B.E.) to data for the United States following Prescott (1986) and Cooley and Prescott (1995). We show that our benchmark economy features businesscycle properties consistent with business-cycle statistics for the United States. 4.1. Calibration Our benchmark economy is calibrated to the US data. The length of a period is assumed to be one year because of sectoral data limitations for a large cross-section of countries. Our calibration procedure consists of three parts. First, we calibrate a set of parameter values without solving the model using direct information from the US data. Second, we calibrate another set of parameter values to long-run observations of the United States by solving for the deterministic steady state of the model. The third component of the calibration is the estimation/calibration of the stochastic process for technology shocks. The following parameter values are determined directly by US data. The exogenous growth of population η is 1.012% from the average annual growth of working-age population. The exogenous growth of productivity γ is 1.016% from the average annual growth of GDP per working-age person. The income share of capital in non-agriculture θ is 0.4 (including durable consumer goods and government capital) from the calculations in Cooley and Prescott (1995). It is estimated that people allocate 1/3 of their productive time to market work. Since the share of employment in agriculture is small and the employment ratio is 66 percent in the US economy, 1/3 total hours of work implies that hours of work in non-agriculture h¯ n is 0.5. (See Hansen, 1985.) We calculate the income share of labor in agriculture φ to be the same as in non-agriculture using data from the US Department of Commerce (2000). In doing this calculation, we follow Gollin (2002) and adjust labor income by the income of self-employed people in agriculture. This adjustment of labor compensation is needed in the US data for agriculture since self-employment is roughly 46 percent of total employment in agriculture.5 Hence, we assume φ = (1 − θ ) which 5 Using data for the United States from 1987 to 2000, we divide employee compensation by the number of full-timeequivalent employees and then multiply this value by the number of people employed (employees plus self-employed). We divide total labor compensation by national income to obtain the income share of labor in agriculture. This adjustment implicitly assumes that there are no systematic differences (in earnings ability and hours of work) between employees and self-employed people and that the labor market is not segmented across these two types of workers. We think these implicit assumptions are reasonable in the context of the US economy. (See Gollin, 2002 for an application of this adjustment to the aggregate economy for a cross section of countries.)

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implies that φ is 0.6. The income share of land in agriculture 1 − φ − μ is 0.1 from estimates of production functions in agriculture in Hayami and Ruttan (1985). The total factor productivity parameter in non-agriculture λn and the supply of land T are both normalized to one and the preference parameter a to 0.5. Changes in these three parameters do not affect the properties of business cycles after the model is calibrated to match a set of targets in the data as described below. The values of the 5 parameters δ, β, h¯ a , λa , and b are chosen so that the deterministic steady state of the model matches the following 5 statistics from the US data: An investment to output ratio of 25 percent, a capital to output ratio of 3.3, an employment ratio in agriculture of 2 percent, a share of output in agriculture of 2 percent, and an employment ratio of 66 percent. Our choice for the structure of shocks in the economy is based on two observations of business cycles in the United States. First, there is almost no correlation of employment and output in agriculture (0.09). This lack of correlation arises despite large fluctuations in employment in agriculture. Second, there is almost no correlation of employment across sectors (−0.02). The first observation suggests that agriculture features shocks to output that do not induce changes in employment in this sector. For instance, “weather” shocks to agriculture may present this property since these shocks affect production in agriculture after labor and capital inputs are in place. Moreover, these shocks are not highly persistent. The second observation suggests that shocks to technology do not induce labor reallocation across sectors. Because of these observations, we assume two components of the stochastic process for technology shocks in agriculture: Shocks that are known prior to factor allocation decisions za and shocks that occur after economic decisions ν. Notice that because estimates from Solow residuals in agriculture cannot identify the properties of each of these shocks, we need to follow an alternative empirical strategy. The shocks to technology in non-agriculture zn are estimated using Solow residuals for non-agriculture as is standard in the real business cycle literature. The ex ante shocks to agriculture za are calibrated to match the lack of correlation between employment across sectors. This implies, in addition to assuming no cross persistence between zn and za shocks, choosing values for ρa , σεa , and corr(εn , εa ). The ex post shock to agriculture ν is calibrated so that the implied Solow residual in agriculture in the model is as volatile as in the data. Sectoral Solow residuals are computed from US data as SRi = log(RGDPi ) − ξi log(Li ) − γi log(Ki ), where for each i ∈ {a, n}, RGDPi is real GDP in sector i, Li is employment in sector i, Ki is the physical capital stock in sector i, ξn = (1 − θ ), ξa = φ, γn = θ , and γa = μ. An OLS regression of the Solow residual in non-agriculture against itself lagged one period implies ρn = 0.829 and σεn = 1.74%. We find that ρa = 0, σεa = 2σεn , and corr(εn , εa ) = 0.564 implies an almost zero correlation of employment across sectors.6 The parameters of the ex ante technology shock process z are as follows,

6 If the two sectors were identical then a common ex ante shock would suffice to produce no reallocation of resources across sectors. Since capital income shares are different between agriculture and non-agriculture and investments goods can only be produced in non-agriculture, high volatility of za relative to zn is needed to generate the lack of resource reallocation across sectors in the benchmark economy.

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 0.83 0.00 ρ= , 0.00 0.00



0.01742 Ω= 0.564 × 2 × 0.01742

469

 0.564 × 2 × 0.01742 . (2 × 0.0174)2

The standard deviation of the i.i.d. shock to agriculture σν is set to 7.5 percent in order for the standard deviation of the implied Solow residual in agriculture in the model to match the same statistic in the data (this implies that the model closely matches the volatility of agricultural output relative to non-agricultural output in the data). Finally, the parameter governing the elasticity of substitution in consumption between agricultural and non-agricultural goods e is chosen to match the relative fluctuations of employment in agriculture and non-agriculture of 1.6. This target implies e = 0.52. We discuss in a sensitivity analysis in the next section the implications of this parameter for our results. A summary of calibrated parameters values and targets is presented in Table 2. Notice that our calibration procedure implies that hours of work in agriculture h¯ a is 0.36. Therefore, if the workweek is normalized to 40 hours in non-agriculture this implies that people in our model work 29 hours per week in agriculture. We think that this difference in hours of work across sectors is reasonable. However, other than with our calibration procedure, it is difficult to justify numbers for hours of work in agriculture since most of the reported hours of work across sectors are for employees and, as discussed previously, employees represent only a half of total employment in US agriculture. Household data from the Current Population Survey that includes employees and self-employed people suggest that hours of work are roughly similar between agriculture and non-agriculture (although this survey only includes people working more than 15 hours a week in family related businesses). Nevertheless, given the limitations surrounding data for hours of work in agriculture, we explore via sensitivity analysis in Section 5.4 the implications for our results of setting h¯ a = h¯ n as an alternative assumption. We find that the quantitative impact of agriculture in aggregate business cycles are magnified under this alternative specification of hours of work.

Table 2 Benchmark parameter values Parameter Data US

h¯ n γ η θ φ 1−φ−μ λn , T a ρ and Ω

0.5 1.016 1.012 0.4 0.6 0.1 1.0 0.5 see text

δ β h¯ a λa b σν e

0.05 0.96 0.36 0.03 0.36 0.075 0.52

Hansen (1985) GDP per capita growth rate Population growth rate Capital income share US Department of Commerce (2000) Hayami and Ruttan (1985) Normalization Normalization Sectoral Solow residuals Targets Investment–output ratio 25% Capital–output ratio 3.3 Ag. output share sa = 0.02 Ag. employment πa = 0.02 Employment ratio 66% Std. of Solow residual in agriculture σπa /σπn = 1.6

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4.2. Results of the benchmark economy We compute decisions rules and business cycle statistics following the linear quadratic procedure described in McGrattan (1990).7 As in the data, all time series of the model are de-trended using the Hodrick–Prescott filter with λ = 100 and the de-trended series are used to compute statistics from simulations. Table 3 presents a summary of business cycle statistics for the US data and the benchmark economy. The calibrated economy roughly matches the data in important dimensions. First, the aggregate economy fluctuates more than in the data (2.60 in the model vs. 2.12 in the US data). Second, the relative volatility of aggregate employment is close to the data (0.68 in the model vs. 0.63 in the data).8 Third, the correlation of aggregate employment and output is close to the data (0.95 in the model vs. 0.82 in the data). In addition, the benchmark economy reproduces some salient features of sectoral business cycles: First, employment in agriculture fluctuates more than in the data (2.88 in the model vs. 2.28 in the data) and the correlation of employment in agriculture and aggregate output closely matches the data (−0.07 in the model vs. −0.14 in the data). Second, the model reproduces the lack of correlation between output in agriculture and output in non-agriculture (0.04 in the model and −0.01 in the data). As a target in our calibration procedure, the model matches the lack of correlation between employment in agriculture and non-agriculture (−0.02 in the model and the data).9

Table 3 Business cycles in the benchmark economy US data

B.E.

σx

σx /σy

ρ(x, y)

σx

σx /σy

ρ(x, y)

Output Employment Non-ag. employment Ag. employment

2.12 1.34 1.39 2.28

1.00 0.63 0.66 1.08

1.00 0.82 0.83 −0.14

2.60 1.76 1.82 2.88

1.00 0.68 0.70 1.11

1.00 0.95 0.96 −0.07

Non-ag. employment Ag. employment Non-ag. output Ag. output

1.39 2.28 2.16 5.48

0.66 1.08 1.02 2.56

0.82 −0.14 1.00 −0.01

1.82 2.88 2.64 8.79

0.70 1.11 1.02 3.33

0.96 −0.11 1.00 0.04

Note. σx is the standard deviation of the log of variable x, y is aggregate GDP, yn is GDP in non-agriculture, and ρ(x, z) is the correlation of variables x and z.

7 We thank Ellen McGrattan for providing us with versions of her programs. 8 It is well known that models of the business cycle with indivisible labor induce larger fluctuations in output and

employment relative to the divisible-labor model. (See Hansen, 1985.) In particular, Hansen shows that output and employment fluctuations increase by 30 and 93 percent in the indivisible-labor model relative to the divisible-labor model. 9 Notice that if instead we assume only ex ante technology shocks z and estimate the process using data on Solow residuals across sectors (standard approach in real business cycle theory), we obtain similar aggregate implications from the model (fluctuations in output of 2.52, relative volatility of employment of 0.68, and a correlation of output and employment of 0.95). However, the sectoral implications of the model are markedly different: Fluctuation of output and employment in agriculture of 14.92 and 7.80, a correlation of employment across sectors of −0.40, and a correlation of employment and output in agriculture of 1.00. These implications across sectors are at odds with the evidence for the United States and, as discussed previously, are likely reflecting a mis-specification of the stochastic process of technology shocks in agriculture. We discuss in detail the cross-country implications of this alternative approach in Section 6.

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5. Cross-country experiments We design and implement a number of experiments to assess the quantitative role of agriculture in business cycles across countries. In particular, in this section we ask: Is the share of agriculture in economic activity important for the observed differences in business cycles across countries? Our results suggest that the share of agriculture in the economy accounts for an important portion of business cycle differences across countries. We find that an increase in the employment ratio in agriculture from 2 to 30 percent in our model increases fluctuations in aggregate output by almost 40 percent. This increase is roughly 2/3 of the difference in aggregate fluctuations between countries such as Turkey and the United States. 5.1. Description of experiments We implement four stylized experiments that feature different deterministic steady-state shares of employment in agriculture. In particular, we consider economies with shares of employment of 10, 15, 20, and 30 percent, while keeping the aggregate employment ratio constant across these economies. We calibrate these experiments by choosing values for the preference parameter of agricultural goods (1 − a) to target the employment to population ratio in agriculture and the preference parameter of leisure b to keep the aggregate employment ratio constant to 66 percent as in the benchmark economy. All other parameter values remain the same as in the benchmark economy. The values for the targets and the resulting values for the calibrated parameters are reported in Table 4. Notice that we focus on fluctuations around a deterministic steady state as opposed to fluctuations around a transitory path towards a balanced growth path. We recognize that countries such as Turkey and even the United States are undergoing a process of structural transformation (from agriculture to non-agriculture) and that Turkey may be lagging behind in this transitory path. However, our simplification is a tractable way of implementing our research question about the role of agriculture in aggregate business cycles. 5.2. Quantitative results Aggregate implications Table 5 summarizes the results of the experiments along with the results for the benchmark economy. The table reports business cycle statistics as well as steady-state implications. We summarize the results of these experiments as follows: (1) Fluctuations in aggregate output increase with the employment ratio in agriculture: Fluctuations in aggregate output in experiment 4 are 37 percent higher than in the benchmark Table 4 Calibration of experiments B.E. Targets: πa π a + πn Parameters: a b

Experiments 1

2

3

4

0.02 0.66

0.10 0.66

0.15 0.66

0.20 0.66

0.30 0.66

0.50 0.36

0.28 0.35

0.23 0.35

0.20 0.34

0.14 0.33

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Table 5 Aggregate implications across economies B.E. πa σY σL σL /σY ρ(Y, L) K/Y h Rel. Y /L

0.02 2.60 1.76 0.68 0.95 3.28 0.33 1.00

Experiments 1

2

3

4

0.10 2.67 1.69 0.63 0.92 3.21 0.32 0.96

0.15 2.81 1.64 0.58 0.88 3.16 0.31 0.93

0.20 2.99 1.58 0.53 0.82 3.11 0.30 0.92

0.30 3.56 1.46 0.41 0.70 3.00 0.29 0.86

Note. σx is the standard deviation of the log of variable x, Y is aggregate GDP, L is aggregate employment, πi is the employment ratio in sector i, ρ(x, z) is the correlation of variables x and z, and h is aggregate hours worked (h = h¯ n πn + h¯ a πa ).

economy (3.56 vs. 2.60), which represents about 2/3 of the difference in fluctuation of aggregate output between countries such as Turkey and the United States. (2) The relative volatility of employment decreases with the employment ratio in agriculture, from 0.68 in the benchmark economy to 0.41 in experiment 4, which represents more than 1/2 of the difference between countries such as the United States and Turkey (0.63 and 0.23). (3) The correlation of aggregate output and employment decreases with the employment ratio in agriculture. The correlation of aggregate output and employment is 0.70 in experiment 4 and 0.95 in the benchmark economy, while this correlation is 0.13 and 0.82 in Turkey and the United States.

Sectoral implications Our experiments indicate that sector-level fluctuations change across economies with different employment to population ratios in agriculture (see Table 6): (1) In the model, an increase in the employment ratio in agriculture from 2 to 30 percent implies an increase in fluctuations of output in non-agriculture of more than 30 percent and a slight decrease in fluctuations of output in agriculture. Similarly, the increase in the employment ratio in agriculture produces an increase in the volatility of employment in non-agriculture in almost 50 percent and a decrease in the volatility of employment in agriculture of more than 40 percent. (2) The size of agriculture in the economy changes the correlation of factor inputs and output in non-agriculture. Whereas the correlation of capital and output in non-agriculture in the benchmark economy is close to 0, it is 0.62 in the Experiment-4 economy. (See Figs. 8 and 9.) (3) The size of agriculture in the economy changes the amount of reallocation of employment across sectors: Whereas the correlation of employment in agriculture and non-agriculture is −0.02 in the benchmark economy, it is −0.26 in the Experiment-4 economy. (See Table 6 and Figs. 8 and 9.) The intuition for these patterns is simple. In a one-sector model, shocks to technology are propagated by the inter-temporal substitution of consumption over time. In a two-sector model, there is an extra margin of substitution: intra-temporal substitution of consumption across sec-

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Table 6 Sectoral implications across economies B.E. πa σYn σYa σπn σπa ρ(πa , πn )

0.02 2.64 8.79 1.82 2.88 −0.02

Experiments 1

2

3

4

0.10 2.81 8.58 1.99 2.55 −0.12

0.15 2.93 8.53 2.12 2.38 −0.16

0.20 3.08 8.37 2.27 2.13 −0.21

0.30 3.48 8.13 2.69 1.66 −0.26

Note. σx is the standard deviation of the log of variable x, Yi is output in sector i, πi is employment in sector i, and ρ(x, z) is the correlation of variables x and z.

Fig. 8. Sectoral fluctuations—benchmark economy.

Fig. 9. Sectoral fluctuations—Experiment-4 economy.

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tors. The amount of intra-temporal substitution hinges on the importance of agriculture in the economy. For a given stochastic process of ex ante shocks z, as the share of agriculture in the economy declines to zero, the economy only substitutes consumption inter-temporally and, therefore, converges to the behavior of a one-sector economy. When the share of agriculture increases, the importance of agriculture in the economy increases and the amount of intra-temporal substitution of consumption alters the sectoral properties of business cycles. 5.3. Discussion Our results regarding the role of agriculture in aggregate business cycles relate to a strand of the business-cycle literature assessing the role of different factors in accounting for businesscycle patterns across countries. For instance, Conesa et al. (2002) assess the quantitative role of home production in accounting for the differences in the standard deviation of the log of output across countries. The home production model is successful in accounting for differences in aggregate output fluctuations across countries. The model implies that countries with large amounts of home production activities have higher market output fluctuations. However, the model also implies that countries with large home production have higher market employment fluctuations. Differences in the relative volatility of employment between European countries and the United States are often cited as evidence of the importance of labor market institutions in accounting for labor market fluctuations in Europe. (See Danthine and Donaldson, 1993 and Kollintzas and Fiorito, 1994.) Maffezzoli (2001) explores the role of non-competitive labor markets in Italy and is successful in accounting for the difference in the relative volatility of employment between Italy and United States, but even with monopolistic competition in the labor market the model cannot account for the low correlation between aggregate employment and output in Italy. The role of agriculture in business cycles complements this literature by generating implications for aggregate business cycle statistics that are consistent with the cross-country data in output and employment. Our experiments illustrate that the model with agriculture is able to generate the main patterns of aggregate business cycles across countries: High fluctuations in aggregate output, low relative volatility of employment, and low correlation of employment and output observed in countries intensive in agriculture. Moreover, these results on aggregate business cycles are generated by the impact of the size of agriculture on sectoral fluctuations. We emphasize that our experiments are not generated by only changing the parameter related to the share of employment in agriculture (i.e., by lowering the preference parameter a). If we generate economies that differ only on a the implied aggregate employment ratio in the deterministic steady state of the model would be higher and affect business cycle properties of the model with regard to the labor market: Fluctuations in employment and the correlation of aggregate employment and output would increase with the share of employment in agriculture. These implications of the model do not conform well with the cross-country evidence discussed previously. However, the implications of the model in terms of aggregate output fluctuations would be similar to the experiments discussed in this section. 5.4. Sensitivity analysis Substitution of consumption goods The parameter e determines the elasticity of substitution between consumption of agricultural and non-agricultural goods. Because this parameter affects the response of factor allocation across sectors to changes in productivity, we restricted this parameter in our baseline calibration to roughly match the volatility of employment in agriculture

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relative to non-agriculture. Nonetheless, because elasticity parameters of this type are crucial for business-cycle analysis in home production models and for development analysis in models of the process of structural transformation, it is of interest to illustrate the implications for our results of different parameter values for e. We proceed by changing the parameter value e and calibrating the benchmark economy to the same targets as before except that we leave untouched the structure of shocks. In particular, we compare economies that have the same employment ratio in agriculture (2 percent in the benchmark economy and 30 percent in the Experiment-4 economy). Recall that the value of e in our baseline calibration is 0.52. In Table 7 we summarize the results. For the benchmark economy, the aggregate implications of different values of e are essentially the same as in our baseline calibration. The noticeable variations occur at the sectoral level: Output in agriculture fluctuates much more as we increase the value of e. However, this larger volatility in agriculture is not reflected to a large extent in the aggregate economy because the share of employment and output in agriculture in all these economies is small. In panel B of Table 7, we report the cross-country results for different values of e. In particular, we report the results for the Experiment-4 economy that has an employment ratio in agriculture of 30 percent. While there is some variation in the aggregate results across different values of e, the main quantitative properties emphasized with our baseline calibration hold. In particular, lower values for e decrease by a small percentage the amount of aggregate fluctuations implied by the model for an economy intensive in agriculture. Hours of work in agriculture Recall that our baseline calibration of the benchmark economy implies that hours of work in agriculture are almost 30 percent lower than in non-agriculture Table 7 Implications of different values for e A. Benchmark economy e σY σL σL /σY ρ(L, Y ) σYn σYa σπn σπa σpa

−3.0 2.57 1.74 0.68 0.96 2.60 7.02 1.80 2.36 27.86

0.1 Aggregate implications 2.57 1.75 0.68 0.95 Sectoral implications 2.61 7.56 1.80 0.32 6.84

0.52

0.9

2.60 1.76 0.68 0.95

2.60 1.80 0.69 0.94

2.64 8.79 1.82 2.88 4.28

2.67 17.33 1.85 14.65 1.78

0.52

0.9

3.56 1.46 0.41 0.70

3.79 2.63 0.69 0.65

B. Experiment-4 economy e σY σL σL /σY ρ(L, Y )

−3.0 3.52 1.35 0.38 0.59

0.1 Aggregate implications 3.56 1.38 0.39 0.66

Note. σx is the standard deviation of the log of variable x, Y is aggregate GDP, L is aggregate employment, Yi is output in sector i, πi is employment in sector i, pa is the relative price of agriculture, and ρ(x, z) is the correlation of variables x and z.

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Table 8 Implications of hours of work in agriculture h¯ a B.E.

Experiment 4

h¯ a

0.36

0.5

0.36

0.5

σY σL σL /σY ρ(L, Y )

2.60 1.76 0.68 0.95

2.60 1.78 0.69 0.95

3.56 1.46 0.41 0.70

4.12 1.63 0.40 0.58

Note. σx is the standard deviation of the log of variable x, Y is aggregate output, L is aggregate employment, and ρ(x, z) is the correlation of variables x and z.

(0.36 vs. 0.5). It is difficult to obtain reliable measures of hours of work in agriculture because a large fraction of employment in this sector is self-employment. The available evidence from household survey data suggests that hours of work are roughly equal in agriculture and nonagriculture (although this data only includes people working more than 15 hours per week in family-related businesses). Therefore, it is of interest to investigate the extent to which our crosscountry business-cycle results depend on our calibration of hours of work in agriculture. We proceed by setting hours of work equal across sectors, i.e., h¯ a = h¯ n . We keep all other parameter values the same as in our baseline calibration. This alternative assumption about hours of work in agriculture implies that the share of output in agriculture is now 3 percent in the benchmark economy as opposed to 2 percent. For all other statistics, the benchmark economy under the alternative assumption for h¯ a are roughly the same. We report in Table 8 the business-cycle implications for aggregate variables for the two different assumptions regarding hours of work in agriculture. For the benchmark economy, aggregate business cycle implications are roughly the same under the two assumptions. For the economy intensive in agriculture however, the aggregate implications of agriculture are magnified under the assumption of equal hours of work across sectors, in particular, when the employment ratio in agriculture increases from 2 to 30 percent, fluctuations in aggregate output increase much more when hours of work are equal across sectors. Equal hours of work across sectors also implies that in the deterministic steady state of the model aggregate hours of work and relative output per worker are the same across economies that differ in the employment ratio in agriculture, while this was not the case in our baseline calibration. 6. The role of agriculture In order to illustrate the importance of agriculture in aggregate business cycles across countries, in this section we perform the same experiments as in Section 5 with changes in the nature of the stochastic process for agriculture. The importance of ex post shocks ν The lack of correlation observed between employment and output in agriculture suggested a feature for fluctuations in output in agriculture that is independent of labor allocations. For this reason, in our baseline calibration we considered an i.i.d. shock to technology in agriculture that is realized after factor input allocations are made. Table 9 illustrates the importance of this shock for the cross-country implications of our model. The table reports business cycle statistics for the benchmark economy and for the economy with a higher share of agriculture (experiment 4) for two different scenarios: With ex post shocks (σν = 0.075 as in the baseline calibration) and without (σν = 0). Ex post shocks have virtually no effect in ag-

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Table 9 The role of ex post shocks in agriculture ν B.E.

σν 0.075 σY σL σL /σY ρ(L, Y ) ρ(πa , πn ) ρ(πa , Ya )

2.60 1.76 0.68 0.95 −0.02 0.60

Experiment 4 0 2.59 1.76 0.68 0.96 0.00 0.98

0.075 3.56 1.46 0.41 0.70 −0.26 0.52

0 2.64 1.47 0.52 0.96 −0.26 0.97

Note. σx is the standard deviation of the log of variable x, Y is aggregate output, Yi is output in sector i, L is aggregate employment, πi is employment in sector i, and ρ(x, z) is the correlation of variables x and z.

gregate business-cycle statistics in the benchmark economy. The reason for this result is that the share of agriculture is small in the benchmark economy and, therefore, fluctuations in agriculture have negligible effects on sectoral reallocation and aggregate statistics. For the economy in experiment 4, however, the shock has an important impact on the aggregate properties of business cycles, in particular, output in this economy fluctuates more, relative volatility of employment is lower, and the correlation of aggregate employment and output is lower when the ex post shock is present. We conclude that despite the irrelevance of ex post shocks to agriculture for aggregate business cycles in the benchmark economy, these shocks are central to our findings across countries. The importance of ex ante shocks z Recall that ex ante shocks to agriculture za are calibrated to match the lack of employment correlation in agriculture and non-agriculture in the United States. We evaluate the importance of this shock for the cross-country implications of the model. Table 10 reports business cycle statistics for the benchmark economy and the economy in experiment 4 for the case in which σν = 0 and za follows the same properties as zn for different values of the correlation of innovations to the shocks corr(εn , εa ). Notice that without ex post shocks and with σεa = σεn , the volatility of aggregate output in the economy intensive in agriculture falls relative to the benchmark economy for all values of the correlation of innovations of ex ante shocks. As Table 10 shows, the correlation of innovations of the shocks has little impact on the aggregate properties of business cycles in the benchmark economy. However, for economy intensive in agriculture, fluctuations of output and employment are lower than in the benchmark economy. Notice in particular that uncorrelated or negatively correlated innovations of ex ante shocks (i.e., corr(εn , εa )  0) are not enough to generate higher fluctuations of aggregate output when the share of employment in agriculture is higher. Table 11 illustrates the importance of the volatility of innovations to ex ante shocks in agriculture for the case without ex post shocks, ρa = ρn , and corr(εn , εa ) = 0. The volatility of εa does not influence aggregate business cycles in the benchmark economy, but it has substantial effects on the properties of aggregate business cycles across countries. With a high volatility of shocks in agriculture, fluctuations in aggregate output are high but the stochastic process of shocks implies a large negative correlation of employment across sectors and relatively high fluctuations in sectoral output. An alternative specification of shocks In the economy with only ex ante shocks z, the shock process can be estimated using Solow residuals from the US data as discussed previously. This

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Table 10 The correlation of innovations to ex ante shocks corr(εa , εn ) B.E.

corr(εa , εn ) σY σL σL /σY ρ(L, Y ) ρ(πa , πn ) ρ(πa , Ya )

Experiment 4

1.0

0.0

−1.0

1.0

0.0

−1.0

2.61 1.77 0.68 0.95 0.92 0.61

2.55 1.73 0.68 0.95 −0.63 0.97

2.52 1.72 0.68 0.95 −0.96 0.99

2.51 1.39 0.55 0.95 0.93 0.57

2.04 1.28 0.63 0.93 −0.74 0.95

1.40 1.13 0.81 0.92 −0.97 0.99

Case: σν = 0; ρa = ρn ; σεa = σεn . Note. σx is the standard deviation of the log of variable x, Y is aggregate output, Yi is output in sector i, L is aggregate employment, πi is employment in sector i, and ρ(x, z) is the correlation of variables x and z.

Table 11 The volatility of innovations to shocks in agriculture σεa B.E.

σεa σY σL σL /σY ρ(L, Y ) ρ(πa , πn ) ρ(πa , Ya ) σYn σYa

Experiment 4

σεn

4 × σεn

8 × σεn

σεn

4 × σεn

8 × σεn

2.56 1.74 0.68 0.95 −0.62 0.97 2.64 3.45

2.56 1.75 0.68 0.95 −0.27 1.00 2.65 12.02

2.60 1.77 0.68 0.95 −0.22 0.99 2.68 24.73

2.05 1.28 0.63 0.93 −0.74 0.95 3.75 2.74

3.02 1.38 0.46 0.85 −0.70 0.99 4.15 9.72

5.14 1.66 0.32 0.84 −0.84 1.00 5.22 19.47

Case: σν = 0; ρa = ρn ; corr(εa , εn ) = 0; and σεn = 1.74%. Note. σx is the standard deviation of the log of variable x, Y is aggregate output, Yi is output in sector i, L is aggregate employment, πi is employment in sector i, and ρ(x, z) is the correlation of variables x and z.

estimation procedure yields: ρa = 0, σεa = 8% and corr(εn , εa ) = −0.25, in addition to the parameters for non-agriculture described in the calibration section. Using this process without ex post shocks, Table 12 documents the results across countries in our model. Notice that even though the ex ante shocks are estimated using sectoral data for the United States, this process implies that the benchmark economy differs from the data in important dimensions, in particular, the benchmark economy displays a large negative correlation of employment across sectors, a large positive correlation of employment and output in agriculture, and a high volatility of output in agriculture relative to non-agriculture. Across countries, the process implies higher fluctuations in output as we increase the share of employment in agriculture. It also implies lower relative volatility of employment, and a lower correlation of employment and output. While the direction of these effects is similar to the results from our baseline calibration, the quantitative magnitude of the effects are different. Moreover, as discussed previously, the aggregate volatility of output in these economies is partly the result of larger relative volatility of output in agriculture than observed in the data.

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Table 12 Cross-country experiments with only ex-ante shocks z B.E. πa σY σL σL /σY ρ(L, Y ) ρ(πa , πn ) ρ(πa , Ya ) σYn σYa

0.02 2.52 1.72 0.68 0.95 −0.40 1.00 2.66 14.92

Experiments 1

2

3

4

0.10 2.44 1.58 0.65 0.94 −0.59 1.00 3.06 14.19

0.15 2.52 1.54 0.61 0.93 −0.65 1.00 3.36 13.72

0.20 2.65 1.48 0.56 0.92 −0.71 1.00 3.66 13.17

0.30 3.22 1.40 0.43 0.86 −0.76 1.00 4.45 11.96

Case: σν = 0; ρa = 0; ρn = 0.83; corr(εa , εn ) = −0.25; σεa = 8%; and σεn = 1.74%. Note. σx is the standard deviation of the log of variable x, Y is aggregate output, Yi is output in sector i, L is aggregate employment, πi is employment in sector i, and ρ(x, z) is the correlation of variables x and z.

7. Conclusions There are substantial differences in business cycle fluctuations across countries. In this paper, we show that these differences are systematically related to the share of agriculture in the economy. In particular, economies intensive in agriculture feature high fluctuations in aggregate output, low relative volatility of aggregate employment, and low correlation of output and employment. In addition, agriculture has certain distinctive features over the business cycle: output and employment in agriculture are more volatile than and not positively correlated with output and employment in the rest of the economy and output and employment are less correlated in agriculture than non-agriculture. Because of these features, agriculture plays an important role in accounting for aggregate business cycles across countries. We calibrated a two-sector indivisiblelabor business cycle model with agriculture and non-agriculture to aggregate and sectoral data for the United States. We found that an increase in the employment ratio in agriculture from 2 to 30 percent in our model increases fluctuations in aggregate output by almost 40 percent. This is about 2/3 of the difference in aggregate fluctuations between countries such as Turkey and the US. Our results regarding the role of agriculture in aggregate business cycles across countries have two important implications. First, our results suggest caution in comparing business cycles across countries if the countries have different economic structures, in particular with regard to the size of agriculture in the economy. Second, the process of structural transformation of the economy (from agriculture to manufacturing) may provide an explanation for the recent historical decline in business cycle fluctuations in the United States and other developed countries as documented by Backus and Kehoe (1992). Acknowledgments We are grateful to Richard Rogerson for many discussions and suggestions. We also thank the comments of an anonymous referee, Javier Díaz-Giménez, Margarida Duarte, Ig Horstmann, José-Víctor Ríos-Rull, and seminar participants at the University of Toronto, Universidad Carlos III de Madrid, and the 2002 Society for Economic Dynamics Meetings in New York. All

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remaining errors are our own. Da-Rocha acknowledges the financial support from the Ministerio de Ciencia y Tecnología and Xunta de Galicia. Restuccia acknowledges the support from the Connaught Fund and the Institute for Policy Analysis at the University of Toronto and the Social Sciences and Humanities Research Council of Canada. Da-Rocha thanks Universidad Carlos III de Madrid for their hospitality during a visit where part of this research was undertaken. Appendix A. Data: definitions, sample periods, and sources We obtain data for OECD countries from the following sources: National Accounts, Main Aggregates and Detailed Tables, OECD (various issues (b)) and Labor Force Statistics, OECD (various issues (a)). The sample periods for each country are as follows: UK (1966–1997), Canada (1966– 1996), Australia (1966–1997), Japan (1970–1996), Austria (1966–1995), Belgium (1966–1996), Denmark (1966–1995), Finland (1970–1997), France (1969–1997), Greece (1966–1995), Italy (1969–1997), Netherlands (1966–1995), Norway (1972–1996), Portugal (1974–1991), Turkey (1974–1996), Spain (1976–1996), Sweden (1966–1997), US (1966–1996). Variables for which statistics are reported in the tables below and in the paper are as follows: Aggregate real Gross Domestic Product (GDP) denoted as Y ; Real GDP in agriculture (including hunting, forestry and fishing) denoted as Ya ; Real GDP in non-agriculture denoted as Yn ; Aggregate civilian employment denoted as L; civilian employment in agriculture (including hunting, forestry and fishing) denoted as La ; civilian employment in non-agriculture denoted as Ln ; Population within 15 to 64 years old (working-age) denoted as N . In addition, data is reported for the share of output in agriculture as the ratio of GDP in agriculture to aggregate GDP denoted as sa and the employment ratio in agriculture as the ratio of employment in agriculture working-age population denoted as πa . Table A.1 Cross-country business cycle fluctuations Country

Average

Standard deviation σx

sa

πa

Y

Yn

Ya

L

Ln

La

sa

πa

Y /L

Yn /Ln

Ya /La

US Canada Australia Japan Austria Belgium Denmark Finland France Greece Italy Netherlands Norway Portugal Spain Sweden Turkey

0.02 0.03 0.04 0.04 0.03 0.02 0.04 0.07 0.05 0.13 0.04 0.03 0.03 0.07 0.06 0.02 0.19

0.02 0.04 0.04 0.07 0.06 0.02 0.06 0.09 0.05 0.18 0.07 0.03 0.06 0.17 0.07 0.04 0.30

2.12 2.20 2.07 2.19 1.51 1.81 1.85 3.81 1.80 2.27 1.85 2.14 1.94 3.22 2.31 1.93 3.25

2.16 2.27 2.15 2.24 1.58 1.88 2.12 4.01 1.83 2.66 1.95 2.22 2.05 3.45 2.37 1.95 3.72

5.48 4.11 7.33 4.26 3.09 3.84 11.95 5.21 4.27 4.58 2.83 3.31 4.71 6.44 5.77 4.63 2.55

1.34 1.75 1.91 0.78 0.83 1.07 1.90 3.06 0.96 1.05 1.23 1.24 1.94 1.60 3.29 1.63 0.75

1.39 1.83 1.97 0.94 0.82 1.12 2.13 3.29 1.14 0.91 1.32 1.33 1.95 2.30 3.89 1.85 1.54

2.28 2.19 2.47 2.33 2.94 1.32 3.62 3.97 1.42 2.71 2.26 1.38 3.69 2.81 2.70 3.11 2.14

5.81 4.75 7.51 4.20 3.53 4.82 12.83 5.65 4.11 4.81 3.61 4.15 5.38 7.03 5.46 4.46 2.72

2.25 2.44 2.35 2.38 2.87 1.29 3.53 3.98 1.39 2.63 2.31 1.41 3.67 2.69 2.75 3.11 2.28

1.28 1.91 1.46 1.76 1.83 1.22 1.46 2.21 1.21 2.83 1.83 2.21 1.44 3.03 1.25 1.45 3.24

1.28 1.93 1.40 1.67 1.83 1.24 1.56 1.91 1.14 2.64 1.90 2.29 1.43 3.23 1.73 1.36 3.28

5.75 4.57 8.23 5.18 3.66 4.06 12.46 5.31 4.50 5.32 3.13 3.42 6.11 6.63 5.50 5.33 3.75

Average

0.05

0.08

2.31

2.45

4.94

1.57

1.76

2.65

5.35

2.63

1.92

1.94

5.56

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481

For the US additional information is collected on the capital stock across sectors from the US Department of Commerce (2000). We obtain the series for real non-residential fixed private assets for farms in the case of agriculture and non-farm manufacturing for the case of non-

Table A.2 Cross-country business cycle correlations Country

Correlation with aggregate output ρ(x, Y ) Yn

Ya

L

Ln

La

sa

πa

Y /L

Yn /Ln

Ya /La

US Canada Australia Japan Austria Belgium Denmark Finland France Greece Italy Netherlands Norway Portugal Spain Sweden Turkey

1.00 1.00 0.99 1.00 1.00 1.00 0.98 1.00 0.99 0.96 1.00 1.00 1.00 0.99 0.99 1.00 0.99

0.03 −0.05 0.05 0.28 −0.07 −0.38 −0.42 0.25 0.30 0.15 −0.15 −0.12 −0.17 0.06 0.33 0.30 0.58

0.82 0.56 0.73 0.68 −0.14 0.76 0.70 0.82 0.78 −0.36 0.35 0.23 0.72 0.36 0.96 0.69 0.13

0.83 0.57 0.74 0.74 −0.05 0.77 0.75 0.87 0.81 0.22 0.39 0.26 0.74 0.41 0.96 0.74 0.49

−0.14 −0.13 0.30 −0.09 −0.30 −0.36 −0.43 −0.05 −0.44 −0.49 0.03 −0.28 0.31 −0.23 0.04 −0.63 −0.27

−0.33 −0.50 −0.22 −0.24 −0.49 −0.67 −0.53 −0.45 −0.13 −0.33 −0.63 −0.61 −0.51 −0.40 −0.08 −0.12 −0.65

−0.13 0.06 0.21 −0.16 −0.22 −0.24 −0.45 −0.04 −0.34 −0.42 0.08 −0.23 0.32 0.01 0.06 −0.62 −0.24

0.80 0.65 0.46 0.94 0.98 0.82 0.36 0.59 0.87 0.94 0.78 0.84 0.37 0.87 −0.67 0.51 0.97

0.79 0.63 0.48 0.92 0.89 0.81 0.31 0.58 0.79 0.89 0.75 0.82 0.42 0.77 −0.80 0.43 0.89

0.09 0.02 −0.04 0.27 0.18 −0.24 −0.27 0.28 0.42 0.38 −0.16 0.00 −0.32 0.15 0.32 0.63 0.55

Average

0.99

0.06

0.52

0.60

−0.17

−0.41

−0.33

0.66

0.62

0.13

Table A.3 Other cross-country business cycle observations Country

σx /σYn

ρ(x, Yn )

ρ(x, Ya )

Ya

Ln

La

Ya

Ln

La

US Canada Australia Japan Austria Belgium Denmark Finland France Greece Italy Netherlands Norway Portugal Spain Sweden Turkey

2.53 1.83 3.47 1.91 2.01 2.08 6.33 1.34 2.32 1.98 1.50 1.52 2.38 1.96 2.45 2.35 0.76

0.65 0.81 0.93 0.42 0.53 0.61 1.12 0.84 0.62 0.39 0.70 0.61 0.99 0.70 1.65 0.94 0.46

1.06 0.98 1.17 1.04 1.91 0.72 1.92 1.02 0.77 1.17 1.20 0.63 1.86 0.85 1.15 1.58 0.65

−0.01 −0.10 −0.07 0.21 −0.14 −0.41 −0.57 0.15 0.19 −0.12 −0.21 −0.17 −0.24 −0.07 0.21 0.24 0.47

0.83 0.57 0.77 0.74 −0.06 0.77 0.73 0.88 0.80 0.19 0.38 0.25 0.75 0.43 0.96 0.75 0.47

0.09 0.05 −0.22 −0.17 0.26 0.00 0.01 0.36 0.00 0.00 0.26 0.13 −0.05 −0.50 0.33 0.10 −0.28

Average

2.23

0.75

1.16

−0.03

0.60

0.06

482

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