Business Cycle during Structural Change: Arthur Lewis' Theory from a Neoclassical Perspective

Layer 1: Overview

This paper asks why the nature of business cycles changes systematically as economies develop and shed their large agricultural sectors. The motivation is both empirical and theoretical. Empirically, countries with large declining agricultural sectors—most prominently China—exhibit business cycle patterns that depart sharply from the textbook procyclical-employment pattern seen in mature economies: aggregate employment is acyclical with respect to GDP, nonagricultural employment is strongly procyclical, agricultural employment is countercyclical, and the labor productivity gap between nonagriculture and agriculture narrows during booms. These cross-country regularities hold in a sample of 63–66 countries using ILO sectoral employment data over 1970–2015, with the correlation between aggregate employment and GDP declining monotonically as the agricultural employment share rises. The cross-country correlation between the agricultural employment share and log GDP per capita is −0.84. For China specifically over 1978–2012, the correlation between HP-filtered agricultural employment and GDP is −0.69, while the correlation for nonagricultural employment with GDP is 0.73. Agricultural employment fell from about 62.4% of total Chinese employment in 1985 to 33.6% in 2012.

The authors construct a unified neoclassical model of growth, structural change, and business cycles. The economy produces a CES aggregate of agricultural and nonagricultural output (elasticity of substitution epsilon), with agriculture itself being a CES aggregate of modern and traditional sub-sectors (elasticity omega). Modern agriculture uses capital and labor (Cobb-Douglas), whereas traditional agriculture uses only labor. This nested structure means the effective elasticity of substitution between capital and labor in agriculture is variable and declines as the traditional sector shrinks—formalizing the Lewisian surplus-labor mechanism within a neoclassical framework. A time-invariant tax wedge tau on nonagricultural wages captures rural-urban earnings gaps and keeps agriculture inefficiently large.

The deterministic model is estimated using Simulated Method of Moments on Chinese data from 1985 to 2012, targeting seven moment sequences: employment share in agriculture, capital share in agriculture, agricultural output-to-GDP ratio, agricultural expenditure share, aggregate GDP growth, the aggregate capital-output ratio path, and the change in the productivity gap. Key findings from estimation: the elasticity of substitution between agricultural and nonagricultural goods epsilon is estimated at 3.6 (significantly greater than 1 at 1% level), and the elasticity between modern and traditional agriculture omega is also very large. The estimated subsistence level in a Stone-Geary extension is small (11% of agricultural production in 1985), so nonhomothetic preferences play only a minor quantitative role. Nonagricultural TFP growth gM is estimated at 6.5% per year; modern-agricultural TFP growth gAM at 6.1% per year; traditional-sector TFP growth gS at 0.9% per year. The estimated labor wedge tau implies persistent misallocation.

Stochastic TFP shocks (VAR(1) for each of the three sectors) are then estimated from observed data by exploiting the model’s equilibrium conditions. The persistence parameters are 0.63 (nonagriculture), 0.90 (modern agriculture), and 0.42 (traditional agriculture). The model, simulated 1,000 times starting in 1980, reproduces the salient Chinese business cycle features: the standard deviation of GDP is 1.7% (matching the data), agricultural employment is countercyclical (model correlation with GDP: −0.25; data: −0.23), nonagricultural employment is strongly procyclical (model: 0.99; data: 0.73), and aggregate employment has a low correlation with GDP (model: 0.42; data: 0.10). A variance decomposition shows nonagricultural TFP shocks account for approximately 95% of GDP fluctuations.

The key mechanism is that a large traditional sector provides an elastic labor supply to nonagriculture at low marginal cost (a neoclassical Lewisian buffer). Positive TFP shocks to nonagriculture draw labor out of traditional agriculture, raising average capital intensity and labor productivity in agriculture—hence the countercyclical productivity gap. As structural change progresses and the traditional sector shrinks, this labor buffer disappears, the effective labor supply elasticity declines, and business cycle properties converge toward those of a standard neoclassical (Hansen-Prescott) economy. Out-of-sample simulations confirm this convergence: the correlation between total employment and GDP rises from around 40% to near 100% as the agricultural employment share falls below 10%. The paper also shows that positive TFP shocks in agriculture slow structural change, consistent with empirical evidence from the Green Revolution (Foster and Rosenzweig 2004; Bustos et al. 2016; Moscona 2018; Jayachandran 2006).

Elasticity estimates using CES production functions for the US, Japan, and China from consumption value-added data yield epsilon of 2.49, 1.58, and 1.70 respectively, all significantly above unity at the 1% level—supporting the labor-pull interpretation of structural change. The authors find that imposing the symmetry restriction (epsilon = epsilon_ms) used by Herrendorf et al. (2013) replicates their near-zero estimate for the US, but relaxing that restriction reveals the agriculture-nonagriculture elasticity to be large while the manufacturing-services elasticity is near zero.

Layer 2: Deep Dive

What are the four key business cycle stylized facts documented for countries with large agricultural sectors?

The paper documents four regularities that hold across 63–66 countries (ILO data, 1970–2015): (1) aggregate employment is less correlated with GDP and less volatile; (2) agricultural employment is countercyclical; (3) the labor productivity gap (nonagriculture/agriculture) is negatively correlated with nonagricultural employment; (4) consumption is highly volatile relative to GDP. All four are quantitatively documented for China and compared with the US.

What is the core theoretical mechanism distinguishing this paper from earlier structural-change models?

The paper adds an internal split of the agricultural sector into modern (capital-using Cobb-Douglas) and traditional (labor-only) sub-sectors that are imperfect substitutes. This nested structure generates a variable effective elasticity of labor supply to nonagriculture: when the traditional sector is large, labor can be released to industry at near-constant marginal cost (a continuous Lewisian surplus), dampening wage and price fluctuations and decoupling aggregate employment from GDP. As the traditional sector shrinks through capital accumulation and differential TFP growth, the effective labor-supply elasticity falls, progressively transforming the economy into a standard neoclassical one.

How does the paper handle the lack of a steady state for the business cycle analysis?

Because structural change is ongoing in China, approximating the model around a balanced growth path is infeasible. The authors instead solve the model recursively over 250 periods back from an assumed one-sector asymptotic balanced growth path (ABGP), using a 27-state Tauchen Markov chain for the three TFP shocks and piecewise linear decision rules on a 75-point grid for each of the two continuous state variables (kappa and kappa-tilde). They simulate 1,000 economies and compute rolling 28-year window statistics, which are then compared to the data.

What is the identification strategy for the elasticity of substitution epsilon, and what are the main threats?

The primary strategy is Simulated Method of Moments on 143 moment conditions from Chinese data 1985–2012 (28 annual observations each for five moment series plus two level/change moments). A second strategy uses IFGNLS estimation of a Stone-Geary demand system for three countries (US, Japan, China) using both consumption value-added (Herrendorf et al. method) and production value-added (GGDC data). The main threats acknowledged: (a) endogeneity—both sides of the demand equations are driven by unobserved productivity and preference shocks with opposite sign implications (addressed by turning to exogenous Green Revolution shocks); (b) measurement error; (c) the symmetry restriction in prior work; (d) the model is closed-economy and abstracts from demand shocks.

What role do agricultural TFP shocks versus nonagricultural TFP shocks play in GDP fluctuations?

A variance decomposition shows nonagricultural TFP shocks (ZM) account for approximately 95% of GDP fluctuations in the benchmark economy over 1985–2012. The logic is that positive TFP shocks to ZM reduce misallocation by drawing labor from the (inefficiently large) agricultural sector to nonagriculture, amplifying the GDP response. In contrast, positive TFP shocks to agriculture partially offset the direct productivity gain by worsening misallocation (labor stays in agriculture), so GDP barely responds. In the low-elasticity (epsilon = 0.5) alternative model, agricultural TFP shocks account for about half of GDP fluctuations—one reason the authors reject this alternative.

How does the model’s prediction for business cycle evolution as structural change progresses compare to cross-country evidence?

Using rolling 28-year windows of simulated data from 1985 to 2185, the paper documents four monotone transitions as the agricultural employment share falls: (a) the correlation between agricultural employment and the productivity gap falls toward zero; (b) the correlation between agricultural and nonagricultural employment rises from large and negative (around −0.75 for China’s current employment share of 40–50%) toward zero; (c) the correlation between total employment and GDP rises from about 40% to nearly 100%; (d) the volatility of employment relative to GDP rises toward the level of mature economies. All four patterns match the cross-country empirical patterns documented in Figure 5.

What does the labor-push versus labor-pull debate imply for the estimated elasticity, and how is it resolved?

With epsilon > 1 (gross substitutes), nonagricultural TFP growth attracts labor from agriculture (labor pull), whereas agricultural TFP growth keeps workers on farms and slows structural change. With epsilon < 1 (complements), agricultural TFP growth would instead push workers into industry. The structural estimate epsilon = 3.6 > 1 strongly favors the labor-pull interpretation. This is confirmed by the Green Revolution evidence: Foster and Rosenzweig (2004), Moscona (2018), Bustos et al. (2016), and Jayachandran (2006) all find that positive agricultural TFP shocks slow industrialization and expand agricultural employment—consistent with epsilon > 1 and inconsistent with epsilon < 1.

What robustness checks are run on the business cycle model?

Four robustness exercises: (1) Low elasticity epsilon = 0.5 with a large food subsistence level—this version fails to generate the observed countercyclicality of the productivity gap and implies an empirically incorrect response to agricultural TFP shocks. (2) Sectoral capital adjustment costs (quadratic, kappa = 2.5)—improves the cyclical behavior of aggregate employment and consumption but makes investment too smooth. (3) Raising the persistence of traditional-sector TFP shocks to match that of modern agriculture (phi_S = phi_AM = 0.90)—reduces aggregate labor volatility and makes the relative volatility of employment monotonically increasing with development. (4) Orthogonal shocks (zero cross-sector correlation)—results are negligibly different from the benchmark. These exercises indicate that the qualitative conclusions are robust across specifications.

How is the productivity gap between nonagriculture and agriculture generated by the model, and does it match the data?

In the model, the productivity gap (nonagricultural output per worker divided by agricultural output per worker) declines with development because the traditional, labor-intensive sector shrinks, raising average labor productivity in agriculture. This is both a long-run trend prediction and a business-cycle prediction: positive TFP shocks to nonagriculture draw workers from the traditional sector, raising agricultural capital intensity and productivity, thereby reducing the gap. The model successfully captures the falling trend in the productivity gap for China. The correlation between the HP-filtered productivity gap and nonagricultural employment in the model is −0.74, close to the empirical value of −0.54 for China. The model predicts lower volatility of the productivity gap than observed in the data.

What is the estimated role of nonhomothetic preferences?

The authors extend the baseline homothetic CES model to allow Stone-Geary preferences (agricultural good as a necessity). The estimated subsistence level c-bar corresponds to only 11% of agricultural production in 1985, making the income effect through nonhomotheticity quantitatively small. The estimated epsilon falls only marginally when Stone-Geary preferences are introduced. The remaining structural parameters are virtually unchanged. The authors interpret this as evidence that, at the macroeconomic level, technological factors (TFP growth differences and capital accumulation) rather than nonhomothetic preferences are the primary drivers of structural change in China—a finding consistent with Alvarez-Cuadrado and Poschke (2011).

How does this paper relate to Acemoglu and Guerrieri (2008) and Herrendorf et al. (2013)?

The model builds on Acemoglu and Guerrieri (2008) in having capital deepening and differential TFP growth drive reallocation from agriculture to nonagriculture, but adds the traditional sector (absent in Acemoglu-Guerrieri), which generates the Lewisian surplus-labor mechanism and the declining productivity gap. With respect to Herrendorf et al. (2013): their three-sector CES model imposes a common elasticity across agriculture, manufacturing, and services, yielding a near-Leontief (epsilon near zero) estimate for the US. The authors show this estimate is an artifact of the symmetry restriction: when that restriction is relaxed, the agriculture-nonagriculture elasticity is large (2.32–2.49 for the US) while the manufacturing-services elasticity is near zero. The asymmetric three-sector estimates for the US (2.49), Japan (1.58), and China (1.70) are all above unity at the 1% significance level.

What are the main limitations and open questions?

The paper explicitly identifies several limitations: (1) the business cycle analysis is restricted to productivity (TFP) shocks only and does not include demand shocks; (2) the model is closed-economy and ignores trade; (3) the distinction between traditional and modern agriculture is not directly observed in the data—the traditional sector’s TFP process is estimated indirectly, introducing potential measurement error that may exaggerate the volatility and understate the persistence of traditional-sector shocks; (4) the prediction that agricultural value added is positively correlated with nonagricultural labor (and negatively with agricultural labor) is inconsistent with Chinese data, a failure the paper acknowledges. Future work is flagged on demand shocks and open-economy extensions.

What cross-country empirical evidence beyond China is presented?

Using ILO sectoral employment data for 63–66 countries over 1970–2015 (requiring at least 15 consecutive years of observations), the authors document: the correlation between agricultural and nonagricultural HP-filtered employment shifts from positive for countries with small agricultural sectors to strongly negative for countries with large sectors; the correlation between total employment and GDP declines monotonically with the agricultural employment share; the productivity gap is negatively correlated with nonagricultural employment in countries with large agricultural sectors (correlation of −0.54 for China) but near zero in mature economies; consumption volatility relative to GDP declines with development. The US historical time series (1929–2015) shows that before 1960 NBER recessions were associated with reversals in structural change—mirroring today’s China—while this pattern ceased after 1960.

Key Concepts

Traditional agriculture (subsistence sector): A sub-sector of the agricultural sector that uses only labor (no capital) and produces an imperfect substitute for modern agricultural output. Its presence generates a reserve pool of labor that can move to nonagriculture at low marginal cost, creating the Lewisian surplus-labor property within a neoclassical framework. As the economy develops, this sector is crowded out by capital-intensive modern agriculture.

Modern agriculture: A Cobb-Douglas sub-sector within agriculture that uses both capital and labor. Its expansion—crowding out the traditional sector—constitutes the modernization of agriculture. As workers leave the traditional sector, average capital intensity and labor productivity in agriculture rise, generating the procyclical productivity-gap pattern observed in developing economies.

Asymptotic Balanced Growth Path (ABGP): The long-run equilibrium toward which the model economy converges, characterized by a fully modernized (traditional sector vanished), small agricultural sector, constant growth rates of sectoral capitals, and standard neoclassical business cycle properties. The paper establishes conditions under which the ABGP is asymptotically stable.

Labor wedge (tau): An exogenous, time-invariant tax on nonagricultural wages that prevents equalization of marginal products of labor across sectors, standing in for a variety of frictions (migration barriers, rural overpopulation, institutional barriers) that keep agriculture inefficiently large. Its presence means that positive TFP shocks to nonagriculture both raise productivity directly and reduce misallocation by drawing workers out of the oversized agricultural sector.

Elasticity of substitution between agriculture and nonagriculture (epsilon): The elasticity governing substitution between agricultural and nonagricultural goods in aggregate CES production. When epsilon > 1 (gross substitutes, as estimated: epsilon = 3.6 for China), positive TFP shocks to nonagriculture pull labor from agriculture (labor-pull structural change), while positive shocks to agriculture slow structural change—consistent with Green Revolution evidence. When epsilon < 1 (complements), the opposite holds, implying counterfactual predictions.

Productivity gap: The ratio of average labor productivity in nonagriculture to average labor productivity in agriculture. In the model and the data this gap declines over the course of development (because agriculture modernizes and raises its average productivity) and also narrows during booms in countries undergoing structural change (because booms draw workers from low-productivity traditional agriculture). The model relates the gap formally to the ratio of labor income shares: APLM/APLG = (1−tau) × (LISM/LISA)^(−1).

Sullying effect of recessions on agriculture: The paper’s terminology for the pattern—documented empirically for China by Zhang et al. (2001)—whereby recessions induce workers to return to or remain in the agricultural sector, reversing structural change and lowering average agricultural productivity. This is the cyclical analog of the Lewisian adjustment: in downturns, the labor buffer of traditional agriculture absorbs displaced workers, cushioning aggregate employment but impairing agricultural productivity.