Ebook Specialization, Economic Development and Aggregate Productivity Differences
Cross-country labor productivity differences are large in agriculture and much smaller in non-agriculture relative to aggregate differences (Caselli, 2005; Restuccia, Yang and Zhu, 2008). Development accounting exercises have shown that these sector productivity differences are key in accounting for aggregate productivity differences. If agricultural labor productivity were hypothetically raised to the U.S. level in every country, or if the share of labor in agriculture were hypothetically lowered to the U.S. level, then international variation in aggregate productivity would be virtually eliminated (Caselli, 2005). These results suggest that understanding productivity differences in agriculture and non-agriculture are at the heart of understanding world income inequality.
In this paper we provide a theory of why labor productivity differences are larger in agriculture and smaller in non-agriculture than in the aggregate. We argue that these sector productivity differences arise when sector-neutral efficiency differences combine with subsistence food consumption needs to generate variation in the extent to which workers specialize in the sector where they are most productive.
The basic idea is that countries with low efficiency must deploy a large fraction of their work-force into the agriculture sector to satisfy subsistence food needs. As a result many of those working in agriculture are those whose comparative advantage is not in agricultural work, but rather in non-agricultural tasks such as writing newspaper articles, doing economic research, or teaching yoga classes. In countries with high efficiency, in contrast, a smaller fraction of workers are in agriculture, and those remaining in agriculture are those who are relatively most productive at farm work. As a result, physical productivity differences are larger in agriculture than in the aggregate. In non-agriculture the mechanism leads to exactly the opposite result, namely that productivity differences are smaller than in the aggregate.
We formalize our theory by embedding the Roy (1951) model of selection into a simple two sector general-equilibrium growth model. Our theory has two main ingredients. First, workers are heterogenous in their ability to produce output in the two sectors and choose where to work. Second, preferences have a subsistence food requirement. Countries differ only in a sector-neutral efficiency term; preferences and the distribution of ability are identical across countries. Qualitatively, the model can generate productivity differences in agriculture that are larger than aggregate differences, and non-agriculture productivity differences that are smaller than in the aggregate. The novel feature of this result is it follows from optimal behavior only, as opposed to exogenous country-specific sectoral productivity differences, or barriers to agricultural production, as emphasized by other studies (e.g. Restuccia, Yang, Zhu, 2008).
Our main question of interest is whether the theory can quantitatively generate productivity differences that are substantially larger in agriculture than non-agriculture, as in the data. To answer this question we calibrate the model using parametric assumptions on the distribution of worker ability and observations on the distribution of wages in agriculture and non agriculture in recent U.S. data. We show that the dispersion in ability for each sector is pinned down by the variances of wages for workers within the two sectors, while the correlation of the ability draws is disciplined by the ratio of average sector wages.
Our main exercise is to vary sector-neutral efficiency in the model so as to generate aggregate productivity differences equal to those found in the 90th and 10th percentile of the country income distribution, namely a factor of 22. We then compute the model’s predictions for agriculture and non-agriculture productivity across countries and compare them to the data. If the model had no predictive power, it would predict that these sector productivity differences equalled those in the aggregate. We find that, to the contrary, the model generates a factor of 39 difference in agriculture productivity and a factor 9 difference in non-agriculture. In the data the corresponding sector productivity gaps are a factor of 45 in agriculture and 4 in non agriculture. Thus, our model explains roughly three quarters of the difference between agriculture productivity gaps and aggregate gaps, and only slightly less of the difference between non-agriculture productivity gaps and those in the aggregate. We conclude that efficiency differences that affect each sector in the same way may nonetheless lead to agriculture differences that are much larger than those outside of agriculture.
We also show that the model performs quantitatively well in matching relevant development facts for the cross-section of counties. Specifically, the model is largely consistent the relationship between income per capita and the share of labor and GDP in agriculture, and performs moderately well in matching the relationship between income per capita and relative agricultural prices. We show that relative agricultural prices are higher in poor countries, with countries around the 10th percentile of the income distribution having prices around 2.5 times higher than countries in the 90th percentile. The model predicts this ratio should be around 4. We also compare our model’s predictions to the same set of statistics for the U.S. time series, and show that the model’s predictions are in line with the data. Finally, we show that the model’s wage distribution closely resembles the current distribution of wages in United States.
To test the robustness of the model’s predictive power, we ask what happens under a more conservative calibration of the model’s most important two parameters, namely the variances of the two ability distributions. While this ability variance is disciplined in the benchmark model by cross-sectional wage variance in the United States, some economists have argued that some fraction of wage dispersion is unrelated to ability differences. Postel-Vinay and Robin (2002), for example, argue that around half of wage variation is due instead to labor market imperfections. To address this concern we recalibrate the model to have half the ability variance as the baseline calibration. In this more conservative calibration we still find that our model explains around 50 percent of the productivity differences in agriculture and non-agriculture, relative to aggregate differences, between the 90th and 10th percentile of countries.
We conclude by providing direct evidence that our mechanism was at work in the development experiences of the United States and Britain. Two dimensions in which sector abilities are observable are sex and age: historians and development economists have argued that women and children have a comparative disadvantage in agricultural work relative to adult men. Our theory thus predicts that, during a structural transformation, women and children leave farm work and enter the industrial sector at a faster rate than men. We cite evidence that this is in fact what happened in Britain and the United States in the 18th and 19th centuries.
Our theory has new implications for the way economists think about aggregate productivity in the developing world. Concretely, our model suggests that low aggregate productivity is not caused by large fractions of workers working in the relatively unproductive agriculture sector. Instead, low measured productivity in agriculture and large agricultural labor shares are consequences of low sector-neutral productivity. The distinction is important because it helps determine the extent to which future research efforts on aggregate productivity differences should focus on the determinants of productivity in agriculture per se, as opposed to more general potential determinants. The policy implications between the two views are different as well. While accounting exercises suggest that fixing agriculture is crucial to raising overall productivity, our theory predicts that improvements in technology, institutions, or social infrastructure (Hall and Jones, 1999; Acemoglu, Robinson and Johnson, 2002) are the key to improving living standards.
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