Allocative inefficiency and sectoral allocation of labor: Evidence from U.S. agriculture

Highlights

• A multi-sector, multi-region model with land as a region-specific factor is considered.

• The model is calibrated using state-level data from the United States.

• Factor specificity accounts for the large differences in farm TFP across U.S. states.

• Large TFP differences across producers do not necessarily imply large inefficiencies.

Abstract

Are productivity differences across producers in an industry a good indicator of allocative inefficiency? If so, what are the welfare consequences of reallocating labor from lesser to more productive producers? This paper addresses these questions in the context of factor specificity, which generates endogenous distribution of total factor productivity across producers, and reallocation of labor across sectors, as well as within a sector. The paper builds a multi-sector, multi-region general equilibrium model with land as a region-specific factor, and calibrates it using state-level U.S. data from 1960 to 2004, a period with considerable reallocation of labor out of agriculture. The results show that large and persistent differences in agricultural productivity across U.S. states are consistent with factor specificity due to geoclimatic conditions and do not correspond to economically significant allocative inefficiencies.

Introduction

Are total factor productivity (TFP) differences across producers in an industry a good indicator of allocative inefficiency? If so, what are the welfare consequences of reallocating labor from lesser to more productive producers? In recent years, there has been a renewed interest among economists on allocative efficiency, and especially toward understanding the implications of inefficient allocation of resources across plants for aggregate productivity.¹ This literature typically starts from the well-documented observation that there are large TFP differences across plants in the manufacturing industry. Using these TFP differences as an indicator of allocative inefficiency, this literature measures the consequences of reallocation of resources for productivity within the corresponding manufacturing industry.

However, there are two issues that this literature has not so far satisfactorily addressed. First, reallocation of resources from lesser to more productive producers within a given industry is not the only alternative available to the economy. In an economy consisting of several distinct sectors, reallocation can also take place between sectors.² Accounting for such sectoral factor flows is important because, as resources relocate, there would be endogenous changes in prices and demand, and it would be necessary to account for these general equilibrium effects before one can be definitive about the destination of those resources released by less efficient plants. Existing literature has so far sidestepped this possibility and simply viewed allocative efficiency within the narrow confines of manufacturing industries alone and in a partial equilibrium setting.

Of course, one could argue that at least some of the resources used in manufacturing industries are sector-specific and may not have alternative uses outside that industry. While this argument is probably correct for specialized machinery and equipment, it is less persuasive for labor. Moreover, reallocation of labor across sectors may have non-negligible general equilibrium effects. Thus, given the possibilities that exist outside manufacturing, the focus on allocative inefficiency within manufacturing industries appears unduly restrictive.

The second issue that arises in the allocative efficiency literature is the source of total factor productivity differences across plants. There is widespread agreement that plants are not homogenous in terms of their productivity levels due to a variety of reasons, including plant-specific factor endowments (Bartelsman and Doms, 2000). Ignoring these plant-specific factors may distort the true magnitude of productivity differences across plants and the economic significance of allocative inefficiency. In fact, one may be even tempted to rationalize all productivity differences across plants by appealing to plant-level factor specificity.

Of course, others would argue that if there is indeed such an extensive factor specificity, then we should be able to observe its consequences in factor prices. So, to make a convincing case about the impact of factor specificity on productivity, one should observe physical quantities of factors of production and output, as well as prices of these specific factors. Since most studies on allocative efficiency do not have factor price data, they inevitably treat their factor inputs as homogenous across plants, with largely unexplored implications of factor specificity for resource allocation and efficiency.

It appears then that, to understand the welfare implications of allocative inefficiency, it might be important to allow for sectoral reallocation of labor in the presence of producer-level factor specificity. In this paper, I conduct a quantitative analysis of allocative inefficiency by adopting a framework with two core ingredients. First, I consider a multi-sector framework in which labor can be reallocated across sectors. This general equilibrium approach allows me to take into account labor reallocation across sectors in response to allocative inefficiency. Second, I consider a multi-region framework which allows for productivity differences in agriculture across regions due to factor-specificity. Agriculture is a natural context to think about specific factors: land is an immobile factor, and the quality of agricultural land and the corresponding climate (geoclimatic conditions) vary substantially even across short distances.³

Starting from such a framework, I develop a general equilibrium model with land as a region-specific factor, and calibrate it using state-level U.S. data. The model captures factor specificity through differences in land-specific (or land-augmenting) productivity across farm regions. These differences in land productivity across regions in turn manifest themselves as differences in farmland rents and in TFP. The data necessary to calibrate this model are total factor productivity estimates and factor prices for farm regions. For productivity, I use agricultural TFP estimates of Ball et al. (2010) on 48 contiguous U.S. states from 1960 to 2004. For factor prices, I construct a novel database on farmland rents and farm wages by state covering the same period. In the data, there are substantial differences in farmland rents across regions, and there is substantial reallocation of labor out of U.S. agriculture.

Even after factoring in land-specificity into TFP differentials, the calibrated model points to significant deviations from allocative efficiency in U.S. agriculture, and that some states employ “too much” agricultural labor, while others employ “too little” labor. Although both of these cases correspond to inefficient allocation of labor, the results indicate that in terms of quantities, the net benefit of moving to an efficient allocation of labor in agriculture would have amounted to less than 1% of total agricultural output per year.⁴ Even after one allows for alternative uses of labor outside agriculture, the welfare costs of inefficient allocation of labor remain low: over the sample period, the welfare costs amount to less than 0.25% permanent reduction in non-farm consumption. These findings suggest that seemingly large within-sector productivity differences across producers may not necessarily have large aggregate welfare implications, and the U.S. structural transformation of the last 50 years was essentially driven by factors other than responses to inefficient allocation of resources.

Within the recent literature on the economic consequences of productivity differences across plants, the paper by Basu et al. (2010) is the closest to the approach taken here. They also study the welfare implications of resource reallocation using equilibrium modeling. However, their data are from the manufacturing industry, and they do not consider factor specificity. This paper is also related to the literature on the conventional accounts of structural change in the United States that has exclusively focused on between-sector labor reallocation. These accounts emphasize labor reallocation from inefficient to efficient sectors, and sectoral differences in productivity growth and income elasticity of demand. For instance, in a highly influential account of U.S. agriculture, Schultz (1945) defines the “farm problem” as an inefficient allocation of labor between agriculture and the rest of the economy.⁵ To allow for these effects, this paper studies the allocation of labor both within-agriculture and across sectors.

The rest of the paper is organized as follows. Section 2 documents the distribution of agricultural TFP across U.S. states from 1960 to 2004. Section 3 presents a multi-sector general equilibrium model which frames the question of allocative inefficiency relative to a benchmark. Section 4 quantifies the degree of allocative inefficiency both across farm regions and across sectors. Section 5 discusses the interaction between allocative inefficiency and policy distortions toward agriculture. Section 6 concludes. Discussion of data sources and several technical issues are contained in three separate appendices. The online supplementary material contains detailed information on dataset construction and derivations.