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3.1 Resource Misallocation: Theoretical Underpinnings
40 b oostin G Pro D u C tivity in s ub- sA h A r A n Afri CA
Resource misallocation refers to distortions in the allocation of inputs (capital, land, and labor, among others) across production units of different sizes. This misallocation typically occurs when the different production establishments are taxed at different rates. This strand of the literature assumes that aggregate output is produced by several producers (N) with different levels of productivity (Ai). Firm i’s technology is summarized by a production function (f) that is strictly increasing and strictly concave. There is a fixed cost of operation (c) for any producer. Given an aggregate demand of labor (H) and capital (K), there is a unique allocation of labor and capital across producers that maximizes total output net of fixed operating costs.
According to this framework, lower values of Ai reflect either slow adoption or inefficient use of technology. The efficient allocation in this economy maximizes final output and is characterized by two decisions: (a) the number of operating establishments (that is, establishments that can pay the fixed cost, c); and (b) the allocation of capital (K) and labor (H) across the operating establishments. If either of these decisions is distorted, the economy will have lower output and hence lower aggregate total factor productivity (TFP)—because the aggregate factor inputs (K and H) in the industry are constant.
The allocation of inputs that maximizes output across production units (say, either firms or farms) takes place when, conditional upon their operation, the marginal (and average) products are equal across all production units. In this equilibrium, no output gains would be acquired by reallocating inputs of production (say, capital, land, and labor) from production units with low marginal products to those with high marginal products. In the efficient allocation, the most productive operating establishments will demand a greater amount of inputs. In other words, a production unit’s productivity and size are positively associated in the efficient allocation. In addition, production units with similar levels of productivity command the same amount of inputs and are of identical size.
Deviations from the efficient allocation of resources across firms may have implications on aggregate output and productivity. Input choices that are different from the efficiency model, even if they allocate more factors to the more-productive production units, will generate lower aggregate output. Given the constant aggregate amount of inputs (say, capital, land, and labor), the output loss associated with an inefficient allocation is also an aggregate TFP loss. In this context, misallocation refers to situations were resources are not allocated efficiently across production units, and the cost of misallocation is typically measured in terms of aggregate output or TFP losses.
Theoretically, inefficiencies in the allocation of labor and capital across heterogeneous producers will affect aggregate output and productivity through three different channels: • The technology channel—the higher the productivity for all firms, the greater the output • The selection channel—based on the choice of operating producers • The misallocation channel—based on the allocation of capital and labor among operating producers.
These three channels are not independent: any policy or institution that distorts the allocation of resources across producers will potentially generate additional effects through both the selection and technology channels.
If the misallocation of resources across these different producers helps explain cross-country differences in aggregate productivity levels, it is then crucial to investigate the sources of misallocation. Resource misallocation across different production units might reflect the following (Restuccia and Rogerson 2017): • Statutory provisions, including some features of the tax code and regulations—for instance, provisions of the tax code that vary with firm characteristics (say, age or size); tariffs targeting certain groups of goods; employment protection measures; and land regulations, among others • Discretionary government (or bank) provisions that favor or penalize specific firms—for instance, subsidies, tax breaks, or low-interest loans granted to specific firms; preferential market access; and unfair bidding practices for government contracts, among others • Market imperfections—for instance, monopoly power; market frictions (such as in credit and land markets); and enforcement of property rights.
Resou R ce Misallocation in s ub- s aha R an a f R ica: f i RM - l evel e vidence 41
The resource misallocation literature examines (a) the extent of factor misallocation in the economy, (b) its impact on TFP differences across countries and over time, and (c) the underlying factors driving misallocation. Two main approaches have been followed to tackle these questions—the direct approach and the indirect approach (Restuccia and Rogerson 2013, 2017).a
The direct approach seeks to ascertain the underlying sources of misallocation and evaluates their consequences through a structural model. Assessing the degree of misallocation requires computation of a counterfactual. However, the direct approach also requires quantitative measures of the source of misallocation. If the main drivers of misallocation come from discretionary rather than statutory provisions, there will be severe measurement problems. Furthermore, the complexity of measuring drivers such as regulation (especially its differences across industries) may make it complicated to build, calibrate, and simulate a structural model.
The indirect approach quantifies the extent of resource misallocation and does not dig deeply into the underlying factors that generate the distortions driving the inefficient allocation of resources. It measures the total net effect of these distortions without fully identifying their main sources. The efficient allocation of resources equalizes their marginal products across all operating production units. A direct examination of the dispersion of marginal products provides a measure of the degree of misallocation. This approach does not require a full structural model; however, it needs the specification of the technology of production. Still, the indirect approach faces an important challenge: efficient allocations may not require that marginal products be equalized across production units at every point in time—especially if input choices precede the realization of the individual productivity shock or are in the presence of adjustment costs.
In sum, resource misallocation is closely related to a specific model economy and to a benchmark allocation relative to that economy. In this model economy, inputs are homogeneous, and the only source of heterogeneity among productive units is the productivity of their operating establishments. The output-maximizing allocation of factors in the model economy is the commonly used benchmark.
It is not optimal to allocate the entire endowment of inputs to any individual production unit—even if it is the most productive one—because the increase in output for a given increase in inputs declines as the size of the establishment increases. Resource misallocation can arise both across production units with different levels of productivity and across units with similar productivity. An important interpretation of misallocation is that production units effectively face different prices or wedges to their inputs or output. That is, production units face idiosyncratic distortions (Restuccia and Rogerson 2008). These wedges or distortions support the observed allocation, which differs from the efficient allocation, as an equilibrium outcome.
Sources: Restuccia 2011; Restuccia and Rogerson 2008, 2013, 2017. a. The direct and indirect approaches have been commonly applied to census data on manufacturing firms. See Restuccia and Rogerson (2008), Hsieh and Klenow (2009), and the empirical literature that arose from those seminal papers.
of resources across farmers rather than agronomic endowments. The most productive farms cannot command more factors of production, and their growth is impeded. Resource misallocation also has dynamic implications for agricultural productivity by disincentivizing the adoption of new technologies and reducing the farmers’ ability to learn new techniques.
In manufacturing, the large dispersion of revenue productivity (TFPR) is an indication of severe misallocation across manufacturing firms in select Sub-Saharan African countries.2 This dispersion is greater than in other low- to middle-income countries (China and India) as well as that of the global efficiency benchmark (the United States). Furthermore, the positive correlation between TFPR and quantity (or physical) productivity (TFPQ)3 across Sub-Saharan African manufacturing firms indicates that the region’s more-productive firms tend to
