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Aggregate productivity growth and the allocation of resources over the business cycle
Introduction
Recessions are often viewed as time where the economy is “cleansed”: the least productive firms are forced to exit the market, allowing resources to be reallocated towards more productive uses. This Schumpeterian view of recessions, which has been emphasized by Caballero and Hammour (1994), suggests that the efficiency in the allocation of resources improves during recessions. While the theoretical literature has focused on the contribution of entry and exit, the dynamics of aggregate productivity could also be driven by changes in the efficiency of resource allocation across existing firms. Is allocative efficiency an important determinant of aggregate productivity changes over the business cycle? To answer this question, I propose a novel approach to separate out the variations in aggregate productivity which are due to within-firm productivity changes from those due to changes in the allocation of resources between incumbents, entering and exiting firms. To this end, I derive the link between micro and aggregate productivity dynamics in a framework where firms are heterogeneous and where market frictions distort the allocation of resources across firms. This approach extends the Solow (1957) growth accounting exercise to a framework with firm heterogeneity and allocative inefficiency.
The importance of resource reallocation for aggregate productivity growth has been docu-mented in many empirical papers (Baily et al., 2001; Foster et al., 2001; Griliches and Regev, 1995; Bartelsman et al., 2009). However, all these papers focus on long run productivity changes and therefore provide little evidence on the contribution of resource reallocation at business cycle frequency. Furthermore, their decomposition relies on an aggregate produc-tivity index computed as the weighted average of firm-level total factor productivity (TFP). The contribution of input reallocations is then measured by the correlation between changes in input shares and firm-level productivity.1 In this paper, I argue that this correlation is not a well-defined measure of allocative efficiency. Once decreasing marginal productivity of inputs is accounted for, shifting resources towards high TFP firms may reduce allocative efficiency and lower aggregate production. In the general case, aggregate productivity is not equal to average productivity and must be derived from an aggregate production function. When derived from the aggregation of firm-level production functions, the contribution of input reallocation is exactly equal to the change in the efficiency of resource allocation and depends on the dispersion in the marginal products of capital and labor, not on the corre-lation between input shares and firm-level TFP. In fact, resources are efficiently allocated when the value of marginal productivities are equalized across firms. The level of allocative inefficiency in then measured with respect to this first-best benchmark as the dispersion in labor and capital marginal productivities. In this paper, I propose a measure of changes in allocative efficiency based on this criterion. Contrary to the existing decompositions, the real-location component captures only the shifts in input shares that lead to a change in the level 1The decompositions found in this literature slightly differ from one another by the weights used (previous or/and current period, labor or market shares) and whether or not firm-level productivity is normalized (relative to the aggregate productivity index) of allocative inefficiency.
The decomposition of aggregate productivity growth is derived in a model where frictions in output and input markets generate production inefficiencies. For a given level of aggregate inputs, a higher level of output could be reached if resources were more efficiently allocated. Following Restuccia and Rogerson (2008) and Chari et al. (2007), I do not specify the frictions that induce this resource misallocation. Rather, the frictions are modelled as wedges between the firms’ marginal products. The model therefore encompasses various sources of distortions such as adjustment costs, search frictions, financial constraints or distortionary regulation. Within this framework, I show how to aggregate the heterogenous production functions into an aggregate production function. The aggregation of heterogeneous production functions is a classical problem in macroeconomics. It is well known that if one allows the individual firm inputs to take any values, the aggregation of firm-level technological constraints is impos-sible unless very restrictive conditions are imposed. The usual solution consists in defining the aggregate production function as the efficient frontier of the production possibilities set (e.g. Fisher (1969), Houthakker (1955)). As the focus is on misallocation and production inefficiencies, this is not the approach considered here. Following Malinvaud (1993), I define the aggregate production function as the relation between aggregate output and input for a given allocation of resources. Computed from this aggregate production function, aggregate productivity growth captures the variations in output that are due to changes in resource allocation, as well as those due to within-firm productivity change2. Then, using a method similar to the index number approach, I decompose aggregate productivity growth between productivity changes at the firm-level, changes in allocative efficiency, and changes in the pattern of entry and exit.
The decomposition of aggregate productivity growth is estimated from 1991 to 2006 on French firm-level data from the manufacturing sector.3 I use a dataset collected annually by the tax administration and combined with survey data in the INSEE unified system of business statis-tics (SUSE). The empirical analysis leads to the following findings: 1) entry and exit contribute very little to the dynamics of aggregate productivity growth. 2) movements in allocative effi-ciency are somewhat countercyclical, with a correlation to real value added growth of -0.25. 3) within-firm productivity changes are procyclical, with a correlation coefficient equal to 0.64. These results differ substantially from those obtained when implementing the decomposition proposed by Foster et al. (2001). Using their decomposition, the extensive margin accounts for a larger share of aggregate productivity growth and the reallocation component appears procyclical.
The finding that entry and exit flows have a negligible role for aggregate productivity growth contrasts sharply with the literature on the cleansing effect of recession (Caballero and Ham-mour, 1994; Barlevy, 2003; Ouyang, 2009). While the cleansing effect would imply a counter-cyclical extensive margin component, I find that, not only is the contribution of entry and exit small, it is also positively correlated to real value added growth. In fact, it is the reallocation of resources between incumbents, and not that between entering and exiting firms that tends to raise aggregate productivity during recessions. Despite the heterogeneity between sectors, the countercyclicality of allocative efficiency also holds for most sectors. This finding suggests new directions for future theoretical work as very little is known on the mechanisms behind the cyclical patterns of allocative efficiency.
This paper is not the first to advocate the use of a well-defined measure of allocative efficiency. Several recent papers (Petrin and Levinsohn, 2005; Basu et al., 2009; Petrin et al., 2011) have emphasized that the reallocation component should capture changes in the allocation of inputs between firms with different marginal values. None of these papers investigate the role of the extensive margin. More importantly, the methods used, as well as the results obtained are substantially different from these papers. Their decompositions are based on the Solow residual measure of productivity at the firm-level. They all build on Basu and Fernald (2002)’s insight that, under some conditions, the Solow residual approximates the welfare change of a representative consumer even when the allocation of resources is distorted by imperfect competition. Their measure of aggregate productivity growth therefore includes the effects of changes in aggregate input reflecting the fact that, under imperfect competition, welfare increases with aggregate input use. Moreover, their measure of allocative efficiency only captures the consequences of reallocation across firms with different markups and therefore does not account for all changes in the dispersion of marginal products. Basu et al. (2009) compute this decomposition for several European countries over the period 1995-2005 and find that allocative efficiency is not an important component of aggregate productivity. In particular, for France, they find that within-firm productivity changes explain all the changes in the Solow residual. This contrasts with my results in which allocative efficiency reduces by 51% the volatility of sectoral productivity growth. Contrary to Basu and Fernald (2002), I explicitly address the aggregation issue to investigate the link between the Solow residual and firm-level productivity change. By taking explicit account of firm heterogeneity and microeconomic frictions, I provide a complementary analysis to Hall (1991) who highlights the consequence of market imperfections for the measure of aggregate productivity growth in a representative firm framework. I show that the Solow residual gives a biased measure of productivity change when the heterogeneity in factor elasticities is accounted for, even when resources are efficiently allocated.
This paper is also closely related to Hsieh and Klenow (2009) who study the role of resource misallocation in explaining the TFP differential between China, India and the United States. As in their paper, resource misallocation is captured by the dispersion in the marginal prod-ucts of capital and labor. However, both the objective and the decomposition differ from their paper. They analyze TFP differentials across countries, and quantify misallocation by measuring the distance between observed and first-best TFP levels. By contrast, I focus on TFP variation across time, and propose a decomposition of observed TFP using an approach similar to the index number theory. Furthermore, contrary to Hsieh and Klenow (2009), I use a unified approach at both the sectoral and aggregate levels. This allows me to provide an estimation of allocative efficiency not only within sectors but also between sectors.
The paper is organized as follows. Section 2 lays out the framework and shows how to aggregate heterogeneous production units to derive the aggregate productivity index. Section 3 presents the decomposition of aggregate productivity both within and between sectors. Section 4 presents the estimation method and the results obtained on French firm-level data. Section 5 concludes.
Aggregation of heterogenous production units
Aggregate productivity is a concept which is intrinsically related to the production function. Aggregate productivity is defined as the change in real output not accounted for by the change in real input. To analyze changes in aggregate productivity, it is therefore necessary to derive the link between aggregate inputs and aggregate output. This section lays out the setup and shows how to derive the aggregate production function in a framework where producers are heterogeneous and face allocation frictions.
Table of contents :
Introduction générale
1 All you need is loan. Credit market frictions and the exit of firms in recessions
1.1 Introduction
1.2 A model of firm dynamics and credit market frictions
1.2.1 Technology and timing of decisions
1.2.2 The frictionless economy
1.2.3 The economy with credit market frictions
1.2.4 Entry, stationary distribution and aggregate output
1.3 Distortion of the exit decision
1.4 Aggregate implications of firm exit under credit market frictions
1.4.1 Benchmark calibration
1.4.2 Steady state capital and exit behavior
1.4.3 Imperfect selection and average productivity
1.4.4 Amplification at the exit margin
1.4.5 The role of idiosyncratic productivity
1.5 Conclusion
2 Aggregate productivity growth and the allocation of resources over the business cycle
2.1 Introduction
2.2 Aggregation of heterogenous production units
2.2.1 Framework
2.2.2 Aggregation
2.3 Accounting for changes in aggregate productivity
2.3.1 Decomposition of sectoral productivity
2.3.2 Decomposition across sectors
2.4 Estimation
2.4.1 Data description
2.4.2 Estimation method
2.4.3 Empirical results
2.5 Conclusion
3 Matching frictions, unemployment dynamics and the cost of business cycles
3.1 Introduction
3.2 Asymmetry in the unemployment dynamics: a reduced form approach
3.2.1 Framework
3.2.2 The analysis of the non-linearities in the unemployment dynamics
3.2.3 Quantifying the employment loss
3.3 Endogenizing the job finding rate: a structural approach
3.3.1 A canonical matching model
3.3.2 Non-linearities, welfare cost and employment loss: the rigid wage case
3.3.3 Quantifying the business cycles costs
3.3.4 Simulation
3.4 Robustness
3.4.1 A flexible-wage approach
3.4.2 Unemployment and non-linearity: a test on panel data
3.5 Structural policy as a stabilizer
3.6 Conclusion
Conclusion générale
