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## Estimation of the parameters

I now describe how I infer the parameters used in the theoretical framework from the dataset. In a perfect economy with no frictions one would naturally approximate the elasticity of output with respect to labor by the share of nominal value-added devoted to nominal expenditure on labor. But as the whole analysis relies on the existence of distortions driving the economy away from an e cient optimum one cannot separately identify di erences in technology and di erences in distortions from di erences in factor expenditure shares. I assume that on average rms within a given industry are undistorted (even if a particular rm still may face a distortion in a particular year). More precisely, I compute for each year and for each rm operating in industry s its labor expenditure share28 and I assume that the median of this variable over the years and over the rms re ects the true value of the elasticity of output with respect to labor. Then under the assumption of constant return to scale it is straightforward to deduce for each industry the elasticity of output with respect to capital.29 As stressed by Hsieh and Klenow (2009) another issue that arises when deducing production elasticities from factor shares is that we have to take into account the markups associated with the market power of the rms in workers skills. However di erences in wages may also be explained by rent sharing and by wage bargaining between the rms and the workers. I will use this alternative speci cation as a robustness check.

27The average number of hours worked by employee for a given year, the investment de ators and the value-added de ators are taken from the INSEE database (available online), although the data are given for a broader level of aggregation than the three-digit level.

28 Payments to labor used to compute labor expenditure shares include the wage bills, fringe bene ts and employer social security contributions.

29 I do not use standard semi-parametric methods such as Olley and Pakes (1996) and Levinsohn and Petrin (2003) for two reasons. First these methods require assumptions on rms capital and labor demands, whereas one advantage of the structural framework I develop is that it does not require any hypothesis on how rms behave. Second, these methods frequently provide very low elasticities for capital, because this input is notoriously more prone to measurement errors than labor.

in these di erentiated good industries. I assume that rents coming from these markups are divided between workers and capital owners proportionally to the factor expenditure shares, and directly appear in the payments to labor used to deduce output elasticities.

In order to measure sectors’ shares s I compute for each year and for each sector the ratio of the sectoral nominal value added to total nominal value added in the economy. These parameters are time-varying.

Most empirical studies in the misallocation literature set the elasticity of substitution be-tween goods s equal to an arbitrary value, considered as the same for all sectors in the economy. In line with these studies I set s equal to 3 in my baseline computations. However this assump-tion may seem unsatisfying, as the value of the elasticity of substitution is bound to vary across sectors and probably impacts the magnitude of the results. As a matter of fact, it determines the sectoral aggregates (equation 2.11), the elasticity of the individual demand equations (equa-tion 2.14) and the measures of idiosyncratic productivity (equation 2.15). Allowing elasticities to vary across sectors constitutes therefore an important step forward. As a robustness check I estimate sector speci c elasticities, using an econometric strategy inspired by De Loecker (2011) (see appendix 2.9).

**Empirical results**

I now apply the theoretical framework developed in section 2.2 to the FIBEN dataset in order to quantify the evolution of misallocation over time and its contribution to the variation in observed TFP.

To guard against the e ect of mismeasurement I follow Hsieh and Klenow (2009) and trim the top and bottom 1% outliers of both physical and revenue productivity for each year and within each sector. After trimming the dataset includes 945,014 rm-year observations.

### Distortions and rm characteristics

Tables 2.3 and 2.4 respectively present univariate comparisons of key descriptive variables by labor distortion and capital distortion quartiles. The quartiles are constructed each year and for each sector. All variables except log distortions are normalized by their sector-year means.

30 I do not claim that this econometric strategy enables me to control for all sources of endogeneity bias. Moreover it relies on arguably strong (although standard) assumptions. The main point here is to get reasonable estimates and to examine whether my main empirical results still hold when allowing for sector speci c elasticities.

I am interested in whether the characteristics of rms which su er from a lack of resources (i.e., rms with high labor or capital distortions) di er from those which should be granted less inputs (i.e., rms with low labor or capital distortions).

Firms’ value added and capital stock increase monotonically with labor distortions. It suggests that for a given distribution of capital labor should optimally be reallocated from rms with relatively low nominal VA and capital stock to rms with relatively high nominal VA and capital stock: the mean rm in the fourth quartile produces 41% more and owns a capital stock 52% higher than its sector-year average, while the mean rm in the rst quartile produces 43% less and owns 44% less capital. As for labor input itself the pattern is not so clear: the mean increases until Q3 but then decreases for the fourth quartile, while the labor input of the median rm is decreasing with labor distortions. The same observation applies to the age variable, both the mean and the median increasing until Q3 and then decreasing for the fourth quartile.

Regarding capital distortions, the mean of value-added, labor and capital decreases mono-tonically (although the median for value-added and labor in Q1 is lower than in Q2). It suggests that for a given distribution of labor one can increase output by reallocating capital from rms with high nominal VA, high labor input and high capital stock to rms producing less with less inputs. The results for the capital variable are particularly striking: the capital stock of the mean rm in Q1 is 2.5 times larger than the sector-year average, while the mean rm in Q4 owns a capital stock more than 7 times smaller. Considering the age variable, it is again hard to draw any rm conclusion, both mean and median increasing then decreasing with capital distortions.

Tables 2.3 and 2.4 also provide useful information on the dispersion of both MRP distribu-tions, and on the correlation with rms’ productivity. On one hand substracting the median log-distortion in Q1 from the median log-distortion in Q4 indicates that the MRPK dispersion is higher than the MRPL dispersion (2.094 versus 0.809 for the di erence between median log-distortions, 2.354 versus 0.946 for the di erence between mean log-distortions). It suggests that there is relatively more room for capital reallocation than for labor reallocation if one wants to improve allocational e ciency. On the other hand TFPQ increases monotonically with both distortions, meaning that rms su ering from a lack of resources are also the most produc-tive ones. However, the productivity gap between low MRPL and high MRPL rms is more pronounced: the mean rm in the fourth ( rst) labor distortion quartile is 59.8% more (46% less) productive than its sector-year average, while the mean rm in the fourth ( rst) capital distortion quartile is only 9.7% more (10.8% less) productive. Other things equal, this bigger productivity gap would make labor misallocation relatively worse than capital misallocation.

#### Misallocation and contribution to the variations in TFP

Table 2.5 presents the magnitude of capital, labor and total misallocation as de ned in section 2.2. First it is interesting to notice that the mean TFP losses one can attribute re-spectively to labor and capital distortions are very similar: in both cases, equalizing marginal revenue products when there are no distortions for the other input would boost aggregate TFP by 14.1% on average. As for total misallocation, I nd that the mean TFP gap between the e cient inputs allocation and the observed one is equal to 28.6%. My results are compara-ble to those in Bellone and Mallen-Pisano (2013) who also focus on the French manufacturing sector: the TFP loss I estimate is equal to 24.3% in 1998, 30% in 2001 and 30.7% in 2005, while they nd a TFP gap of respectively 30.5%, 27.5% and 30.5%. As recently emphasized by Bils, Klenow, and Ruane (2018), measurement errors in revenue and inputs may impact the magnitude of the TFP losses that are attributed to misallocation. On the other hand and as long as mismeasurement stays stable over time, dynamics of allocational e ciency should be una ected by such measurement errors. I focus hereafter on the evolution of misallocation and on its e ect on aggregate productivity.

Table 2.5 shows that misallocation seems to worsen over time. Capital misallocation is minimal in 1990, and culminates in 2012; labor misallocation reaches its minimum in 1991 and 1992, and is maximal in 2015; total misallocation is minimal in 1991, and reaches a peak in 2008. However, because rms appear in the dataset only when their sales exceed 750,000 euros, entry and exit between two consecutive years re ect this threshold e ect and not necessarily rms shutting down their businesses. These arti cial entry and exit make it hard to properly assess the evolution of misallocation over time, and its impact on productivity.

In order to cope with this issue I make use of additional data available at the banque de France, keeping track of the main judicial or administrative stages in the life of the rms, and gathered from registrars of commercial courts, journals of legal notices, or from the compa-nies themselves. I focus on events associated with entry ( rst registration at the register of commerce) and exit (cessation of activity, judicial liquidation). To evaluate the change in mis-allocation between year t and year t + 1 I consider the set of rms appearing either at t, t + 1, or both; I drop from the sample rms which disappear in year t + 1 but for which I have no event associated with exit at this date, and rms which appear in year t + 1 but for which I have no event associated with entry at this date. Using this procedure I may drop from the sample rms which really stop their activities or which really start a business, but do not report it to legal institutions, and for which I have therefore no information. Thus I cannot claim that I do not drop any actual entry or exit; but I make sure that I drop every arti cial ones. Then I compute the variation (in log) of misallocation and of its three components between t and t + 1. Finally I assess the evolution of misallocation over time by summing the variations for all consecutive years.

**Table of contents :**

**1 General Introduction **

1.1 The great productivity slowdown

1.2 Misallocation before, during, and after the Great Recession

1.3 Granular borrowers

1.4 Bank lending shocks, credit allocation, and capital allocation

**2 Misallocation before, during, and after the Great Recession **

2.1 Introduction

2.2 Theoretical framework

2.2.1 The ecient allocation

2.2.2 Production functions and output aggregators

2.2.3 Capital, labor and the log-normality assumption

2.2.4 Misallocation and aggregate TFP

2.3 Data

2.3.1 Data description

2.3.2 Estimation of the parameters

2.4 Empirical results

2.4.1 Distortions and rm characteristics

2.4.2 Misallocation and contribution to the variations in TFP

2.5 Robustness checks

2.6 Conclusion

2.7 Tables and gures

2.8 The log-normality assumption

2.9 Sector-specic elasticities of substitution

**3 Granular Borrowers **

3.1 Introduction

3.2 Granular borrowers

3.2.1 Presentation of the data set

3.2.2 Credit concentration: evidence at the bank and aggregate level

3.3 Estimating rm and bank shocks

3.3.1 Presentation of the methodology

3.3.2 Single- and multiple-bank borrowers

3.3.3 Aggregation and normalization of the shocks

3.3.4 External validation of the rm components

3.4 Granular borrowers and the cyclicality of aggregate credit

3.4.1 Granularity and cyclicality

3.4.2 Dissecting the cyclicality of aggregate credit

3.4.3 Granular shocks and granular trends

3.4.4 Robustness checks

3.5 Bank liquidity risk and borrower concentration

3.5.1 Can banks pool borrower idiosyncratic risk?

3.5.2 Borrower concentration as a source of synchronization

3.6 Conclusion

3.7 Tables and gures

**4 Bank lending shocks, credit allocation, and capital allocation **

4.1 Introduction

4.2 Data

4.3 Estimation of bank credit shocks

4.4 Main variables and descriptive statistics

4.5 Results

4.5.1 Aggregate bank shocks and credit allocation

4.5.2 Average real eects of bank shocks on rm-level outcomes

4.5.3 From credit allocation to resource allocation

4.6 Conclusion

4.7 Figures

4.8 Tables