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## Aggregate productivity and domestic and export activity

An important feature of the French woodworking industry is that about 75% of total produc-tion is distributed on the domestic market, i.e., most firms only export very little w.r.t. their total sales.34 For this reasons it seems important to relate aggregate productivity growth not only to firms’ export status, but also their volumes of sales in the domestic and export market. Section 2.3.2 presented the aggregate productivity decomposition for this purpose. Remember that I here simply split firms’ sales shares into its domestic and export compo-nent, respectively. I then apply the static Olley-Pakes productivity decomposition to contin-uing firms, i.e., without taking market entry and exit effects into account that are studied in the previous sections. In this manner I am able to investigate, to which extend productivity growth dynamics are related to the domestic and export economic activity.

Table 2.11 presents the corresponding the results. The table shows that especially dur-ing the first two periods, 1994-2000 and 2001-2007, total growth is mainly driven by firms’ domestic activity. For instance, considering the period 1994-2000, the contribution to aggre-gate productivity growth of firms’ domestic activity is given by 7.2% (sum of within and between contribution) whereas aggregate productivity growth from firms’ export activity is only given by 2.16%. Here, in particular, firms’ within growth related to domestic activity contributes considerably to the aggregate productivity growth. A similar pattern is mea-sured for the period 2001-2007. For the period of economic distress, 2009-2012, as well as for 2013-2016, the within contribution related to both domestic and export activity is measured to be negative. Here, compared to the first two periods, especially the within contribution related to domestic activity reduces dramatically, given by -0.22% and -1.86%, respectively. Over the last period, I measure a considerable positive between contribution related to both firms’ domestic and export activity, indicating that after the crisis, domestic and export sales shares were considerably reallocated from less to more productive firms.

The key message from this section is that firms domestic activity is a crucial driver for aggregate productivity growth, which is induced by the high share of sales distributed in the domestic market. That is, while exporting firms exhibit higher productivity levels and a more sustainable aggregate productivity growth, domestic economic activity states the most important pillar for the industry’s productivity growth. Generally, my results suggest that a higher degree of internationalization of the French woodworking industry could have two positive effects. Fist, more firms would benefit from export-learning increasing their indi-vidual productivity (Bellone et al., 2008). Second, by higher export sales shares aggregate productivity would be less vulnerable to domestic economic distress, thus, allowing for a more sustainable aggregate productivity and economic growth.

**Conclusion**

This chapter investigates productivity dynamics in the French woodworking industry be-tween 1994 and 2016. More specifically, it analyses the effect of market entry and exit on aggregate productivity growth as well as the relation between firms’ export status (i.e. ex-porting or non-exporting) and export volumes and aggregate productivity growth in the in-dustry. For this purpose I use French firm-level data covering the period from 1994-2016 and estimate firm-level productivity based on a value added Cobb-Douglas production function, following Ackerberg et al. (2015).

Compared to more recent periods, I find that the industry’s total aggregate productivity growth is considerably higher for the periods 1994-2000 and 2001-2007. During the period of worldwide economic distress, 2008-2012, a remarkable slowdown in productivity growth took place, with some improvement during the period after the economic crisis, 2012-2016, which goes in line with other studies considering productivity of the French economy (Cette et al., 2017; Ben Hassine, 2019; De Monte, 2021). The analysis further shows that an impor-tant driver for these dynamics is the contribution of the group of incumbent firms, where market entry and exit reveals a much lower contribution. Moreover, investigating aggregate productivity growth separately w.r.t. firms export status, i.e. non-exporting and exporting firms, I find that the group of exporting firms feature higher aggregate productivity growth rates compared to the group of non-exporting firms. This result is similar to the findings by Harris and Li (2008), who investigate UK firms. Further, applying the concept of first order stochastic dominance, exporter show higher productivity levels on the whole range of the productivity distribution, where I measure exporters’ median productivity as 7% and 9% higher compared to non-exporters. However, when decomposing aggregate productiv-ity into the part contributed by firms’ domestic and export activity, the results suggest, that domestic activity contributes considerably more to aggregate productivity growth for the periods 1994-2000 and 2001-2007, compared to the contribution of export activity. This is due to the fact that by far the largest part of firms’ production is for the domestic market. That is, the slowed aggregate productivity growth is mainly transmitted by firms’ domestic activity. Therefore, given firms learn and improve through exporting (Bellone et al., 2008; De Loecker, 2013), my results suggest that a more international orientation of the French woodworking industry promotes a higher and more sustainable aggregate productivity growth, which would, in turn, also be more resilient to domestic economic distress. More-over, as the French woodworking industry exhibits a considerable trade deficit (Levet et al., 2014), losing sales share on the global market (Koebel et al., 2016), further research should be done to better understand the barriers preventing firms from engaging in export activity and to evaluate what policy measures would be best suited to support firms’ competitiveness in the global market.

The analysis performed in the chapter leaves room for improvement in several ways. First, the use of a value added Cobb-Douglas production function, implying constant output elasticities across firms, is restrictive. More general models, such as a translog production technology (De Monte, 2021; De Loecker and Warzynski, 2012) and/or nonparametric es-timation approaches of production functions (Demirer, 2020; Doraszelski and Jaumandreu, 2018), would allow for more flexibility. Second, firm productivity is estimated from revenue data and as such it conflates price-setting effects with physical productivity. In other words, a firm might be considered productive as it is cost-effective or because it has significant mar-ket power. Using firm-level price indicators (Morlacco, 2017) or physical output/input data would be possible ways to avoid this issue. Third, the measure of market entry and exit is only based on firm observations in the data but not on the legal activity status of a firm, which might bias the effect of firm entry and exit on aggregate productivity.

### Merging of the data sets FICUS and FARE

For the analysis the two fiscal firm-level data sets FICUS and FARE are merged, covering the periods from 1994 to 2007, and 2008 to 2016, respectively. Both in FICUS and FARE firms are classified by a 4-digit sector nomenclature « NAF » (nomenclature d’activité française). However, from 2008 onward, the FARE sectoral nomenclature changed: new sectors ap-peared (some FICUS sectors were split), some FICUS sectors disappeared (were merged into a FARE sector). In FICUS, the nomenclature was organized according to « NAF 1 », while in FARE the nomenclature is organized according to « NAF 2 ». In this study a single data set is constructed, 1994 – 2016, by extending the sector nomenclature NAF 2 throughout the whole period. That is, the current 4-digit sector nomenclature NAF 2 are assigned retrospectively to all firms observed in FICUS. For firms that are observed both in FICUS and FARE or only in FARE their 4-digit sector according to NAF 2 is known. However, for firms that have exited the market before 2008 we do not know to which NAF 2 4-digit sector they would have belonged to if they had continued their activity. To also classify these firms by the NAF 2 4-digit nomenclature the following methodology is used: First only those firms that are observed in both data sets, FICUS and FARE, are considered. From these observations a transition matrix is built where each row represents a 4-digit sector according to NAF 1 and each column represents a 4-digit sector according to NAF 2. Each cell of the transition matrix contains the number of firms transiting from a specific 4-digit sector in FICUS (NAF 1) to the new 4-digit sector in FARE (NAF 2). Table 2.12 shows an exemplifying transition matrix, choosing the NAF 1 4-digit sectors 201A – 205C, i.e. the manufacture of wood and products of wood. For instance, it can be seen that there are 2060 firms observed that were classified in FICUS in 201A (first row) and in FARE in the sector 1610 (third column), while there are only 46 observations that were classified in 201A and in FICUS in 0220 (first column). From these observed transition frequencies the transition probabilities are then calculated by sim-ply dividing each element of the matrix by the sum of its corresponding row. That is, the NAF 1 – NAF 2 transition probabilities are calculated by where n is a firm observed in both FICUS and FARE, I and J are specific 4-digit sectors according to NAF 1 and NAF 2, respectively. 1 is an index variable equal to 1 if the condition in parenthesis is fulfilled. Table 2.13 contains the transition probabilities according to the observed transitions Table 2.12. It can be seen that those 4-digit transitions between FICUS and FARE that were more frequently observed obtain accordingly higher probabilities. In a second step, firms only observed in FICUS belonging to a specific NAF 1 4-digit sector, are a All figures represent averages over the whole period 1994-2016. b Shares and rates are given in %.

c Size group is given in terms of number of employees. NA denotes the group of firms for which the number of employees is not available.

**Appendix B: Descriptive statistics**

#### Share of the French woodworking industry w.r.t. the overall manufactur-ing industry

Table 2.15 provides some quantitative information mentioned in the introduction, concern-ing the importance of the woodworking industry w.r.t. the overall French manufacturing industry. The table is based on the sample without any restriction on observations in terms of firm size or other variables and figures are calculated for the whole period 1994-2016. The table shows that the share of firms active in the woodworking industry accounts for about 10%, w.r.t. all firms active in the French manufacturing. Further, the woodworking industry’s share of turnover and exports is given by 4.6% and 3.2%, respectively. As also mentioned in the main text, these shares are however decreasing over time, as can be seen in Figure 2.7, illustrating the share of the French woodworking industry in terms of the number of firms, workers, turnover, and exports w.r.t. the overall manufacturing industry. All shares show a decreasing tendency over time, indicating a lower economic importance of the woodworking industry.

**Table of contents :**

**1 General introduction **

1.1 Motivation

1.2 Overview of the thesis

1.2.1 Chapter 2: Productivity dynamics and exports of the french woodworking industry

1.2.2 Chapter 3: Productivity, markups, entry, and exit: evidence from French manufacturing firms

1.2.3 Chapter 4: Cournot equilibrium and heterogenous firms

1.2.4 Chapter 5: Nonparametric instrumental regression with additive fixed effects

**2 Productivity dynamics and exports in the French woodworking industry**

2.1 Introduction

2.2 Literature review

2.2.1 Productivity and resource allocation

2.2.2 Productivity and international trade

2.2.3 Studies with focus on France and/or the woodworking industry

2.3 Empirical framework

2.3.1 Production function estimation

2.3.2 Aggregate productivity growth, firm entry and exit, and export status

2.4 Data and variables

2.4.1 Production function and export variables

2.4.2 Definition of firm entry and exit

2.5 Descriptive statistics

2.6 Empirical results of structural stability and productivity distribution

2.7 Empirical results of aggregate productivity dynamics

2.7.1 Aggregate productivity with market entry and exit

2.7.2 Aggregate productivity and export status

2.7.3 Aggregate productivity and domestic and export activity

2.8 Conclusion

2.9 Appendix A: Data

2.9.1 Merging of the data sets FICUS and FARE

2.9.2 Data cleaning

2.10 Appendix B: Descriptive statistics

2.10.1 Share of the French woodworking industry w.r.t. the overall manufacturing industry

2.10.2 Evolution of value added, inputs, and exports by 4-digit sectors

2.11 Appendix C: Production function estimation

2.11.1 Chunk code

2.11.2 Production function estimates

2.11.3 Distribution of the production function residual

2.12 Appendix D: Productivity distribution and dispersion by 4-digit sector

2.13 Appendix E: Productivity decomposition

2.13.1 Annual aggregate productivity with entry and exit

2.13.2 Aggregate productivity and entry and exit w.r.t. 4-digit sectors

2.13.3 Aggregate productivity and firms’ export behavior

**3 Productivity, markups, entry, and exit: evidence from French manufacturing firms from 1994 to 2016 **

3.1 Introduction

3.2 Related literature

3.2.1 Productivity

3.2.2 Markups

3.3 Theoretical background

3.4 Empirical framework

3.4.1 Production function estimation

3.4.2 Firm-level markups

3.4.3 Discussion

3.5 Data and descriptive statistics

3.5.1 Data

3.5.2 Descriptive statistics

3.6 Decomposing aggregate productivity and markups with entry and exit

3.6.1 Decomposition approach

3.6.2 Empirical decomposition of aggregate productivity

3.6.3 Empirical decomposition of aggregate markups

3.7 Heterogeneity in aggregate productivity and markup across sectors

3.8 Distribution and convergence patterns of productivity and markups

3.8.1 Distribution over time of productivity and markups

3.8.2 Convergence patterns of productivity and markups

3.9 Relation between markups, productivity, firm entry and exit

3.10 Conclusion

3.11 Appendix A: Data

3.11.1 Descriptive statistics

3.11.2 Measuring firm entry and exit at a yearly basis

3.12 Appendix B: Translog production function estimation

3.13 Appendix C: Decomposition analysis

3.13.1 Derivation of the DOPD approach

3.13.2 Decomposition tables for both aggregate productivity and markups

3.14 Appendix D: Robustness checks

3.14.1 Production function specification

3.14.2 Aggregate productivity

3.14.3 Aggregate markups

3.15 Appendix E: Further material

**4 Cournot equilibrium and welfare with heterogeneous firms**

4.1 Introduction

4.2 Short-run Cournot equilibrium with heterogeneous quadratic cost functions

4.3 The long-run Cournot equilibrium

4.4 The welfare consequences of entry and exit at LRCE

4.5 Data and descriptive statistics

4.6 Inverse output demand estimates

4.7 Cost function estimation with heterogeneity in fixed and variable costs

4.7.1 Empirical specification

4.7.2 Identification

4.7.3 Estimation results

4.8 Conclusion

4.9 Appendix A: Proof of the propositions

4.10 Appendix B: Further information on the data and descriptive statistics

4.10.1 Data cleaning

4.10.2 Further descriptive statistics

4.11 Appendix C: Reparameterization of the cost function

**5 On nonparametric instrumental regression with additive fixed effects **

5.1 Introduction

5.2 Related estimation methods

5.2.1 Fève and Florens (2014)’s estimator: instrumental regression with FE

5.2.2 Lee et al. (2019)’s estimator: FE only

5.3 Another estimation procedure for instrumental regression with FE

5.3.1 Setup of the estimator

5.3.2 Estimation and implementation

5.3.3 Discussion

5.4 Simulation and finite sample behavior

5.4.1 Data Generating Process (DGP)

5.4.2 Estimation results

5.4.3 Finite sample behavior

5.5 Application to the estimation of the inverse demand function

5.5.1 Inverse demand specification

5.5.2 Data

5.5.3 Estimation results of the inverse demand function

5.6 Conclusion

5.7 Appendix A: Bandwidth selection via leave-one-out cross-validation

5.8 Appendix B: Estimation of the inverse demand

**6 Conclusion**

6.1 Summary of the dissertation

6.2 Limitations and extensions

6.2.1 Estimating firm-level productivity

6.2.2 Measuring market entry and exit

6.2.3 Modeling firm competition à la Cournot

6.2.4 Nonparametric estimation with endogenous variables