Productivity growth and resource (mis)allocation in France: New insights from bankruptcy and inference 

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Economic-based efficiency measurement of bankruptcy frameworks

Considering type I errors, they can occur because of barriers to exit, which are the obstacles firms face that make market’s exit costly for them such as sunk costs. However, unlike firms’ voluntary exit, firms do not initiate bankruptcies, but the Court imposes it to them due to the creditors’ request. Thus, if type I errors happen, it should be related to the creditors. Indeed, since they are the main plaintiffs, if they decide not to ask the Court to trigger a proceeding, the procedure might not start. Zombie firms are a good example of the type I errors. Zombie firms are defined in the literature as mature firms that are not able to cover their interest rates with their operational profits for more than three years. According to Ben Hassine et al. (2019), zombie firms are not a minor phenomenon. They show, out of a panel of firms that are defaulting, zombie or both defaulting and zombie, that zombies firms that are not defaulting, namely type I errors, account for 43% of them. In the whole French economy, Coface (2018) evaluates their occurrences between 4% and 5%. This is more than in Germany but less than in Italy and Spain. Thus, even if it is not the best performing framework, the French framework seems to discriminate firms that should enter into the bankruptcy procedure better than others.
On the contrary, type II errors could ensue from the preferences of the legisla-tors. Indeed, we can distinguish two types of performances. One relies on economic indicators such as the apparent productivity of labor, or the total factor productivity (the part of the production not explained by labor and capital), and the other relies on financial indexes, like the financial performances. Since the bankruptcy is trig-gered based on financial indexes, it is possible that relatively economically efficient firms face financial difficulties due to a shock (a crisis) or due to delay of payment from some important clients. In such cases, firms might not face their creditors’ claims while being well suited for operating in the market. If the framework is too biased towards the creditors’ reimbursement, the Court would likely decide to liquidate firms that are economically efficient enough.
To sum up, when type I errors arise, firms that should exit the market remain active. If the bankruptcy system does not evacuate these firms, they use inputs less efficiently than the other firms, reducing the economy’s growth potential, the loans available for more performing firms, and the labor force available. On the contrary, when the type II errors occur, efficient firms have to leave the market where they operate. This error implies that potential growth is lost because the Court was too prompt to liquidate the firms. Therefore, both of these errors are sub-optimal situations. In order to start assessing the French framework, we might first approach type II errors. While in a debtors-friendly framework one should avoid type II errors, France’s proportion of direct liquidations is important, as it is next to 70% out of the procedures.10 Moreover, half of the firms involved in a safeguard or a reorganization procedure are liquidated after three years and two-third after eight years. This high proportion of liquidation might be due to the high effectiveness of the mutual agreement procedures. This procedure allows firms with a high likelihood of sur-viving to avoid the other bankruptcy proceedings or to prepare a plan with higher chances of success. Hence, even firms involved in procedures created to help them reorganize themselves and survive are likely to exit the market definitively: they cannot be saved before the cessations of payments occur, so they exit the market all together, explaining the high liquidation rate in a debtor-friendly framework. On the one hand, it appears that the French framework performs well to avoid type I errors. Indeed, as Adalet McGowan et al. (2018) show, firms considered as zombies account for around 2% of the firms in 2012. This number is one of the lowest one among the countries they considered. This low proportion of zombie firms in the whole economy is also confirmed by Ben Hassine et al. (2019), even if the share is at around 5% and higher than that in Coface (2018). On the other hand, the screening of firms in difficulty and the mutual agreement proceedings before bankruptcy are the reasons to explain the low type II errors, as stated by the French Senate (2005). As a consequence, this framework seems to generate minor economic growth losses due to type II errors.

Export sunk costs: an identification using propensity score matching

Theoretically, we can make a clear distinction between the sunk costs supported by firms to access the domestic market and those supported to access the export market (Melitz, 2003, Yi and Wang, 2012). By contrast, in the data, we can control only for the presence of overall sunk costs, without the distinction between the sunk costs related to the domestic activity and export one.
We propose to measure the sunk costs with a new methodology. The sunk costs directed to the export activity can be viewed as the difference between the global sunk costs of the exporting firm and the sunk costs linked to the domestic market. This difference can be estimated due to the matching methodology, which allows comparison between treated firms and their constructed counterfactuals. In addition, knowing that the decision to export is not a random process, matching the firms will allow us to randomize the treatment allocation. Using this property, we can extract the sunk costs of non-exporters, which are statistically identical to exporters. We will consider this difference to be the sunk costs directly linked to export activity.
This methodology will allow us to compute the two types of sunk costs for each exporting firm each year. Thus, because we will calculate it by firm and by year, Mundlak’s methodology (Mundlak, 1978) allows us to control the individual unobserved heterogeneity in our primary model. The critical steps are the matching methodology used and the variable choice. We will perform PSM, and the model retained will be discussed later.
The literature frequently uses the method of PSM proposed by Rosenbaum and Rubin (1983). This is a convenient methodology because it allows us to obtain a single index built from the observed characteristics of firms to match treated firms with non-treated firms. Its central component is the choice of independent vari-ables, so we have complete independence between the unobserved characteristics and the outcome, the sunk costs related to firms’ export activity. Consequently, we must use all the explanatory variables of the decision to export in the model to discriminate properly the sunk costs related to exports. Hence, we can see this approach as a way to explain the difference in export status between two firms that are statistically identical, where the decision to export is a random process. This probability is estimated with a probit using the data available between 2006 and 2014. P ( Export ′ ′ ′ (1.4) =1∣ )=Φ( 0++ ̄ + + ).
Since the choice of the covariates is crucial to obtaining a good quality of match-ing, we follow Roberts and Tybout (1997) and Vicard (2014) to predict the export choice. We use a set of industry dummies at the two-digit NACE level (Sit), a dummy of foreign ownership, and a dummy of importer status. We also use the logarithm of continuous variables, such as the lag of the productivity index of the firm.

Sunk costs fallacy or real options model

In Table 1.3 we estimate models with the number of destination and the share of destinations according to the difficulty of the market, which help us to illustrate how firms deal with risk, as in real options models. In the column (1) to (6), the destination considered is the European Union, since it is easier to access the market of countries inside the Single Market. In the column (7) to (12), we took the OECD membership as an easy market, because countries part of OECD are more similar in term of economic development than the other countries and can be seen as a robustness check. Overall, we do not find a decrease in exports to “more difficult markets”.14. Nevertheless, the heterogeneity of economic activities and opportunities within EU countries can be too large to consider all of them as easy markets. When considering the OECD destination, i.e. columns (7) to (12), only the number of destinations at the time of default has a positive impact on the default probability, thus we can consider our findings robust.
Considering that only the number of destination estimations in t is significant, our findings seem to be in line with the predictions of real options model theory. As O’Brien and Folta (2009) notes, the inertia we find here can be logically ex-plained, especially when sunk costs are high. When facing great uncertainty and a high amount of sunk costs, poorly performing firms will not exit the market. Since exiting the market means losing the stock of the wide variety of sunk costs, such as “strategic asset stocks”, and knowledge, steadily accumulated through the company’s exporting history. Thus, exiting and re-entering the market when the economic environment is more favorable also means losing competitiveness com-pared to the pre-exit situation, even if the firm does not perform well (Dierickx and Cool, 1989, O’Brien and Folta, 2009). For this reason, firms will stay in an inaction zone, hoping for better times. It can be mistaken with the sunk costs fallacy, but with our results and the difference in exports towards difficult destinations before and after the procedure is triggered (Table A.4.1), it seems that the incompleteness of information, and thus the range of possible outcomes, is important enough for those firms to stay in a supposedly more difficult and risky business. However, we the significant impact of the number of destination in t point towards an exit from the inaction zone to refocus the efforts on easier markets. This description seems to be in line with the first explanation of the positive relation between the default and export sunk costs: the inertia of export activity. However, when the firm is in de-fault, the manager does not make decisions anymore. An administrator nominated by the court now owns the decision power to save the company. The administrator needs to improve the firm’s situation as quickly as possible. For these reasons, it is logical to reduce the number of markets to which the firm exports in order to focus on the company’s historical export market, as shown in Appendix A.4. We observe a similar phenomenon for the amount of sunk costs after the triggering of the procedure (Figure 1.2 and Table A.5.1).
In Table 1.3, the signs and significance of our productivity index and the sunk costs linked to the export market and domestic market coefficients do not change compared to Table 1.2. We still find a positive correlation between firms’ default probability and their level of sunk costs and a negative correlation with their pro-ductivity. Therefore, the slight decrease in destinations when a firm is, or will be, in default, as seen in Section 1.5.1, does not seem to hold when we take into account multiple factors, such as productivity or sunk costs.However, only modeling the probability of default in the next 3 years do not allow us to really detect the existence of the inaction zone. To be sure that it is either the sunk cost fallacy, the real options model or a mix of them, we have to rely on the the probability of entering into a collective proceeding. The results displayed in Table 1.4 show that the results are mixed. At first, there is a significant and positive impact on the probability of defaulting the years before the entry into a procedure of the sunk costs linked to the export activity. In the year of the default, this effect is globally insignificant. These results point toward a sequential effect: i) at first firms invest more than their non-defaulting counterparts and are in trapped a sunk costs fallacy; ii) then the firm knowing it will become defaulting are cutting the losses, entering in an inaction zone. This result might reflect the will of the firm to not lose the investment made to establish themselves into the foreign market. But, by doing so, they keep having a consistently higher level of sunk costs linked to the export activity than the others, which rises the amount of illiquid assets they have. This, in turn, increases the likelihood that these companies will exit the market.


Decompositions and Standard Errors

Decompositions of productivity can be classified according to two basic specifi-cations with refinements. The first branch is the OP decomposition, with the aver-age productivity and a co-variance term of productivity and market share. MP use this static decomposition and convert it into a dynamic one, which allows assessing the contribution of entry and exit of firms. The other branch takes roots in the BHC decomposition, which proposed a decomposition of the productivity growth into four components: two for the incumbents (a within-effect term, a reallocation-effect term), and two others for the net entry (an entry term and an exit term). The decomposition of GR and FHK are refinements of the BHC one. While the first uses the average aggregate productivity between the two periods considered be-tween the two periods, the seconds use the average aggregate productivity at the beginning of the period considered. Moreover, the FHK decomposition introduces a covariance term. We present this decomposition below: Δ = ∑ Δ + ∑Δ ( − − )+ ∑Δ Δ (3.2) ∈ ∈ ∈.
Within effect Between effect Covariance + ∑ ( − − ) − ∑ , − ( , − − − ) ∈ ∈ Entry effect Exit effect Net entry effect Where is the average productivity in year t, is the productivity of the firm i in year t and is the weight of the firm i in the market at the year t. As a productivity measure, we use the total factor productivity in logarithm. C subset encompasses the continuing firms of the sample, i.e., firms that stay in the market from t-k to t, X the exiting firms, i.e., the firms in the market in t-k but not in t, and N the subsample of firms entering the market, and still performing on the market in t. The ”within” term represents the share of productivity resulting from the evolution of the continuing firms while performing in the market, namely the learning effect. The second term (between) modifies the aggregate productivity growth following a change in the market composition, while the third one (covariance) is an interac-tion term between productivity changes and size changes between the two periods. This term can be interpreted as a misallocation since it shows if the market and the productivity grow in the same direction. For example, a firm with an important dynamic of productivity enhancement should also be the one with a market share growing rapidly. However, if this term can be understood as part of the reallocation effect, it does not mean the most productive firms will have the biggest growth. Finally, the last terms encompass the contribution of both the entry and the exit. The entry part is positive when entering firms are more productive than the average aggregate productivity in t-k. Therefore, they should be more productive than the overall firms previously producing, including the exiting firms. The exiters’ con-tribution is the difference between their productivity in t-k, i.e., the last time we observe them, and the overall productivity at the same period. If the exiters have lower productivity than the average of the firms, then it contributes positively on the productivity growth. These last two terms are the Schumpeterian “cleansing effect” contribution to the evolution of aggregate productivity.

Exit term: usual definition vs. decomposition

In the results displayed in Table 3.3, we see that, there are a lot of heterogene-ity across periods and terms. By focusing first on the full 2006-2013 period for the whole French economy, we see that, for the incumbent firms the reallocation inside firms and the reallocation between firms bear opposite signs. The first one reflects the ability of firms to learn and progress over time, while the reallocation to con-tinuing firms encompass both between-effect and covariance terms. The learning term is negative, and the second one is positive, but is insufficient to compensate the poor performance of the learning effect.
Considering the net entry on the whole period, i.e. the addition of entry and exit, the contribution is negative, at -2.549 percentage points (pp thereafter) for the FHK decomposition and -1.745pp for the MP one. In both cases, this is mainly due to the effect of entering firms that do not perform as well as either the aver-age firms or the average incumbent in the market. But the exiting firms, if they contribute positively on the productivity growth, they do not have the same contri-bution according to the way they exit.
Defaulting firms contribute positively the reallocation of resources (1.320pp for FHK and 1.387pp for MP), while non-defaulting firms have a negative contribu-tion on productivity growth (-0.297pp and -0.144pp for FHK and MP respectively). Therefore, it seems that defaulting firms are, on average, firms that had to exit the market. By doing so, they help firms that are more efficient to access the produc-tion factors they should have (mis)used if they stayed in the market. In contrast, the fact that the other exiting firms seem to contribute negatively, on average, the productivity growth points toward the exit of firms that should not have left the market, but did anyway. This might be due to other form of exits, such as merger-and-acquisitions, that make well-performing firms disappear from the database. However, both signs and magnitude of the different effects differ across industries.
As shown in Table C.2.1, when we analyze the incumbents’ contributions in each sector, we see that the terms have globally opposite contribution on the real-location of resources. On the one hand, for the learning effect, we see that, if the majority of sectors have negative values for this term, in food products, beverages and tobacco industries, information and communication industries, financial activ-ities and insurance industries and especially in the wood and paper industries, the learning effect on productivity growth is positive. In the wood and paper industries it is even the effect that drives the productivity growth in this sector. On the other hand, the reallocation between incumbents contributes almost always positively to-wards productivity growth. Only financial activities and insurance industries have a negative contribution of reallocation between incumbent firms. Nonetheless, the magnitude of this term is mainly low, thus it does not drive the reallocation in the different sectors, with the notable exception of electric, electronics, and informatics products industries.
After taking into account the role of incumbent, we can see the contribution of the creative-destruction process through the effect of both entering and exiting firms from the market. Considering the first category, we see that, overall, the firms that are entering into the market seem to be less efficient than the average firms in the market at the end of the period. The fact that only two sectors have positive contribution of their entering firms over the period (namely wood and paper industries and real estate activities) points toward a deficit of performances for entering companies in almost all sectors in the economy. The other side of the creative-destruction process, the exits of firms, have an inverse conclusion. Apart from the legal, accounting, management architectural, engineering, control and technical analysis activities, the exit of the firms allows the industries to reallocate their resources towards better-suited firms. When entering into further details of the exit, we see that defaulting firms’ contribution on productivity growth is always positive, even if the magnitudes are not especially large.
The results are more mixed concerning the other exiting firms’ contributions. It can either be positive or negative. In some cases it can even drives the exit terms value. The only sector contributing negatively to the overall exit term also has the highest value, in absolute terms, and is negative. Therefore, it outweighs the pos-itive contribution of the defaulting firms’ exits. Then, we clearly see a distinction between the contributions of the two types of exits. In one case we have evidence that, on average, the defaulting firms exiting the market are less performing than the average firms in their market. In the other case, the results are more hetero-geneous. If the contribution of exiting firms on resource reallocations can be both large and positive, it can also be negative. In this latter case, firms that do not suffer from a lesser competitiveness exit the market. If the decomposition of productivity growth at the sectoral level is informative, the period might be too important and encompass different realities. Indeed, prior to 2008’s economic crisis, both economy and productivity growth where hindered. For these reason, we divide the time span in two periods: a first one from 2006 to 2009, and a second one between 2010 and 2013. The first time period en-compasses the transition between the periods prior to the economic crisis to the beginning of it, while the second one cover the period post crisis. The results are displayed in Table 3.3 for all sectors and Tables C.2.2 and C.2.3 for a sectoral-level decomposition.
The main difference between the two periods is the magnitude of the incum-bents’ terms, both learning and reallocation ones. In the 2006-2009 period, the overall average effect of the productivity growth’s learning component is at -23.766pp and the reallocation is at 28.566pp for FHK and -24.259pp and 29.548pp, respec-tively, for MP. From 2010 to 2013, the learning term is still negative and the reallo-cation one is still positive but the magnitudes of both terms for each decomposition dropped drastically.

Table of contents :

1 Why would exporters in difficulty not exit? 
1.1 Introduction
1.2 Literature review
1.3 The probit model
1.4 Export sunk costs: an identification using propensity score matching
1.5 Results
1.6 Conclusion
2 R&D expenditures and firm survival 
2.1 Introduction
2.2 Relationship between R&D expenditure and survival
2.3 Empirical strategy
2.4 Results
2.5 Conclusion
3 Productivity growth and resource (mis)allocation in France: New insights from bankruptcy and inference 
3.1 Introduction
3.2 Literature review
3.3 Empirical strategy
3.4 Results
3.5 Conclusion
General Conclusion
Appendix A Appendix for Chapter 1 
A.1 Legal procedures
A.2 Total factor productivity
A.3 Distribution of firms according to productivity
A.4 Export behavior according to the firm’s default status
A.5 Sunk costs per category and industry
A.6 Propensity score matching
Appendix B Appendix for Chapter 2 
B.1 Total factor productivity
B.2 Panel Fixed-effect estimation of TFP
B.3 Average amount invested in BERD
B.4 Turning points with TFP cross-term
B.5 Statistics by sectors
Appendix C Appendix for Chapter 3 
C.1 Production function
C.2 Sectoral decomposition
C.3 Sectoral decompositions with bootstrap . .


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