Credit Shocks, Employment Protection, and Growth: Firm-Level Evidence from Spain

We offer new evidence on the real effects of credit shocks in the presence of employment protection regulations by exploiting a unique provision in Spanish labor laws: dismissal rules are less stringent for Spanish firms with fewer than 50 employees, lowering the cost of hiring new workers. Using a new dataset, we find that during the financial crisis, healthy firms with fewer than 50 employees borrowing from troubled banks grew faster in sectors where capital and labor were sufficiently substitutable. This result does not obtain when we use a different cut-off for Spain or the same cut-off for firms in Germany. Our evidence suggests that labor market flexibility can dampen the negative effect of credit shocks by allowing firms to keep growing by substituting labor for capital.


Introduction
Flexible labor market institutions are a standard fixture in neoclassical economic theory.
They are often credited with delivering large economic benefits to liberalizing countries, such as the UK in 1989, Italy in 1997-2003, or Germany in the early 2000s (Boeri, 2011;Dustmann et al., 2014). Conversely, high employment protection is often seen as one reason why economies lose their ability to adapt to negative shocks (Blanchard and Portugal, 2001; Alesina and Giavazzi, 2006). 1 While empirical evidence to the success of labor market reforms abounds, it mostly focuses on the up phase of the cycle (e.g., Engellandt and Riphahn, 2005;Ichino and Riphahn, 2005;Autor et al., 2007). This approach is consistent with Haltiwanger's (1990, 1992) seminal work on the importance of labor reallocation for growth and macroeconomic fluctuations. At the same time, there are equally good arguments to expect that flexible labor markets will deliver large benefits to a country's economy during downturns, by facilitating the process of "creative destruction" (Caballero and Hammour, 1994) and by allowing otherwise healthy credit constrained firms to keep growing. Yet, to our knowledge, there is little evidence on the firm-level benefits of labor market flexibility during recesions.
We go to the heart of this question by studying the impact of employment protection on firms' ability to absorb large negative credit shocks during the Spanish credit crisis of 2008-09. We do so by constructing a new dataset that merges two data sources, the firm-level Amadeus database and the Kompass database of bank-firm relationships. The final dataset contains around 140,000 Spanish firms with full balance sheet information, observed both before and after the crisis, and it covers the full size distribution of firms, from 1 employee to over 1,000 employees.
Our identification strategy has three crucial ingredients. First, labor regulation in Spain is characterized by a well-defined distortion whereby dismissal rules vary by firm size.
Specifically, according to Spanish law, employment protection is notably more stringent for firms with more than 50 employees, greatly increasing firing costs. 2 In turn, firing costs can be seen as a fixed per-employee cost impeding firm growth by reducing firms' incentives 1 For excellent early reviews of the role played by differences in the level of employment protection, unemployment benefit systems, payroll taxes and subsidies on labor, as well as wage setting institutions, in explaining the higher level and duration of unemployment in Europe vis-a-vis the US, see Bean (1994), Nickell (1997), Bertola (1999), Blanchard (2006). 2 Spain has for long been an outlier in labor market protection, especially firing costs. This is often thought to have contributed to its structurally high unemployment (see, e.g., Bover et al., 2000). to hire new workers (Bentolila and Bertola, 1990). Second, the credit crunch of 2008-09 constitutes a well-defined shock to firms' borrowing costs. Spanish banks were unequally affected by the crisis, and some required large recapitalizations, of the overall order of 1.1% of GDP. While during the crisis the supply of credit declined across the board, new credit issued by affected savings banks declined significantly more than new credit issued by nonaffected banks. 3 Firms borrowing from affected banks thus experienced a larger increase in the rental cost of capital, giving them an incentive to substitute labor for capital. The combination of these two factors gives rise to a well-defined empirical mechanism: all else equal, firms with fewer than 50 workers should have grown faster than firms with more than 50 workers after the start of the financial crisis in Spain, because lower firing costs allowed them to keep growing by hiring more workers, thus making up for the decline in capital use.
At the same time, there is plenty of evidence that small firms face stiffer credit constraints during a credit crunch, for reasons related to their higher credit risk and information opacity (e.g., Haltiwanger et al., 2013). This could also be true for firms borrowing from the same bank, as well as over an arbitrarily narrow window around the 50-employee cut-off, as long as risk and opacity increase monotonically with firm size. As a result, this "credit-constraints" effect could eclipse the "employment-protection" effect for small firms, leading the econometrician to erroneously fail to reject the hypothesis that employment protection does not matter. Therefore, we add a third ingredient to our identification strategy whereby we distinguish across firms depending on their technological ability to substitute labor for capital. For firms whose elasticity of substitution between labor and capital is low, an increase in the user cost of capital will lead to a decline in employment, too. Therefore, in the class of firms with fewer than 50 employees, the "credit-constraints" effect will dominate the "employment-protection" effect. However, for firms whose elasticity of factor substitution is high (i.e., relative to the median across sectors) , an increase in the user cost will result in an increase in employment as firms substitute labor for capital, allowing us to identify the "employment-protection" effect. Our empirical hypothesis then is that (otherwise healthy) credit constrained firms that benefit from firm-size-specific employment protection will grow faster than credit constrained firms subject to stricter employment protection, as long as their elasticity of substitution between labor and capital 3 For recent evidence, see Bentolila et al. (2018). is large enough. 4 We focus on sales growth as a measure of firm performance, but we also examine employment growth as the main transmission channel.
Our methodological approach rests on a number of conditions. First, bank-borrower relationships need to be sticky over the cycle, a fact that has already been established in the literature in various contexts, such as the US (e.g., Chodorow-Reich, 2014), andimportantly for our paper-Spain (Bentolila et al., 2018). Second, the cross-sectional variation in banks' willingness to lend during the crisis needs to be orthogonal to firm characteristics and to pre-crisis labor market trends. The advantage of focusing on bank-specific credit supply shocks is that they are unlikely to be related to both individual borrowers' conditions and to pre-crisis labor market conditions. Third, the measure of capital-labor substitution should not be picking up variation in the demand for finance. To make sure that we have abstracted from this channel, we calculate industry-specific elasticities of substitution using US data, and we also control for the financial dependence of the firm.
Our main finding is that Spanish firms with fewer than 50 employees grew relatively faster during the financial crisis when exposed to a negative credit shock than similarly credit constrained, but larger firms in sectors with a technologically higher substitutability between labor and capital. This result is robust to controlling for time-varying firm-specific factors that can affect firm growth in the absence of credit shocks or firm-size-specific labor regulation, such as cash flows and net worth. It is also robust to controlling throughout for unobservable firm heterogeneity with firm fixed effects, and for unobservable sectorspecific trends with interactions of sector and year dummies. The main effect still obtains when we compare smaller and larger firms that are closer to the 50-employee threshold; when we control for other underlying industry characteristics, such as dependence on external finance; when we look at firms with a credit relationship with only one bank; and when we drop all firms in Construction, a sector where some of the problems of the Spanish banks originated. Crucially, the effect still obtains when we control for the potentially confounding effects of firm size and of firm quality, as well as when we control for unobservable shocks to local demand with region×sector×time fixed effects. We also find that firms subject to less stringent employment protection in sectors with high substitutability between labor and capital experience higher rates of employment growth, while their investment growth exhibits a similar trend as investment growth at firms subject to stricter 4 A higher value of substitution thus denotes a higher degree of flexibility with which labor can be adjusted to absorb shocks (an argument that goes back to Hicks (1932)). employment protection. Finally, the main effect is much more pronounced for firms with higher sales growth before the crisis started. The totality of our results suggests that lax employment protection benefits (especially healthy) firms faced with an exogenous shock to their user cost of capital, by enabling them to substitute labor for capital and continue growing.
We also perform three separate falsification tests of the underlying credit and labor market mechanisms. First, we repeat the main test on the same sample of firms, but in the absence of a credit shock (i.e., before the financial crisis). Second, we compare how sales growth adjusts to credit shocks, depending on the firm's elasticity of substitution between labor and capital, for firms smaller and larger than another arbitrary firm-size threshold that does not capture a firm-size-specific employment protection rule. Third, we compare sales growth across the 50-worker threshold, for credit-constrained versus unconstrained firms and depending on their elasticity of factor substitution, in Germany where employment protection is not different for firms with fewer and with more than 50 workers. In all three cases, the main effect goes away, suggesting that we are indeed capturing a genuine interaction of credit shocks and labor regulation in determining firm growth.  Kluve and Schmidt, 2002;Black et al., 2003). More closely related are papers that have studied the impact of employment protection laws on firm demand for labor. For example, Bentolila and Bertola (1990) argue that high firing costs can help explain the dynamic behavior of European employment, including the persistence of unemployment, in the 1970s and 1980s. 5 We make two contributions to the literature relative to the 5 Boeri and Jimeno (2005) study the effects of employment protection on dismissal probabilities and on the equilibrium size distribution of firms. They find that workers under permanent contracts in firms with less restrictive employment protection are more likely to be dismissed, while at the same time there is no effect of the exemption threshold on the growth of firms. Garibaldi and Violante (2005) study empirically the two separate dimensions of firing costs-the transfer from the firm to the laid-off worker, and the tax paid outside the firm-worker pair-and show that they do not have the same effect in the presence of wage rigidities. Messina and Valanti (2007) use firm level data of manufacturing and non-manufacturing industries to study the impact of firing restrictions on job flow dynamics across 14 European countries, and find that more stringent firing laws make job turnover less counter-cyclical. Marinescu (2009) uses a 1999 British reform that increased job security for workers with 1-2 years of tenure, and finds that the firing hazard for these workers decreased by 26% relative to the hazard for workers with 2-4 years of tenure. Schivardi and Torrini (2008) and Cingano et al. (2016) exploit a firm-size cut-off to identify the effects of employment protection in Italy where firing cited papers. First, we study the interaction between employment protection and credit constraints on firm growth, whereby we take advantage of the firm's technological ability to substitute labor for capital when relative factor prices change. Second, we study the benefits of employment protection during a financial crisis when some firms with healthy growth prospects are held back by worsening credit market frictions.
More generally, our paper contributes to the literature on the real effect of financial frictions, and specifically their effects on firm employment. Much of this literature has focused on the impact of negative shocks to the firm's borrowing capacity on its demand for labor. Some studies have relied on indirect measures of credit constraints such as firm size or debt to identify the effect of monetary policy and the business cycle on employment (e.g., Sharpe, 1994;Nickell and Nicolitsas, 1999). Lichtenberg and Siegel (1990) provide evidence that a leveraged buyout is followed by a reduction in employment and wages. Hanka (1998) shows that highly levered firms reduce employment more often and pay lower wages. Falato and Liang (2016) show that loan covenant violations are followed by simultaneous cuts in employment and wages. Most recent studies have attempted to gauge the effect of shocks to external finance on employment using more direct measures.
For example, Benmelech et al. (2011) find that following the large decline in real estate values in Japan, unemployment increased by about 1% in U.S. metropolitan state areas dominated by Japanese-affiliates banks. 6 In addition, several recent studies have used micro data to estimate the response of employment to credit constraints. For example, Campello et al. (2010) show that firms with credit constraints plan to cut investment and employment more than unconstrained firms. While Chodorow-Reich (2014) uses syndicated loan data to show that small firms that before the crisis were borrowing from banks that subsequently became impaired, reduced employment more than small firms associated with healthier banks. 7 Our contribution is to show how credit constraints interact with employrestrictions are more stringent for firms with more than 15 employees. 6 Greenstone and Mas (2012) show that the predicted decline in small business lending at the regional US level maps into lower rates of new business formation and higher unemployment. Boeri et al. (2012) shows that more leveraged sectors exhibit higher employment-to-output elasticities during banking crises. Pagano and Pica (2012) show that during banking crises, employment grows less in industries more dependent on external finance. 7 Acharya et al. (2014) find that large firms with higher exposure to syndicated lending by European periphery banks experienced lower growth of employment, sales, and capital expenditures. Duygan-Bump et al. (2015) find that during recessions, workers in small firms are more likely to become unemployed in industries with high external financial needs. Bentolila et al. (2017) show that Spanish firms with credit relationships with weak banks reduced employment substantially more than firms borrowing from non-affected banks. Popov and Rocholl (2017) show that German firms borrowing from savings banks that during 2007-2008 had to provide funds for the recapitalization of their head institutions reduced employment and average wages, both in ment protection to determine the firm's choise of inputs of production, and ultimately, its growth.
The remainder of the paper is organized as follows. Section 2 discusses the institutional details with respect to labor regulation and the impact of the financial crisis in Spain. Section 3 details the calculations of the industry-specific elasticity of substitution between labor and capital. Section 4 describes the data. Section 5 presents the empirical methodology and identification strategy. Section 6 provides the main test, alongside an exhaustive battery of falsification and robustness tests, and we investigate the mechanisms involved. Section 7 concludes.

Employment protection in Spain
The Spanish labor legislation at the time of the financial crisis included two dismissal rules which by default affected firms differently depending on their size. The first one applied to negotiation between the employer and workers' representatives. According to this regulation, if a collective dismissal is going to be carried out, workers' representatives or ad hoc designated workers' representatives are entitled to negotiate the collective redundancy process. Therefore, the employer needs to first apply for authorization and open a period of consultation with the representatives of the workers. The period of required consultation is 15 days in enterprises of less than 50 workers, but 30 days in enterprises with more than 50 workers. During negotiations with the workers' representatives, the employer must consider alternative measures to reduce the number of terminations, and agree on the selection criteria. As in the case of individual redundancy, the severance pay is set at 20 days of salary per year of service (capped at 12 months' pay). However, oftentimes during the negotiations with the workers' representatives, severance per employee is increased.
In addition, in enterprises with more than 50 employees, a collective dismissal should be accompanied by a social plan aiming to mitigate the consequences for the affected workers. Such firms carrying out a collective dismissal should offer the affected employees an external replacement plan through the authorized employment agencies. This plan, designed for a minimum period of 6 months should include: the short and in the medium term.
-measures intended to avoid or reduce the effects of restructuring, for instance, internal redeployment, functional or geographical mobility, or a substantial modifications of contractual conditions; -measures aimed at reducing the effects of restructuring on employees; -external relocation; -promotion of self-employment; -financial compensations for geographical mobility; -economic, technical, organizational and other types of measures intended to make the continuation of the undertaking and its activity possible.
Companies also have to carry out a special training and redeployment plan of at least 6 months, implemented by means of an authorized outplacement company, if the collective dismissal affects over 50 employees. The cost of carrying out this plan is borne by the firm, and not by the workers. Non-compliance with this obligation could result in a legal claim for its compliance by the workers. Importantly, companies with fewer than 50 workers do not have to implement a social plan aiming to support dismissed workers.
The longer negotiating period and the need to provide workers with a social plan makes it considerably more costly for firms with more than 50 employees to dismiss workers. As a consequence, the cost of hiring the marginal worker, given that she may have to be let go in the future, is higher for such firms. It is therefore plausible to hypothesize that firms with fewer than 50 employees will be more inclined to hire more workers if they need to expand. This logic goes back to studies such as Bentolila and Bertola (1990) who argue that employment protection laws -in their view, the main source of firing costs in Europehave a significant effect on firms' propensity to fire, as well as to hire.
One immediate concern is that this type of regulation may be too weak to present a binding constraint on firms' expansion. Figure   During this period, savings banks were forced to transform into commercial banks, and the European Financial Stability Facility provided financial assistance for the recapitalization of a number of banks. Overall, a total of 71 banks were subject to some kind of intervention (see also appendix Table C.1). For the purpose of the analysis, we classify as "affected" all firms that in 2008 had a credit relationship with a bank that was subject to government intervention at any point during the financial crisis.
It is important to note that during the crisis, banks became troubled for reasons that are not related to their credit relationship with a particular firm or a segment of the Spanish corporate landscape. In many cases, inefficient supervision exacerbated problems that could have been dealt with earlier and more forcefully. Savings banks in particular were subject to the same regulation and supervision by the Bank of Spain as commercial banks, however, they had a very different ownership and governance structure. Because they were not listed on the stock market, savings banks were less exposed to market discipline than commercial banks, while at the same time their ability to raise capital in response to the crisis was more limited. Moreover, they were de facto controlled by regional governments, which introduced a number of political inefficiencies in their operation and led to delays in their restructuring. 8 As a result of balance sheet problems, new credit issued by affected savings banks de- substantially higher average interest rates than healthy banks (see Bentolila et al., 2018).
Splitting banks into affected and non-affected based on clear criteria allows us to analyze the overall impact of the initial balance sheet shock, including latent losses not officially recognized until much later. While the Spanish banking sector as a whole reduced lending during the crisis, to a large degree because of a drop in credit demand, an "affected" bank is one with a relatively stronger deterioration in its balance sheet and lending capacity, affecting firm growth through the channel of reduced credit access.

Estimation of the sectoral capital-labor elasticities
A key parameter in our analysis is firms' factor substitution possibilities: how easy it is to shift ("substitute") between factors (typically, capital K and labor L) is captured by the elasticity of factor substitution. This provides a powerful tool for answering analytical questions about the distribution of income and the response of the economy to various shocks.
To illustrate, for production function Y = F (K, L) the elasticity is given by the formula . In other words, it is the percentage change in factor proportions due to a unit change in the marginal rate of technical substitution (MRTS) (along a given isoquant). Under the assumption that the marginal productivities (F K , F L ) reflect factor prices, the MRTS would match up with the wage/capital rental ratio.
Accordingly, if there is a 'shock' to relative factor prices (i.e., one factor becomes more expensive compared to another), then optimizing firms respond by changing their factor intensity. The extent to which they can do so is captured by 'σ'. To illustrate, increasing the minimum wage in sectors in which the substitution elasticity is 'high' (say above unity) would, ceteris paribus, contract labor demand since the representative firm could shift into (now relatively cheaper) capital inputs. Likewise, and more relevant in our context, a firm which faced higher or more variable capital costs, may react by increasing its demand for labor (to the extent allowed by its substitution elasticity, and prevailing regulations).
Following León-Ledesma et al. (2010) we estimate sectoral production characteristics using a normalized system of equations containing the production function and factor demands with cross-equation parameter constraints. The full details are relegated to A of the appendix but the general principles are straightforward to motivate. Consider that real output Y for a given sector can be described by a Constant Elasticity of Substitution (CES) production function (suppressing time subscripts for notational convenience), where π ∈ (0, 1) is a distribution parameter that determines the relative importance of factors in the production of the final good, and terms a and b capture the level of technical progress associated to the capital and labor, respectively. 9 The CES function is attractive since it flexibly nests other well-known production types. 10 In the Leontief case (σ → 0), substitution between factors is not possible: capital and labor must always be used in fixed proportions. In the linear case (σ → ∞), substitution is such that factors are essentially indistinguishable from one another. Cobb Douglas (σ → 1) is an intermediate case. Figures 2 and 3 illustrate the mechanism. For firms which cannot substitute labor for capital, an increase in the user cost of capital results in a decline in both factors of production ( Figure 2). However, for firms with a high(er) elasticity of substitution, an increase in the user cost of capital can result in an increase in employment (Figure 3), as firms substitute labor for capital, with overall output declining less than in the Leontief case.

Firm-level data from ORBIS
Our firm-level data come from the ORBIS dataset provided by Bureau van Dijk (BvD). OR-BIS contains financial and ownership data for more than 170 million firms from more than 100 countries world-wide. Financial data include balance sheet information and income statements, while ownership data contains information about the company's ultimate owner and shareholders. The database has been compiled since 2004 by BvD and is currently updated quarterly. Every vintage contains a history of up to ten years of financial 9 Note that capturing technical progress is a by product of the CES function estimation. However the Monte Carlo study of León-Ledesma et al. (2010) demonstrated that production-function estimation without allowing for technical progress substantially biases the estimation of the substitution elasticity. 10 An additional advantage of the CES function is that by allowing for an unconstrained elasticity of substitution, it facilitates a better fit to the data. For instance a well-known property of the unitary-elasticity Cobb-Douglas production function is that factor income shares are constant, given that movements in factor prices are exactly offset by commensurate movements in factor volumes. However, for most of the sectors in our database this is strongly counterfactual, and indeed we always statistically reject the Cobb-Douglas case in our estimations at 1% or less. information for an individual firm. In addition to this product, BvD offers to link the latest vintage with historical vintages going back to 2004. The analysis in this paper is based on the vintage as of the second quarter of 2004 linked with all historical files available from BvD.
A common case in ORBIS is that financial information for a given firm and year is updated from one vintage to the next. When constructing the historical files, special care is taken to put the latest available information for any given year and company. The resulting dataset contains many more firm-year observations than are available in the latest vintage. This is because there are more years of data for many firms. In addition, there are about 30 percent more companies in the historical files compared to the latest vintage. The reason is that BvD deletes companies that do not report for a certain period from each vintage.
Such companies are nevertheless included in the linked historical files thereby reducing the survival bias that is present in a single vintage. This is crucial because any empirical estimates would be biased if the least productive firms in a country during a particular year are ultimately removed from the data. At this stage the dataset contains about 100 million firm-year observations, but about a quarter of those relate to firms that have not provided financial information in any given year.
For our analysis, we take Spanish companies with financial data in the period 2004-2013 and we work with unconsolidated accounts. We first make sure that firms' balance sheet items pass a standard consistency test, after which inconsistent firm-year observations are dropped. Our consistency checks make sure that balance-sheet identities hold within a small margin and entries are meaningful from an accounting point of view. Following Kalemli-Özcan et al. (2015), we drop firm-year observations in which total assets, fixed assets, intangible assets, sales, long-term debt, loans, creditors, other current liabilities or total shareholder funds and liabilities that have negative values.
Next, we drop firm-year observations for which some basic accounting identities are violated by more than 10%. 11 We also drop country-specific sectors, such as agriculture and mining; sectors with high government ownership, such as public administration; and heavily regulated sectors, such as finance. year observations if there are less than 10 firms in each NACE Rev. 2 digit 4 sector. In addition, we remove firm-year observations that have loans or long-term debt exceeding total liabilities. Then we drop all firms for which we do not have at least 5 years of consecutive non-missing observations of sales. This leaves us with a total of 231,843 unique firms, for a total of 1,849,170 observations. Finally, we focus on those firms that are observed at least once before and at least once after the beginning of the financial crisis in 2007. This is done for the purpose of comparing firms that experienced a tightening of credit constraints after the crisis started to those that did not, and studying the extent to which such tightening translates into a decline in firm growth, based on the firm's size and sector of operation.
This reduces the sample to 135,799 unique firms, for a total of 1,351,331 observations.
In terms of firm-specific information that we use in the regressions, we make use of a wide range of variables which we summarize in Table 1. The main dependent variable in the paper is 'Sales growth' which denotes the log difference in the firm's total sales between this period and the previous one. On average, firms over the sample period posted a year-on-year decline in sales of about 3.2 percent, which is consistent with the overall performance of the Spanish economy which posted negative GDP growth for five years in a row between 2009 and 2013. The median firms experienced an even larger decline in sales (3.6 percent), suggesting a negatively skewed distribution of sales growth. Looking at the growth of inputs in production, we also note that employment declined considerably less during the same period, on average by 0.7 percent year on year, with the median firm neither growing nor declining. At the same time, firm-level capital investment declined on average by 5.2 percent year-on-year, with the median firm posting an even larger decline (6.7 percent). This is the first indication in the raw data that the financial crisis had a more significant impact on capital than on labor. All growth variables are winsorized at -100 percent and at 100 percent.
We then use the employment data to construct the main explanatory firm-level variable which is a dummy variable equal to 1 if the firm has fewer than 50 employees. This definition is based on a piece of regulation which makes it considerably easier for smaller firms to fire employees, making it less costly for them to expand their labor force. Comparing firms below and above this threshold is a direct test of the hypothesis that firms can cush-ion the impact of a credit shock on production by substituting labor for capital, but only if labor rules do not penalize them for hiring workers. In order to make sure that we are not simply picking a small firm vs. large firm effect that has to do with differences in technology or opportunities, and not with labor regulation, we create other cut-offs, for example, a dummy equal to one if the firm has fewer than 10 employees. As Table 1 demonstrates, the firms in our dataset are on average very small, with 89.4 percent having fewer than 50, and 43.5 percent fewer than 10, employees. We also employ a set of standard controls for size and net worth. They take the logarithm of total sales and the logarithm of total assets, as well as the ratio of cash flow to total assets and of net worth to total assets.

Firm-bank shock
One of the main blocks of our identification strategy is trying to compare firms across size bins and sectors in terms of whether they are credit constrained or not. While the Spanish banking sector as a whole experienced a large negative shock during the crisis, mostly deriving from its exposure to the country's pre-crisis housing boom, there were large differences across banks in pre-crisis exposure and within-crisis performance. We exploit this margin by making use of a variable called 'BANKER', available from Orbis through Kompass, which displays the name of the bank(s) with which the firm has a relationship. Each firm reports up to 10 credit institutions with which it has a relationship. We then match these bank names with a publicly available list-provided by the Bank of Spain-of all banks which during the financial crisis were subject to government intervention in the form of a liquidity injection, recapitalization, or a take over. 12 The firms in the final dataset report a credit link to a total of 1,506 different credit institutions. Out of these, 71 were subject to a government intervention during the crisis, and hence are classified by us as affected. Consequently, we create a dummy variable 'Shock' which is equal to one after 2007 for all firms with a credit relationship with at least one affected bank. 13 Table 1 reports the percentage of firms in our sample that are associated with one or with multiple banks. On average, 51 percent of firms in the final dataset have a credit association with at least one affected bank, translating into 26 percent of all observations. Of course, having a credit association with an affected bank is less of an issue for firms with multiple banking relationships. For this reason, in robustness tests we look at firms attached to a single bank only. In the case of these, the variable Shock is equal to one in 18.9 percent of all cases (corresponding to 40.3 percent of all such firms). We estimate the technological elasticity of substitution between labor and capital by using data on the US. An argument going back to Rajan and Zingales' (1998) seminal work states that the production and factor choices of firms will be least distorted by credit constraints in an economy that is backed by highly developed and liquid financial markets.

Elasticity of substitution between labor and capital
Moreover, the US has one of the most flexible set of labor regulations in the OECD, suggesting that factor adjustment in response to changes in factor prices will not be distorted by labor market rigidities. 14 Therefore, backing out sector-level elasticities of substitution between labor and capital for US sectors should produce a reasonable empirical proxy for the sectors' "natural" elasticities of substitution. However, even putting aside this argument, estimating sectoral elasticity for Spain faces data limitations. 15 There are two vintages of the US KLEMs database, one from 1947-2010, the other from 1970-2007. 16 In this application, we rely on the more popular longer dataset. However, for robustness we also consider the shorter variant which ends just prior to the financial crisis. Although they follow the same classification, the two databases represent different 14 See http://www.oecd.org/els/emp/oecdindicatorsofemploymentprotection.htm. 15 For example in the case of KLEM's sectoral data for Spain, their "Capital services, volume indices" and "Labor services, volume indices" only start in 1995. The sectoral Value Added series starts in 1970 (although there are back-casted (from 1995) estimates based on the 2012 EU KLEMS release (ISIC Rev.4/ESA 95)). vintages of the underlying BEA data and some slightly different statistical methods. Generally, though, we find that both datasets give qualitatively similar values for the sectoral elasticity values. Table 2 shows that the elasticity of substitution values across the selected sectors. They range from 0.36 (Coke subsector) to 1.96 (Construction), with a (unweighted) across-industry median of 0.85. In all but four cases, the elasticity is below unity. Moreover, although there is an elasticity value relatively close to unity in four other cases (e.g., σ = 0.9 in Textiles, textile, leather, and footwear, see appendix table B.1), we conclude that in no case can a unitary elasticity not be rejected. Given the prevalence of below-unity results, there are many sectors which are (compared, say, to the Cobb-Douglas benchmark) constrained in their ability to substitute factors for one another in the face of economic shocks or changes to relative factors prices.

Empirical methodology and identification
Our identification strategy is based on three separate arguments. The first argument is that a firm's sales growth will be negatively affected if it experiences a negative credit shock that raises the cost of renting capital. Such a shock can materialize when, for example, the firm's creditor is experiencing balance sheet problems and needs to cut lending. The second argument is that a firm's decline in sales following a credit shock will be less pronounced if its production function exhibits a high elasticity of substitution between capital and labor.
In this case, a firm can substitute relatively cheaper labor for capital, maintaining similar levels of output. This would not be possible with a Leontief production function where firms need to employ capital and labor in fixed proportions. The third argument is that this mechanism is more likely to be activated if the cost of hiring is low. This will be the case when, for example, labor regulation does not impose strong restrictions on firing, making it easier for firms to expand their employment base if they need to.
Our estimand of interest is the average treatment effect of a credit shock on firms' growth, as well as on their employment and investment decisions. We exploit both the discontinuity in employment protection at the 50-employee threshold and the credit shock in 2008, to build a regression-discontinuity design combined with a difference-in-differences strategy to estimate the causal effect of the credit shock in the presence of firm-specific employment protection on various firm-level outcomes. The assumption required to interpret the effect of firm-specific employment protection as causal is that any other variable that affects firm growth is either continuous at the threshold or its discontinuity is constant over time. In this case, the average trend of sales among firms marginally above the 50-employee threshold represents a good counterfactual for the trend of those just below the threshold.
We model the sales growth of firm f in sector s in year t using the following regression: 17 The main dependent variable, ∆Sales f st denotes the change in the total sales of firm f in sector s between year t − 1 and year t. We calculate the variable as a log difference, but our results are robust to constructing the variable as a percentage change instead.
We now turn to the main explanatory variables. Shock f t is a dummy variable equal to one if firm f is borrowing from a bank that was affected during the financial crisis and later required government assistance. For firms linked to an affected bank, the dummy variable becomes one in 2008. While the majority of firms in the dataset are single-bank firms, more than a third of firms report a credit relationship with more than one bank. In the latter case, Shock f t is equal to 1 after 2008 as long as the firm has a credit relationship with at least one affected bank. The variable < 50 employees f is a dummy equal to one if the firm has fewer than 50 employees. This definition is based on the regulatory cut-off discussed in Section 4, whereby firms with fewer than 50 employees face substantially lower firing restrictions. In falsification tests, we move the firm-size cut-off around to test for whether we are not capturing a spurious difference between small and large firms rather than a true discontinuity effect.
Next, σ s is the estimated industry-specific elasticity of substitution between capital and labor whose construction we detailed in Section 3. Its inclusion in the model is crucial because it allows us to identify industries where firms can plausibly adjust the production process across inputs, in response to changes in relative prices, and sectors where firms are technologically unable to do so, therefore they keep employing production inputs in fixed 17 With the advance of micro-level datasets, triple interactions (as here) have become increasingly common in economics and finance literatures -see for instance Antràs  proportions before and after input price shocks. This technological benchmark is different from the ratio of capital to labor, which at each point in time is an equilibrium outcome of shocks to input prices. σ s thus allows us to identify firms' growth response to changes in the cost of capital for one segment of firms (with 'high' capital-labor elasticity) compared to another segment of firms (with lower capital-labor elasticities).
In addition to these three variables and the interactions thereof, we include a set of controls to make sure that we are isolating an effect that is driven by the interplay of a credit shock, firm-size-specific labor regulation, and the firm's technology. For one, we include a vector of time-varying firm-specific variables X f t . For a start, it contains a polynomial of third degree in firm employment. Given this, all effects can be read as holding labor constant. X f t also includes the logarithm of the firm's sales, the ratio of the firm's cash flow to assets, and the ratio of the firm's net worth to assets. These variables capture the firm-specific impact on growth of size, cash flow from operations, and agency problems.
By including them in the regression, we control for the possibility that firms just above and just below the 50-employee threshold may differ across other dimensions that can have an impact on firm growth. All variables are lagged 1-period. Second, we include a vector of firm fixed effects µ f . This allows us to net out the independent effect of firm-specific characteristics potentially unobservable to the econometrician, such as the propensity to take risk or managerial quality, that might be fixed over the short-to-medium term and that might explain a large share of the cross-sectional variation in firm growth. We also include a matrix of sector-year fixed effects θ st . These are crucial as they wash out any variation in the firm growth that is common to all firms in the same sector at the same point in time (e.g., shock to the demand for residential property). 18 In later robustness tests, we control even more tightly for shocks to local demand by including region×sector×year fixed effects that should wash out all unobservable variation common to firms operating in the same narrowly defined geographic area and in the same sector during the same year. We specify two-way clustered standard errors at the sector and year level (Petersen, 2009). Finally, we estimate model (2) using OLS. 19 18 Note that we cannot estimate the direct effect of the interaction variable 50 employees f × σs because it is subsumed in the fixed effects. 19 In estimation, we use cluster robust standard errors. Since we introduce σs from a separate regression, we examined the robustness of our results to bootstrap procedures. For a standard bootstrap, there were no change in the inference of the parameters in the table. Since we have two fixed effects in our case, however, the wild bootstrap breaks down. We thank Dimitris Georgarakos and David Roodman for discussion on these issues.
The contribution of this paper is the analysis of the growth of firms experiencing a shock to their credit access by firm size and elasticity of substitution between labor and capital (or sigma). By specifying a firm-size threshold at 50 employees, we are not comparing small to large firms, but rather exploiting, in a regression discontinuity sense, a firm-size-specific labor regulation. Thus, the coefficient of interest is β 1 . It captures the difference in sales growth between a firm attached to an affected and a firm attached to a healthy bank, depending on size and industry. A positive coefficient β 1 would imply that a firm with fewer than 50 employees borrowing from an affected bank is experiencing a smaller decline in sales growth if it is in a high-sigma sector. The economic interpretation in this case would be that in sectors where firms can substitute across inputs in production, flexible labor market rules act to counter the negative impact of credit shocks.
Distinguishing across firms' technological ability to substitute between factors of production is crucial for identification. Balance sheet shocks lead banks to reduce credit to their borrowers, and a large literature has argued that smaller firms are affected more forcefully by this process as their investment projects are more opaque and uncertain (e.g., Berger and Udell, 1995). This firm-size effect would imply that after the shock to their creditor, firms with fewer than 50 employees may suffer more in terms of growth as banks tighten credit relatively more for them. Figure 4 plots growth rates before and after the credit shock for the firms in our sample. It clearly shows that while firms with fewer than 50 employees and firms with more than 50 employees, both of which became affected during the crisis, were growing at approximately the same rate up to 2007, in 2008 and 2009 sales growth declined considerably more at smaller firms. However, Figure 5 demonstrated that this divergence in growth rates is driven by firms in sectors with below-median elasticity of substitution between capital and labor. At the same time, for firms in sectors with above-median elasticity of factor substitution, affected firms with fewer than 50 employees post relatively higher growth than affected firms with more than 50 employees. This suggests that in the absence of substitutability between the factors of production, the firm-size effect can dominate the employment-protection effect, and that only firms that can technologically substitute labor for capital will benefit from lax employment protection when the user cost of capital goes up.
The sample period is 2006-2009, including two years before and two years after the beginning of the financial crisis. The underlying assumption is that from an identifica-tion point of view, any effect of tightening credit constraints on individual firms would be immediate, while starting in 2010, as a result of the unfolding sovereign debt crisis, there would be more forces at play affecting firms' growth. Nevertheless, in robustness tests, we look at a longer period, to capture more medium-term effects.
One final concern with our identification strategy is that small firms that are more likely to be exposed to shocks can choose to stay below a size of 50 to avoid high firing costs, introducing a possible selection bias. However, Figure 1, where we plot the firm size distribution for the firms in our sample, shows no bunching of firms around 50 employees in the data, alleviating concerns related to the self-selection of firms into a particular size class.

Credit shocks, employment protection, and firm growth: Empirical results
In this section, we present the full battery of empirical tests employed to evaluate the relationship between credit constraints, employment protection, and firm growth. In 6.1, we present the headline results based on 2. In 6.3, we present estimates from a set of falsification tests. In 6.4, we perform robustness tests using alternative cut-offs within our regression discontinuity set-up, as well as alternative empirical proxies, sample periods, and samples. Finally, 6.5 tests for the underlying mechanisms that are activated to deliver the main result.

Main result
We begin by testing more parsimonious versions and gradually building towards the most saturated version of model 2. In that way, we are able to evaluate all underlying mechanisms that we had in mind when formulating our empirical model. All of these tests are reported in Table 3.
The first underlying mechanism relates credit constraints to firm growth. In particular, we postulate that ceteris paribus, tightening credit constraints due to balance sheet problems at the firm's creditor have a negative impact on firm growth. We evaluate this prediction in column (1) where we only include the variable Shock, alongside firm and Sector×Year fixed effects. The point estimate is negative and significant at the 5 percent statistical level, confirming the main intuition. In addition, the effect is economically meaningful, too: all else equal, a firm with a credit relationship with an affected bank experiences a decline in its sales growth by around 30 percent of the sample mean. Note that this is a conservative estimate because we have included in the sample both single-bank firms and firms that can substitute across creditors.
We next proceed to evaluate how credit shocks interact with the other components of the triple interaction in model 2. In column (2) we add the interaction of the variable Shock with the < 50 employees dummy which is equal to one if the firm has less than 50 employees. The estimates from this regression make it clear that only small firms experience a decline in their sales growth when their creditor experiences balance sheet problems. In this case, the decline in sales growth is 1.09 percentage points, or 0.34 percent lower than the sample mean sales growth. In column (3), we instead add the interaction of the variable Shock with the empirical estimate of the technological elasticity of substitution between capital and labor in the sector in which the firm operates. This test makes it clear that the direct effect of the credit shock is statistically indistinguishable across high-sigma and low-sigma sectors.
In column (4), we introduce the triple interaction together with the two estimable double interactions and the fixed effects. This regression strongly rejects the null hypothesis that employment protection and the technological substitution between labor and capital are not associated with changes in firm growth in the presence of credit shocks. Namely, we find that all else equal, a credit shock reduces sales growth more for small firms, which are the firms that are by default more dependent on bank credit for their operations. We also find that all else equal, a credit shock reduces sales growth more for firms in high-sigma industries. Crucially, the impact of a credit shock is reduced for firms with fewer than 50 employees in high-sigma industries. Recall that these are the firms that can substitute labor for capital, because their technology allows them to do so. These are also the firms for which it is less costly to substitute labor for capital because employment legislation makes it easier for them to fire employees. Therefore, we conclude that we have identified a positive impact on firm growth of laxer labor regulation in the presence of credit shocks.
In column (5), we add the polynomial of third degree in firm employment. Its inclusion changes very little the main coefficients of interest, suggesting that the regressiondiscontinuity effect is remarkably stable. Finally, in column (6) we estimate our preferred specification which includes on the right-hand side the triple interaction, the estimable double interactions, the variable Shock, the fixed effects as specified, and the set of firm-specific time-varying controls. We find that larger firms have on average lower sales growth, while firms with higher net worth have on average higher sales growth. These results are logical and they also serve to validate the data we are using. Importantly, we find that all variables of interest used to identify the main effect have the expected sign, just as in columns (4) and (5). Namely, we confirm that a credit shock reduces sales growth more for small firms and for firms in high-sigma industries, but its impact is reduced for small firms in high-sigma industries, which are the firms that both can and are allowed to substitute labor for capital.
In terms of economic magnitudes, our empirical strategy allows us to compare firms across industries based on their technological ability to substitute between labor and capital (σ). Consider two industries, one at the 75th percentile of σ (Chemicals and chemical products) and another at the 25th percentile of σ (Rubber and plastic). The difference in technological capital-labor elasticity between the two sectors is 0.33. The point estimate on the triple interaction Shock f t × < 50 employees f × σ s in column (5)

Controlling for the effect of firm size and firm quality
We now address two first-order concerns with our results. First, it is possible that our results capture the effect of firm size as opposed to employment protection. Although Spanish labor legislation contains a sharp employment-protection threshold at 50 employees, 50 employees is a threshold used in different laws to discriminate between firms in Spain.
For instance, the SMEs definition in Spain, until the end of 2013 at least, required, among other factors, that companies have no more than 50 employees in two consecutive years; a workers council is required for companies with more than 50 workers; and firms with more than 50 employees are required to have a canteen. Examples like this one suggests that firms with more than 50 employees face higher per-worker labor costs that are not necessarily related to employment protection. Thus it is possible that the effect reported in Table 3 is not necessarily due to dismissal costs, compromising our empirical strategy.
In order to alleviate this concern, we now include in our regression controls for firm size (namely, employment and the logarithm of total tangible assets) in interaction with Shock f t and with Shock f t × σ s . Column (1) of Table 4 demonstrates that controlling for employment, sales growth at firms with more tangible assets declines more after being exposed to a credit shock. The coefficients on the main variables of interest, however, are remarkably stable: we still find that the impact of a credit shock is lower for small firms in high-sigma industries, which are the firms that both can and are allowed to substitute labor for capital. The effect is still significant at the 5 percent statistical level, suggesting that other factors that make firms with more than 50 employees different from those with fewer employees do not explain away the positive impact of laxer employment protection during a credit shock.
Second, there may be non-trivial selection issues. With regard to the possible selection bias arising from the non-random assignment of banks to firms, we have argued that the credit supply shock is orthogonal to credit demand. However, it is possible that more affected banks are more likely to grant loans to worse firms (e.g., Bentolila et al., 2018). In order to address this issue, we next augment our main regression to account for the independent effect of firm quality. In practice, we include in our regression the firm's ratio of cash flow to assets (a proxy for profitability) and the firm's net worth (a proxy for credit quality), in interaction with Shock f t and with Shock f t × σ s . Column (2) of Table 4 suggests that conditional on a credit shock, more profitable firms grow faster, suggesting that indeed firm quality exerts an independent effect on the growth of firms hit by a shock to their borrowing capacity. Crucially, we still find that the impact of a credit shock is lower for small firms in high-sigma industries, and the effect is still significant at the 5 percent statistical level, suggesting that the potential selection of lower-quality firms to more affected banks does not explain the main result in the paper.
Finally, we include all those double and triple interactions in a horse race in column (3) of Table 4. We find that while both firm size and firm quality matter for the relative performance of credit-constrained firms with fewer than 50 employees, the interaction of a firm-size-specific employment protection threshold and the technological ability to substitute labor for capital still explains a large share of the variation in growth across credit constrained firms.

Falsification tests
In this Section, we report the estimates from a number of falsification tests. In particular, the results we document should disappear once we perform our tests on samples where the labor regulation and the credit shock we base our analysis on no longer bind. Recall that the underlying mechanisms we test is that-controlling for technology-firms with fewer than 50 employees reach different outcomes than larger firms when faced with a credit shock. We now perform three different tests where we arbitrarily move first the credit shock, then the firm-size cut-off, and finally perform our test on a sample of firms derived from a different country (Germany) where some firms during the crisis are subject to a credit shock, but there is no discontinuity in labor regulation at 50 employees. We report the estimates from these tests in Table 4.
In order for the credit shock we use to be valid, it has to bite only during the financial crisis once banks were suddenly hit by balance sheet problems. In other words, it should not have an effect before the financial crisis when the Spanish banking sector posted healthy growth in both lending and profitability. To test this underlying assumption, in column (1) we perform our underlying test of model 2 on the period 2004-2007, using the same sample of firms, the same firm-bank matches, and the same definition of an affected bank. The only difference thus is that we are performing our diff-in-diff-in-diff on a sample period fully preceding the financial crisis. This should result in a random assignment of nonexisting credit shocks to firms, and should yield no significant association between the shock and its interaction with firm size and firm technology with firm growth. Column (1) reports that this is indeed the case. Not only is there no statistical correlation between the shock and firm growth, but randomly "shocked" firms are also not more likely to experience different sales growth rates regardless of their size and of their technological ability to substitute labor and capital in the production process.
In column (2), we subject to a falsification test the assumption that what the 50-employee cut-off is measuring is the impact of firm-size-specific labor regulation which makes it cheaper for firms with fewer than 50 employees to hire workers when they need to. An alternative explanation is that the results we reported in Table 3 simply capture a difference between small and large firms, in that smaller firms find it naturally easier to substitute labor for capita. If so, our results would still hold when we move the size cut-off around. In column (2), we perform a test of this hypothesis. We replace the < 50 employees dummy with a < 10 employees dummy equal to 1 if the firm has fewer than 10 employees. We preserve the other components of our tests unchanged, namely, we assign firms the same credit shock and the same industry-specific elasticity of substitution between capital and labor. The data fail to reject the hypothesis that there is no difference between small and large firms when we alter the definition of "small", suggesting that firm size indeed works through the impact of firm-size-specific employment protection.
While this test suggests that the 50-employee cut-off is materially different from another way of separating small from large firms, it could still be the case that firms with fewer than 50 employees differ from larger firms in ways that are unobserved to the econometrician and are common across the global corporate landscape. However, if this is the case, then we can run model 2 on a sample of firms in a country without a 50-employee employment protection rule. If we continue getting a significant association between the firm-size cutoff, the firm's elasticity of substitution between capital and labor, the credit shock, and firm growth, then the underlying mechanism we have in mind will be compromised.
To address this point, we download from Orbis the exact same balance sheet information for the universe of firms in Germany. We choose this country for two different reasons.
For one, during the financial crisis it experienced a similar type of credit shock whereby five of its State clearing banks, Landesbanken, needed to be recapitalized by their daughter savings banks because they had overinvested in the US mortgage-backed-securities market. The remaining 7 Landesbanken, and therefore their daughter savings banks, did not experience this shock. 20 This makes it possible to determine which firms are linked to "affected" banks and therefore credibly experiencing a negative credit shock. 21 This makes the sample of German firms similar to the sample of Spanish firms that we are using in 20  that some firms are subjected to an exogenous credit shock thanks to their pre-crisis association with banks which during the crisis experienced balance sheet problems. The second reason is that there is no labor regulation in Germany that distinguishes between firms with more and firms with fewer than 50 employees. If our identifying assumptions are wrong and there is an (unobservable) difference between firms with more and firms with fewer than 50 employees that is independent of labor regulation, we should register in the sample of German firms the same effect that we observe in the sample of Spanish firms. The point estimates reported in column (3) strongly suggest that this is not the case: the same firm-size cut-off that works in Spain does not affect the interaction between the credit shock, the firm's technology, and firm growth.
We conclude that the data provide us with no reason to believe that our results are due to choosing a definition of a credit shock and of a firm-size cut-off that are associated with forces which have affect firm growth outside of their impact through the relative cost of credit and the relative cost of hiring.

Alternative empirical proxies and model robustness
In Table 6, we proceed to address a number of concerns related to the construction of our main explanatory variables. We start with the estimated elasticity of substitution between labor and capital. As we noted already, we use data on the inputs in production from the US KLEMs database. This database provides two separate data series, one encompassing the period 1947 to 2010, and one encompassing the period 1970 to 2007. In the tests so far we rely on the longer dataset which is both more popular and provides for a more robust estimation of the underlying sector-specific elasticities. An argument in favor of the second series is that it captures a period of more mature industrial development, aligning it more closely to the technological characteristics of Spanish firms during the 2000s. Although it follows the same classification, the second database represent a different vintage of the underlying BEA data and some slightly different statistical methods.
To test for whether our main result is not driven by a particular choice of data in calculating sector-specific benchmarks for the elasticity of substitution between labor and capital, we re-estimate 2 using the second, shorter data series. Then we use the resulting sector-specific values to re-estimate model 2. The estimate from this regression is reported in column (1) of Table 6. They strongly suggest that statistical association between the credit shock, labor regulation, the firm's technology, and firm growth is not a feature of the particular data series we choose to construct sector-specific elasticities of substitution between labor and capital.
In column (2), we address a similar point by noting that the distribution of estimated σ s has a median value of 0.77. At the same time, the economically relevant value is 1: when σ > 1, firms find it easier to substitute between labor and capital, while when σ < 1, capital and labor start being more of complements in production. To address this point, we use the main estimates of the sector-specific elasticities to create a dummy variable equal to 1 if for a particular sector, σ > 1, and to zero otherwise. In this way, only 4 of the 23 sectors in the dataset are defined as high-sigma. Our estimates strongly suggest that it is indeed firms in high-sigma sectors with fewer than 50 employees for whom a credit shock has a weaker impact on sales growth.
Our empirical model is based on the interaction of labor regulation and a credit shock with a particular technological property that allows for the identification of the growth impact of labor regulation during a credit crunch through the substitution of labor for capital.
Nevertheless, a high degree of technological substitutability between labor and capital can correlate with another industry characteristic which, if concurrently active, can introduce bias in our results. One such property is the sector's technological dependence on external finance. An argument going back to the seminal paper by Rajan and Zingales (1998) is that for technological reasons, some sectors are able to finance their operations to a higher degree with internal funds, while others rely more on external finance. Evidence from the financial crisis suggested that small firms in such sectors tend to be more affected by a credit shock as they have few alternative funding sources, and so a reduction of access to bank credit causes them to cut both employment and investment (e.g., Duygan-Bump et al. 2015; Popov and Rocholl, 2017). If the production function of firms in such sectors is also characterized by a technology where capital and labor are close substitutes, then our estimates of β 1 would partially be capturing the impact of external financial dependence.
In column (3), we put this concern to the test. We first obtain data on the sectors' ex- Finally, we employ an alternative empirical proxy for an exogenous shock to the firm's borrowing capacity. In our main specifications, the treatment group comprises firms attached to banks that required a government intervention of some type during the financial crisis, and the control group comprises firm attached to banks that did not. While government intervention should be highly correlated with bank health, this approach lumps together firms linked to banks with potentially varying levels of (poor) health. Moreover firms linked to unhealthy banks that did not require government assistance may be included in the control group. To correct for such potential misclassification, we use as alternative measure of bank health a dummy variable equal to one if the firm's credit has a total capital ratio of less than 10% in 2008, and to 0 otherwise. In this way, we split firms depending on the extent to which they are likely to experience a negative shock to their cost of funding originating from a weakening of the balance sheet of their lenders. The test reported in Table 6, column (4) suggests that the main finding of the paper is not affected by the approach used to classify weak banks.

Sample robustness
The main advantage of the empirical design that we are using is that we are exploiting a clear policy-driven discontinuity along the firm size distribution. Namely, while all firms with fewer than 50 employees find it easier to fire workers-making it in return cheaper for them to hire workers they can then fire-this becomes more difficult for firms with more than 50 employees which for whom regulation makes collective dismissals much more costly.
For this policy discontinuity to bite, we would ideally have to estimate our model for firms close to the cut-off. Otherwise, we would be running the risk of comparing a subsample dominated by very large firms (e.g., with more than 1000 employees) to a subsample of very small firms (e.g., with less than 5 workers), a concern our test in column (2) of Table 5 does not address.
To address this potential issue, in column (1) of Table 7 we report estimates from tests where we have restricted the sample to a narrower window around the 50-employee cutoff. In particular, we restrict the sample to firms with more than 30 and firms with less than 750 employees, which corresponds to 4 percent of the sample on each side of the 50-employee cut-off. The point estimate on the triple interaction is still positive and significant, reinforces the previous finding that a credit shock which increases the price of renting capital has a smaller impact on firms that can substitute labor for capital and are allowed to do so by labor rules.
Next, we extend the sample period on both sides, by one year (column (2)) and by two years (column (3)). In our main tests, we deliberately chose a sample period ending in 2010, so that our estimates are not contaminated by the sovereign debt crisis which erupted in 2010. At the same time, we would like to know how persistent the effect that we document is. In particular, the benefits of flexible labor regulation would be smaller if firms can only substitute across inputs of production in the short-run. However, the estimates from model 2 suggest that the increase in firm growth coming from the substitution of labor for capital does not disappear in the medium run, and moreover that it becomes even larger once we look at a longer period after the initial shock. This suggests that the benefit of flexible labor regulation during times of credit distress extend beyond impact and provide longer-term benefits to firms.
Another concern associated with our sample is that it includes firms from all sectors, including construction. It has been well-established that a number of Spanish banks had become excessively exposed to local construction, and so they encountered severe problems once the Spanish housing bubble burst (e.g., Bentolila et al., 2018). In the case of construction firms attached to troubled banks, the argument can be made that the direction of the shock ran from the real to the banking sector, which questions our assumption about the exogeneity of the credit shock. To address this concern, we drop all firms operating in the construction sector (i.e., firms with NACE codes 41, 42, and 43). Column (4) of Table 7 reports the estimates of this test, and it suggests that our main results are not sensitive to inclusion of construction firms in the dataset.
There is one final, data-related concern we need to address. We have classified firms as affected by a credit shock if they have a credit association with at least one affected bank.
This might be inaccurate in the context of multiple banking relationships that firms can substitute across. It is true that the potential bias goes in our favour: if firms can substitute across banks, it makes it more difficult to find any effect of the credit shock on firm growth. However, if firms could perfectly substitute away from affected banks, but we still find an effect of association with an affected bank, it would imply that the correlation between supply shocks and firm responses that we have captured is a spurious one.
To that end, in column (5) of Table 7, we reduce the sample to firms with a single bank relationship. Such firms will be unable to make up for the decline in credit from their main creditor by borrowing from another bank, and due to their size, they will find it difficult to substitute for the decline of bank credit by accessing a non-bank funding source. Our estimates imply that the negative effect of the credit shock on small firms' growth holds for the sub-sample of firms that only bank with one creditor, too. The magnitude of this effect is substantially larger than in column (6) of Table 3, confirming the intuition that single-bank firms are more affected by the same credit shock than firms that can substitute across creditors. Importantly, the decline in firm growth is significantly lower for firms that are not subject to restrictions on collective dismissal, and this effect is significant at the 10 percent statistical level. We thus confirm that the statistical association between changes in financing access and changes in firm growth that we have uncovered is not spurious in that it also holds in the extreme case when firms cannot substitute between affected and non-affected banks.

Controlling for local demand
There could be systematic differences across firms stemming from different shocks to local demand across Spanish regions. The divergence in growth trends across affected and nonaffected firms could in theory be due to the activation of mechanisms that affect firms' local growth prospects. One such mechanism is related to shocks to investment opportunities: because regional governments may have participated in the recapitalization of troubled banks, regional budgets may have been adversely affected. Regions may, as a result, have postponed investment in infrastructure and limited social services, all of which should lead to a reduction in investment opportunities. An alternative mechanism is a feedback effect from retail lending which declined in the wake of the crisis: if credit to households is reduced, making them feel poorer, they can cut back on local spending, leading firms to reduce sales. Such mechanisms can have a material impact on our results if, for example, affected firms with fewer than 50 employees in low-sigma industries are more likely to operate in more affected regions.
In order to allay such concerns, we modify our main regression in two different ways.
For a start, we download regional information for all firms in the dataset for which such information is available. There are 50 NUTS3 regions in the dataset, corresponding to the 50 provinces of Spain. With this information at hand, we can add region×year fixed effects to the regressions. The inclusion of this interaction term should net out all trends that are region-specific but common to all firms within a region. Even more tightly, we can add region×sector×year fixed effects, washing away unobservable heterogeneity that is common to all firms within a region and an industry at the same point in time. Columns (1) and (2) of Table 8 report that our main results are robust to these alternative procedures. Moreover, the main coefficients of interest are remarkably stable, suggesting that unobservable time-varying regional heterogeneity does not play an important role in explaining changes in firms' performance.

Distinguishing between high-and low-growth firms
The main identifying mechanism in our paper is that when the user cost of capital goes up because of an inward shift of the supply of credit, firms with healthy growth prospects want to substitute labor for capital in order to keep growing, and they can only do so if both their technology and employment protection allow them to do so. This mechanism rests on the assumption that firms have healthy growth prospects which are not affected by the same background forces which generate the credit crunch. If this assumption would is violated, there is no reason to expect that firms would want to substitute between factors of production and keep growing, in which case we may have detected a spurious correlation between credit shocks, employment protection, the elasticity of substitution between labor and capital, and firm growth.
To address this concern, in Table 9 we split the sample between firms with belowmedian and firms with above-median sales growth in 2007. It is reasonable to assume that firms which were growing in a healthy fashion right before the credit shock were also facing better growth prospects a year later. The evidence in Table 9 suggests that the mechanism we identify is only relevant for these firms. In particular, within the sample of high-growth firms, smaller firms are more affected than larger firms by the credit shock, but they benefit more if they are in high-sigma sectors, suggesting that they indeed substitute labor for capital in order to keep growing (column (1)). We detect no such patter in the data when we zoom in onto the sample of low-growth firms (column (2)), validating the underlying assumption behind our empirical strategy.

Empirical channels
We now turn to the empirical channels that are plausibly activated to cause the increase in firm growth as a result of flexible labor regulation. The underlying hypothesis is clearly that as firms are faced with a shock to external credit that raises the cost of renting capital, those which can substitute labor for capital-because both their technology and the regulatory framework make it possible-will do so. Therefore, conditional on being subject to a credit shock, we should observe higher labor growth in firms with fewer than 50 employees in high-sigma industries, relative to firms with more than 50 employees and/or firms in low-sigma industries. The same argument should not apply to capital investment, which should decline for both types of firms, regardless of whether they can substitute labor for capital or not. Table 10 presents a direct test of this hypothesis. We modify model 2 in two ways. In column (1), we replace the dependent variable with employment growth, i.e., the log difference in the firm's total employment between this period and the previous one. In column (2), we replace the dependent variable with investment growth, i.e., the log difference in the firm's total tangible assets between this period and the previous one. Our estimates clearly show that size-dependent labor regulation has a strong impact on labor demand. In particular, firms subject to a credit shock are considerably more likely to hire more workers if their technology allows them to do so (i.e., capital and labor are substitutes) and if labor regulation reduces their cost of hiring (i.e., they have fewer than 50 employees and so are not subject to strict collective dismissal restrictions). At the same time, firm-size-specific labor regulation does not appear to have a differential impact across firm sizes on capital investment, which is consistent with our prior. 22 22 Appendix Table C.2 reports estimates from another robustness test whereby we restrict the sample to firms with a credit relationship with an affected bank, observed after the crisis (i.e., in 2008 or in 2009). This allows us to modify 2 such that the main explanatory variable is an interaction between a dummy variable equal to 1 for firms with fewer than 50 employees and the sector-specific elasticity of substitution sigma. The point estimates clearly show that after the crisis, smaller credit constrained firms grew more slowly than otherwise comparable larger firms, however, the effect of firm size is reversed in high-sigma industries (column (1)). Columns (2) and (3) further suggest that the higher growth of small firms in high-sigma industries is entirely due to higher employment growth and not to higher investment growth, confirming the motivating empirical mechanism. Because this regression model is based on a double interaction, it is easier to interpret. Nevertheless, throughout the paper we give preference to the triple-interaction-based model 2 because it allows to

Conclusions
The recent financial crisis resulted in a dramatic increase in unemployment, 23 sparking interest in the ability of flexible labor markets to help the economy withstand negative shocks and to sustain employment and output growth. While recessions may have cleansing effects, with some role for creative destruction, deep and long recessions such as the one in Spain can generate major scars with negative long-run effects. This naturally raises the question whether more flexible labor regulation benefits firms not during the upside, but also during the downside of the business cycle.
We show that Spanish firms with fewer than 50 employees grew relatively faster during the financial crisis when exposed to a negative credit shock than larger firms in sectors with a technologically higher substitutability between labor and capital. Since firms with less than 50 employees face lower dismissal costs on account of labor regulation, these results support the view that labor market flexibility enhances the ability of firms to absorb large negative shocks during recessions. These results hold only for firms in sectors with a relatively high substitution elasticity which are firms that offer more flexibility to adjust labor following an increase in the user cost of capital. The main result is robust to controlling for time-varying firm-specific factors that can affect firm growth in the absence of credit shocks or firm-size-specific labor regulation, such as size, cash flows, and net worth. It is also robust to controlling throughout for unobservable firm heterogeneity with firm fixed effects, and for unobservable sector-specific trends with interactions of sector and year dummies. We continue to obtain our main effect when we compare smaller and larger firms that are closer to the 50-employee threshold, when we control for other underlying industry characteristics, such as dependence on external finance, and when we look at firms with a credit relationship with only one bank. Importantly, the effect is only present for high-growth firms, which suggests that during a credit crunch, lax employment protection mainly benefits firms with good growth prospects by enabling them to substitute labor for capital when the user cost of capital has increased. In terms of underlying channels, we find that the effect operates primarily through affecting employment, not capital, which indicates that the ability to substitute labor for capital is an important driver of firm growth control for the impact of unobservable time-invariant firm heterogeneity, as well as to compare constrained to unconstrained firms. during a credit crunch.
Our results tend to support the adoption of flexible labor laws. While such labor market reforms do not come without pain for incumbent workers, they allow firms to recover more quickly from a deep recession whose roots are in the banking sector. Since the financial crisis, Spain has indeed embarked on a package of labor market reforms with a view to make labor markets more flexible and in particular ease the cost of dismissals for firms.
This has led to a reduction in the wage bill of the average firm and generated an economic recovery and a fall in the exorbitantly high levels of unemployment.   Only firms that report a credit association with at least one bank are included. 'Sales growth' denotes the log difference in the firm's total sales between this period and the previous one. 'Employment growth' denotes the log difference in the firm's total employment between this period and the previous one. 'Investment growth' denotes the log difference in the firm's total tangible capital between this period and the previous one. 'Shock' is a dummy variable equal to one in 2008 and in 2009 and if the firm has a credit association with at least one bank which required public assistance during the financial crisis. '<50 employees' is a dummy variable equal to one if the firm had fewer than 50 employees before the financial crisis. '<10 employees' is a dummy variable equal to one if the firm had fewer than 10 employees before the financial crisis. 'Employment' denotes the number of the firm's employees. 'Log (Sales)' denotes the logarithm of the firm's total sales, 1-period lagged. 'Cash flow / Assets' denotes the ratio of the firm's cash flow to the firm's total assets, 1-period lagged. 'Net worth / Assets' denotes the ratio of the firm's net worth, calculated as the difference between total assets and total liabilities, to the firm's total assets, 1period lagged. 'Log (Assets)' denotes the logarithm of the firm's total tangible assets, 1-period lagged. 'Shock' is a dummy variable equal to one if the firm has a credit relationship with a bank that received government assistance during the financial crisis. 'Sigma' denotes the sector's technological elasticity of substitution between labor and capital; see Section 3 for a description of how sigma is calculated. 'External dependence' denotes the sector's technological dependence on external finance, using the calculations in Duygan-Bump, Levkov, and Montoriol-Garriga (2015).     Table reports the point estimates from OLS regressions where the dependent variable is the firm's annual sales growth. 'Shock' is a dummy variable equal to one if the firm has a credit relationship with a bank that received government assistance during the financial crisis. '<50 employees' is a dummy variable equal to one if the firm has less than 50 employees. 'Sigma' is the sector's technological elasticity of substitution between labor and capital, calculated using KLEMs data over the period 1947-2010. 'Log (Sales)' is the logarithm of the firm's one-period-lagged total sales. 'Cash flow / Assets' is the ratio the firm's one-period-lagged cash flow to the firm's one-period-lagged total assets. 'Net worth / Assets' is the ratio of the firm's net worth, calculated as the difference between total assets and total liabilities, to the firm's total assets. In all regressions, only firms with at least one observation before and at least one observation after 2008 are included. The sample period is 2006-2009. Standard errors clustered at the sector level are reported in parentheses where ***, **, and * indicate significance at the 1 percent, 5 percent, and 10 percent statistical level, respectively.  Table reports the point estimates from OLS regressions where the dependent variable is the firm's annual sales growth. 'Shock' is a dummy variable equal to one if the firm has a credit relationship with a bank that received government assistance during the financial crisis. '<50 employees' is a dummy variable equal to one if the firm has less than 50 employees. 'Sigma' is the sector's technological elasticity of substitution between labor and capital, calculated using KLEMs data over the period 1947-2010. 'Log (Sales)' is the logarithm of the firm's one-period-lagged total sales. 'Cash flow / Assets' is the ratio the firm's one-period-lagged cash flow to the firm's one-period-lagged total assets. 'Net worth / Assets' is the ratio of the firm's net worth, calculated as the difference between total assets and total liabilities, to the firm's total assets. All firm controls from Table 3, column (6) are also included in the regression. In all regressions, only firms with at least one observation before and at least one observation after 2008 are included. The sample period is 2006-2009. Standard errors clustered at the sector level are reported in parentheses where ***, **, and * indicate significance at the 1 percent, 5 percent, and 10 percent statistical level, respectively.  Table reports the point estimates from OLS regressions where the dependent variable is the firm's annual sales growth. 'Shock' is a dummy variable equal to one if the firm has a credit relationship with a bank that received government assistance during the financial crisis. '<50 employees' is a dummy variable equal to one if the firm has less than 50 employees. '<10 employees' is a dummy variable equal to one if the firm has less than 10 employees. 'Sigma' is the sector's technological elasticity of substitution between labor and capital, calculated using KLEMs data over the period 1947-2010. All firm controls from Table 3 (4)). In column (3), the test is performed on a sample of German firms. Standard errors clustered at the sector level are reported in parentheses where ***, **, and * indicate significance at the 1 percent, 5 percent, and 10 percent statistical level, respectively.  Table reports the point estimates from OLS regressions where the dependent variable is the firm's annual sales growth. 'Shock' is a dummy variable equal to one if the firm has a credit relationship with a bank that received government assistance during the financial crisis (columns (1)-(3)) and a dummy variable equal to one if the firm has a credit relationship with a bank with a capital ratio of less than 10% before 2008 (column (4)). '<50 employees' is a dummy variable equal to one if the firm has less than 50 employees. 'Sigma' is the sector's technological elasticity of substitution between labor and capital, calculated using KLEMs data over the period 1947-2010. All firm controls from Table 3, column (6) are also included in the regression. In all regressions, only firms with at least one observation before and at least one observation after 2008 are included. In column (1), sigma is calculated on a shorter, precrisis time period . In column (2), sigma is replaced with a dummy equal to one if sigma is more than 1, and to zero otherwise. The sample period is 2006-2009. Standard errors clustered at the sector level are reported in parentheses where ***, **, and * indicate significance at the 1 percent, 5 percent, and 10 percent statistical level, respectively.  Table reports the point estimates from OLS regressions where the dependent variable is the firm's annual sales growth. 'Shock' is a dummy variable equal to one if the firm has a credit relationship with a bank that received government assistance during the financial crisis (columns (1)- (7)) and a dummy variable equal to one if the firm has a credit relationship with a bank with a capital ratio of less than 10% before 2008 (column (8)). '<50 employees' is a dummy variable equal to one if the firm has less than 50 employees. 'Sigma' is the sector's technological elasticity of substitution between labor and capital, calculated using KLEMs data over the period 1947-2010. All firm controls from Table 3 (3)). In column (1), only firms with between 30 and 750 employees (4% of the sample on each side of 50) are included. In column (4), firms in the construction sector are excluded. In column (5), only firms with a credit relationship with a single bank are included in the regressions. Standard errors clustered at the sector level are reported in parentheses where ***, **, and * indicate significance at the 1 percent, 5 percent, and 10 percent statistical level, respectively.  Table reports the point estimates from OLS regressions where the dependent variable is the firm's annual sales growth. 'Shock' is a dummy variable equal to one if the firm has a credit relationship with a bank that received government assistance during the financial crisis. '<50 employees' is a dummy variable equal to one if the firm has less than 50 employees. 'Sigma' is the sector's technological elasticity of substitution between labor and capital, calculated using KLEMs data over the period 1947-2010. All firm controls from Table 3, column (6) are also included in the regression. In all regressions, only firms with at least one observation before and at least one observation after 2008 are included. The sample period is 2006-2009. Standard errors clustered at the sector level are reported in parentheses where ***, **, and * indicate significance at the 1 percent, 5 percent, and 10 percent statistical level, respectively.  Table reports the point estimates from OLS regressions where the dependent variable is the firm's annual sales growth. 'Shock' is a dummy variable equal to one if the firm has a credit relationship with a bank that received government assistance during the financial crisis, and the firm is observed after 2008. '<50 employees' is a dummy variable equal to one if the firm has less than 50 employees. 'Sigma' is the sector's technological elasticity of substitution between labor and capital, calculated using KLEMs data over the period 1947-2010. All firm controls from Table 3, column (6) (1)) and the firm's annual investment growth (column (2)). 'Shock' is a dummy variable equal to one if the firm has a credit relationship with a bank that received government assistance during the financial crisis, and the firm is observed after 2008. '<50 employees' is a dummy variable equal to one if the firm has less than 50 employees. 'Sigma' is the sector's technological elasticity of substitution between labor and capital, calculated using KLEMs data over the period 1947-2010. All firm controls from Table 3, column (6) are also included in the regression. In all regressions, only firms with at least one observation before and at least one observation after 2008 are included. The sample period is 2006-2009. Standard errors clustered at the sector level are reported in parentheses where ***, **, and * indicate significance at the 1 percent, 5 percent, and 10 percent statistical level, respectively.
Given this, the optimal labor and capital income shares are, respectively,

B Full Sectoral Estimates
We now show more detailed estimates of our core results for the chosen KLEMs US sectors.
For estimation of the non-linear system of equations, we mainly used three different estimators: non-linear seemingly unrelated regression, feasible generalized non-linear least squares and the iterated feasible generalized non-linear least squares. These estimators account for cross-equation parameter restrictions as well as cross-correlated errors. Of the three, iterated feasible generalized non-linear least squares tends to be the one reported in the main text.
For additional robustness we also estimated separately the production function (A.1), individual factor demands (A.2, A.3), or the ratio of the two factor demands. In most cases these single equation approaches did not fit the data as well, but where feasible they provided a cross check on our main results. We also (for cross checking purposes) used two and three stage non-linear least square estimators (we used lags of output and capital and the labor input as instruments). 27    1.000*** 1.037*** 0.984*** 1.093*** 1.015*** 1.008*** 1.027*** 1.042*** 1.000***

B.1 Robustness
In each of the non-linear cases, we systematically varied the initial parameter conditions to ensure the attainment of a global optimum (e.g., for the substitution elasticity, we use a grid of σ 0 ∈ [0.2, 0.4, 0.8, 1.2, 1.6]). For additional robustness we also estimated separately the production function (A.1), individual factor demands (A.2, A.3), or the ratio of the two factor demands. In most cases these single equation approaches did not fit the data as well, but where feasible they provided a cross check on our main results. We also used two and three stage non-linear least square estimators (we used lags of output and capital and the labor input as instruments). 28 An example (for one particular sector) is given in appendix table B.2. In that case, there are some variations in σ (although all significantly below one) with a labor augmenting growth rate of around 2% per year and a statistically zero growth rate in capital augmenting technical progress. The case IFGNLS ∀σ 0 is favored across the discriminatory metrics. 28 Details of all our estimation forms and results are available on request. Note σ < 1|σ0 > 1 (likewise σ > 1|σ0 < 1) constitutes especially strong evidence for the estimated σ given the discontinuity of the production function estimation around the unitary substitution elasticity region.       (1)), the firms annual employment growth (column (2)) and the firms annual investment growth (column (3)). ¡50 employees is a dummy variable equal to one if the firm has less than 50 employees. Sigma is the sectors technological elasticity of substitution between labor and capital, calculated using KLEMs data over the period 19472010. All firm controls from Table 3, column (6) are also included in the regression. In all regressions, only firms with at least one observation before and at least one observation after 2008 are included. All regressions are run on the sub-sample of firm with a credit relationship with a bank that received government assistance during the financial crisis. The sample period is 2008 and 2009. Standard errors clustered at the sector level are reported in parentheses where ***, **, and * indicate significance at the 1 percent, 5 percent, and 10 percent statistical level, respectively.