Aggregate Effects of Collateral Constraints

Transcription

1 Aggregate Effects of Collateral Constraints VERY PRELIMINARY VERSION DO NOT CIRCULATE Thomas Chaney Zongbo Huang David Sraer David Thesmar October 2, 2015 Abstract This paper provides a quantitative exploration of the aggregate effects of an important source of financing friction, collateral constraints. We develop a general equilibrium model of firm dynamics with collateral constraints and adjustment costs, which we structurally estimate using administrative data on French firms. The model is estimated using the joint firm-level dynamics of capital and labor observed following exogenous shocks to the value of collateral. We find that welfare increases by 5.4% when collateral constraints are removed. 25% of these welfare gains come from an improved allocation of inputs across heterogenous firms; 75% are derived from an aggregate increase in capital. Interestingly, removing collateral constraints has little effect on aggregate employment, as financially constrained firms tend to substitute labor for capital. We are grateful to conference and seminar participants in Berkeley, Capri, HBS, NYU-Stern, Stanford, the LSE, the Chicago Fed, the FED Board for their insightful comments. We warmly thank Toni Whited for sharing her fortran code with us. All errors are our own. Toulouse School of Economics and CEPR ( thomas.chaney@gmail.com) Princeton ( congerhuang@gmail.com) Berkeley, NBER and CEPR ( sraer@berkeley.edu) HEC and CEPR ( thesmar@hec.fr) 1

2 There is an accumulating body of evidence showing the causal effect of financing frictions on firms investment and employment decisions at the micro-level. 1 In this paper, we use a quantitative model to investigate the aggregate effects of a pervasive source of financing friction collateral constraints. Our approach expands on the existing literature by combining several features: (1) we provide clean firm-level evidence that collateral constraints causally affect investment and employment decisions, (2) we use this well-identified relationship to estimate a dynamic model that includes both adjustment costs and collateral constraints, and (3) we nest this model in a general equilibrium framework with heterogenous firms to study aggregate effect of collateral constraints. Our estimated model shows that even in a developed country like France, collateral constraints significantly reduce aggregate welfare. In a counterfactual economy where collateral constraints are removed, we find that aggregate welfare increases by 5.4% relative to its actual level. Of these welfare gains, about a quarter come from the better allocation of inputs among heterogenous firms 2. The remaining welfare gains can be attributed to the fact that the aggregate capital stock increases when firms become unconstrained. Importantly, we find that the removal of collateral constraints has little effect on aggregate employment: collateral constrained firms typically substitute labor for capital since labor requires less up-front financing; when the financing constraint is removed, these previously constrained firms grow by expanding their capital to labor ratio, which leaves the aggregate stock of labor used in equilibrium almost unchanged. The paper starts by documenting how, at the firm-level, capital and labor respond to shocks to collateral values. Since real estate is a sizeable asset on firms balance sheet, our empirical strategy uses variations in local real estate prices as shocks to the collateral value available to land-holding firms. Precisely, we measure how firms investment and hiring decisions respond to each additional dollar of real estate that the firm actually owns. Because variations in local house prices may simply reflect changing investment opportunities or demand shocks, we benchmark 1 See, among many others, Lamont (1997), Rauh (2006), Chaney et al. (2012a), Blanchard et al. (1994) for the effect of financial frictions on investment and Benmelech et al. (2010) or Chodorow-Reich (2013) for the effect of financial frictions on employment 2 These gains from the reallocation of input in the economy are the focus of Hsieh and Klenow (2009), Moll (2014), Midrigan and Xu (2014) 2

3 the investment and hiring response of land-holding firms to that of local firms with no real estate assets on their balance sheet. This empirical strategy is akin to a difference-in-difference strategy: treated firms (i.e. land-holding firms) are benchmarked agains a control group (i.e. non landholding firms located in the same area); local variations in house prices constitute the treatment, which induces variations in collateral values only for land-holding firms, i.e. firms in the treated group. We show that a e1m increase in collateral value leads the average French firm to raise its investment by e190k and to create an additional 1.5 job. At the microeconomic level, collateral constraints represents a strong impediment to firms investment and hiring decisions. To assess whether these micro-level elasticities have significant aggregate implications, we then develop a structural model of firms dynamics. The model builds on the standard neo-classical model of investment with adjustment costs (Jorgenson (1963), Hayashi (1982)). We add three key ingredients. First, firms face decreasing returns to scale. This assumption is natural given our sample of mostly small, private, firms. Second, firms face a collateral constraint: the amount they can borrow every period is limited by how much tangible assets they own. Tangible assets are decomposed into real estate and other productive assets. Each period, the value of real estate assets fluctuates randomly, creating variations in the collateral constraint for firms that own land and thus mimicking our reduced-form empirical design. 3 Third, we introduce adjustment costs to labor in addition to adjustment costs to capital. While adjustment costs to labor have been previously analyzed in the investment literature, 4 our choice is motivated by the relative response of employment and capital observed in our reduced-form exercise: for a given increase in collateral value, capital growth is on average about ten times larger than employment growth. In the absence of adjustment costs, the static first-order condition on labor suggests that the response of capital to collateral shocks should be at most twice larger than the response of employment. It is not surprising that labor adjustment costs play a role in firm dynamics in France, given the well-documented rigidity of the French labor market. 3 While we do not explicitly micro-found the collateral constraint, it emanates naturally from limited enforcement models (Hart and Moore (1994)). 4 See, among many others, Caballero et al. (1997), Hall (2004b), or more recently Bloom (2009) 3

4 The model is then embedded in a general equilibrium framework. Our economy consists of a large number of local economies, which all faces idiosyncratic shocks to house prices. Firms produce intermediate goods, which are combined into a CES-composite final good. This market for intermediate inputs operates under monopolistic competition. A representative consumer consumes the final good, and supply labor elastically. The final good market and the labor markets are assumed to be competitive national markets. Given the large number of local economies, the final good price and the equilibrium wage do not depend on the realization of the idiosyncratic house price shocks. Importantly and this is a current limitation of our analysis shocks to the local housing markets are exogenous in the model. We estimate this model through a Simulated Method of Moments (SMM), which simply minimizes the distance between actual targeted moments and moments simulated through our structural model. In addition to the standard moments used in the structural corporate finance literature, our estimation procedure explicitly targets the coefficient estimates obtained in our reduced-form analysis, namely the relative response of land-holding firms labor, capital and debt stock to variations in local house prices. We show that these moments are crucial to identify parameters related to the collateral constraints and inputs adjustment costs. In particular, an estimation based solely on standard targeted moments would be inconsistent with the reducedform moments This procedure provides us with estimates of structural parameters governing the adjustment costs to labor and capital, as well as governing the pledgability of real estate and tangible assets in the collateral constraint. We show that the model manages to fit quite precisely the targeted moments. We also demonstrate the model s external validity by showing that the model can replicated several features of the data not used in the estimation. The estimated model is then used to assess the aggregate effect of collateral constraints. We simulate an economy in which firms face no borrowing constraints. In this counterfactual, welfare is larger than the estimated welfare of the actual economy by 4.5%. There are two reasons that can explain these welfare gains. First, the collateral constraint limits the amount of capital and labor that can be purchased by firms and thus creates some efficiency losses. Second, the borrowing 4

5 constraint creates a misallocation of inputs across heterogeneous producers (Hsieh and Klenow (2009), Moll (2014), Midrigan and Xu (2014)). Standard measures of misallocation proposed in the literature do not apply in our context, which entails decreasing returns to scale, adjustment costs and a borrowing constraint. We thus propose a novel decomposition of the welfare gains from removing the collateral constraints, which accounts separately for reallocation gains and the gains from increased aggregate resources. To this end, we compute the welfare that a planner could achieve by reallocating resources in the actual economy, keeping the aggregate inputs at their actual level. The difference between this hypothetical welfare and the welfare of the actual economy corresponds to the welfare gains that are achieved purely through a reallocation effect. The difference between the welfare in the counterfactual economy and this hypothetical welfare corresponds to the welfare gains that are achieved by increasing aggregate inputs, holding the cross-sectional allocation of inputs efficient. We find that the misallocation of resources is responsible for 1.3 percentage point of the 5.3% welfare costs of collateral constraints. This is because in the presence of large adjustment costs, there is little efficiency gains to be achieved by reallocating capital from the least to the most efficient units of production in the economy. The remaining 4% welfare costs of collateral constraints are attributed to a 17% reduction in the aggregate capital stock. Interestingly, the removal of collateral constraints only increases aggregate employment by about 1%. This surprising result comes from the asymmetry of capital and labor in terms of financing costs: while capital needs to be funded ex ante, labor can be rented every period. Therefore, constrained firms, in particular firms with no real estate assets on their balance sheet, tend to substitute labor for capital. When these firms get unconstrained access to outside financing, they optimally increase their capital to labor ratio, which leaves the aggregate demand for labor almost unchanged. Related Literature. Our focus on collateral constraints is rooted in large array of empirical evidence on the importance of collateral constraints. It is well documented that collateral plays a key role in financial contracting. More redeployable assets receive larger loans and loans with lower interest rates (Benmelech et al. (2005)). The value of collateral affects the relative ex post 5

6 bargaining power of borrowers and lenders (Benmelech and Bergman (2008)). Beyond these effects on financial contracting, collateral values also affect real outcomes at the micro-economic level: firms with more valuable collateral invest more (Gan (2007), Chaney et al. (2012a)); individuals with more valuable collateral are more likely to start up new businesses (Schmalz et al. (Forthcoming)). Additionally, many empirical evidence point to the prevalence of real estate collateral in loan contracts (Davydenko and Franks (2008), Calomiris et al. (2015)). Our paper adds to the literature by bridging the gap between microeconomic evidence on the role of collateral constraints and the macroeconomics of financial frictions. Our paper also contributes to the long-standing literature in corporate finance investigating the real effects of financing frictions. This literature has traditionally explored the effect of financing frictions on corporate investment. The empirical challenge is to find exogenous variations in financing capacity that are not correlated with investment opportunities. For instance, Lamont (1997) overcomes this challenge by showing that non-oil divisions of oil conglomerates increase their investment when oil prices increase. Rauh (2006) shows that firms with underfunded defined benefit plans need to make financial contributions to their pension fund, depriving them of available cash-flows and leading to reduced investment. 56 A more recent incarnation of this literature investigates the effects of credit constraints on labor demand. Using individual data from the US Current Population Survey, Duygan-Bump et al. (2010) show that employees of small firms that rely heavily on external finance, were more likely to lose their jobs during the great recession. Looking at survey evidence from US managers during the same period, Campello et al. (2011) show that firms reacted to financing constraints by reducing investment, R&D spending, and employment. Chodorow-Reich (2013) uses firm-level data to show that firms borrowing from banks most affected the US banking crisis tended to reduce employment the most. Finally, Benmelech et al. (2010) use three different credit supply / cash-flow shocks to identify the effects of credit 5 See Bakke and Whited (2012) for a discussion of this identification strategy. 6 The literature on this topic is extensive. For some important contributions, see Fazzari et al. (1988), Erickson and Whited (2000), Kaplan and Zingales (1997), Almeida and Campello (2007), Blanchard et al. (1994), Campello et al. (2010), Chaney et al. (2012b), Kaplan and Zingales (2000), Peek and Rosengren (2000), Campello et al. (2011). 6

7 constraints on the labor demand of US listed firms. Relative to this literature, our paper provides a joint estimation of the effect of financing friction more precisely of collateral constraints on both investment and employment growth. We also contribute to this literature by providing a quantitative interpretation of our well-identified reduced-form evidence based on a structural approach. Several important papers have developed a structural quantitative approach to estimate the effect of financing frictions. This literature is reviewed in Strebulaev and Whited (2012). In a seminal contribution, Hennessy and Whited (2007) apply SMM to a dynamic model to infer the magnitude of financing costs. They find that for small firms, estimated marginal equity flotation costs is about 10.7% and bankruptcy costs equal to 15.1% of capital. Hennessy and Whited (2005) develop a dynamic trade-off model, which they structurally estimate to explain several empirical findings inconsistent with the static trade-off theory. Lin et al. (2011) examines the impact of the divergence between corporate insiders control rights and cash-flow rights on firms external finance constraints via generalized method of moments estimation of an investment Euler equation and show that the agency problems associated with the control-ownership divergence can have a real impact on corporate financial and investment outcomes. Nikolov and Whited (2014) estimate a dynamic model of finance and investment with different sources of agency conflicts between managers and shareholders to analyze the role of agency conflicts in corporate policies and investment. Relative to this literature, our contribution is twofold. First, we include coefficient estimates from a reduced-form regression identifying the effect of collateral constraints on employment, investment and debt as targeted moments. We show that these moments are crucial in identifying the strength of financial frictions in our data. Second, we nest our investment model into a general equilibrium model, which allows us to account for general equilibrium effects in our counterfactuals. In contrast, the literature typically only considers partial equilibrium counterfactuals. Finally, our paper contributes to the important macroeconomic literature on the aggregate effects of financial frictions. Restuccia and Rogerson (2008), Hsieh and Klenow (2009) and Bar- 7

8 telsman et al. (2013) emphasizes that the misallocation of resources across heterogenous firms can have important effect on aggregate TFP and welfare. Midrigan and Xu (2014) focuses on financing frictions as a source of misallocation. They calibrate a model of establishment dynamics with financing constraint and find that financing frictions cannot explain large aggregate TFP losses from misallocation. In contrast, Moll (2014) shows that for a TFP persistence parameter in the empirically relevant range, financial frictions can matter in both the short and the long run. Buera et al. (2011) develop a quantitative framework to explain the relationship between aggregate/sector-level TFP and financial development across countries and show that financial frictions account for a substantial part of the observed cross-country differences in output per worker, aggregate TFP, sector-level relative productivity, and capital-to-output ratios. Beyond misallocation, a large literature has investigated the effects of financing friction on aggregate TFP growth and welfare. Jeong and Townsend (2007) develop a method of growth accounting based on an integrated use of transitional growth models and micro data and find that in Thailand, between 1976 and 1996, 73 percent of TFP growth is explained by occupational shifts and financial deepening. Amaral and Quintin (2010) present calibrated simulations of a model of economic development with limited enforcement and find that the average scale of production rise with the quality of enforcement. Eisfeldt and Rampini (2006) study the costly reallocation of capital across heterogenous firms. They infer the cost of reallocation from a calibrated model and show that reallocatoin cost need to be largely countercyclical to be consistent with the observed dispersion of productivity. We make two distinct contributions to this literature. First, we base our quantification exercise on an estimation procedure that targets moments from a reduced-form analysis exploiting exogenous shocks to financing capacity. We show that standard calibrations cannot account for the joint dynamics of labor and capital following such shocks and thus lead to erroneous inference of the parameters related to the collateral constraint. Second, our paper combines adjustment cost to both labor and capital with financing friction, in an economy where firms are heterogeneous in TFP. Asker et al. (2014) consider the effect of adjustment costs on static misallocation measures, but their economy does not feature a financing friction. In contrast, our 8

9 approach delivers interesting implications on the interaction between adjustment costs and credit frictions. We present reduced form evidence of the effect of collateral values on both investment and employment in Section 1. We present our formal model of firm dynamics with collateral constraints in Section 2. We structurally estimate the model using French firm level data in Section 3. Section 4 presents our counterfactual analysis. Section 5 concludes. 1 Reduced form evidence In this section, we describe our dataset, we explain how we construct a measure of the value of real estate holdings at the firm level, and we present reduced form evidence on the impact of real estate collateral shocks on firms investment and labor demand. In the next Sections, we will then use these results as moments to identify adjustment costs and collateral constraints in a structural model. 1.1 Data Our sample is an administrative dataset of all French firms from 1998 to We describe the sample construction in detail in Appendix A. Accounting items come from tax files. The definitions of capital, investment, cash-flows and other accounting items are designed to match existing US studies on COMPUSTAT. The tax files also provide us with the book value of buildings, gross and net of depreciation. We use a 2-digit industry classification similar to the SIC2 classification in the US. Our firm-level employment measure comes from plant-level employment counts, aggregated at the firm level. We focus most of our analysis on single-plant firms for which the location of real estate assets is known with the highest precision possible but as we show in our robustness checks, our estimates are similar when including multi-establishment firms. Our starting sample has about 1 million observations, corresponding to about 100,000 firms every year. Because we restrict ourselves to firms present in 1998, the final sample size goes down to 750,000 observations. 9

10 Our results are robust to including new entrants in the sample. Following Chaney et al. (2012a), our main test to gauge the importance of the collateral channel for labor and capital demand consists of regressing investment and employment on real estate value (RE Value). Real estate value is computed as follows: for each firm-year observation (i, t), we first retrieve the gross and net values of buildings in 1998, i.e. the starting year of our sample. Assuming linear depreciation over 25 years, we estimate the average age of buildings a i for firm i in For each year t in the sample, we then take the gross accounting value of buildings in 1998 and multiply it by cumulative real estate inflation between t a i and t in the location where the buildings are located. This provides us with a proxy for the market value, in year t, of the real estate assets held by the firm in Constructed this way, our measure of real estate value only varies because local house prices vary. It thus eliminates variations in real estate value coming from the purchase of new buildings or the sell of existing buildings. Real estate prices are measured as residential real estate prices in the département where the firm s single plant is located. 7 This leads us to an estimate of the market value of the real estate held by the firm. In our sample, the average value of a firm s real estate is equal to about 30% of its book physical capital (equivalent to property, plants and equipment in US data). During the period, this ratio goes up from 25% to 35% as house prices increased nationally though at different paces in different location (Figure E.1). Summary statistics for our sample are provided in Table Reduced form estimation Specification. For firm j, in département d, at date t, we estimate: Y jdt P P E jd,t 1 = a j + b dt + β RE Value jdt P P E jd,t 1 + controls jdt + ɛ jdt (1) where a j is a firm fixed effect, and b dt a fixed effect designed to control for département-level shocks. RE Value jdt is the measure of the value of real estate described above. We cluster error 7 A French département is approximately the size of a US MSA; There are 95 départements in France. 10

11 terms at the département level (95 clusters). This clustering level is designed to capture that our source of variation of RE Value is partly but not only driven by département level house prices. Y jdt is a measure of investment or change in employment for firm j in year t. β is the coefficient of interest in Equation (1). Its estimation relies on a strategy similar in spirit to a difference-in-differences identification. The treatment group consists of firms that own some real estate assets; the control group consists of firms with no real estate assets. The (continuous) treatment is the house-price growth in the département. A rise in house prices increases the collateral value available to land-holding firms, whereas it leaves leasersâăź debt capacity unaffected. Our identifying assumption is that land-holding firms face the same local shocks and investment opportunities as renters, so that leaserâăźs input choices serve as a useful benchmark for the effect of local economic activity on firm-level hiring and investment and β captures the causal effect of the collateral channel on firm outcome Y. This identification strategy uses two sources of variation in the data to identify β: (1) in a given year, some dèpartment experience larger house-price growth than others, so that β is identified by comparing the difference in investment/hiring between land-holding firms and renters across these regions with different house-price growth; (2) within a given département, house-price growth varies in the time-series, so that β is also identified by comparing, within each region, how the difference in investment and hiring between land-holding firms and leasers varies as house-price growth evolves. A positive β indicates that, in regions with high house-price growth, land-holding firms invest or hir more than leasers, relative to regions with smaller house-price growth. The null hypothesis is that β = 0, which would indicate that collateral values do not affect firms input choices. By contrast, if collateral facilitates investment or hiring, we should expect a positive estimate, β > 0. Since variations in house prices, both cross-sectionally and in the time-series, are crucial to identification, We report house price indices by département in Figure E.1. Panel A plots the trends for all départements taken together. Panel B plots trends for the top 20 départements in terms of number of firms in Altogether, these départements account for half of the firms in 11

12 1998. These two panels show that real estate inflation varies considerably across départements, from about 50% to more than 150%. Investment. We measure investment as capital expenditure ( Immobilisations Productives which corresponds to property plants and equipment in US data), so that our dependent variable in Equation 1 is CAP EX t /P P E t 1. We first replicate the results of Chaney et al. (2012a), which look at the impact of RE value on investment, using a sample of publicly listed firms in the US. We thus verify here that their baseline investment regression still works (1) in a different country and (2) on a sample of smaller, unlisted firms where real estate assets are precisely located. The results are reported in Table 2, columns 1-4. Column 1 only includes firm and year fixed effects. β is estimated at.17 and is statistically significant at the 1% confidence level. One issue with our approach at this point is that real estate ownership is endogeneous. Land-holding firms could share some characteristics that explain both why they hold real estate assets and why their investment co-vary more with the local housing cycle. For instance, firms in retail trade may be more likely to own their stores relative to firms in wholesale trade; at the same time, investment in the retail industry may be more sensitive to the local housing cycle. As in Chaney et al. (2012a), we do not have a firm-level instrument for real estate ownership. We thus simply address this issue by controlling for various firm-level observable characteristics that are likely to correlate with the own vs. lease decision. Precisely, Column 2 includes as further control four firm-level characteristics measured in 1998 (2-digit industry dummies, size measured as log of total assets, return on assets, leverage) interacted with dèpartement-level house price growth from 1998 to year t. These interacted controls ensure that our effects is not simply driven by the endogeneous selection of firms into land-holding based on these observables. Importantly, Column 2 shows that these controls do not change the point estimate, suggesting that there is very little selection into real estate ownership based on observables. In column 3, we add one additional timevarying control: the cash-flow to capital ratio, which is a standard determinant of investment in the literature on financial constraints (Fazzari et al. (1988)). β is now estimated at.15 and is 12

13 still significant at the 1% confidence level. The investment literature typically uses the firm-level book-to-market ratio as a proxy for marginal Q and thus existing investment opportunities. We cannot use this approach since most of our firms are not listed. Instead, we include industry dèpartement year dummies in order to capture industry-level, local, time variation in investment opportunities. In spite of this restrictive set of controls (11 years 95 regions 20 industries = 20,900 different dummies, in addition to firm-fixed effects), our baseline estimate is unaffected at.15. We find larger effects in the sample of French firms than in our previous US study. The fully saturated specification in column 4 estimates that a e1 increase in the value of real estate assets leads to an increase in investment by some.15 Euro. In our sample of publicly listed US firms, we found that a $1 increase in real estate wealth led to a $0.06 increase in capital expenditures. Hence, the effect on French firms that we estimate here is about three times larger. This difference is consistent with the fact that (1) we observe real estate with greater precision in the French sample, thus reducing attenuation bias (2) our French sample consists mostly of privately-owned, small firms, which are more likely to be financially constrained than large, publicly-traded corporations in the US. We also show that, consistent with the collateral channel, the increase in real estate collateral value lead to increased debt issuance. To this end, we simply estimate Equation 1 using change in total debt (bank-financed and trade payables) normalized by lagged tangible assets as a dependent variable. The results are reported in Table 2, column 5-9, which follow the same specification as column 1-4 respectively. A e1 increase in the value of real estate collateral leads to 20 cents of additional debt, remarkably close to the 15 cents obtained for the investment equation (Column 8). Labor demand. We explore two distinct specifications looking at how labor demand respond to shocks to the value of real estate collateral. First, we simply use the ratio of employment change to lagged capital, Emp t /P P E t 1 as a 13

14 dependent variable in Equation 1. These results are reported in Table 3, columns 1-4, which again follow the specifications of Table 2, column 1-4 respectively. In the most restrictive specification (column 4), β is estimated at 1.5 and is statistically significant at the 1% confidence level. Since our dependent variable is multiplied by 1,000 (to facilitate the reading of the table), this point estimate implies that, for a e1 Million increase in real estate value, firm-level employment increases by 1.5 employee. Second, to facilitate the comparison with the investment response to shocks to collateral value, we use symmetrized employment growth, defined as 2 Emp t / (Emp t + Emp t 1 ) as an alternative dependent variable. Estimates are reported in Table 3, columns 5-8. The most restrictive specification (column 8) shows that an in increase in real estate value by 10 percentage point of the previous year capital stock leads to increased employment growth of 0.25 percentage points ( ). This effect is in line with estimates from columns 1-4, as we discuss in detail in Section Magnitudes The results in Table 2 and 3 show that variations in collateral values affect significantly input choices by firms. They also suggest that the aggregate effects implied by the collateral channel have the potential to be large. For instance, from 2002 to 2007, RE Value jdt P P E jd,t 1 increases by about 10 percentage points. Given our estimates from Table 2, this translates into an increase in investment by about 1.5 percentage points due to the collateral channel (.15.1). This direct effect corresponds to about 1/8 of the cumulative growth in aggregate investment over the same period. 8 Looking at employment, a similar calculation shows that during the sample period, the average additional employment growth due to the collateral channel could be equal to 0.25 percent ( ). Given that total employment in France is around 20m, this suggests that the collateral channel may have led to the creation of approximately 50,000 jobs between 2002 and 2007, as much as 10% of aggregate job growth during the same period. 8 During this period, French national accounts report that non-financial corporate investment grew by 16.5%. 14

15 These aggregate quantifications are of course invalid, since they ignore potential GE effects like, for instance, investment of collateral-rich firms crowding out investment by collateral-poor firms. But it is suggestive that these micro-estimates could have significant effect at the macro-level. We investigate this question formally within the context of our quantitative model in Section Robustness We provide numerous robustness checks to our main results in Tables D.1-D.5. Sample selection. Potentially endogenous attrition is unlikely to be a concern. Our estimates are unaffected when we run regressions on a balanced sample of firms continuously present between 1998 and 2007, on a panel of firms with at least 5 employees, when restricting our analysis to firms that do not belong to a business group, or when we expand our sample to include multiple establishment firms. 9 All results are presented in Table D.1. Placebo Test. We assess the robustness of our estimation procedure but perform a placebo test using simulated data under the null that investment and RE Value are uncorrelated. Intuitively, we want to reallocate firms to another département and see whether in this simulated sample, investment and variations in house prices are still correlated for land-holding firms. To make the exercise simple, we restrict ourselves to the balanced panel. Using the actual empirical distribution of the time series of investment and of RE Value across firms, we draw, for each fictitious firm in our synthetic sample, one sequence of investment choices and one sequence of RE Value. We create enough fictitious firms so that the number of observations in the synthetic sample matches that of our real sample. We then estimate our baseline regression on this synthetic sample. We repeat this procedure 50 times. As we show in Figure E.2, we find a distribution of the coefficient β that is tightly located around zero, very far from our point estimate Variable definition. In Table D.2, we experiment alternative variable definitions, using standard employment growth ( Emp/Emp t 1 ) instead of a symmetrized measure of employment 9 To compute the market value of real estate holdings of multi-establishment firms, we simply weight each local house price index by the number of employees working for the firms in each locality. 15

16 growth, and using various treatment for outliers. Changing the definition of employment growth does not alter our results. Estimates are a bit sensitive to the treatment of outliers, but always remain strongly significant. Large vs small firms. Tables D.3 and D.4 show that the estimated collateral channel on labor is not a tiny firm effect. The estimates vary little across terciles of firm size, or across terciles of sectors ranked according to their export ratio. If anything, larger firms and firms operating in more global sectors are more sensitive to the value of their collateral. Dynamics. Table D.5 explores the dynamics of the collateral channel on labor. For k between 0 and 5, we regress Emp t+k /P P E t+k 1 on RE V alue t. The maximum effect of a e1 million increase in collateral is reached after 1 year (2.7 jobs created per million Euro of collateral), decreases afterwards, and becomes insignificant and small after 3 years. Control for local economic cycle. House prices reflect local economic activity. Our identifying assumption is that the investment and hiring decisions of firms with and without land holding depend in a similar way on local economic activity. If this assumption is violated, then our approach is invalid: β could simply reflect the different sensitivity of land-holding and non-land holding firms on local economic activity. To assuage this concern, we control for the interaction of a dummy equal to one for land-holding firms and two proxies for local economic activity, namely the yearly change in unemployment rate at the département level and the yearly change in regional-level GDP. As shown in Table D.6, these two additional interactions do not change our main results at all. Taken together, our reduced form regressions suggest a strong and significant effect of the real estate collateral channel for investment and labor demand. When the value of a firm s real estate assets, everything else equal, the firm invests and hires more. To assess the quantitative importance of the real estate collateral channel, and in particular its aggregate effects, we turn in the next section to a structural model of the firm. 16

17 2 The Model We present a neoclassical model of investment with three additional ingredients: (1) decreasing returns to scale (2) adjustment costs to both capital and labor, including fixed costs of adjustment (3) a collateral constraint limiting firms debt capacity. 2.1 Technology Each firm produces output combining capital and labor into a Cobb-Douglas production function subject to decreasing returns to scale, ( ) F (A t, K t, L t ) = A t K α t Lt 1 α ν (2) with A t the firm s total factor productivity; L t total employment in efficiency units; K t capital; α the share of capital in production; and ν < 1 the degree of decreasing returns to scale. The firm faces a downward sloping demand curve with constant elasticity σ, Q t = B t P σ t (3) The total revenue of the firm is then, R (z t ; K t, L t ) = exp (z t ) ( ) Kt α Lt 1 α θ (4) The returns to scale parameter θ ν (1 1/σ) combines both the technological returns to scale (ν) and the demand elasticity (1 1/σ). The revenue shifter term exp (z t ) A 1 1/σ t B 1/σ t combines both supply (A t ) and demand (B t ) shocks. For simplicity, we will refer to this term as productivity, while keeping in mind it contains any shock that affects the firm s revenue, both from the demand and supply sides The demand shifter term B t contains information on aggregate demand. In this section, we take aggregate demand as given. We calibrate the process for exp (z t ) to match French firms dynamics when we confront the model 17

18 2.2 Adjustment costs The firm s capital stock depreciates at a constant rate δ K. For a gross investment I t, the firm s capital stock evolves as, K t+1 = K t + I t δ K K t (5) Workers leave the firm at a rate δ L. This worker attrition captures both voluntary quits, and workers who leave the firm at the end of a fixed term contract, a feature prevalent in the French labor market. For a gross hiring E t, the firm s employment evolves as, L t = L t 1 + E t δ L L t 1 (6) The firm mechanically wants to invest and hire to replace depreciated capital and worker attrition. In addition, the firm s productivity is stochastic, so that the firm will want to adjust capital and employment in response to productivity shocks. When the firm changes its stock of capital by investing or disinvesting, or its level of employment by hiring or firing workers, it faces adjustment costs. To match both the lumpiness and skewness of investment and labor changes, we assume adjustment costs contain both a fixed cost and a quadratic adjustment cost. A firm with productivity z t, an existing stock of capital K t and existing workers L t 1, which wants to change its capital and employment to (K t+1, L t ) must pay the following adjustment cost upfront, Adj. Cost t = exp (z t ) ( ( ) ) Kt α L 1 α θ t f K 1 ( I t >0) + f L 1 ( ) E K t >0 + c K t L t 1 2 It 2 + c L K t 2 E 2 t L t 1 (7) The parameters (f K, f L ) and (c K, c K ) control the fixed and variable adjustment costs. Note a few assumptions built into the definition of the adjustment cost function. First, in keeping with the literature on costly adjustment since Lucas (1967), the variable adjustment cost to the data in section 3. We explicitly model the general equilibrium of the model, including the endogenously determined aggregate demand buried inside the B t demand shifter when we perform counterfactuals in section 4. 18

19 function is homogenous of degree one in (I t, K t ) and in (E t, L t 1 ), and convex in the size of the adjustment (I t or E t ). Second, the fixed cost is scaled by the revenue of the firm. This assumption ensures the problem of the firm is independent of firm size. The presence of fixed costs is necessary to match the lumpiness in labor and capital present in the data (Cooper and Haltiwanger (2006), Bloom (2009)). Third, we assume a one period time to build for capital as is conventional in the macro literature (Hall (2004a), Bloom (2009)): the firm pays in period t for capital that will only be used in production in period t + 1. Fourth, we assume no lag between the time a worker is hired and she starts working: a worker hired in period t starts working right away. There are two reasons for this assumption. The first is our data and our simulated model is at an annual frequency, so a one period time to start working would seem implausibly long. The second and more important reason is we want to analyze a special case where labor is freely adjustable. A one period lag to start for new workers would make labor a dynamic input even if f L = c L = Financing frictions Collateral constraint. The firm may raise debt from outside investors in order to fund its financing deficit. We assume that debt has a maturity of 1 period and set up the model such that it is risk-free. The firm may issue debt or hold cash instead, where cash is understood as negative debt. However, due to unmodeled frictions, e.g. limited enforcement as in Hart and Moore (1994), the firm cannot commit to repay its debt. We assume the firm can pledge some of its assets as collateral to mitigate this constraint. In the event of default, the financier seizes and liquidates the firm s collateral. The firm uses two types of assets as collateral: physical assets (K) and real estate assets (H). We abstract from issues related to the purchase or sale of real estate by firm and assume the amount of real estate H is constant throughout the life of each firm, but may differ across firms. 19

20 This assumption is made to simplify the exposition of the model. In our simulations, we assume in practice that the choice of H is endogeneous and time-varying, but faces adjustment costs that are so high that firms never change their holdings. The choice of a constant H is primarily motivated by the fact that in our dataset, very few firms change their real estate ownership status. Another motivation is that we can focus on the effect of real estate shocks on hiring and investing. Indeed, endogenizing real estate purchases in the model is feasible and simple, but it would interact with investment and hiring in a subtle way. For instance, firms may choose to purchase real estate in anticipations of events of high productivity and low debt capacity (Froot et al., 1993). It would be interesting to see how such a behavior would affect the moments of interest, but we defer this analysis to future research. The price of capital is normalized to 1. The price per unit of real estate is p t. In the event of liquidation, only a fraction s K of capital and s H of real estate can be recovered. Denoting by D t the amount of debt the firm will have to repay in period t, the firm faces the following collateral constraint on borrowing, D t s K K t + s H min (p t p t 1 ) H t (8) The term min (p t p t 1 ) guarantees repayment even if the lowest real estate price is realized. 11 Thus, debt is a risk-free investment for lenders. In addition to this collateral constraint, the firm faces two other financing frictions. Equity issuance. We forbid our firms from issuing equity. Denoting by e t the cash flows generated by the firm in period t, we impose a non negativity constraint on e, e t 0 (9) In our sample of mostly medium sized French firms, the vast majority of firms do not raise equity. Imposing a strict constraint of no equity issuance allows for a simpler characterization of the 11 We assume a discrete process for p t so that min (p t+1 p t ) is always correlated with p t. This means a shock to real estate prices at time t always has an impact on the debt capacity in period t. 20

21 optimal firm strategy. When we turn to our simulated model in the next section, we impose a milder assumption of a very large but finite cost of raising equity. Cost of debt. The interest rate the firm receives on cash is lower than the interest rate it has to pay on its debt. This spread between lending and borrowing rates allows us to pin down the choice of debt by the firm else, the firm would be indifferent across levels of D t as long as constraint (8) is satisfied. Formally, the firm receives/pays an interest rate r when it holds cash/owes debt, with r defined as, r if D < 0, r = r (1 + m) if D 0. (10) The borrowing premium m controls the spread between lending and borrowing rates. 2.4 Stochastic shocks and timeline Stochastic shocks. The firm is subject to two independent stochastic shocks, one for its productivity z, and one for real estate prices p. Both variables follow a discretized AR(1) process, where the persistence and volatility of the underlying processes are (ρ z, σ z ) and (ρ p, σ p ) respectively. Productivity shocks are firm specific. Real estate prices are region specific, so that all firms in the same region face the same price. Timeline. The timing of the firm s actions is as follows. The firm enters period t with an operational stock of capital, K t, an existing employment stock, L t 1, and outstanding debt that needs to be repaid, D t. At the beginning of period t, the productivity and real estate price shocks (z t, p t ) are realized. The firm pays back its debt. It chooses optimally the level of employment for the current period, L t, the stock of capital for the next period, K t+1, and the amount of debt to issue/cash to hoard, D t+1. The firm produces using existing capital and newly hired labor (K t, L t ), and pays the adjustment cost on capital and labor. 21

22 2.5 Optimal debt, investment and employment The firm is infinitely lived as long as it is not hit by an exogenous death shock which occurs with probability d each period. Capital, labor and debt are chosen optimally to maximize a discounted sum of per period cash flows, subject to a collateral and a no equity issuance constraint. The firm takes as given its productivity, local real estate prices, and forms expectation for future productivities and real estate prices according to their actual stochastic processes. Define as V (S t ; X t ) the value of the discounted sum of cash flows given the exogenous state variables X t = {z t, p t, H} and the past endogenous state variables S t = {K t, L t 1, D t }. This value function V is the solution to the following Bellman equation, V (S t ; X t ) s.t. { = max e (St, S t+1 ; X t ) + 1 de [V (S S 1+r t+1; X t+1 ) X t ] } t+1 D t+1 s K K t+1 + s H min (p t+1 p t ) H e (S t, S t+1 ; X t ) 0 with e (S t, S t+1 ; X t ) = exp (z t ) ( ) Lt 1 α Kt α θ wlt I t + 1 Adj. Cost t = exp (z t ) ( ( ) ) Lt 1 α Kt α θ f K 1 I t >0 + f L 1 E K t >0 t L t 1+ r t+1 D t+1 D t Adj. Cost t + c K 2 I 2 t K t + c L 2 E 2 t L t 1 I t = K t+1 (1 δ K ) K t E t = L t (1 δ L ) L t 1 r t+1 = r if D t+1 < 0, (1 + m) r if D t+1 0 (11) Due to decreasing returns to scale and downward sloping demand, firms have an optimal scale of production. A firm initially below this level accumulates capital and hires workers. Once the target scale is reached, firms replace depleted capital and lost workers. When faced by a productivity shock, the firm adjusts towards its new desired steady state. Convex adjustment costs prevent the firm from adjusting factors instantaneously. Fixed adjustment costs make investment and employment changes lumpy. 22

23 Spending on adjusting capital and labor is bound by the collateral constraint. When the value of a firm s real estate assets increases, the collateral constraint is relaxed, and the firm finances more of the cost of adjusting towards its desired scale. This feature of the model will allow us to jointly estimate the structure of adjustment costs and of the collateral constraint by matching the sensitivity of investment and employment changes to real estate collateral. 2.6 Motivation for capital and labor adjustment costs We introduce adjustment costs to labor and capital in our model based on the reduced-form results presented in Section 1. Assume that there were no adjustment costs to labor, so that (f K, c K 0; f L, c L = 0) In our model, labor does not require financing because workers work as soon as they are hired. In the absence of labor adjustment cost, only capital is therefore directly affected by the collateral constraint. But because labor and capital are complement, labor demand is indirectly affected by the ease with which the firm can finance investment. To see this formally, notice that in the absence of labor adjustment costs, labor is determined by the static first order condition R L = w, so that: ( ) 1/(1 θ+αθ) ( ) w z t L t = exp K αθ 1 θ+αθ t (12) (1 α) θ 1 θ + αθ where K t is determined in the previous period. This equation makes it clear that, when collateral makes it easier to expand K, the firm also hires: machines need workers to be operated. Even without labor adjustment costs, labor demand reacts to real estate shocks. However, for plausible parameters, the model cannot replicate our reduced form results of Section 1. To visualize this, let us log-differentiate equation (12): L t L t = αθ K t + 1 θ + αθ K t 1 1 θ + αθ z t (13) This equation predicts labor moves with capital. It moves less than one for one because of de- 23