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 (e-mail: thomas.chaney@gmail.com)
‡
Princeton (e-mail: congerhuang@gmail.com)
§
Berkeley, NBER and CEPR (e-mail: sraer@berkeley.edu)
¶
HEC and CEPR (e-mail: thesmar@hec.fr)
1
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
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
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
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
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.
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
6
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 Bar7
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
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 2007. 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
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 ai for firm
i in 1998. 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 − ai 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 1998. 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 1.
1.2
Reduced form estimation
Specification.— For firm j, in département d, at date t, we estimate:
RE Valuejdt
Yjdt
= aj + bdt + β ×
+ controlsjdt + jdt
P P Ejd,t−1
P P Ejd,t−1
(1)
where aj is a firm fixed effect, and bdt a fixed effect designed to control for département-level
shocks. RE Valuejdt 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
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.
Yjdt 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 1998. Altogether, these départements account for half of the firms in
11
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 EXt /P P Et−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
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, ∆Empt /P P Et−1 as a
13
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∆Empt / (Empt + Empt−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
(≈ 0.025 × 0.10). This effect is in line with estimates from columns 1-4, as we discuss in detail in
Section 1.3.
1.3
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 Valuejdt
P P Ejd,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 (≈
0.025 × 0.10). 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
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 4.
1.4
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 0.15.
Variable definition.— In Table D.2, we experiment alternative variable definitions, using standard employment growth (∆Emp/Empt−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
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 ∆Empt+k /P P Et+k−1 on RE V aluet . 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
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 (At , Kt , Lt ) = At Ktα Lt1−α
ν
(2)
with At the firm’s total factor productivity; Lt total employment in efficiency units; Kt 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,
Qt = Bt Pt−σ
(3)
The total revenue of the firm is then,
R (zt ; Kt , Lt ) = exp (zt ) Ktα Lt1−α
θ
(4)
The returns to scale parameter θ ≡ ν (1 − 1/σ) combines both the technological returns to scale
1−1/σ
(ν) and the demand elasticity (1 − 1/σ). The revenue shifter term exp (zt ) ≡ At
1/σ
Bt
combines
both supply (At ) and demand (Bt ) 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.10
10
The demand shifter term Bt contains information on aggregate demand. In this section, we take aggregate
demand as given. We calibrate the process for exp (zt ) to match French firms dynamics when we confront the model
17
2.2
Adjustment costs
The firm’s capital stock depreciates at a constant rate δK . For a gross investment It , the firm’s
capital stock evolves as,
Kt+1 = Kt + It − δK Kt
(5)
Workers leave the firm at a rate δL . 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 Et , the firm’s employment evolves as,
Lt = Lt−1 + Et − δL Lt−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 zt , an existing stock of capital Kt and
existing workers Lt−1 , which wants to change its capital and employment to (Kt+1 , Lt ) must pay
the following adjustment cost upfront,
Adj. Costt = exp (zt )
θ
Ktα L1−α
t
fK 1 It >0 + fL 1
Kt
Et
Lt−1
>0
cK It2
cL Et2
+
+
2 Kt
2 Lt−1
(7)
The parameters (fK , fL ) and (cK , cK ) 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 Bt demand shifter when we perform counterfactuals in section 4.
18
function is homogenous of degree one in (It , Kt ) and in (Et , Lt−1 ), and convex in the size of the
adjustment (It or Et ).
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 fL = cL = 0.
2.3
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
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 pt . In the event of
liquidation, only a fraction sK of capital and sH of real estate can be recovered. Denoting by Dt
the amount of debt the firm will have to repay in period t, the firm faces the following collateral
constraint on borrowing,
Dt ≤ sK Kt + sH min (pt |pt−1 ) Ht
(8)
The term min (pt |pt−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 et the cash flows
generated by the firm in period t, we impose a non negativity constraint on e,
et ≥ 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 pt so that min (pt+1 |pt ) is always correlated with pt . This means a shock to
real estate prices at time t always has an impact on the debt capacity in period t.
20
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 Dt as long
as constraint (8) is satisfied. Formally, the firm receives/pays an interest rate r̃ when it holds
cash/owes debt, with r̃ defined as,
r̃ =



r
if D < 0,
(10)


r (1 + m) if D ≥ 0.
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 (ρz , σz ) and (ρp , σp ) 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, Kt , an existing employment stock, Lt−1 , and outstanding debt that
needs to be repaid, Dt . At the beginning of period t, the productivity and real estate price shocks
(zt , pt ) are realized. The firm pays back its debt. It chooses optimally the level of employment
for the current period, Lt , the stock of capital for the next period, Kt+1 , and the amount of debt
to issue/cash to hoard, Dt+1 . The firm produces using existing capital and newly hired labor
(Kt , Lt ), and pays the adjustment cost on capital and labor.
21
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 (St ; Xt ) the value of the discounted sum of cash flows given the exogenous state
variables Xt = {zt , pt , H} and the past endogenous state variables St = {Kt , Lt−1 , Dt }. This value
function V is the solution to the following Bellman equation,



V (St ; Xt )









s.t.















with



























= max e (St , St+1 ; Xt ) +
St+1
1−d
E [V
1+r
(St+1 ; Xt+1 ) |Xt ]
Dt+1 ≤ sK Kt+1 + sH min (pt+1 |pt ) H
e (St , St+1 ; Xt ) ≥ 0
θ
e (St , St+1 ; Xt ) = exp (zt ) Lt1−α Ktα − wLt − It + 1+r̃1t+1 Dt+1 − Dt − Adj. Costt
I2
Et2
1−α α θ
Adj. Costt = exp (zt ) Lt Kt
fK 1 It >0 + fL 1 Et >0 + c2K Ktt + c2L Lt−1
Kt
Lt
It = Kt+1 − (1 − δK ) Kt
Et = Lt − (1 − δL ) Lt−1
r̃t+1 = r if Dt+1 < 0, (1 + m) r if Dt+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
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
(fK , cK ≥ 0; fL , cL = 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 RL = w, so that:
Lt =
w
(1 − α) θ
−1/(1−θ+αθ)
exp
zt
1 − θ + αθ
αθ
Kt1−θ+αθ
(12)
where Kt 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):
αθ
∆Kt
1
∆Lt
=
+
∆zt
Lt
1 − θ + αθ Kt
1 − θ + αθ
(13)
This equation predicts labor moves with capital. It moves less than one for one because of de-
23
creasing returns to scale (θ < 1). For a standard calibration, e.g. α = 1/3 and θ = 3/4 (returns
to scale ν = 0.95 and demand elasticity σ = 5), the elasticity of labor w.r.t. capital, holding
productivity unchanged, would be around 1/2.
If labor and capital were chosen contemporaneously, i.e. capital is not a dynamic input, any
shock, such as a change in RE Value, that affects investment today will also affect labor changes
today. Equation (13) predicts a 2 to 1 ratio of the sensitivity of investment to RE Value relative
to that of labor. In the data, we find a 10 to 1 ratio of those sensitivities (a coefficient of .19
for investment in Table 2, and .02 for the labor in Table 3). So a simple version of our model
with freely adjustable labor and capital chosen contemporaneously would over-predict the ratio of
coefficients by a factor 5.
If capital is chosen one period in advance, i.e. capital is a dynamic input, then equation (13)
ties the change in labor in period t (∆Lt ) to investment in period t − 1: ∆Kt is chosen one period
in advance. If RE Value at time t − 1 affects investment at time t − 1, it only affects labor with a
one period lag. With serially correlated real estate prices with persistence ρp = .65 as we calculate
in the data, equation (13) implies that the sensitivity of investment to real RE Value ought to be
about 3 times larger than that of labor. This 3 to 1 predicted ratio is still too large compared to
the 10 to 1 ratio we find in the data.
To further close the gap between the data and our model, we need to assume not only that
capital is a dynamic input, but also that labor and capital are subject to adjustment costs. Adjustment costs break the tight link between capital and labor changes implied by the first order
condition (12).
In Appendix B, we derive the first-order conditions that characterize the optimum policies in
the absence of fixed adjustment costs. This allows to derive some theoretical insights on the way
the collateral channel operates in our model.
24
3
Structural estimation
3.1
Estimation procedure
We estimate the key parameters of the model by simulated method of moments (SMM), which
minimizes the distance between moments from real data and simulated data. It proceeds as
follows: we select a vector of moments m computed from the actual data. Given candidate set of
parameters Θ, we solve the policy function, simulate a panel dataset of firms, and compute the
b (Θ). For each candidate Θ, we have a vector of deviations between the
simulated moments m
b (Θ). Under the moment condition that E [m − m
b (Θ0 )] = 0
actual and simulated moments, m− m
b that minimizes the
for the true value of the parameters Θ0 , we search the set of parameters Θ
weighted deviations between the actual and simulated moments,
b = arg min (m − m
b (Θ))0 W (m − m
b (Θ))
Θ
Θ
(14)
where the weight matrix W adjusts for the fact that some moments are more precisely estimated
than others. It is computed as the inverse of the variance-covariance matrix of actual moments
Ω estimated by bootstrap with replacement on the actual data. Under the null that the model
is correct, the optimal weighting matrix is (Ω(1 + 1/k))−1 where k is the number of independent
data simulated. We use 100 départements with independent real estate price processes, so there is
enough randomness in our simulations to use Ω−1 as our weighting matrix (see discussion in Bloom
b we use the standard CMA-ES algorithm. We describe the simulation
(2009)). To search for Θ,
procedure in greater detail in Appendix C.
3.2
Predefined and Estimated Parameters
The model has 20 parameters. We calibrate 14 of them using estimates from the literature or from
direct computation, and estimate the 6 remaining ones.
Predefined parameters.— Our 14 calibrated parameters are as follows. We use estimates from
25
Bartelsman et al. (2013) for the technology and preference parameters: we set the returns to
scale near unity, ν = 0.95, the capital share α = 1/3, and the demand elasticity σ = 5 (which
would lead to mark-ups of 25% in the absence of adjustment costs). Productivity log zt follows a
discretized AR(1) process with persistence ρz = 0.75 and volatility σz = 0.23 for the innovation.
We set the mean productivity log zt so that the steady state capital stock of our simulated firms is
equal to 10 Million euros, which corresponds to the average fixed assets of firms with more than 20
employees.12 Real estate prices log pt follow a discretized AR(1) process. We estimate this AR(1)
process on de-trended logged real estate prices and find a persistence ρp = 0.65 and volatility
σp = 0.06 for log pt . Both AR(1) processes for log zt and log pt are discretized using Tauchen’s
method. The exogenous firm exit rate is set to d = 5%, the rate of obsolescence of capital to
δK = 10%, the labor quit rate to δL = 7.5%, as the average fraction of workers that leave French
firms over 1998-2007, either because they are quitting or because their fixed-term contract ends
(DARES, 2013). The lending rate is set to 3% (return on cash) and the borrowing rate to 4.5%
(cost of debt, risk-free in our model). We fix wages w to 28,000 euros, which corresponds to the
average wage bill (including payroll taxes) over the number of employees for firms with more than
20 employees. We set the fraction of real estate owners at 50%, approximately as in our sample
of firms. We set the average value of real estate assets for owners, E [pt ] H, at 5.2 Million euros to
match the average real estate assets to capital ratio for owners in our sample (52%).
Estimated parameters.— Our 6 estimated parameters control the adjustment costs to capital
(fK , cK ), to labor (fL , cL ), and the pledgeability of capital and real estate (sK , sH ),
Θ = {fK , cK , fL , cL , sK , sH }
12
In the steady state, and assuming no adjustment cost, the FOCs for capital and labor combine into the following
expression for the mean productivity:
A
1−1/σ
B
1/σ
=
R
(1 − α)θ
1−αθ w αθ 1−θ
K
αθ
1+r
where R is the user cost of capital: R = 1−d
− (1 − δK ) ≈ r + δK + d. So if the average K is calibrated, and the
other parameters are known, this also fixes the average productivity.
26
3.3
Choice of Moments
We compute the moments on the sample of firms which have more than 20 employees. We do
this in order to avoid hiring/firing inaction due to worker indivisibility, a phenomenon apparent
in small firm data. In this section, we list the moments and justify their selection based on a
heuristic discussion on identification of the parameter we seek to estimate. We defer a sharper
discussion on identification to the next section.
To estimate our 6 parameters of interest, we match 7 moments in the data.
Moments 1-4 describe the behavior of investment and employment: the frequency of positive
investment; the frequency of labor changes; the average investment rate conditional on investment
being positive; the average absolute employment growth conditional on employment changing.
Those moments inform us on the distribution of investment and employment changes, both their
lumpiness and their average size.
Moment 5 is simply the average debt to asset ratio across firms. This moment is informative
about firms’ debt capacity and in particular how tight the collateral constraint is. Moments 6-7
correspond to the regression coefficients from the reduced form evidence discussed in Section 1: the
sensitivity of debt issues, investment and employment growth to the value of real estate collateral.
3.4
Identification
Before turning to the actual results, we discuss formally how our 6 parameters are identified in
practice. We report in Table 5 the sensitivity of moments with respect to model parameters, around
the SMM estimates. The intuition is that, if a given moment is very sensitive to a parameter, the
SMM procedure will estimate this parameter with more precision, since moving away from the
minimum distance estimate will make the simulated moment very different from the targeted data
moment.
The elasticities reported in Table 5 are computed using the following method, similar to Hennessy and Whited (2007). Take the k th parameter, whose SMM estimate is θ̂k , and the nth moment
27
whose data value is mn . We then fix the other parameters k 0 6= k to their SMM value, and simulate
h
i
data for various values of θk around θ̂k . For all simulations with parameter θk ∈ 0.5 × θ̂k ; θ̂k ,
we compute θk− as the average value of the parameter and m−
n as the average simulated moment.
h
i
Symmetrically for all θk ∈ θ̂k ; 1.5 × θ̂k , we compute the average θk+ and m+
n . We then define the
elasticity of the nth moment with respect to the k th parameter as:
n,k =
−
m+
θ̂k
n − mn
+
− ×
mn
θk − θk
Note these elasticities are local, i.e. estimated near the SMM estimates.
Two features are notable in Table 5. First, no parameter is identified from a single moment.
This justifies our SMM approach. Second, the two reduced form regression coefficients depend
strongly not only on the collateral constraint parameters (sK , sH ), but also on the adjustment cost
parameters (fK , fL , cK , cL ). This justifies our reduced form regressions.
The impact of the adjustment costs on the investment and labor moments (M1-M4) are intuitive. With larger fixed adjustment costs to labor, the firm adjusts labor less frequently, but
by more when it does so. For instance, a 10% increase in the fixed labor adjustment cost (fL )
reduces the frequency of labor changes by 1%, but increases the average labor change conditional
on hiring by 1%. The variable adjustment cost plays exactly a symmetric role. For instance, a
10% increase of the labor variable cost cL increases the frequency of positive investment by 1%,
but decreases the average investment conditional on investing by 2%.
The debt to capital ratio is crucially affected by the pledgeability parameters. When assets
(capital and real estate) are more pledgeable, leverage increases: a 10% increase in the pledgeability
of land (sH ) leads to a 29% increase in the leverage ratio; a similar increase in the pledgeability of
capital (sK ) leads to an 8% increase in leverage. That leverage is more sensitive to sH than to sL
is consistent with the view that real estate is more redeployable than standard productive capital
(Calomiris et al. (2015)). The leverage ratio is also negatively affected by all the adjustment costs.
For instance, a 10% increase in the variable capital adjustment cost cK reduces the debt ratio
28
by 12%. This is intuitive as higher variable adjustment costs imply lower investment ratios and
thus lower financing needs. The impact of the fixed adjustment costs is ambiguous. On the one
hand, with higher fixed costs, the firm adjusts inputs less frequently, and requires less debt. On
the other, the fixed costs have to be financed upfront, sometimes with debt. Around our SMM
estimates, the first effects dominates: for instance, a 10% increase in the fixed labor adjustment
cost fK decreases the debt ratio by 6%.
Interestingly, the effect of the pledgeability parameters (sK , sH ) on the reduced form regression
coefficients M6 and M7 is ambiguous. On the one hand, a higher sK or sH relaxes the firm’s borrowing constraint, and allows it to make investment and hiring decisions solely based on efficiency
consideration, and not on the collateral value of its assets. That first effect lowers the regression
coefficients. On the other hand, a higher sH makes the debt constraint more sensitive to the
value of real estate prices; for those firms that still face a binding debt constraint, it makes their
investment and hiring decisions more sensitive to the value of their real estate. This second effect
increases the regression coefficients. In the vicinity of our SMM estimates, the first (negative)
effect dominates: both regression coefficients are negatively affected by the collateral value of capital and real estate. A 10% increase in sH lead to a 1% decline in the coefficient of investment on
real estate value and a 4% decline in the coefficient of hiring on real estate value.
The effect of adjustment costs on the reduced form regression coefficients is also ambiguous.
On the one hand, adjustment costs to capital and labor make input choices less sensitive to
a relaxation/tightening of the collateral constraint. This first effect lowers both reduced form
coefficients with the fixed adjustment costs (less frequent adjustments), and with the convex
adjustment costs (smaller adjustments). On the other hand, adjustment costs have to be financed
upfront, and are subject to the collateral constraint. This second effect increases both reduced form
coefficients with the adjustment costs. In the vicinity of our SMM estimates, a 10% increase in the
fixed labor adjustment cost fL increases the labor coefficient by 16% (the second effect dominates),
while a 10% increase in the variable capital adjustment cost cK decreases the investment coefficient
by 24% (the first effect dominates).
29
3.5
Estimation Results
Results are reported in Table 6. Panel A shows the actual moments from the data, and the
simulated moments from the estimated model. Panel B shows the estimated coefficients. To
clarify intuitions about estimation, we estimate four variants of the model: with adjustment
costs on both capital and labor (“All”), with capital adjustment costs only (“Capital”), with labor
adjustment costs only (“Labor”) and with no adjustment costs (“None”).
Looking at the model without capital adjustment costs (“Labor”, fK , cK = 0), the estimation
procedure seeks to match moments by taking a very low value of pledgeability for capital (sK
small). A low sK acts as a substitute for capital adjustment costs, as the firm avoids losing the
little collateral value it gets from its capital stock. This ensures that investment does not react too
much to productivity shocks, so that the estimation manages to match the investment moments.
But the consequence is that firms need to preserve debt capacity in case they need it, so that
the leverage is low (9%), at odds with the data (19%). The estimates of the model without labor
adjustment costs show the opposite picture (“Capital”, fL , cL = 0). Compared to the data, the
model generates adjustments to labor that are too frequent (98% versus 84% in the data), and
too large (27% versus 14% in the data). When adjustment costs on both capital and labor are set
to zero (“None”, fK , cK , fL , cL = 0), all simulated moments are off: firms adjust capital too rarely
(70% versus 96% in the data), labor too frequently (98% versus 84% in the data), they adjust
capital and labor too much when they do so (by 28% and 27% versus 15% and 14% in the data),
their debt ratio is too low (5% instead of 19%), and both reduced form regression coefficients are
too large (0.25 versus 0.18 for capital, and 0.07 versus 0.04 for labor).
When we allow for both capital and labor adjustment costs (“All"), we can match all moments
well. In particular, the regression coefficients estimated in our simulated data precisely match
those in the data (0.19 in simulated data versus 0.18 in the actual data for the coefficient of
investment on real estate value, and 0.05 versus 0.04 for the labor coefficient). We under-predict
the frequency of positive investment (89% versus 96% in the data), and the debt to capital ratio
30
(13% versus 18% in the data).
Consistent with most of the literature, we estimate a fixed adjustment cost of capital that is
rather low (fK = 0.02) and a large variable cost to adjusting capital (cK = 0.42).13 We also find
a relatively large fixed cost of adjusting labor (fL = 0.09, so that adjusting labor represents on
average 9% of the firm’s annual sales), and a low variable adjustment cost on labor (cL = 0.06).
Finally, we find that while the collateral value of $1 of capital is fairly low (sK = 0.14), real estate
assets are easily pledgeable (sH = 0.87). This is consistent with the fact that real estate assets
are more easily redeployable than productive assets, and therefore a better source of collateral;
importantly, these numbers are in line (Calomiris et al., 2015).
Note in passing that 0.87 is very different from the measured sensitivity of investment to real
estate collateral (0.14). This difference is a reminder that parameters in reduced forms are not, in
general, deep structural parameters. In particular, it is important to remember that the sensitivity
of investment to collateral values is a non-monotonic function of sH : If sH is large, owners are
not constrained, and their investment decisions do not depend on the collateral value of their real
estate. This would lead to lower sensitivities.
We gauge the model fit by focusing on a particular relevant moment that we do not use in
the estimation procedure, the sensitivity of debt to real estate value. On our simulated data, a
regression of firm debt issuance (Dt+1 − Dt )/Kt on real estate value leads to a point estimate of
.22: a $1 increase in real estate value on debt issuance is about 22 cents (see Column (8) of Table
D.4). On our actual sample, the estimate is .2.
The estimated parameters can be compared with existing studies, summarized in Bloom (2009).
Compared to Bloom (2009), we find a similar level for the fixed capital adjustment cost (2% of
annual sales versus 1.5% in Bloom), and a larger fixed labor adjustment cost (9% of annual sales
versus 2.1% in Bloom). Our larger estimate for the fixed labor adjustment cost may be due to the
more rigid labor market regulations in France compared to the US, and to the fact that we use an
13
fK = .02 implies that the firm needs to spend 2% of sales to invest; cK = .42 implies that to invest $1, and
considering an investment ratio of around 10%, the firm needs to pay about 4 cents.
31
administrative dataset of mostly mid-sized French firms while Bloom uses only larger US publicly
traded firms. Our model (and Bloom’s) assumes fixed costs scale with firm size; any additional
fixed cost which does not would tend to lower the effective fixed adjustment cost for larger firms.
We find that a model with quadratic adjustment costs to capital and labor performs better at
matching our data than a model with linear adjustment cost. Our estimates for the quadratic
adjustment costs are therefore not directly comparable to Bloom’s, who assumes both linear and
quadratic variable costs. But we find the same larger variable adjustment cost on capital than
on labor as Bloom and the rest of the literature do. One notable exception is Hall (2004a), who
finds no evidence of variable adjustment costs on either capital or labor. To the extent he uses
aggregate (sectoral) data, his estimates are not directly comparable to our firm level evidence.
3.6
Dynamic Behavior of the Model
We investigate the partial equilibrium dynamic behavior of the model in Figures 1 and 2. Figure
1 reports the response of firms to a permanent shock to house prices (a one standard-deviation
shock). We proceed as follows: We start with the simulated data. We then regress Dt+1 , Kt+1
and Lt on (Dt+1 , Kt+1 , Lt , zt , pt ) using OLS. We thus obtain a linear approximation of the optimal
policy rule implied by our SMM estimate of the model. We then use this estimated policy function
to show the response of debt, capital and labor to a one-off one standard deviation shock to p,
keeping z constant. We report separate impulse response functions for owners and renters. As
expected, renters do not react to a real estate price shock (the small deviations correspond to
numerical errors leading to non zero estimation of the policy function). Owners however react by
increasing debt by about 14%. This increase takes about 10 years to take place. Over the same
period, they increase capital by about 2.2% and labor by 1%. These IRFs are consistent with our
reduced-form strategy: investment, hiring and borrowing all respond to changes in house prices
for owning firms.
Figure 2 investigates the reaction of capital, labor and debt to a one s.d. shock in productivity.
When the firm experiences a positive productivity shock, it borrows, invest and hires. The salient
32
feature is that owners respond by increasing their borrowing more, investing more, but hiring less
than renters. The intuition for this is that owners have enough spare debt capacity to withstand
future negative productivity shocks, and thus can afford to increase leverage more. Owners can
invest and disinvest more easily because of their additional debt capacity. They thus has an
incentive to adjust to productivity shocks with capital more than labor, whose adjustment costs
are bigger.14
This feature is more apparent in Figure 3, which shows the relative difference of borrowing,
capital and labor between owners and renters, for each value of z. Consistently with the interpretation that looser borrowing constraints reduce the cost of adjusting capital, owners adjust their
capital more to the level of productivity. They have less capital than renters when z is low, and
more capital when z is high. They also borrow much more than renters, in particular when z > 0.
When facing a positive productivity shock, owners are less reluctant to borrow in order to invest,
as they have enough spare debt capacity to disinvest if z decreases. A second salient feature is
that owners tend to have lower employment levels than renters, unless z is very high. This is
indicative of capital-labor substitution effects induced by financing constraints and adjustment
costs. Owners choose to hold, across the productivity cycle, more capital and less labor, because
capital is relatively easier to adjust (thanks to their looser borrowing constraint) than labor.
4
Counterfactual experiments
Equipped with a fully specified and parametrized model, we are now ready to perform a series of
counterfactuals. Those counterfactuals shed light on how the model works, and they allow us to
assess the quantitative importance of the collateral constraint.
14
In the absence of labor adjustment costs, it turns out the labor and capital reaction to z of owners and renters
are nearly identical. We show impulse responses in Figure E.3: To construct them, we simulate data with SMM
parameters, except that we set cL = fL = 0. Clearly, constrained and unconstrained firms display the same reaction
of L and K. In the absence of labor adjustment costs, owners do not feel the need to substitute capital for labor.
33
4.1
General equilibrium
In order to perform counterfactual experiments, we need to re-compute the full general equilibrium
for each counterfactual, accounting for changes in factor prices and aggregate goods demand and
labor supply. To close the model, we make the following simple assumptions.
Firms produce intermediate inputs, Qit for firm i at time t. All intermediates are combined
into a CES-composite final good through the following CRS production function,
Yt =
X
σ−1
σ
σ
! σ−1
Qit
(15)
i
The price of good Yt is Pt =
P
i
Pit1−σ
1
1−σ
which we normalize to 1.
The final good (Yt ) is used for final consumption (Ct ), paying for the adjustment costs (Adj. Costt ),
and investment into new capital (It ),
Yt = Ct + Adj. Costt + It
with Adj. Costt =
P
i
(16)
Adj. Costit , and aggregate investment, It =
P
i Iit .
15
A representative consumer has inter-temporal preferences over consumption and labor,
1+ 1
Us =
X
− 1
t
β Wt with Wt = Ct − L̃
t≥s
Lt 1 + 1
(17)
where Ct are units of the composite final good, Lt are aggregate hours worked, L̃ is a simple scaling
constant, and is the Frisch elasticity of labor supply. With quasi-linear preferences, the Hicksian,
Marshallian and Frisch elasticities of labor supply are all equal to . Following Chetty (2012), we
set = 0.50. Since we only consider steady state equilibria such that aggregate consumption and
labor supply are constant over time, Us = Wt /β, ∀ (s, t), we use the flow utility Wt as our measure
15
Our assumption in section 2 that the price of the investment good is normalized to 1 is satisfied here, as
investment is composed of units of the composite final good, with a unit price Pt normalized to 1.
34
of welfare to be compared across counterfactuals.
The consumption Euler equation ties the equilibrium interest rate rt to the discount rate β,
and so we take interest rate rt as given throughout all counterfactuals.
Labor supply, LS , depends on the relative price of labor and consumption. Labor demand,
LD , emanates from all firms.



LS
t


LD
t
= L̃
=
wt
Pt
P
i
(18)
Lit
The final good and labor markets are competitive. The market for intermediates operates
under monopolistic competition. Each firm faces the following demand function,
Qit =
Pit
Pt
−σ
Yt
(19)
1−1/σ
1/σ
Under the normalization Pt = 1, we recover exactly our revenue equation R (zt ; Kt , Lt ) = At
Bt
θ
exp (zt ) Ktα L1−α
as in (4), with the demand shifter, Bt = Yt (the same for all firms), and our
t
“productivity” shock,
1−1/σ
exp (zit ) = Ait
1/σ
Yt
(20)
We adjust the endogenous Yt term in the firms’ productivity shock across counterfactuals, while
1−1/σ
the scaled TFP term Ait
always follows (in logs) the same AR(1) process.
S
To clear the goods market (Yt = Ct + Adj. Costt + It ) and the labor market LD
t = Lt , we
normalize the goods price Pt to 1 and solve for the equilibrium wage wt . All preference and technological parameters except the labor adjustment costs are kept constant across counterfactuals.
Quantities of interest.— For our benchmark economy and for each counterfactual, we compute
the following quantities. With our normalization Pt = 1, all measures are in real terms. Our
measure of aggregate welfare is given by Wt . Aggregate output, Yt , and aggregate consumption,
Ct , are both informative about aggregate efficiency. Aggregate labor, Lt , and wages, wt , inform
us about the functioning of the labor market.
35
Ktα L1−α
t
4.2
4.2.1
Counterfactuals: description
Main Counterfactual and Welfare Decomposition
Our main counterfactual experiment removes entirely the financing friction for all firms, owners
and renters. To do so, we allow firms to borrow up to a non-binding level. The aggregate variables
in this counterfactuals are shown in Column (3) of Table 7, as percentage changes relative to
the benchmark economy with the borrowing constraint. We see that in the steady state of the
economy with no borrowing constraints, welfare is higher by 5.4% than in the steady state of our
benchmark economy. The most striking feature of the counterfactual economy is the large rise in
aggregate capital relative to the benchmark economy – there is 17.2% more capital employed in the
counterfactual economy relative to the benchmark economy. Interestingly, aggregate employment
increases only slightly after financial frictions have been removed. One interpretation is that
financially constrained firms tend to distort their input choices toward using more labor and less
capital; when financial frictions are removed, these firms optimally substitute capital for labor,
leading to the large observed increase in the aggregate stock of capital, while leaving the aggregate
stock of labor almost unchanged.
The literature on the aggregate effects of financial constraints has emphasized that credit
frictions lead to substantial misallocation of resources across heterogeneous firms (Moll (2014),
Midrigan and Xu (2014) among others). In our dynamic economy, two channels may explain why
welfare increases following the removal of the collateral constraint: (1) in the cross-section of firms,
capital is better allocated when firms can borrow freely, i.e. more productive firms are able to
invest and hire more than they can in the constrained equilibrium (2) on average, all constrained
firms are able to invest and hire more, which increases the steady state output, consumption and
hence welfare. This last channel would operate even in an economy with a representative firm.
To assess quantitatively the relative contribution of these two channels to the 5.3% welfare gains
estimated in Table 7, we compute the equilibrium aggregate quantities in the following counterfactual economy: the borrowing constraint is removed again, but we impose uniform linear taxes
36
on labor and capital to ensure that the aggregate stock of capital and labor in this counterfactual
is similar to the benchmark economy. In other words, this new economy has no credit frictions
and uses the same amount of capital and labor in the aggregate than the benchmark economy. It
thus approximately represents the welfare gains that can be achieved through a better allocation
of resources, holding aggregate resources constant. Note however that this new economy may still
experience misallocation despite the absence of the credit friction, because of the linear taxes and
the fixed cost of adjustment to labor and capital. Section C.6 in the Appendix details how we
compute this new counterfactual and the welfare decomposition we propose.
The aggregate quantities in this economy are shown on Column (2) of Table 7, again as
percentage changes relative to the benchmark economy. The welfare in this counterfactual is 1.3%
higher than in the benchmark economy, although the aggregate stock of capital and labor remain
the same as in the benchmark economy. Thus, of the 5.3% overall welfare gains from removing
the borrowing constraint, 24% (1.3/5.3) can be attributed, according to this decomposition, to
improved allocation of capital and labor across heterogenous firms; the remain 76% come from
the large increase in the capital stock.
4.2.2
Additional Counterfactuals
To get a better sense of the quantitative importance of the adjustment costs to labor, we consider a
counterfactual where these adjustment costs are entirely removed. For this counterfactual (and this
one only), in order not to tautologically find that removing a wasteful adjustment cost increases
aggregate consumption, we assume for the benchmark economy (with fL , cL > 0) that all the
spending on labor adjustment costs is rebated lump-sum as consumption to the representative
consumer. This way, any increase in welfare will come from a more efficient use of resources, and
not simply from having removed a wasteful source of spending by firms.
In the same spirit, we propose a counterfactual where both the borrowing constraints and
labor adjustment costs are removed. This counterfactual is designed to get a better sense of the
interaction of these two crucial ingredients in our quantitative model.
37
Relaxing labor market rigidities.— The results are presented in column (2) of Table 8. When
all labor adjustment costs are lifted, labor becomes a static input. Firms can adjust labor instantaneously in response to productivity shocks. To the extent that capital is still subject to adjustment
costs, firms also get the option to adjust labor instead of capital in response to shocks. This increased flexibility allows for a more efficient allocation of resources across firms. We see that there
is a large aggregate increase in output (∆Y /Y = +9.9%), a large increase in adjusted consumption
(∆C/C = +9%). It also induces a reallocation of input demand away from capital and towards
labor, so that real wages increase substantially (∆w/w = +20%), inducing an increase in the aggregate labor supply (∆L/L = +9.3%). The increase in consumption more than compensates the
increased labor supply, and welfare increases (∆W/W = +5.9%).
Removing both financing frictions and labor adjustment costs.— Removing both frictions jointly
increases the aggregate efficiency even further. Comparing column (3) of Table 8 and column (3)
of Table 7, we see that about half of the aggregate gains (in welfare, production and consumption)
are obtained from removing financing constraint, the other half from further removing adjustment
costs to labor.
5
Conclusion
This paper provides a quantification of the aggregate effects of a particular source of financing
friction, collateral constraints. We present clean reduced form evidence that increases in the value
of collateral available to firms lead to increases in investment and labor demand. We build a
dynamic general equilibrium model that we estimate to be consistent with the firm-level joint
dynamic of labor and capital in response to shocks to collateral value. The model is then used to
simulate an economy where borrowing constraints are removed. We find that in this counterfactual
economy, welfare increases by 5.3%. We propose a decomposition of these welfare gains into
reallocation gains – more productive firms are able to obtain more funding when the borrowing
constraint is removed, holding aggregate inputs fixed – and gains from increased aggregate inputs.
38
Quantitatively 24% of these welfare gains can be traced to the increased allocation of resources
across hetereogeneous firms.
One limitation of this analysis is that the shocks to collateral value that we use to identify the
effect of collateral constraints at the firm-level are exogenous in the model. Yet, house prices are
an endogenous outcome and increased investment and hiring at the local level will clearly feed
back, in equilibrium, into local house prices. Additionally, since households are to some extent
mobile across regions, variations in house prices will induce variations in wages faced by firms,
which will affect their local input choices. Endogenizing the housing market and incorporating it
into our quantitative analysis is an important step that we plan to tackle in further research.
39
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6
Tables and Figures
Figure 1: Reponse to a Permanent Real Estate Price Shock
0
1
2
3
Panel A: Borrowing
0
10
20
30
year
Renter
Owner
Panel C: Labor
92
7.8
8
94
96
8.2
98
8.4
8.6
100
Panel B: Capital
0
10
20
30
0
year
Renter
10
20
30
year
Owner
Renter
Owner
Note: We first estimate the linearized policy function from data simulated using SMM parameters (500
firms in 100 departments over 10 years. Using this simulated panel, we regress (Dt+1 , Kt+1 ), Lt ) on Dt
, Kt , Lt−1 , zt and pt . We then use these parameter to simulate the response of the firm to a one s.d.
positive permanent shock to p. The firm is assumed to start from the average value of each of the five
state variables. This procedure (including the calculation of averages and policy function estimation) is
done separately for firms renting and firm owning real estate. Panel A is for debt, Panel B for the capital
stock and panel C for total employment. The red line is the impulse response of owning firms, and the
blue line the impulse response for renting ones. Renting firms do not react –beyond rounding errors– to
real estate prices. Their IRF is presented for comparison and is supposed to be perfectly flat.
44
Figure 2: Reponse to a Permanent Productivity Shock
0
1
2
3
4
5
Panel A: Borrowing
0
10
20
30
year
Renter
Owner
Panel C: Labor
80
8
100
10
120
12
140
14
160
Panel B: Capital
0
10
20
30
0
year
Renter
10
20
30
year
Owner
Renter
Owner
Note: We first estimate the linearized policy function from data simulated using SMM parameters (500
firms in 100 departments over 10 years. Using this simulated panel, we regress (Dt+1 , Kt+1 ), Lt ) on Dt
, Kt , Lt−1 , zt and pt . We then use these parameter to simulate the response of the firm to a one s.d.
positive permanent shock to z. The firm is assumed to start from the average value of each of the five
state variables. This procedure (including the calculation of averages and policy function estimation) is
done separately for firms renting and firm owning real estate. Panel A is for debt, Panel B for the capital
stock and panel C for total employment. The red line is the impulse response of owning firms, and the
blue line the impulse response for renting ones.
45
Difference between renters and owners
-.4
-.2
0
.2
Figure 3: Debt, Capital and Employment: Difference between Owners and Renters
-.3
-.2
-.1
0
Productivity (zt )
Employment (Lt )
Borrowing (Dt+1 )
.1
.2
.3
Capital stock (Kt+1 )
Note: This figure presents the percentage difference of debt, capital and labor between owning and renting firms,
as a function of productivity parameter z. We construct these measures using simulated data (500 firms in 100
regions over 10 years, using SMM parameters and at the steady state). We first compute, for each value of z,
the average debt, employment and capital of renting and owning firms More specifically, given the notations of
the model, “Employment” is measured as (Lot − Lrt ) /Lm
t where r stands for renting and o for owning firm and
r
o
o
r
m
Lm
t = (Lt + Lt ) /2. “Capital stock” is constructed symmetrically as (Lt − Lt ) /Lt . “Borrowing” is normalized by
o
r
m
capital: (Dt − Dt ) /Kt . Reading: For low values of z, renting firms tend to have a level of capital about 10%
higher than owning firms.
46
47
0.01
0.00
0.00
0.00
0.00
1.24
0.28
0.11
0.60
0.00
0.02
0.28
1.38
0.85
Owner Dummy
Assets
ROA
Leverage
0.44
9.28
0.06
0.16
0.00
9.15
0.05
0.11
0.00
3.74
-0.43
0.00
-0.73
0.00
0.75
-2.67
-0.72
-28.55
-2.66
-0.93
∆(Debt)
P P Et−1
1.00
19.03
0.53
1.08
0.73
1.82
3.25
4.79
0.72
28.55
2.67
1.09
0.00
8.49
0.01
0.04
-0.06
0.00
1.05
0.05
-0.06
-2.21
-0.19
0.02
p25
1.00
9.93
0.11
0.23
0.08
0.36
1.64
0.97
0.08
3.64
0.35
0.23
p75
125,065
86,228
86,228
86,228
1,059,840
1,078,211
1,078,211
1,078,211
1,062,435
1,078,211
1,078,211
1,078,211
N
is the change in total debt normalized by previous year PPE.
0.50
1.19
0.12
0.17
0.23
0.49
0.46
1.29
0.23
13.01
1.05
0.28
sd
is the standard growth rate of employment. RE Valuet is our proxy for the market value of firms’ real estate assets. Dep.
t
Index is the real estate price index defined at the département level. PCash
P Et−1 is the ratio of current cash flows to previous year PPE. Owner dummy
is a dummy equal to 1 if the firm owns some real estate assets in 1998. Assets is total assets. ROA is a return on asset computed as EBIT normalized
by total assets. Leverage is total debt normalized by total assets.
∆(Emp)
Empt−1
is the change in total employment normalized by previous year PPE (in million Euro). 2 Emp∆(Emp)
is the symmetric growth rate
t +Empt−1
is Capital Expenditure normalized by previous year PPE.
of employment.
CAP Xt
P P Et−1
∆(Employment)
P P Et−1
Note:
0.08
0.19
Panel B: Sample of firms in 1998
Casht
P P Et−1
RE_Value
Dep. Index
CAP Xt
P P Et−1
∆(Debt)
P P Et−1
∆(Employment)
P P Et−1
2 Emp∆(Emp)
t +Empt−1
∆(Emp)
Empt−1
mean median
min
max
Panel A: Sample of all firms from 1998 to 2007
Table 1: Descriptive Statistics
48
Yes
Yes
No
382507
(1)
.17***
(9.4)
-.02**
(-2.4)
Yes
Yes
No
325656
(2)
.17***
(9.2)
-.037***
(-2.7)
.0016
(1.2)
-.052**
(-2.5)
-.027
(-1.1)
Yes
Yes
No
(3)
.15***
(8.8)
-.052***
(-4.1)
.0033***
(2.6)
-.033*
(-1.8)
-.034
(-1.4)
.043***
(16)
325656
Yes
Yes
Yes
.0035***
(4.6)
-.038***
(-3.6)
-.034***
(-5.2)
.042***
(18)
330389
(4)
.15***
(29)
Yes
Yes
No
382507
(5)
.29***
(7.5)
-.13***
(-2.9)
Yes
Yes
No
325656
(6)
.3***
(7.3)
-.22*
(-1.7)
.0089
(.77)
.14***
(2.8)
.0027
(.023)
Yes
Yes
No
(7)
.2***
(5.5)
-.3**
(-2.5)
.018*
(1.7)
.25***
(4)
-.038
(-.33)
.25***
(15)
325656
∆(Debt)
P P Et−1
Yes
Yes
Yes
.021***
(3.7)
.25***
(4.7)
-.031
(-.79)
.25***
(24)
330389
(8)
.2***
(14)
Note: The dependent variable is Capital Expenditure normalized by previous year PPE (Column 1 to 4) and Changes in total debt normalized by
previous year PPE (Column 5 to 8). RE Valuet is our proxy for the market value of firms’ real estate assets. See Section 1.1 for the construction of
this proxy. Dep. Index is a département-level residential price index. Log(Assets98 ) is the log of the firm’s total assets in 1998. ROA98 is the firm’s
Return on Asset in 1998. Leverage 98 is the firm’s leverage in 1998. Casht is operating cash flows. Column 2 to 4 and 6 to 8 include industry and
département fixed effects interacted with the département-level real estate price index. All specifications include year and firm fixed effects. Column
4 and 8 include département-industry-year fixed effects. Our industry classification has 20 groups. Standard errors are clustered at the département
level. T-statistics are reporter in parenthesis.***, ** and * means significant at the 1, 5 and 10% significance level.
Year FE
Firm FE
Dep. × Industry× Year FE
Observations
Casht
P P Et−1
Leverage98 × Dep. Prices
ROA98 × Dep. Prices
Log(assets)98 × Dep. Prices
Dep. Prices
RE Valuet
CAP Xt
P P Et−1
Table 2: Investment, Capital Structure and Collateral Value
49
No
No
Yes
Yes
No
382507
Yes
Yes
Yes
Yes
No
325656
(2)
1.9***
(8.5)
-7.4***
(-6.2)
.64***
(4.3)
-2.5*
(-1.7)
-.54
(-1.1)
Yes
Yes
Yes
Yes
No
(3)
1.5***
(7.8)
-7.8***
(-6.6)
.69***
(4.5)
-2
(-1.4)
-.73
(-1.5)
1.2***
(14)
325656
Yes
Yes
Yes
Yes
Yes
.71***
(9.3)
-2***
(-3.1)
-.6**
(-2)
1.2***
(15)
330389
(4)
1.5***
(11)
No
No
Yes
Yes
No
382507
(5)
.032***
(6.4)
-.02***
(-3.2)
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
No
2 Emp∆(Emp)
t +Empt−1
(6)
(7)
.03***
.024***
(6.4)
(5.7)
-.027*** -.033***
(-2.8)
(-3.4)
.0012
.0018
(.9)
(1.4)
-.024
-.017
(-1.2)
(-.96)
-.023*** -.026***
(-3)
(-3.2)
.016***
(15)
325656
325656
Yes
Yes
Yes
Yes
Yes
.0021***
(2.8)
-.017*
(-1.9)
-.025***
(-4.6)
.015***
(16)
330389
(8)
.025***
(11)
Note: The dependent variable is Change in employment normalized by previous year PPE (Column 1 to 4) and symmetric growth rate of employment
(Column 5 to 8). RE Valuet is our proxy for the market value of firms’ real estate assets. See Section 1.1 for the construction of this proxy. Dep.
Index is a département-level residential price index. Log(Assets98 ) is the log of the firm’s total assets in 1998. ROA98 is the firm’s Return on Asset
in 1998. Leverage 98 is the firm’s leverage in 1998. Casht is operating cash flows. Column 2 to 4 and 6 to 8 include industry and département
fixed effects interacted with the département-level real estate price index. All specifications include year and firm fixed effects. Column 4 and 8
include département-industry-year fixed effects. Our industry classification has 20 groups. Standard errors are clustered at the département level.
T-statistics are reporter in parenthesis.***, ** and * means significant at the 1, 5 and 10% significance level.
Industry FE × Dep. Index
Dep. FE × Dep. Index
Year FE
Firm FE
Dep. × Industry× Year FE
Observations
Casht
P P Et−1
Leverage98 × Dep. Prices
ROA98 × Dep. Prices
Log(assets)98 × Dep. Prices
Dep. Prices
RE Valuet
(1)
2.4***
(8.4)
-1.7***
(-3.6)
∆(Employment)
P P Et−1
Table 3: Employment Changes, Employment Growth and Collateral Value
Table 4: Pre-defined parameters
Parameter
ν
α
σ
θ
ρz
σz
ρp
σp
d
δK
δL
r
r (1 + m)
w
E [pt ] H
Value
Description
0.95
Returns to scale
1/3
Capital share
5
Demand elasticity
3/4
ν σ−1
σ
0.5
Frisch elasticity of labor supply
0.75
Persistence of log zt shocks
0.23
Volatility of log zt shocks
0.65
Persistence of log pt shocks
0.06
Volatility of log pt shocks
5%
Exogenous exit rate
10%
Obsolescence rate of capital
7.5%
Exogenous worker attrition rate
3%
Lending rate
4.5%
Borrowing rate
28K euros Wage
5.2M euros Average value of real estate
50
Table 5: Elasticity of Moments w.r.t. Parameters
Frequency of Positive Investment
Frequency of Labor Changes
Average Investment Conditional on Positive
Average Labor Change Conditional on Non-Zero
Average Debt to Assets
Coefficient of Investment on Real Estate Value
Coefficient of Hiring on Real Estate Value
fK
fL
cK
cL
sK
sH
0
0
0
0
-.6
0
-.4
0
-.1
0
.1
-.3
1
1.6
.1
0
-.2
0
-1.2
-2.4
-.4
0
0
-.1
-.1
-.8
-.5
-.9
0
-.1
-.1
0
.8
-1.7
-1.2
0
-.1
0
.1
2.9
-.1
-.4
Note: This table reports the elasticity of various moments with respect to the structural parameters that
we estimate. To make the table easier to read, all elasticities are rounded to the first decimal point, so
b of the
zeroes stand for elasticities below 0.05 in absolute value. First, we start with the SMM estimate Θ
parameters Θ. For each k = 1, · · · , 6, we set θl = θ̂l for all l 6= k, and vary the parameter θk around the
estimated θ̂k . We then simulate datasets with these various levels of parameter θk , and for each dataset,
compute the simulated moments m = (m1 , · · · , m7 ). For each moment mn , we then compute the elasticity
of the moment w.r.t. parameter θk as
n,k =
−
m+
θ̂k
n − mn
+
− × m̂
θk − θk
n
where m̂n is the nth data moment. m+
n is the average of moments based on data simulated with parameters
−
θk between θ̂k and 1.5 × θ̂k . mn is the average of moments based on data simulated with parameters
θk between 0.5 × θ̂k and θ̂k . θk+ and θk+ are averages of the θk ’s in these two ranges. Reading: Around
the SMM estimate, a 1% increase in cK is associated with a 0.1% increase in the frequency of positive
investment in simulated data.
51
52
fK
cK
fL
cL
sK
sH
Actual
P [I/K > 0]
0.96
P [|∆L/L| =
6 0]
0.84
E [I/K|I/K > 0]
0.15
E [|∆L/L| ||∆L/L| > 0]
0.14
E(B/K)
0.19
coeffI/REV alue
0.18
coeffL/REV alue
0.04
All Capital
0.02
0.01
0.42
0.48
0.09
0.06
0.14
0.19
0.87
1.00
All Capital
0.89
0.81
0.80
0.98
0.13
0.15
0.12
0.27
0.13
0.29
0.19
0.15
0.05
0.08
Labor
0.08
0.17
0.07
0.55
Labor
0.72
0.82
0.20
0.11
0.09
0.19
0.04
None
0.01
0.46
None
0.70
0.98
0.28
0.27
0.05
0.25
0.07
Calculations are based on a sample of nonfinancial firms from French tax files. We restrict ourselves for firms with more than 20 employees. The
sample period is 1998 to 2006. Estimation is done with SMM, which chooses structural model parameters by matching the moments from a simulated
panel of firms to the corresponding moments from the data. The simulated panel of firms is generated from the model in Section 2, and contains
100 departments, each with 500 firms over 200 time periods. For each firm, we then drop the first 190 periods to remove transition dynamics, and
therefore only end up with 500,000 simulated observations. The first panel reports the simulated and estimated moments. The second panel reports
the estimated structural parameters.
Fixed Adjustment Cost on Capital
Quadratic Adjustment Cost on Capital
Fixed Adjustment Cost on Labor
Quadratic Adjustment Cost on Labor
Collateral Value of Capital
Collateral Value of Real Estate
Panel B: Parameter Estimates
Frequency of Investment
Frequency of Labor Changes
Average Investment
Average Labor Change
Leverage ratio
Coefficient of I/K on Real Estate
Coefficient of labor on Real Estate
Panel A: Moments
Table 6: Simulated Method of Moments Estimation
Table 7: Welfare Gains From Removing Financing Constraints
Benchmark
Welfare
Output
Capital
Employment
Real Wage
Adj. Consumption
(1)
No BC
Same K & L
(2)
No BC
K& L endogeneous
(3)
.
.
.
.
.
.
0.013
0.004
0.018
0.000
-0.025
0.011
0.054
0.058
0.172
0.008
0.015
0.049
Note: This table reports aggregate variables, in percentage deviation with respect to the benchmark (SMM)
economy. We consider two counterfactuals: Column (3) (No BC, K&L endogeneous) removes the borrowing
constraint; Column (2) (No BC, same K&L) removes the borrowing constraint, but imposes linear taxes For
instance, welfare is 5.4% higher than the benchmark in the absence of borrowing constraints. The description of
the general equilibrium setting, and the details of the counterfactuals, are given in section 4.1.
53
Table 8: Additional Counterfactual Experiments
Welfare
Output
Capital
Employment
Adj. Consumption
Real Wage
Benchmark
No adj. cost on L
(1)
(2)
No BC
No adj. cost on L
(3)
.
.
.
.
.
.
0.06
0.099
0.1
0.073
0.093
0.2
0.1
0.17
0.14
0.3
0.1
0.22
Note: This table summarizes the findings of additional counterfactual analyses. We report aggregate variables, in
percentage deviation with respect to the benchmark (SMM) economy. For instance, welfare is 6% higher than the
benchmark in the absence of adjustment costs to labor. The description of the general equilibrium setting, and the
details of the counterfactuals, are given in section 4.1.
54
APPENDIX
This Appendix contains 4 sections. Section A contains a detailed description of how we construct our dataset.
Section B provides some theoretical insight on the special case where there are no fixed costs of adjustment. Section
C describes our SMM estimation procedure in detail. Section D is a list of supplementary Tables that serve as
robustness checks for our reduced form evidence. Section E contains supplementary Figures.
55
A
Data Description
The sample is a large dataset of French firms from 1998 to 2007. We use administrative data sources only, made
available by INSEE, the French statistical office.
Accounting and employment data.— Accounting data come from tax files. To tax authorities, all French firms
which pay the corporate tax under the standard (as opposed to simplified) regime have to report detailed balance
sheet and income statements. We exclude industries directly related to the real estate market: construction, finance
and real estate development: This ensures that real estate prices –hence collateral value– do not obviously proxy
for investment opportunities.
Employment data come from plant-level data. We merge plant-level data on employment with firm-level
accounting data using the firm identifying number. One firm may have several plants. Most of our regressions
restrict the sample to single plant firms, as it makes the determination of the location of a firm’s real estate easier.
We do, however, run robustness checks including multi-plant firms.
The variables are constructed to follow, as much as possible, those used in our previous study on US firms
(Chaney et al., 2012a). As our normalization variable, we used Immobilisations Productives, which measures
physical capital, and is the equivalent to the PPE variable used in all US-based investment papers (“Plant, Property,
and Equipment”). We label it henceforth PPE.
Investment is the ratio of capital expenditures to lagged PPE. Cash flows are the standard measure of Net cash
flows used in the literature: Net Income - Exceptional Items + Depreciation. Investment is Capital Expenditure.
Labor demand is measured with two variables. The first measure is employment change divided by lagged
PPE (∆L/K). This first measure has the advantage of providing a straightforward interpretation our regression
coefficients, and an direct comparison between investment and employment change, as both are normalized by
the same PPE. The second measure is the symmetrized employment growth (2 × (Lt − Lt−1 )/(Lt + Lt−1 )). This
measure of employment growth is taken from Davis et al. (1996). It is bounded above by 2 (from 0 to x jobs)
and below by -2 (from x to 0 jobs), and can accommodate both entry and exit. This second measure has the
advantage of offering an easier theoretical interpretation. Employment growth is less thick-tailed than employment
to physical capital ratio (s.d. equal to 0.23 instead of 1.98). Results are therefore likely less sensitive to extreme
values for our second measure –although all our variables are windsorized. We perform robustness checks to assess
the importance of extreme values.
Our main sample is unbalanced, firms may enter and exit the sample as they start and cease to pay the regular
corporate tax. It contains slightly more than 1m observations - about 100,000 mono-plant firms per year. Entry
and exit may be related to creation and bankruptcy, but it may also be due to the fact that firms cross the size
threshold below which it is optimal to opt for the “simplified” tax regime (a few hundred thousands Euro of annual
turnover, depending on the firm). Firms may exit the sample because they are terminated –more likely for smaller
firms– or acquired by a larger entity –more likely for larger firms. In order to control for observable determinants
of real estate holdings, we also need to run a number of regressions on firms that are present in our sample in 1998.
This allows us to control for such determinants –firm size, industry etc.– as of 1998. This alternative sample is also
unbalanced, but there is by construction no entry after 1998. It has 750,000 observations.
All variables are trimmed: We take out observations whose value is above the 99th or below the 1st percentile.
For most variables, this procedure leads to the suppression of all outliers. One exception is the ratio of employment
change to physical assets ∆L/K, which has a bit more outliers than the other variables. We test that our estimates
are robust to the trimming/windsorizing technique in Table D.2.
Estimating Real Estate Value at the Firm-Level.— Key to our estimates is the calculation of the ratio of real
estate value to physical assets, RE Value. To maximize the precision of our real estate value variable, we first focus
on single plant firms. Because our real estate measure relies on several assumption, we also provide, in robustness
checks, regressions using an “Owner dummy” interacted with house price levels. All our results go through using
this alternative measure, but the advantage of RE Value is that it makes quantification much more intuitive.
For each firm-year observation, we first estimate the date at which the real estate was purchased. To do this,
we use the fact that French tax files provide us with the gross (of depreciation) and the net (of depreciation) book
value of buildings. Assuming linear amortization over 25 years, as is the standard accounting practice, we calculate
one minus the ratio of net building assets divided by gross building assets, and multiply it by 25. This gives us the
implicit average age of buildings held by the firm, which allows us to deduct the date at which the average Euro
56
of building has been purchased. Our methodology thus implicitly assumes that real estate has not been purchased
prior to 25 years before the current date of the observation. There are very few observations with building age
above 20 years, which suggests that this left-censorship of our data is unlikely to be a concern.
We then use local house prices to impute the market value of real estate holdings of each firm. To do this,
we focus on single establishment firms, and assume that all real estate holdings are in the same “département” as
the establishment –there are 95 départments in “mainland France”. We need to make this assumption because our
data does not report the exact location of real estate holdings. We then multiply the book value of real estate at
the time of purchase (measured by the gross book value) by one plus the cumulative price growth of house prices
in the département where the establishment is located.
As commercial real estate price series are unavailable in France, we use house prices. Our previous study on
investment in the US showed that using commercial or residential real estate prices led to similar estimates. Due
to data limitations, we need to make additional assumptions, however. House prices are obtained from INSEE, but
are unfortunately not available back to 1973 (1998-25). They are available at the département-level starting in 1998
–which is why we start our study in 1998. Between 1986 and 1998, we can backfill the series using region-level price
data also available from INSEE –there are 20 regions in France, each of them including on average 5 départements.
Prior to 1986, we use the nationwide inflation index to backfill house price data.
After this procedure, we normalize the value of real estate holdings by physical capital. This number is available
for more than 1m observations. The median RE value is zero: 56% of the observations correspond to firms which
own zero real estate. The average RE value is .28: For the average firm, real estate holdings are worth nearly
a third of their physical capital. Between 1998 and 2007, RE value increases on average by about 10 percentage
points (from .25 to .35). This is because the period that we study is one of rising house prices, in all parts of France
(as shown in Figure E.1).
B
Solution when there are no fixed adjustment costs.
Variable adjustment cost, no fixed cost (cK , cL > 0; fK , fL = 0).— Without fixed costs, the solution to the problem
(11) is characterized by a series of first order conditions for capital and labor, and since the Lagrangian associated
with the problem is linear in debt, a series of corner solutions for debt. Imposing those conditions, denoting by
1−d
1+r λt+1 the Lagrange multiplier in front of the collateral constraint on debt to be repaid in period t + 1, γt the
Lagrange multiplier in front of the non-negative cash flow constraint for period t, applying an envelope condition,
iterating forward the optimality conditions and using the law of iterating expectations, we derive the following
three conditions for the choice of investment, It , new hires Et , and debt, Dt+1 ,
It
(1 + γt ) 1 + cK
=
Kt

X 1 − d s
s−1
(1 − δK )
Et 
1+r
s≥1
(1 + γt+s ) RK +
cK
2
It+s
Kt+s
2 !
!
+ sK λt+s 


X (1 − d)(1 − δL ) s
Et
(1 + γt ) cL
+ Et 
(1 + γt+s ) w =
Lt−1
1+r
s≥0


2 !
X (1 − d)(1 − δL ) s
c
E
L
t+s

(1 + γt ) RL + Et 
(1 + γt+s ) RL +
1+r
2 Lt−1+s
s≥1
57
(21)
(22)
Dt+1 =


if 1−d
sK Kt+1 + sH min (pt+1 |pt ) H,
1+r (1 + r̃t+1 ) (λt+1 + Et [1 + γt+1 ]) < 1 + γt
1−d
(1 + r̃t+1 ) (wLt + Dt + Adj. Cost − Rt ) , if 1+r (1 + r̃t+1 ) (λt+1 + Et [1 + γt+1 ]) > 1 + γt


indifferent,
otherwise.
(23)
The first equation (21) characterizes the optimal investment choice in period t, and equates the marginal cost of
one extra unit of capital (LHS) to its marginal benefit (RHS). The marginal cost is the sum to the direct cost of
equipment goods, and the adjustment cost; both costs (in dollars) are augmented by the Lagrange multiplier on the
non-negative cash flow constraint, γt , as each extra dollar spent on investment is one less dollar of cash flows. The
marginal benefit is the discounted sum of three terms: first, the present value of extra revenues generated by the
new investment; second, the lower adjustment cost for future investment achieved by having scaled up the stock of
capital; both of those terms are augmented by the shadow value of extra revenue, the γt+s ’s; third, by increasing
its capital, the firm relaxes its collateral constraint for all future periods, as captured by the sK λt+s ’s.
The second equation (22) offers a similar characterization for the optimal choice of labor, equating the marginal
cost and marginal revenue of labor. In this model where labor is not freely adjustable, the cost of one worker hired
today is the entire discounted sum of wages paid to this worker, and the benefit contains the entire discounted sum
of marginal product of labor from this extra worker. 16
The third equation (23) characterizes the optimal choice of debt. If the
cost of (1 + r̃t+1 ) extra dollar
marginal
of debt owed at t + 1, composed both of the tighter collateral constraint 1−d
1+r λt+1 and of the present value of the
dollar repaid next period (augmented by the future shadow cost of cash, γt+1 ), is lower than the marginal benefit
of one extra dollars today (augmented by the shadow value of cash today, γt ), then the firm will max out its debt.
If the cost of debt is higher than its benefit, the firm minimizes its debt; if the firm’s revenue exceed its expenses
and existing debt repayment, it accumulates cash. If the cost and benefit of debt are equal, the firm is indifferent
as to how much debt it issues.
Intuitively, this condition ensures that, on the optimal path, the collateral constraint binds more when the
non-negativity
constraint (e >
0) is more binding today than tomorrow, all in present-value, risk-adjusted terms
γt > 1−d
1+r (1 + r̃t+1 ) Et [γt+1 ] . Put differently, when the firm experiences a sudden, temporary, tightening of its
positive cash-flow constraint, it tends to borrow more, thus tightening the collateral constraint. This happens for
instance when the firm has experienced a positive productivity shock, so that it wants to adjust its capital and
labor stock up.
Together, equations (21-23) explain how the collateral channel works in our model. Assume real estate prices
go up, so that collateral constraints, today and in future periods, are relaxed: λt+s decreases for all s ≥ 0.17 From
equation (23), the cost of debt decreases. As it becomes less likely that the firm cannot borrow to cover its costs
and investment, the current non-negativity constraint is relaxed too: γt decreases. This in turn reduces the effective
cost of labor and capital in equations (21) and (22) though the multiplicative term (γt ) on the LHS of these two
equations. Both investment and new hire increase. The effect on investment is bigger because investment requires
up-front financing (the cost at t of investing is 1, while labor is rented at rate w per period only). This asymmetry
comes from the fact that labor can only be rented, while capital only be owned in this model.
In the presence of fixed adjustment costs (fK > 0, fL > 0), the characterization of the optimal strategy of the
firm through first order conditions no longer applies. The presence of fixed adjustment costs makes investment and
labor lumpy, as in the data. But it does not alter qualitatively the main features of the model described above. In
the next section, we resort to numerical simulations to solve the full model, and we estimate the model’s parameter
to match key moments from the data, including the sensitivity of investment and labor demand to real estate
collateral.
16
In the special case of freely adjustable labor (cL = 0), this optimality condition collapses into a series of static
first order conditions RL = w as in the previous special case and equation (12).
17
Remember the discrete process we assume for real estate prices is such that the term min (pt+s |pt ) H which
enters the collateral constraint is always correlated with today’s real estate prices pt .
58
C
SMM Procedure
The SMM procedure consists of three main blocks, which we describe in detail in this Appendix:
• For a given set of parameters, we need to solve the model numerically, which means computing the policy
function of the firm, which maps productivity and real estate prices into hiring, investment and borrowing
decision.
• For a given policy function, create a simulated dataset, which is a panel of firms, located in fictitious
départements, over a certain period of time.
• Use this simulation technique to find the set of model parameters that matches best a set of moments chosen
from the data.
C.1
Numerical Resolution of the Firm’s Problem
In this section, we first describe how we numerically solve the firm’s problem with given parameters. Before we
describe the procedure, two remarks are in order.
First, in principle, the decision to own vs rent the real estate H could be an endogenous variable in the model
described in the main text. The decision of how much real estate to own would in this case depend on a tradeoff
between the cost of borrowing today and the ability to build debt capacity in case of positive productivity shocks.
In this case, the model would have 4 choice variables S = (K, L, B, H) and H, as well as the two state variables
X = (z, p). The large dimensionality of this problem makes it computationally intensive. In addition, it is not
feasible to reduce the state space by normalizing the problem by one state variable –because of decreasing returns
to scale in revenue. This is why we choose to simplify the model by abstracting from the owner/renter choice. This
assumption is supported by the fact that less than 1% firms switch between renting and owning real estate in the
data. In practice, we include H as an additional choice variable in the firm’s program, but assuming very large
adjustment costs to real estate purchase or sale.
Second, in order to solve the model numerically, we need to discretize the state space (S; X). For the AR1
productivity shock z, we use the standard Tauchen method. For real estate prices p, we use a geometrically spaced
grid that roughly mimicks the range of real estate price appreciation in the data. The grid of K is geometrically
spaced using (1 − δ) as the multiplicative ratio. This ensures that the choice of no adjustment after depreciation is
feasible and exact on the grid. Similarly, the grid of L is geometrically spaced, using (1 − 2δL ) as the multiplicative
ratio instead of (1 − δL ) as the model presentation suggests we should do. We use a coarser grid (the multiplicative
coefficient is smaller than it should be) for labor demand in order to reduce grid size. To be able to use this coarser
grid, we assume random labor separation: Firms face a quit rate of 2 × δL with probability 1/2, and no quits at
all with probability 1/2. This ensures that we can use realistically small quit rates (7.5%) while preventing grid
size from exploding. Finally, the grid points of B are equi-spaced as b is one-period debt and has no “physical”
depreciation.
In order to maximize the speed of convergence (see below), we actually use in our iterations two different grids
for the state space (S; X) = (K, L, B, H; z, p). The first one is the “coarse” grid 10 × 5 × 5 × 2 × 5 × 4, of size 10, 000.
The second one is the “fine” grid 46 × 21 × 21 × 2 × 5 × 4, of size 811, 440. The finer grid has a larger number of
potential values of the three endogenous variables (k, l, b) only. The advantage of this twin grid approach is that
we optimize continuation value on the fine grid, conditional on state variables chosen on the coarse grid. So this
approach divides the number of optimizations to perform at each iteration by about 80 (see below).
The numerical procedure to solve the firm’s problem proceeds as follows. First, we compute profit flows
e(S, S 0 ; X) using the production and cost functions, for all possible values of SandXonthecoarsegrid, and, S 0 on the
fine grid. We assume that firms can avoid fixed adjustment cost of capital and/or labor as long as the adjustment
is small (less than 1%). We set e to -10,000 if S, S 0 and X are such that the collateral constraint is violated. Then,
in order to initiate the process, we start with value function v0 (S; X) = 1 for all values of S and X. The value
function is defined on the coarse grid. Then, we iterate the following loop (where n is the number of the loop):
1. Retrieve vn−1 (S; X), the value function obtained from the previous round, and defined for each point of the
coarse grid.
2. Interpolate linearly vn−1 (S; X) over each point of the fine grid.
59
3. For every point (S; X) on the coarse grid, we compute the continuation value
Cn (S, S 0 ; X) = e(S, S 0 ; X) +
1−d
E [vn−1 (S 0 ; X 0 )|X]
1+r
and maximize it w.r.t. to the choice variables S 0 on the fine grid. We obtain the policy function S 0 =
Pn (S; X), but only on the coarse grid. This divides the number of optimizations to perform by 811, 440/10, 000×
81, which accelerates the process considerably.
4. Use the new policy function to update the value function vn (S; X) = Cn (S, Pn (S; X); X), on the coarse grid
only (since the policy function is only defined on the coarse grid).
5. Store the policy function Fn and the value function vn , both defined over the coarse grid and start again.
After enough iterations, through the contraction mapping theorem, one obtains a good approximation of the
value function and the policy function defined over the coarse grid. We then interpolate the vn and Pn over the
finer grid. These two functions are the outcome of this procedure. We also experimented with larger and smaller
grid size. There are some changes in the value function and policy function, but in general our grid is large enough
to achieve good approximation.
C.2
Simulation of data
Given the solved policy function, we simulate a balanced panel of firms solving the dynamic problem with 500,000
observations: 100 départements, each with 500 firms, over 10 consecutive years. We simulate this data in three
steps.
Step 1: We simulate a sequence of real estate price p for each of the 100 department following an assumed
stochastic process. We simulate 200 periods.
Step 2: In the first period, each firm draws a random initial state S0 and X0 . We assume that firms are always
start with zero debt and their capital-labor ratio is not too far from the first best. This ensures the franchise value
of firms being positive in the first period.
For each period t > 1, we first draw the exogenous state variables Xt = (zt , pt )18 , and then use the policy
function to obtain St = P (St−1 ; Xt−1 ) given St−1 and Xt−1 from last period. Since here the choice of previous
period enters as state variable in the next period, we need a policy function that maps from the finer grid to the
finer grid. This is done by interpolation again.
Step 3: We drop the first 190 periods to reach the ergodic distribution, and use the simulation of last 10 periods
to compute relevant moments.
We obtain a simulated balanced panel of 100 départements, each with their own real estate price dynamic, and
each with 5000 observations corresponding to 500 firms operating in steady state over 10 periods.
C.3
Optimization Algorithm
The CMA-ES algorithm is a derivative-free evolutionary algorithm for non-linear optimization problems.19 In each
round we draw n off-springs in the parameter space which are normally distrusted around the mean inherited from
last round. Then we compute the distance between simulated data with each off-spring and actual data as its
fitness. With the fitness at hand, we rank the off-springs by their fitness, and update the mean by the weighted
average of the upper half off-springs. We also update the variance-covariance matrix of multi-dimensional normal
18
We use a discretized AR-1 process with 50 states instead of 5 (as in value function iteration) for zt , and
interpolate the policy function. This helps us to smooth the policy function without increasing the grid size in
value function iteration. Moments are robust to further increase of the number of states.
19
See wikipedia page for instance.
60
distribution that will be used in the next round to draw off-springs20 . We iterate this procedure until the off-springs
are distributed close enough to the mean.
C.4
Standard Errors
TO BE DONE
C.5
Robustness of the Reduced Form Specification
We use our simulated data to run various specification checks of our reduced form regressions. We report the
results in Table D.7. Column (1) and (4) simply re-estimate our reduced form regressions on simulated data,
and consistent with the results in Table 6, we find coefficient estimates that are very close to those estimated on
actual data. Columns (2) and (5) shows that controlling for the past dynamic of house prices has little effect on
the estimated reduced form coefficients. Columns (3) and (6) estimate the reduced form using one year changes
in the investment ratio and in employment growth as dependent variables. This leaves the investment coefficient
unchanged, but we see that the employment regression ceases to be significant.
C.6
Welfare decomposition
TO BE DONE
D
20
Additional Tables
We use the fitness-weighted average of solved value function as the initial guess in the next round for efficiency.
61
62
Yes
Yes
Yes
(1)
1.3***
(10)
.96***
(11)
.43***
(7.7)
-1.5**
(-2)
-.1
(-.32)
174210
Yes
Yes
Yes
2 Emp∆(Emp)
t +Empt−1
(2)
.022***
(10)
.011***
(10)
-.0014*
(-1.8)
-.013
(-1.1)
-.02***
(-3.5)
174210
Yes
Yes
Yes
(3)
1.4***
(13)
1.2***
(24)
.071
(1)
-3.2***
(-9.2)
-.4**
(-2.1)
853932
∆(Emp)
P P Et−1
Yes
Yes
Yes
2 Emp∆(Emp)
t +Empt−1
(4)
.017***
(6.2)
.019***
(16)
-.0041***
(-4.1)
-.018***
(-2.7)
-.024***
(-6.4)
844235
Yes
Yes
Yes
(5)
1.4***
(8.2)
1.2***
(14)
.87***
(8.2)
-2***
(-3.2)
-.78**
(-2.5)
262282
∆(Emp)
P P Et−1
Yes
Yes
Yes
2 Emp∆(Emp)
t +Empt−1
(6)
.022***
(7.6)
.015***
(14)
.0028***
(2.6)
-.021**
(-2.5)
-.028***
(-5)
262282
Yes
Yes
Yes
(7)
1.1***
(11)
.91***
(30)
-.00055
(-.012)
-3.9***
(-14)
-.5**
(-2.4)
786392
∆(Emp)
P P Et−1
Yes
Yes
Yes
2 Emp∆(Emp)
t +Empt−1
(8)
.015***
(5.7)
.017***
(32)
-.0049***
(-6.7)
-.039***
(-6.9)
-.026***
(-6)
776745
Note: The dependent variable is Change in employment normalized by previous year PPE (Column 1 , 3, 5 and 7) and symmetric growth rate of
employment (Column 2, 4, 6 and 8). Column 1 and 2 uses a balanced sample of firms from 1998 to 2007. Column 3 and 4 allows for entry of new
firms in the sample provided these firms have more than 5 employees. Column 5 and 6 use a sample of stand-alone firms, i.e. not affilliated to a
business group. Column 7 and 8 add multi-establishment firms and assign to these firms a real estate price index equal to a weighted-average of
the real estate price index for each plant location, where the weights are the number of employees in the plant. RE Valuet is our proxy for the
market value of firms’ real estate assets. See Section 1.1 for the construction of this proxy. Dep. Index is a département-level residential price index.
Log(Assets98 ) is the log of the firm’s total assets in 1998. ROA98 is the firm’s Return on Asset in 1998. Leverage 98 is the firm’s leverage in 1998.
Casht is operating cash flows. All columns include industry and département fixed effects interacted with the département-level real estate price
indexes well as year, firm and département-industry-year fixed effects. Our industry classification has 20 groups. Standard errors are clustered at
the département level. T-statistics are reported in parenthesis.***, ** and * means significant at the 1, 5 and 10% significance level.
Year FE
Firm FE
Dep. × Industry× Year FE
Observations
Adj. R-Square
Leverage98 × Dep. Prices
ROA98 × Dep. Prices
Log(assets)98 × Dep. Prices
Casht
P P Et−1
RE Valuet
∆(Emp)
P P Et−1
Table D.1: Employment Changes, Employment Growth and Collateral Value: Robustness Checks
I
63
Yes
Yes
Yes
Year FE
Firm FE
Dep. × Industry× Year FE
Yes
Yes
Yes
.0077***
(4.9)
.016***
(17)
.0023***
(2.8)
-.02**
(-2.4)
-.026***
(-4.8)
330389
2 Emp∆(Emp)
t +Empt−1
(2)
Yes
Yes
Yes
.015***
(15)
.0027***
(3.5)
-.021**
(-2.4)
-.029***
(-5.5)
330389
(3)
.027***
(11)
∆(Emp)
Empt−1
Yes
Yes
Yes
1.5***
(17)
.88***
(11)
-2.1***
(-3)
-.8**
(-2.5)
330389
(4)
2.1***
(14)
Yes
Yes
Yes
.46***
(9.3)
.25***
(5.9)
-1.6***
(-4.6)
-.76***
(-3.1)
294175
(5)
.86***
(8.8)
∆(Emp)
P P Et−1
Yes
Yes
Yes
.67***
(13)
.44***
(7.5)
-1.7***
(-4.1)
-.89***
(-3.1)
296483
(6)
1.4***
(12)
Note: The dependent variable is Change in employment normalized by previous year PPE (Column 1, 4, 5 and 6), the symmetric growth rate of
employment (Column 2) and employment growth (Column 3). Owner dummy is a dummy variable equal to 1 if the firm reports some real estate
∆(Emp)
assets in its 1998 balance sheet. Column 4 trims the dependent variable ( P
P Et−1 ) at the median +/- 5 times the interquartile range, Column 5
windsorizes at the 5th and 95th percentiles while Column 6 trims at the 5 and 95th percentiles. RE Valuet is our proxy for the market value of firms’
real estate assets. See Section 1.1 for the construction of this proxy. Dep. Index is a département-level residential price index. Log(Assets98 ) is the
log of the firm’s total assets in 1998. ROA98 is the firm’s Return on Asset in 1998. Leverage 98 is the firm’s leverage in 1998. Casht is operating
cash flows. All columns include industry and département fixed effects interacted with the département-level real estate price index, as well as year,
firm and département-industry-year fixed effects. Our industry classification has 20 groups. Standard errors are clustered at the département level.
T-statistics are reported in parenthesis.***, ** and * means significant at the 1, 5 and 10% significance level.
Observations
Adj. R-Square
Leverage98 × Dep. Prices
ROA98 × Dep. Prices
Log(assets)98 × Dep. Prices
Casht
P P Et−1
.88***
(8.1)
1.2***
(16)
.67***
(8.1)
-2.2***
(-3.5)
-.71**
(-2.3)
330389
(1)
Owner dummy × Dep. Prices
RE Valuet
∆(Emp)
P P Et−1
Table D.2: Employment Changes, Employment Growth and Collateral Value: Robustness Checks
II
64
Yes
Yes
Yes
Log(assets)98 × Dep. Prices
Year FE
Firm FE
Dep. × Industry× Year FE
Yes
Yes
Yes
Medium
(2)
1.1***
(5.1)
.95***
(8.3)
.59***
(4.8)
-2.5**
(-2.4)
-.53
(-1.1)
92754
Yes
Yes
Yes
Large
(3)
1.5***
(5.1)
1.2***
(11)
.65***
(6.5)
-2.7**
(-2)
-.14
(-.25)
90095
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
2 Emp∆(Emp)
t +Empt−1
Small
Medium
Large
(4)
(5)
(6)
.016*** .017*** .032***
(3.2)
(4.7)
(5.6)
.01*** .013*** .019***
(5)
(10)
(11)
-.001
.0032**
.0017
(-.52)
(2.1)
(1.3)
-.016
-.018
-.031
(-1.1)
(-1)
(-1.1)
-.014
-.024*
-.032**
(-1.5)
(-2)
(-2.2)
78429
92754
90095
Note: The dependent variable is Change in employment normalized by previous year PPE (Column 1, 2 and 3) and the symmetric growth rate of
employment (Column 4, 5 and 6). Column 1 and 4 (resp. 2 and 5, 3 and 6) use the sample of firms in the first (resp. second and third) tercile of firm
size as measured by total assets in 1998. RE Valuet is our proxy for the market value of firms’ real estate assets. See Section 1.1 for the construction
of this proxy. Dep. Index is a département-level residential price index. Log(Assets98 ) is the log of the firm’s total assets in 1998. ROA98 is the firm’s
Return on Asset in 1998. Leverage 98 is the firm’s leverage in 1998. Casht is operating cash flows. All columns include industry and département
fixed effects interacted with the département-level real estate price index, as well as year, firm and département-industry-year fixed effects. Our
industry classification has 20 groups. Standard errors are clustered at the département level. T-statistics are reported in parenthesis.***, ** and *
means significant at the 1, 5 and 10% significance level.
Observations
Adj. R-Square
Leverage98 × Dep. Prices
ROA98 × Dep. Prices
Casht
P P Et−1
RE Valuet
Small
(1)
1.3***
(3.7)
1.1***
(6)
.63***
(3.9)
-1.2
(-1.1)
-.33
(-.49)
78429
∆(Emp)
P P Et−1
Table D.3: Employment Changes, Employment Growth and Collateral Value: Variations by Size
65
Yes
Yes
Yes
Log(assets)98 × Dep. Prices
Year FE
Firm FE
Dep. × Industry× Year FE
Yes
Yes
Yes
Interm.
(2)
1.6***
(7)
1.2***
(10)
.76***
(7.9)
-4.3***
(-6.3)
-1.4**
(-2)
143111
Yes
Yes
Yes
Global
(3)
1.7***
(3.3)
.96***
(3.5)
.74***
(4.2)
-6.1**
(-2.3)
-2.1
(-1.2)
29691
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
2 Emp∆(Emp)
t +Empt−1
Local
Interm. Global
(4)
(5)
(6)
.022*** .028*** .036***
(5.7)
(6.6)
(4.5)
.014*** .016*** .014***
(11)
(12)
(4.3)
.0026** .0022**
.002
(2.6)
(2.5)
(.59)
.00047 -.042***
-.03
(.034)
(-4.4)
(-.78)
-.014** -.048*** -.053**
(-2.4)
(-3.8)
(-2)
157587
143111
29691
Note: The dependent variable is Change in employment normalized by previous year PPE (Column 1, 2 and 3) and the symmetric growth rate of
employment (Column 4, 5 and 6). Column 1 and 4 (resp. 2 and 5, 3 and 6) use the sample of firms in the first (resp. second and third) tercile of
industry. Industry trade costs are defined as the average firm-level ratio of export sales to total sales in each 2-digit industry. RE Valuet is our proxy
for the market value of firms’ real estate assets. See Section 1.1 for the construction of this proxy. Dep. Index is a département-level residential
price index. Log(Assets98 ) is the log of the firm’s total assets in 1998. ROA98 is the firm’s Return on Asset in 1998. Leverage 98 is the firm’s
leverage in 1998. Casht is operating cash flows. All columns include industry and département fixed effects interacted with the département-level
real estate price index, as well as year, firm and département-industry-year fixed effects. Our industry classification has 20 groups. Standard errors
are clustered at the département level. T-statistics are reported in parenthesis.***, ** and * means significant at the 1, 5 and 10% significance level.
Observations
Adj. R-Square
Leverage98 × Dep. Prices
ROA98 × Dep. Prices
Casht
P P Et−1
RE Valuet
Local
(1)
1.4***
(5.8)
1.1***
(12)
.68***
(8.9)
-.45
(-.41)
-.34
(-.94)
157587
∆(Emp)
P P Et−1
Table D.4: Employment Changes, Employment Growth and Collateral Value: Variations by Industry trade costs
66
.15***
(29)
.042***
(18)
.0035***
(4.6)
-.038***
(-3.6)
-.034***
(-5.2)
330389
Yes
Yes
Yes
1.5***
(11)
1.2***
(15)
.71***
(9.3)
-2***
(-3.1)
-.6**
(-2)
330389
.13***
(24)
.04***
(12)
.0053***
(4.1)
-.038**
(-2.5)
-.00065
(-.077)
275396
Yes
Yes
Yes
1.7***
(12)
.71***
(8.1)
.75***
(8.3)
-.72
(-1.1)
-.56
(-1.6)
275396
(2)
(1)
.097***
(19)
.018***
(8.1)
.0083***
(4.2)
-.028
(-1.6)
.012
(1.1)
229779
∆(Empt )
on
P P Et−1
Yes
Yes
Yes
1.3***
(7.6)
.12*
(1.8)
.75***
(6.4)
.72
(.69)
-.58
(-.85)
229779
(3)
∆(Empt+2 )
P P Et+1
.053***
(10)
.0061***
(4.2)
.011***
(3.1)
-.0065
(-.26)
.0052
(.26)
191278
common sample
Yes
Yes
Yes
.57***
(2.9)
-.11
(-1.2)
.62***
(3.5)
3.3*
(1.8)
-.38
(-.38)
191278
(4)
∆(Empt+3 )
P P Et+2
.01*
(1.8)
-.00052
(-.48)
.015***
(2.6)
.034
(.96)
-.011
(-.32)
156014
Yes
Yes
Yes
-.044
(-.2)
-.22**
(-2.1)
.47
(1.3)
11***
(2.9)
.67
(.41)
156014
(5)
∆(Empt+4 )
P P Et+3
-.014**
(-2.2)
-.0031
(-1.3)
.02***
(3.7)
.094*
(1.7)
-.057
(-.96)
123596
Yes
Yes
Yes
-.14
(-.36)
-.044
(-.25)
.33
(.61)
17***
(3.7)
.53
(.28)
123596
(6)
∆(Empt+5 )
P P Et+4
Note: In panel A, the dependent variable is Change in employment normalized by previous year PPE from year t+k-2 to year t+k-1 in column k.
In panel B, the dependent variable is the current Change in employment normalized by previous year PPE. In panel B, the regression in column k is
run for the sample where Change in employment normalized by previous year PPE from year t+k-2 to year t+k-1 is defined. RE Valuet is our proxy
for the market value of firms’ real estate assets. See Section 1.1 for the construction of this proxy. Dep. Index is a département-level residential
price index. Log(Assets98 ) is the log of the firm’s total assets in 1998. ROA98 is the firm’s Return on Asset in 1998. Leverage 98 is the firm’s
leverage in 1998. Casht is operating cash flows. All columns include industry and département fixed effects interacted with the département-level
real estate price index, as well as year, firm and département-industry-year fixed effects. Our industry classification has 20 groups. Standard errors
are clustered at the département level. T-statistics are reported in parenthesis.***, ** and * means significant at the 1, 5 and 10% significance level.
Observations
Adj. R-Square
Leverage98 × Dep. Prices
ROA98 × Dep. Prices
Log(assets)98 × Dep. Prices
Casht
P P Et−1
RE Valuet
Panel B:
Year FE
Firm FE
Dep. × Industry× Year FE
Observations
Adj. R-Square
Leverage98 × Dep. Prices
ROA98 × Dep. Prices
Log(assets)98 × Dep. Prices
Casht
P P Et−1
Panel A:
RE Valuet
∆(Empt+1 )
P P Et
∆(Empt )
P P Et−1
Table D.5: Employment Changes, Employment Growth and Collateral Value: Dynamics
Table D.6: Robustness to control for local economic activity
RE Valuet
Owner × ∆Unemp
Owner × ∆ln(GDP)
Casht
P P Et−1
Log(assets)98 × Dep. Prices
ROA98 × Dep. Prices
Leverage98 × Dep. Prices
Observations
Adj. R-Square
Firm FE
Dep. × Industry× Year FE
Note:
CAP Xt
P P Et−1
CAP Xt
P P Et−1
∆(Debt)
P P Et−1
∆(Emp)
P P Et−1
(1)
.15***
(8.7)
.0053
(1.8)
-.088
(-.93)
.042***
(16)
.0034**
(2.6)
-.038*
(-2)
-.034
(-1.3)
324886
(2)
.2***
(5.4)
.043***
(3.5)
.68
(1.3)
.25***
(15)
.02
(1.6)
.25***
(4)
-.032
(-.27)
324886
(3)
1.5***
(8.8)
.68***
(5)
4.4
(.68)
1.2***
(14)
.7***
(4.7)
-2
(-1.4)
-.61
(-1.2)
324886
2 Emp∆(Emp)
t +Empt−1
(4)
.025***
(5.8)
.0036*
(2.1)
.051
(.81)
.015***
(14)
.0021
(1.5)
-.017
(-.87)
-.025**
(-2.9)
324886
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
is Capital Expenditure normalized by previous year PPE.
normalized by previous year PPE.
∆(Employment)
P P Et−1
∆(Debt)
P P Et−1
is the change in total debt
is the change in total employment normalized by previous year
2 Emp∆(Emp)
t +Empt−1
PPE (in million Euro).
is the symmetric growth rate of employment. ∆(Emp)
Empt−1 is the standard growth
rate of employment. RE Valuet is our proxy for the market value of firms’ real estate assets. Dep. Index is the
t
real estate price index defined at the département level. PCash
P Et−1 is the ratio of current cash flows to previous year
PPE. Owner dummy is a dummy equal to 1 if the firm owns some real estate assets in 1998. ROA is a return
on asset computed as EBIT normalized by total assets. Leverage is total debt normalized by total assets. All
specifications include industry and département fixed effects interacted with the département-level real estate price
index. They also include firm fixed effects and département-industry-year fixed effects. Our industry classification
has 20 groups. Standard errors are clustered at the département level. T-statistics are reported in parenthesis.
***, ** and * means significant at the 1, 5 and 10% significance level.
67
68
Cash-Flowt
Kt−1
Yes
400000
.58***
(355)
.0035
(1.6)
.17***
(20)
No
400000
.59***
(338)
.0095***
(3.6)
-.016***
(-6.5)
.19***
(24)
-.055***
(-21)
It
Kt
(4)
Yes
Yes
No
Yes
(298)
350000
-.0002
(-.046)
.0052
(.45)
∆
∆Lt
Lt
(6) (339)
350000
400000
.6***
(337)
-.019***
(-5)
.046***
(17)
.091***
(8.2)
-.12***
(-27)
∆Lt
Lt
.62***
400000
.58***
(385)
-.002
(-.69)
.043***
(5.1)
∆Lt
Lt
.63***
.0058***
(2.6)
.21***
(25)
∆
It
Kt
(3) Hiring
(5)
Yes
400000
.2***
(96)
.014***
(7.9)
.26***
(14)
Yes
400000
.19***
(98)
.012***
(5.3)
.22***
(12)
(8)
Bt+1 −Bt
Kt
(7)
Bt+1
Kt
Debt
Hi
Hi
cashit
+
× pdt + pdt +
+ idt
Kit
Kit
Kit
for firm i in département d at date t. Hi corresponds to the firm’s real estate holdings (assumed fixed), pdt the département-level price, and cashit
the firm’s cash. In columns 1-3, Yidt is investment (defined as Ki,t+1 /Kit − (1 − δ)). In columns 4-6, Yidt is net hires (2(Li,t+1 − Li,t )/(Li,t+1 + Li,t )),
and in columns 7-8, Yidt corresponds to 2 measures of borrowing. Columns 1,4,7 correspond to the reduced form regressions that we run. The other
columns corresponds to alternative specifications (with lagged independent variables in columns 2 and 5; in first differences in columns 3 and 6)
Standard errors are clustered at the département level. T-statistics are reported in parentheses.***, ** and * means significant at the 1, 5 and 10%
significance level.
Yidt = αi +
Note: The simulated panel of firms is generated from the model in Section 2 calibrated with SMM estimates. It contains 100 departments, each
with 500 firms simulated over 200 time periods. For each firm, we then drop the first 190 periods to remove transition dynamics, and therefore only
end up with 500,000 simulated observations. We then run reduced-form investment, labor demand and debt regressions of the form:
Firm FE
N
∆
Cash-Flowt
Kt−1
∆DEP Pricet
DEP Pricet−1
DEP Pricet
∆RE Valuet
RE Valuet−1
RE Valuet
It
Kt
(1)
Investment
(2)
Table D.7: Collateral Regressions on Simulated Data
E
Appendix Figures
Figure E.1: House Price Inflation: 1998-2007
1
1
1.5
1.5
2
2
2.5
2.5
3
Panel B: 20 Departements
3
Panel A: All 95 Departements
1998
2000
2002
2004
Year
2006
2008
1998
2000
2002
2004
Year
2006
2008
Source: INSEE. Note: In Panel A, each line represents the house price index for one of the 95
French départments. In Panel B, we restrict ourselves to the 20 départements which have more
than 2,000 firms in 1998. In 1998, these départements altogether have 62,504 firms, about half of
the 125,065 firms present in our sample that year.
69
0
.5
Density
1
1.5
Figure E.2: Placebo Regressions
-2
-1
0
Coefficient on RE Value
1
2
Note: This figure displays the distribution of coefficient estimates of placebo regressions relative
to our baseline regression (red line). For each regression, we randomly draw from the balanced
sample with replacement the market value of real estate of firms (RE Value) from its empirical
distribution and run the regression corresponding to column 1 in Table D.1 – fully saturated
specification on the balanced sample. We repeat this procedure 50 times.
70
Figure E.3: Reponse to a Permanent Productivity Shock - Model Without Labor Adj. Costs
0
1
2
3
4
Panel A: Borrowing
0
10
20
30
year
Renter
Owner
Panel C: Labor
100
9
120
10
140
11
160
12
13
180
Panel B: Capital
0
10
20
30
0
year
Renter
10
20
30
year
Owner
Renter
Owner
Note: We first estimate the linearized policy function from data simulated using SMM parameters (500
firms in 100 departments over 10 years), except that we set fL = cL = 0. Using this simulated panel,
we regress (Dt+1 , Kt+1 ), Lt ) on Dt , Kt , Lt−1 , zt and pt . We then use these parameter to simulate the
response of the firm to a one s.d. positive permanent shock to z. The firm is assumed to start from the
average value of each of the five state variables. This procedure (including the calculation of averages and
policy function estimation) is done separately for firms renting and firm owning real estate. Panel A is
for debt, Panel B for the capital stock and panel C for total employment. The red line is the impulse
response of owning firms, and the blue line the impulse response for renting ones.
71