eric young, university of virginia flexibility and frictions in

Flexibility and Frictions in Production Networks∗

Jorge Miranda-Pinto

Department of Economics

University of Virginia

Eric R. Young

Department of Economics

University of Virginia

September 12, 2016

Abstract

We establish correlations between ”flexibility” of production (in terms of the elasticity of

substitution within intermediates and between intermediates and value added) and sectoral

bond premia. Bond premia are countercyclical. During normal times no systematic relation-

ship appears, but during recessions sectors with flexibility in their bundle of intermediates

pay higher premia while those sectors with flexibility between intermediates and value added

pay lower premia. We use these facts to guide construction of a multisector model with

occasionally-binding working capital constraints; the facts reveal that high elasticity service

sectors appear to have difficulty financing value added during downturns while low elasticity

manufacturing sectors have difficulty financing intermediates.

1 Introduction

The standard narrative of the Great Recession is one where financial frictions and intercon-

nected sectors translated a small shock to a relatively unimportant sector – often argued to be an

unexpectedly-large number of subprime mortgage defaults – into a large economy-wide decline in

economic activity. Clearly, sectoral linkages are critical for this narrative; recent work has shown

the potential for sectoral productivity shocks to be amplified and propagated strongly when in-

termediate inputs generate tight connections between sectors (Foerster, Sarte, and Watson 2011;

∗We thank Enghin Atalay, Pierre Sarte, James Harrigan, and Felipe Schwartzmann for comments, along with

seminar participants at the Kansas City Fed, the Cleveland Fed, UC Santa Barbara, and CUFE. We also thank

Egon Zakrajsek for providing us with the spread data.

1

Atalay 2015). Bigio and La’O (2016) show how financial shocks can be transmitted through the

network in the presence of working capital financing constraints, leading to declines in measured

aggregate TFP and aggregate labor wedges.

To date, however, this literature has neglected significant sectoral heterogeneity along two di-

mensions. First, the elasticity of substitution in sectoral production functions differs significantly

across sectors, both in terms of the elasticity of substitution between value added (labor and cap-

ital) and intermediates, which we denote ǫQ, as well as between intermediates ǫM ; indeed, with

the exception of Atalay (2015), these elasticities are generally constrained not only to be equal

but also equal to one. Atalay (2015) finds that both elasticities are significantly different than

one, but does not permit them to vary across sectors. We find substantial heterogeneity in both

elasticities, with large differences in particular between manufacturing and service sectors, and a

positive but low correlation between the elasticities for a given sector. We find that manufactur-

ing sectors have lower elasticities than service sectors in general, that elasticities between value

added and intermediates are larger than those within intermediates, and that service sectors have

an average elasticity of substitution between value added and intermediates that exceeds one.

Second, the spread that sectors pay to borrow (over the T-bill rate) also varies substantially

across sectors. Using the bond premium data from Gilchrist and Zakrajsek (2012), we find

two key facts. First, spreads are countercyclical for most sectors, in particular aggregates for

manufacturing and services (see Figure 5). Second, spreads are systematically related to our

estimated elasticities. We find that, during expansions, there is no evidence that either flexible

(high elasticity) or inflexible (low elasticity) sectors pay higher premia, no matter which elasticity

we consider. During recessions, however, things change – sectors that have a relatively diffi-

cult time substituting between value added and intermediates (low ǫQ) will pay higher premia,

which is probably not surprising to most readers, but sectors that have a relatively difficult time

substituting between different intermediates (low ǫM ) actually pay lower premia.

We use these results to guide the construction of a model built on Bigio and La’O (2016). We

allow for sectors to have heterogeneous values for ǫQ and ǫM , and we explore different assumptions

about which inputs are subject to the working capital requirement. To facilitate intuition, we

first study a very simple two-sector model. Sector one uses only labor to produce an intermediate

good for use in sector two. Sector two combines intermediates from both sectors with labor to

2

produce a good that can be consumed or used as an intermediate in sector two. We consider

environments where the firms in sector two are required to finance one or both types of inputs in

advance of production via working capital loans, and these loans must be collateralized by sales.1

When the production function is Cobb-Douglas between material inputs (ǫM = 1), we can

analytically characterize the Lagrange multiplier as a function of sectoral productivity levels, in

the sense that we can sign the derivative with respect to ǫQ. This multiplier can be viewed as

the shadow price of borrowing, which in turn therefore can be interpreted as a spread.2 Our first

result characterizes a key multiplicative ”wedge” between the costs of labor and intermediates

that depends on (i) the share of labor in the production function and (ii) the fraction of sales

that can be credibly pledged as collateral. If this wedge exceeds one, then the particular input is

more costly (in shadow units). We can then show that when the wedge is larger than one, sectors

that must finance intermediates in advance will be more frequently constrained during recessions

if they are a high ǫQ sector, provided ǫQ < 1; that is, among the low elasticity sectors the more

elastic are constrained more often. If, in addition, the price of intermediates is high, these sectors

will also be ”more constrained” in the sense of facing a higher shadow cost conditional on being

constrained. In contrast, sectors that must finance labor in advance will be more frequently

constrained during recessions if they are a low ǫQ sector provided ǫQ > 1; that is, among the high

elasticity sectors the less elastic are constrained more often. If, in addition, the price of labor is

high, these sectors will also be more constrained.

While these results are consistent with our empirical work, the assumption that ǫM = 1 is

definitely not. We then study cases where both elasticities are free to deviate from one. We

have been unable to find analytical results for these cases, but numerical examples have led us to

conclude the following statements are representative of the behavior of our model. The model can

reproduce all three facts – spreads can be countercyclical and systematically related to elasticities.

To match these facts, we need high elasticity service sectors (where ǫQ > 1) to face working capital

requirements that burden the purchase of value-added inputs, while low elasticity manufacturing

sectors (where ǫQ < 1) must face constraints on their purchases of intermediates.

Some additional evidence in favor of our model comes from studying the costs of intermediates

1Formally this arrangement is quite similar to ’Sudden Stop’ models with flow constraints, as in Bianchi (2011)

or Benigno et al. (2013).2Bigio and La’O (2016) derive an equivalence in their appendix.

3

for manufacturing and labor for services. We find that manufacturing costs for intermediates are

countercyclical and labor costs for services are procyclical, which fits our narrative.

Finally, we want to draw attention to international data that also supports our model.

Miranda-Pinto (2016) uses this model to explore the connections between measures of asym-

metry and density in production networks and the higher moments of GDP growth. He finds the

following facts: (i) GDP growth is more volatile in countries whose production networks have a

small number of sectors that purchase a large amount of intermediates (asymmetry in ’in degree’);

(ii) GDP growth is less volatile in countries with production networks that have lots of connections

(density); and (iii) GDP growth is more negatively-skewed in countries with a small number of

sectors that supply most of the intermediates (asymmetry in ’out degree’). Our model here can

reproduce these facts, whereas other models in the literature (Acemoglu et al. 2012, Acemoglu,

Akcigit, and Kerr 2016, Atalay 2015, and Bigio and La’O 2016) cannot.

2 Facts

Our goal in this section is to lay out the connections between the spread that a sector pays (the

median, specifically) and the elasticities of substitution in production for that sector. Suppose

that sectoral production uses an aggregate of capital and labor (value added Vj) and an aggregate

of intermediates (material input Mj) to produce a final good:

Qj = Zj

a1

ǫQ,j

j V

ǫQ,j−1

ǫQ,j

j + (1− aj)1

ǫQ,j M

ǫQj−1

ǫQ,j

j

ǫQj

ǫQ,j−1

where ǫQ,j is the elasticity of substitution and is sector-specific. The material input bundle Mj

is constructed using intermediates from other sectors:

Mj =

(

J∑

i=1

γ1

ǫM,j

ij M

ǫM,j−1

ǫM,j

ij

)

ǫM,j

ǫM,j−1

where ǫM,j is the elasticity of substitution between different material inputs.

To estimate the elasticities we follow Atalay (2015), but we allow for the elasticities to differ

across sectors. We run the OLS regression

∆ log

(

PitMijt

PjtQjt

)

=N∑

j=1

αjDj∆ log

(

PMjt

Pit

)

+N∑

j=1

βjDj∆ log

(

Pjt

PMjt

)

+ ηijt, (1)

4

where Dj are sectoral dummies, Pit and Pjt are sectoral output prices, and PMjt is the price of the

sector j intermediate bundle. We also include buyer-seller and time fixed effects. We can obtain

the elasticities as

ǫQ,j = 1 + βj

ǫM,j = 1 + αj .

We plot the elasticities in Figure (5); the average elasticities are ǫQ = 1.15 and ǫM = 0.5, in line

with Atalay (2015), but there is substantial heterogeneity. Elasticities are positively but weakly

correlated across sectors, so that it is not the case that a sector with flexibility in substituting

different intermediates also can easily substitute between intermediates and value added. We

also find that there is substantial difference between the elasticities in manufacturing and service

sectors – the average elasticities for manufacturing are ǫQ = 0.9 and ǫM = 0.31 while those

for services are ǫQ = 1.3 and ǫM = 0.8. Note that if we used a homogeneous production

function across sectors (in terms of the elasticities, at least), we would infer that value added and

intermediates are substitutes; however, this result only holds on average for service sectors, and

does not hold for all of them – we find both manufacturing and service sectors on either side of

one. Most sectors have ǫM < 1.

Note that we are forced to drop all sectors with negative estimated elasticities; this requirement

causes us to lose a large number of sectors. As a result, we end up with roughly the same number

of sectors as in Atalay (2015), despite starting with many more. As a result, we are working

to aggregate sectors in order to deal with an endogeneity problem. As noted in Atalay (2015),

there is a potential endogeneity problem in that relative prices will be correlated with unobserved

sectoral productivity. However, the instrument used in Atalay (2015), namely sectoral military

spending, is weak and generates a larger bias than OLS if we do not aggregate sectors.

We regress the spread on a constant, time and sector fixed effects, and various controls.

Sectoral bond spreads are obtained from Gilchrist and Zakrajsek (2012), defined as the median

spread of all firms in sector j at time t; the data cover the period 1973Q1-2016Q1. We control

for sectoral sales, the value tangible assets, leverage (total debt divided by sales), the value of

property and plants, and working capital as a fraction of sales; all the controls are plausible

reasons unconnected to the elasticity that a sector might pay a higher premium at a given point

5

in time.

Figures (5)-(5) display scatterplots of the residual of the regression vs the elasticity for 29

sectors (we have dropped some outlier sectors and sectors where our estimates of the elasticity of

substitution are negative). During NBER recessions, we see clearly that sectors with high values

of ǫM pay higher premia on average, while those with high values of ǫQ pay lower premia. In

contrast, outside recessions we find no systematic relationship. We view this result as suggesting

an environment with occasionally-binding constraints; that is, a model where financial frictions

play little role during ”normal” times, but activate during downturns. Furthermore, as we show

in the next section, the different correlations between spreads and the two elasticities can be used

as a guide to the construction of an economic model.

To explore this relationship more formally, we run the regression

rjt = αj + β1DR + β2Ljt + β3ǫQjDRt + β4ǫMjDRt + β5ǫQjLjt + β6ǫMjLjt + γXjt + νjt, (2)

where rjt is the median credit spread for sector j in quarter t, DRt is a recession dummy (or

a banking crisis dummy), Ljt is leverage measured by total debt divided by sales, and Xjt is

the vector of controls from before. In Table 1 we present our estimates; both recession-elasticity

interaction terms are significant when all sectors are pooled together, and most are significant

when manufacturing and services are split.

We use NBER recession dates to identify recessions. Having a high elasticity ǫM leads to

higher spreads during a recession, even controlling for the overall leverage for the sector, and

having a high ǫQ leads to low spreads for the pooled regression and the service sector only (our

regression has few manufacturing sectors so insignificance is not a surprise here).

We find similar results with firm-level data. We match corporate bond yields from TRACE

with Compustat balance sheet data for the period 2002Q2-2015Q4; now our recession dummy

variable only captures the effect of the Great Recession, and our sample is shorter and almost

entirely manufacturing, but we can use firm-level fixed effects (see Table 2). Results are similar.

As a last point, we plot the bond yields for manufacturing and services over time overlaid with

the NBER recession dates; in general, yields rise during recessions (they are countercyclical).

6

3 A Model of Network Production

In this section we provide some intuition for how we use the empirical facts to guide development

of a quantitative model. We suppose there are only two sectors – the first sector produces using

only labor, and the second sector produces using labor and intermediates from both sectors:

Q1 = Z1L1

Q2 = Z2

a

1

ǫQ,2

2L

ǫQ,2−1

ǫQ,2

2+ (1− a2)

1

ǫQ,2

(

γ1

ǫM,2

12M

ǫM,2−1

ǫM,2

12+ γ

1

ǫM,2

22M

ǫM,2−1

ǫM,2

22

)

ǫM,2

ǫM,2−1

ǫQ,2−1

ǫQ,2

ǫQ,2

ǫQ,2−1

.

We suppose that each sector faces a collateral constraint on working capital:

wL1 ≤ η1p1Q1

θw2 wL2 + θm12M12 + θm22p2M22 ≤ η2p2Q2.

The representative household maximizes

U (C,L) =C1−σ − 1

1− σ− ψ

L1+ξ

1 + ξ

subject to the budget constraint

wL+Π ≥ PC + T.

In equilibrium, labor market clearing requires

L = L1 + L2,

and goods market clearing requires

M12 = Q1

C +M22 = Q2.

Note that, for simplicity of the resulting algebra, the output of sector one is not consumed.

Adding capital would not change our results if value added is produced using a Cobb-Douglas

aggregate of capital and labor, so again for ease of presentation we simply ignore it.

We develop intuition through a series of special cases. We vary the values of the elasticities

and examine the relationship between the Lagrange multiplier µ2 on the collateral constraint for

7

sector 2 and the elasticity of interest. We set ψ = 0, σ = 1, and normalize w = 1. The total

labor endowment is normalized to 1, and we set θm22 = 0. Some configurations of parameters yield

uninteresting results. For example, if we set ǫQ = ǫM = 1, we get essentially Bigio and La’O

(2016), where firms are either permanently constrained or unconstrained (since shares of inputs

are constant, the firm can either collateralize enough sales to make its required prepayments or

it cannot, independent of productivity); it turns out that this argument goes through for ǫQ = 1

independent of ǫM , so we ignore both of these cases and focus on cases where ǫQ 6= 1.

Abandoning Cobb-Douglas means we can study (i) which sectors will become constrained

more frequently and (ii) when sectors become constrained which sectors are ”more constrained”.

In contrast, under Cobb-Douglas assumptions sectors are either constrained or unconstrained if

we maintain the assumption of constant returns to scale (for example, a sector is constrained

if η < 1 and θ = 1 since the left-hand-side of the collateral constraint equals revenue at the

unconstrained profit-maximizing point). To deal with this problem while maintaining Cobb-

Douglas production functions, Bigio and La’O (2016) assume sector-specific decreasing returns to

scale; this assumption seems difficult to calibrate empirically, and their strategy is indirect.

3.1 Case 1: ǫQ 6= 1 and ǫM = 1

Proposition 1. Suppose µ2 > 0. Then, if θm12 = 1 and θw2 = 0, we have ∂µ2

∂ǫQ< 0 if p1φm > 1 and

∂µ2

∂ǫQ> 0 if p1φm < 1, where

φm =(1− η2) (1− a2)

η2a2.

Also, if θm12 = 0 and θw2 = 1, we have ∂µ2

∂ǫQ< 0 if φw

p1> 1 and ∂µ2

∂ǫQ> 0 if φw

p1< 1 , where

φw =(1− η2) a2(1− a2) η2

.

Proof. First set θw2 = 0 and θm12 = 1, which implies L2 = 1 − η2 and Q1 = Z1η2. Using the

production function for sector 2 and the first-order condition for L2 we obtain

µ2 =

(

(1− η2) (1− a2)

a2η2

)1−ρQ

ZρQ1

− 1,

where ρQ = (1− ǫQ) /ǫQ. Therefore,

∂µ2∂ǫQ

=1

ǫ2QZ

ρQ1φ1−ρQm ln

(

Z1

φm

)

.

8

If Z1 < φm the derivative is negative, otherwise it is positive. Now set θw2 = 1 and θm12 = 0, which

implies L2 = η2 and Q1 = Z1 (1− η2). Again using the production function and the first-order

condition for L2 we obtain

µ2 =

(

(1− η2) a2η2 (1− a2)

)1−ρQ

Z−ρQ1

− 1,

which implies∂µ2∂ǫQ

= −1

ǫ2QZ−ρQ1

φ1−ρQw ln (Z1φw) ;

if Z1φw > 1 the derivative is negative, otherwise it is positive.

The terms p1φm and p1/φw can be interpreted as friction-adjusted prices of intermediates

relative to labor. If the constraint affects only intermediate purchases (θm12 = 1 and θw2 = 0), then

if intermediates are relatively expensive inflexible firms will face a higher shadow cost for working

capital, as such firms will be unable to easily shift their production away from intermediates.

On the other hand, if intermediates are relatively cheap more flexible firms will choose a higher

intermediate share and therefore face a higher shadow price. Similar intuition applies to the

second part of Proposition 1.

Proposition 2. Let Z∗

1 denote the threshold productivity in sector 1 that results in sector 2 being

constrained. Then, if θm12 = 1 and θw2 = 0, we have∂Z∗

1

∂ǫQ< 0 if φm < 1 and

∂Z∗

1

∂ǫQ> 0 if φm > 1.

Also, if θm12 = 0 and θw2 = 1, we have∂Z∗

1

∂ǫQ< 0 if φw > 1 and

∂Z∗

1

∂ǫQ> 0 if φw < 1.

Proof. Using the solution for µ2 from Proposition 1, we have

Z∗

1 = φ1

1−ǫQm

so that∂Z∗

1

∂ǫQ= φ

1

1−ǫQm

1

(1− ǫQ)2ln (φm) .

The sign depends on whether φm is larger or smaller than 1.

3.2 Case 2: ǫQ 6= 1 and ǫM 6= 1

For this case we have been unable to construct a special case amenable to analysis, so we proceed

using numerical examples. Figures (5)-(5) plot the Lagrange multiplier for sector 2 as a function

9

of the two sectoral productivity levels under a variety of different assumptions about (i) the value

of the two elasticities and (ii) the value of θm12 and θw2 .

Table ?? contains the complete set of results from this case.

3.3 Discussion

The propositions above identify the connection between the elasticities in production (flexibility)

and the multiplier on the working capital constraint, both in terms of the extensive and intensive

margins. Based on the first proposition, when intermediate prices are high, a negative correlation

between ǫQ and the spread is consistent with a working capital requirement for intermediates; in

contrast, a positive correlation would indicate that labor is subject to the working capital require-

ment. Figure (5) plots the relative price of intermediates to labor for a number of manufacturing

sectors; note that this cost spikes up at the beginning of NBER-dated recessions. Using our

model, we would infer that spreads would rise on manufacturing firms, as the rise in the cost

causes the LHS of the collateral constraint to rise while the RHS falls, leading these sectors to

become constrained (or more constrained).

We also looked at the behavior of wages in service sectors; see Figure (5). Consistent with

our model, we find that wages fall during recessions, leading to a rise in the share of expenditures

on labor (note that the drops are obscured a bit by the overall downward trend and the generally

smooth nature of service wages). In this case, the LHS of the constraint falls less than the RHS,

leading again to countercyclical spreads.

4 Monte Carlo Experiment

As discussed earlier, the estimation of elasticities is biased due to unobserved productivity shocks

that are correlated with prices and the input choice. To evaluate how important is this bias, we

use the model as a guide. We simulate series of output, prices, and input demand to estimate the

same OLS regressions as in section 2.3.

The model used for the experiment is a more general version of the two sector model in section

3.

3Feenstra et al. (2014) perform a similar exercise to study how biased are the usual estimates of consumption

elasticities that enter in the definition of trade elasticities.

10

Firms in the intermediate good sector produce according to

Q1 = Z1

a

1

ǫQ1

1L

ǫQ1−1

ǫQ1

1+ (1− a1)

1

ǫQ1 M

ǫQ1−1

ǫQ1

1

ǫQ1

ǫQ1−1

, (3)

where M1 =Mγ1111M1−γ11

21.

Final good firms produce according to

Q2 = Z2

a

1

ǫQ2

2L

ǫQ2−1

ǫQ2

2+ (1− a2)

1

ǫQ2 M

ǫQ2−1

ǫQ2

2

ǫQ2

ǫQ2−1

, (4)

where M2 =Mγ2222M1−γ22

12.

The working capital constraints are

θw1 wL1 + θm1 (P1M11 + P2M21) ≤ η1P1Q1 (5)

θw2 wL2 + θm2 (P1M12 + P2M22) ≤ η2P2Q2. (6)

The market clearing conditions are

Q1 =M11 +M12, (7)

Q2 = C +M21 +M22. (8)

Households solve the same problem as in Section 3.

To derive Equation (1) we solve the cost minimization problem

L = PMj Mj+wLj+λ

Qj − Zj

a

1

ǫQj

j L

ǫQj−1

ǫQj

j + (1− aj)1

ǫQj M

ǫQj−1

ǫQj

j

ǫQj

ǫQj−1

+φ(

Mj −Mγjjjj M

1−γjjij

)

+µCj(

ηjP

(9)

The first-order necessary and sufficient conditions for Mj are

PMj − λ

∂Qj

∂Mj+ µCj ηjPj

∂Qj

∂Mj− µCj θ

mj P

Mj = 0. (10)

or

PMj = Z

ρjj

(

ajQj

Mj

) 1

ǫQjPj

(

1− µCj ηj

)

(

1− µCj θj

) . (11)

11

Let µj =(1−µC

j ηj)(1−µC

j θj). Raising the previous equation to the power of ǫQ2

, taking logs, and rearranging

we obtain Equation (1). For the experiment, the TFP shocks in each sector are assumed to be

either iid standard normal or having persistence by following an AR(1)process with persistence

parameter 0.9. In the first simulation we assume ǫQ1= 1, a1 = 1, a2 = 0.3, and γ22 = 0. Here we

explore the effects of the bias – on what features of the environment does it depend?

In the next experiment we assume γ11 = γ22 = 0.3, η1 = η2 = 1, a1 = a2 = 0.4, θwj = 0, and

θmj = 1. In this experiment one can study if the rank in terms of production flexibility is preserved.

For example, for true pairs of elasticities like (ǫQ1= 0.3, ǫQ2

= 0.8), is the OLS estimation still

preserving the fact that sector 2 is more flexible?

We summarize our results for the bias as (i) there is no bias if the sector under investigation

does not experience shocks; (ii) when estimating only one elasticity estimates are biased toward 1,

even if constraints are not binding, and are exactly equal to 1 if constraints are always binding; (iii)

estimates are biased downward when trying to estimate two elasticities if both sectors experience

shocks. We conclude from these exercises that endogeneity may be an issue. As noted previously,

the weak instrument problem is attentuated if we aggregate as in Atalay (2015); we are currently

exploring whether our results survive aggregation (we have no reason to expect they will not).

5 Conclusion

In this paper we have provided a ’guidebook’ for the construction of multisector business cycle

models with intersectoral linkages through intermediates. To capture the dynamics of sectoral

bond premia one needs high elasticity service sectors to be occasionally constrained in their use

of labor and low elasticity manufacturing sectors to be occasionally constrained in intermediates.

Future work will situate our model in a larger multisector model suitable for dynamic analysis;

results in Miranda-Pinto and Young (2016) suggest a method for computing a model with capital,

many sectors, and occasionally-binding constraints. Our interest in this model lies in studying

the implied dynamics, extending results in Foerster, Sarte, and Watson (2011), Atalay (2015),

and Luo (2016).

12

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13

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14

Table 1: GZ Spreads and Elasticities

Elasticities and Sectoral Spreads 1973-2016

(1) (2) (3)

Regressors All Manu Serv

DR 0.494∗∗∗ 0.561∗∗∗ 0.514∗∗∗

(0.0478) (0.0897) (0.0622)

L 0.400∗∗∗ 0.0409 0.373∗∗∗

(0.0543) (0.166) (0.0707)

ǫQDR −0.0537∗∗∗ 0.0628 −0.0743∗∗

(0.0230) (0.0400) (0.0304)

ǫMDR 0.0619∗∗∗ 0.0833∗∗ 0.0700∗∗∗

(0.0179) (0.0392) (0.0214)

ǫQL −0.0365 −0.398∗∗∗ 0.0905∗

(0.0359) (0.0896) (0.0546)

ǫML 0.165∗∗∗ −0.153∗ 0.281∗∗∗

(0.0334) (0.0781) (0.0459)

Observations 2092 820 1121

R2 0.594 0.625 0.604

Year FE Yes Yes Yes

Sector FE Yes Yes Yes

Sectors 32 11 19

15

Table 2: TRACE Spreads and Elasticities

(1) (2)

VARIABLES Spread Spread

Recession 0.264*** 0.262***

(0.0728) (0.0728)

Leverage 0.281*** 0.203***

(0.0372) (0.0585)

ǫQ · Recession -0.134*** -0.138***

(0.0350) (0.0350)

ǫM · Recession -0.00494 -0.00826

(0.0401) (0.0401)

ǫQ · Leverage -0.0586*

(0.0336)

ǫM · Leverage -0.0626*

(0.0365)

Observations 3,583 3,583

R-squared 0.209 0.211

Year FE Yes Yes

Firm FE Yes Yes

Standard errors clustered at the sector level

*** p<0.01, ** p<0.05, * p<0.1

16

Table 3: Results from the General Case

φm < 1, φw < 1

(φm > 1, φw > 1)

Bold Countercyclical Spreads

ǫQ < 1 ǫQ > 1

M L M L

High ǫM − (−) + (+) + (+) − (−)

High ǫQ − (+) − (+) + (−) + (−)

Table 4: OLS Bias

ǫQ 0.5 0.65 0.8 0.95 1.1 1.25 1.4

Only Z1, iid

OLS uncon 0.5 0.65 0.8 0.95 1.1 1.25 1.4

OLS con 1 1 1 1 1 1 1

(Z1, Z2), iid

OLS uncon 0.93 0.95 0.97 0.99 1.01 1.03 1.05

OLS con 1 1 1 1 1 1 1

(Z1, Z2), persistence 0.9

OLS 0.96 0.969 0.984 0.994 1.011 1.021 1.032

Binding Freq 0.58 0.57 0.57 0 0.42 0.42 0.42

17

Table 5: OLS Bias

ǫQ10.5 0.6 0.5 0.8 ... ... ...

ǫQ21.2 1.2 1 1 ... ... ...

Only Z1, iid

ǫQ1OLS uncon 1.42 1.38 1.42 1.23 ... ... ...

ǫQ2OLS uncon 0.5 0.5 0.5 0.5 ... ... ...

OLS con

Only Z2, iid

ǫQ1OLS uncon 0.5 0.6 0.5 0.8 ... ... ...

ǫQ2OLS uncon 1.42 1.36 1.42 1.29 ... ... ...

OLS con

(Z1, Z2), iid

ǫQ1OLS uncon 0.45 0.79 0.44 0.94 ... ... ...

ǫQ2OLS uncon 0.67 0.93 0.67 1.01 ... ... ...

OLS con

18

1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 20200

2

4

6

8

10

12

Manufacturing

Services

Figure 1: Sectoral Spreads

19

Elasticity ǫ M

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Ela

sticity ǫ

Q

0

0.5

1

1.5

2

2.5

3

3.5

Farms

Oil and gas extraction

Mining support

Utilities

Nonmetallic mineral

Primary metals

Machinery

Electrical equipment

Other transportation equipmentFurniture

Food and beverage Textile mills

Apparel and leather

Paper productsPrinting

Merchandise stores

Other retail

Truck transportation

Publishing industries

Broadcasting and telecommunications

Legal services

Computer systems design

Administrative services

Ambulatory health care

Hospitals

Nursing

Amusements

Accommodation

Other services

Figure 2: Sectoral Elasticities

20

Elasticity ǫ M

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Spre

ad R

esid

ual

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

Farms


Mining support

Utilities

Nonmetallic mineralPrimary metals

Machinery


Other transportation equipment

Furniture

Food and beverage

Textile mills

Apparel and leatherPaper products

Printing

Merchandise stores

Other retail



Broadcasting and telecommunicationsLegal servicesComputer systems design



Hospitals

Nursing

AmusementsAccommodation

Other services

Figure 3: Sectoral Elasticities and Spreads, Expansion

21

Elasticity ǫ M

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Spre

ad R

esid

ual

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

Farms


Mining support

Utilities

Nonmetallic mineral

Primary metals

Machinery



Furniture

Food and beverage

Textile mills

Apparel and leather

Paper products

Printing

Merchandise stores

Other retail




Legal servicesComputer systems design



Hospitals

Nursing


Other services

Figure 4: Sectoral Elasticities and Spreads, Recession

22

Elasticity ǫ Q

0 0.5 1 1.5 2 2.5 3 3.5

Spre

ad R

esid

ual

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

Farms


Mining support

Utilities

Nonmetallic mineralPrimary metals

Machinery



Furniture

Food and beverage

Textile mills

Apparel and leatherPaper products

Printing

Merchandise stores

Other retail



Broadcasting and telecommunicationsLegal services Computer systems design



Hospitals

Nursing


Other services

Figure 5: Sectoral Elasticities and Spreads, Expansion

23

Elasticity ǫ Q

0 0.5 1 1.5 2 2.5 3 3.5

Spre

ad R

esid

ual

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

Farms


Mining support

Utilities

Nonmetallic mineral

Primary metals

Machinery



Furniture

Food and beverage

Textile mills

Apparel and leather

Paper products

Printing

Merchandise stores

Other retail




Legal servicesComputer systems design



Hospitals

NursingAmusements

Accommodation

Other services

Figure 6: Sectoral Elasticities and Spreads, Recession

24

0.05

0.05

0.1

0.1

0.150.20.250.3

Financing Materials: ǫQ

=0.5 and ǫM

=0.3

Z1

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Z2

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

µ 2

Figure 7: Shadow Cost of Borrowing

25

0.0050.01

0.015


=0.9 and ǫM

=0.3

Z1

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Z2

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

µ2


26

0.0050.01

0.015


=0.9 and ǫM

=0.9

Z1

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Z2

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

µ2


27

1985 1990 1995 2000 2005 2010-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

Figure 10: Relative Price of Manufacturing Intermediates

28

1998 2000 2002 2004 2006 2008 2010 20120

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08Service Sector Wages

Figure 11: Wages in Service Sectors

29

eric young, university of virginia flexibility and frictions in

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