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Capital Values, Job Valuesand the Joint Behavior of Hiring and Investment

Eran YashivTel Aviv University

SF Macro conference, JerusalemJune 22, 2014

ERAN YASHIV (TEL AVIV) HIRING AND INVESTMENT JUNE 2014 1 / 71

MOTIVATION AND KEY IDEAS

This paper explores how the joint behavior of hiring andinvestment is governed by capital and job values.

It uses a model of frictions:akin to search models of the labor market;Q-type models of the capital market;it emphasizes the interaction of capital and labor frictions.Relying on structural estimation of private sector U.S. data, itstudies their cyclical behavior, their future determinants and theimplications for U.S. labor market developments.

This paper explores how the joint behavior of hiring andinvestment is governed by capital and job values.It uses a model of frictions:

akin to search models of the labor market;Q-type models of the capital market;it emphasizes the interaction of capital and labor frictions.Relying on structural estimation of private sector U.S. data, itstudies their cyclical behavior, their future determinants and theimplications for U.S. labor market developments.

This paper explores how the joint behavior of hiring andinvestment is governed by capital and job values.It uses a model of frictions:akin to search models of the labor market;

Q-type models of the capital market;it emphasizes the interaction of capital and labor frictions.Relying on structural estimation of private sector U.S. data, itstudies their cyclical behavior, their future determinants and theimplications for U.S. labor market developments.

This paper explores how the joint behavior of hiring andinvestment is governed by capital and job values.It uses a model of frictions:akin to search models of the labor market;Q-type models of the capital market;

it emphasizes the interaction of capital and labor frictions.Relying on structural estimation of private sector U.S. data, itstudies their cyclical behavior, their future determinants and theimplications for U.S. labor market developments.

This paper explores how the joint behavior of hiring andinvestment is governed by capital and job values.It uses a model of frictions:akin to search models of the labor market;Q-type models of the capital market;it emphasizes the interaction of capital and labor frictions.

Relying on structural estimation of private sector U.S. data, itstudies their cyclical behavior, their future determinants and theimplications for U.S. labor market developments.

This paper explores how the joint behavior of hiring andinvestment is governed by capital and job values.It uses a model of frictions:akin to search models of the labor market;Q-type models of the capital market;it emphasizes the interaction of capital and labor frictions.Relying on structural estimation of private sector U.S. data, itstudies their cyclical behavior, their future determinants and theimplications for U.S. labor market developments.

(i) how do capital and labor expected present values behave overthe business cycle and what cyclical hiring and investmentpatterns do they generate?

(ii) how big are these values, i.e., how big are the relevantfrictions?(iii) what determinants drive expected present values?(iv) how can recent U.S. labor market developments – includingthe Great Recession period – be understood in terms of capitaland labor (job) values?

(i) how do capital and labor expected present values behave overthe business cycle and what cyclical hiring and investmentpatterns do they generate?(ii) how big are these values, i.e., how big are the relevantfrictions?

(iii) what determinants drive expected present values?(iv) how can recent U.S. labor market developments – includingthe Great Recession period – be understood in terms of capitaland labor (job) values?

(i) how do capital and labor expected present values behave overthe business cycle and what cyclical hiring and investmentpatterns do they generate?(ii) how big are these values, i.e., how big are the relevantfrictions?(iii) what determinants drive expected present values?

(iv) how can recent U.S. labor market developments – includingthe Great Recession period – be understood in terms of capitaland labor (job) values?

(i) how do capital and labor expected present values behave overthe business cycle and what cyclical hiring and investmentpatterns do they generate?(ii) how big are these values, i.e., how big are the relevantfrictions?(iii) what determinants drive expected present values?(iv) how can recent U.S. labor market developments – includingthe Great Recession period – be understood in terms of capitaland labor (job) values?

Key findings include:

1 a substantial effect of the expected value of capital on hiring2 cyclical behavior of hiring and of investment are markedly

different3 counter-cyclcial job values, hence counter-cyclcial hiring rates4 future returns series are derived and shown to play a dominant

role in determining capital and job values5 U.S. labor market developments, including the inward and

subsequent, Great Recession outward shift of the Beveridge curvecan be accounted for by changes in job values

1 a substantial effect of the expected value of capital on hiring

2 cyclical behavior of hiring and of investment are markedlydifferent

3 counter-cyclcial job values, hence counter-cyclcial hiring rates4 future returns series are derived and shown to play a dominant

different

3 counter-cyclcial job values, hence counter-cyclcial hiring rates4 future returns series are derived and shown to play a dominant

different3 counter-cyclcial job values, hence counter-cyclcial hiring rates

4 future returns series are derived and shown to play a dominantrole in determining capital and job values

5 U.S. labor market developments, including the inward andsubsequent, Great Recession outward shift of the Beveridge curvecan be accounted for by changes in job values

role in determining capital and job values

5 U.S. labor market developments, including the inward andsubsequent, Great Recession outward shift of the Beveridge curvecan be accounted for by changes in job values

LITERATURE

For the labor part – search and matching models (e.g. Pissarides2000)

Investment models – seminal: Lucas (JPE 1967) and Lucas andPrescott (Econometrica 1971); Tobin (JMCB 1969) and Brainardand Tobin (AER 1968); Hayashi (Econometrica 1982).Immediate antecedents: Yashiv (RED 2000); Merz and Yashiv(AER 2007)Recent related: Hall (NBER WP 2014)

LITERATURE

For the labor part – search and matching models (e.g. Pissarides2000)Investment models – seminal: Lucas (JPE 1967) and Lucas andPrescott (Econometrica 1971); Tobin (JMCB 1969) and Brainardand Tobin (AER 1968); Hayashi (Econometrica 1982).

Immediate antecedents: Yashiv (RED 2000); Merz and Yashiv(AER 2007)Recent related: Hall (NBER WP 2014)

LITERATURE

For the labor part – search and matching models (e.g. Pissarides2000)Investment models – seminal: Lucas (JPE 1967) and Lucas andPrescott (Econometrica 1971); Tobin (JMCB 1969) and Brainardand Tobin (AER 1968); Hayashi (Econometrica 1982).Immediate antecedents: Yashiv (RED 2000); Merz and Yashiv(AER 2007)

Recent related: Hall (NBER WP 2014)

LITERATURE

For the labor part – search and matching models (e.g. Pissarides2000)Investment models – seminal: Lucas (JPE 1967) and Lucas andPrescott (Econometrica 1971); Tobin (JMCB 1969) and Brainardand Tobin (AER 1968); Hayashi (Econometrica 1982).Immediate antecedents: Yashiv (RED 2000); Merz and Yashiv(AER 2007)Recent related: Hall (NBER WP 2014)

LITERATURE

Mutual dependence of hiring and investment and the interactionof their costs – Mortensen (Econometrica 1973);

some empirical treatments: Nadiri and Rosen (AER 1969), Shapiro(QJE 1986), and Hall (QJE 2004).Relevant asset pricing literature – Campbell and Shiller (RFS1988); Cochrane (book 2005, JF 2011)

LITERATURE

Mutual dependence of hiring and investment and the interactionof their costs – Mortensen (Econometrica 1973);some empirical treatments: Nadiri and Rosen (AER 1969), Shapiro(QJE 1986), and Hall (QJE 2004).

Relevant asset pricing literature – Campbell and Shiller (RFS1988); Cochrane (book 2005, JF 2011)

LITERATURE

Mutual dependence of hiring and investment and the interactionof their costs – Mortensen (Econometrica 1973);some empirical treatments: Nadiri and Rosen (AER 1969), Shapiro(QJE 1986), and Hall (QJE 2004).Relevant asset pricing literature – Campbell and Shiller (RFS1988); Cochrane (book 2005, JF 2011)

THE MODEL

F.O.C (PE model) for both i and h

yt = f (zt,nt, kt), (1)

kt+1 = (1� δt)kt + it, 0 � δt � 1. (2)

nt+1 = (1� ψt)nt + ht, 0 � ψt � 1. (3)

THE MODEL

F.O.C (PE model) for both i and h

yt = f (zt,nt, kt), (1)

kt+1 = (1� δt)kt + it, 0 � δt � 1. (2)

nt+1 = (1� ψt)nt + ht, 0 � ψt � 1. (3)

THE MODEL

maxfit+j,ht+jg

Et∑∞

�∏

ji=0 ρt+i

� 24 (1� τt+j)�f (zt+j,nt+j, kt+j)

�g�it+j, kt+j, ht+j, nt+j

�� wt+jnt+j

��

1� χt+j � τt+jDt+j

� epIt+j it+j

s.t. k, n dynamicsThe firm takes the variables w, pI , δ, ψ, and ρ as given.

THE MODEL

maxfit+j,ht+jg

Et∑∞

�∏

ji=0 ρt+i

� 24 (1� τt+j)�f (zt+j,nt+j, kt+j)

�� wt+jnt+j

��

� epIt+j it+j

s.t. k, n dynamics

The firm takes the variables w, pI , δ, ψ, and ρ as given.

THE MODEL

maxfit+j,ht+jg

Et∑∞

�∏

ji=0 ρt+i

� 24 (1� τt+j)�f (zt+j,nt+j, kt+j)

�� wt+jnt+j

��

� epIt+j it+j

s.t. k, n dynamicsThe firm takes the variables w, pI , δ, ψ, and ρ as given.

THE MODEL

F.O.C. with asset pricing interpretation

(1� τt)�

git + pIt

�| {z }

8>>>>><>>>>>:

ρt+1 (1� τt+1)26664fkt+1 � gkt+1| {z }

+(1� δt+1)(git+1 + pIt+1)| {z }

9>>>>>=>>>>>;(5)

(1� τt) ght| {z }Pt

8>>>>><>>>>>:

ρt+1 (1� τt+1)26664fnt+1 � gnt+1 � wt+1| {z }

+(1� ψt+1)ght+1|{z}Pt+1

9>>>>>=>>>>>;. (6)

To know what Pt, &Dt are, we need estimates

THE MODEL

F.O.C. with asset pricing interpretation

(1� τt)�

git + pIt

�| {z }

8>>>>><>>>>>:

ρt+1 (1� τt+1)26664fkt+1 � gkt+1| {z }

+(1� δt+1)(git+1 + pIt+1)| {z }

9>>>>>=>>>>>;(5)

(1� τt) ght| {z }Pt

8>>>>><>>>>>:

ρt+1 (1� τt+1)26664fnt+1 � gnt+1 � wt+1| {z }

+(1� ψt+1)ght+1|{z}Pt+1

9>>>>>=>>>>>;. (6)

To know what Pt, &Dt are, we need estimates

THE EMPIRICAL STRATEGY

These relationships include observables and unobservables.

Unlike stock prices and dividends, the equivalents in terms of thismodel are not observed in the markets.Thus, costs are unobserved directly and need to be inferred byestimating the cost function (g).The estimation of this function allows not only to infer currentmarginal costs but also the present value expected when the firmis following optimal policy

QKt = (1� τt)

�git + pI

�(7)

QNt = (1� τt) ght (8)

These relationships include observables and unobservables.Unlike stock prices and dividends, the equivalents in terms of thismodel are not observed in the markets.

Thus, costs are unobserved directly and need to be inferred byestimating the cost function (g).The estimation of this function allows not only to infer currentmarginal costs but also the present value expected when the firmis following optimal policy

QKt = (1� τt)

�git + pI

�(7)

QNt = (1� τt) ght (8)

These relationships include observables and unobservables.Unlike stock prices and dividends, the equivalents in terms of thismodel are not observed in the markets.Thus, costs are unobserved directly and need to be inferred byestimating the cost function (g).

The estimation of this function allows not only to infer currentmarginal costs but also the present value expected when the firmis following optimal policy

QKt = (1� τt)

�git + pI

�(7)

QNt = (1� τt) ght (8)

These relationships include observables and unobservables.Unlike stock prices and dividends, the equivalents in terms of thismodel are not observed in the markets.Thus, costs are unobserved directly and need to be inferred byestimating the cost function (g).The estimation of this function allows not only to infer currentmarginal costs but also the present value expected when the firmis following optimal policy

QKt = (1� τt)

�git + pI

�(7)

QNt = (1� τt) ght (8)

These relationships include observables and unobservables.Unlike stock prices and dividends, the equivalents in terms of thismodel are not observed in the markets.Thus, costs are unobserved directly and need to be inferred byestimating the cost function (g).The estimation of this function allows not only to infer currentmarginal costs but also the present value expected when the firmis following optimal policy

QKt = (1� τt)

�git + pI

�(7)

QNt = (1� τt) ght (8)

The route to be taken in estimation and the study of itsimplications consists of the following:

1 Structural estimation with quarterly data that pertain to theprivate sector of the U.S. economy, in the period 1976-2011.

2 Comparison of the resulting estimates to the findings in therelevant literatures

3 Use of the estimates to study the relationships of hiring andinvestment rates ( ht

nt, it

kt) and their present values (QN

t , QKt ),

including the cyclical behavior of all relevant variables.4 Decomposition of the two present value terms into their

components.5 The implications of model to the study of recent U.S. labor market

developments

nt, it

t , QKt ),

developments

nt, it

t , QKt ),

developments

nt, it

t , QKt ),

including the cyclical behavior of all relevant variables.

4 Decomposition of the two present value terms into theircomponents.

5 The implications of model to the study of recent U.S. labor marketdevelopments

nt, it

t , QKt ),

components.

5 The implications of model to the study of recent U.S. labor marketdevelopments

nt, it

t , QKt ),

developments

nt, it

t , QKt ),

developments

RESULTS

GMM estimation of the two F.O.C

Functions

f (zt,nt, kt) = ezt ntαk1�α

t , 0 < α < 1. (9)

g(�) =

266664f1

itkt+ f2

+ e1η1( it

kt)η1

+ e2η2( ht

nt)η2

+ e3η3

�itkt

�η3

377775 f (zt, nt, kt). (10)

Estimate scale ( f1, f2, e1, e2, e3) and power (η1, η2, η3) parametersPreferred specification: f� standard α estimate (0.67), g� nolinear terms, quadratic η1 = η2 = 2, linear interaction η3 = 1

RESULTS

GMM estimation of the two F.O.CFunctions

t , 0 < α < 1. (9)

g(�) =

266664f1

itkt+ f2

+ e1η1( it

kt)η1

+ e2η2( ht

nt)η2

+ e3η3

�itkt

�η3

377775 f (zt, nt, kt). (10)

RESULTS

t , 0 < α < 1. (9)

g(�) =

266664f1

itkt+ f2

+ e1η1( it

kt)η1

+ e2η2( ht

nt)η2

+ e3η3

�itkt

�η3

377775 f (zt, nt, kt). (10)

RESULTS

t , 0 < α < 1. (9)

g(�) =

266664f1

itkt+ f2

+ e1η1( it

kt)η1

+ e2η2( ht

nt)η2

+ e3η3

�itkt

�η3

377775 f (zt, nt, kt). (10)

Estimate scale ( f1, f2, e1, e2, e3) and power (η1, η2, η3) parameters

Preferred specification: f� standard α estimate (0.67), g� nolinear terms, quadratic η1 = η2 = 2, linear interaction η3 = 1

RESULTS

t , 0 < α < 1. (9)

g(�) =

266664f1

itkt+ f2

+ e1η1( it

kt)η1

+ e2η2( ht

nt)η2

+ e3η3

�itkt

�η3

377775 f (zt, nt, kt). (10)

RESULTS

In the preferred specification total costs are 1.4% of GDP onaverage, with a standard deviation of 0.2%.

Marginal investment costs add about 6% on average to the pricepI

t of a unit of capitalMarginal hiring costs are on average the equivalent of 1.6 weeksof wages.

RESULTS

In the preferred specification total costs are 1.4% of GDP onaverage, with a standard deviation of 0.2%.Marginal investment costs add about 6% on average to the pricepI

t of a unit of capital

Marginal hiring costs are on average the equivalent of 1.6 weeksof wages.

RESULTS

In the preferred specification total costs are 1.4% of GDP onaverage, with a standard deviation of 0.2%.Marginal investment costs add about 6% on average to the pricepI

t of a unit of capitalMarginal hiring costs are on average the equivalent of 1.6 weeksof wages.

RESULTS

The standard specifications posit higher costs, up to 3% of output.

High costs of investment (2.33 or even 1.39 vs 0.75)In other words, 17% to be added to pI (vs. 6%)

RESULTS

The standard specifications posit higher costs, up to 3% of output.High costs of investment (2.33 or even 1.39 vs 0.75)

In other words, 17% to be added to pI (vs. 6%)

RESULTS

The standard specifications posit higher costs, up to 3% of output.High costs of investment (2.33 or even 1.39 vs 0.75)In other words, 17% to be added to pI (vs. 6%)

RESULTS HIRING, INVESTMENT AND THEIR PRESENT VALUES

HIRING, INVESTMENT AND THEIR PRESENT VALUES

Using η1 = η2 = 2, η3 = 1

1(1� τt)(e1e2 � e2

� e3QK

+ e3(1� τt)pI

1(1� τt)(e1e2 � e2

+ e2QK

� e2(1� τt)pI

1(e1e2 � e2

ghtftnt

� e3gitftkt

1 2htnt

e1e2�e23

�ght

��e3

e1e2�e23

�gitftkt

1 mean 0.13 relative mean 0.58 0.42

2 std 0.01 relative var 7.9 3.9

3 relative cova �5.38

1(e1e2 � e2

ghtftnt

+ e2gitftkt

1 2itkt

��e3

e1e2�e23

�ght

e1e2�e23

�gitftkt

1 mean 0.02 relative mean 0.32 0.68

2 std 0.003 relative var 0.85 3.50

3 relative cova �1.67

It ensues that the cross effects are asymmetric: the investmentterms play a bigger role in hiring than the hiring terms ininvestment.

The scope statistic g(0, hn )+g( i

k ,0)�g( ik , h

g( ik , h

The cost of doing investment and hiring sequentially(g(0, h

n ) + g( ik , 0)) sums up to about 3.3% of GDP;

the cost of doing them simultaneously is about 1.4% of GDP, i.e., itis 1.9% of GDP cheaper.e3 < 0, there is complementarity: higher investment (hiring)lowers hiring (investment) costs

k ,0)�g( ik , h

g( ik , h

k ,0)�g( ik , h

g( ik , h

the cost of doing them simultaneously is about 1.4% of GDP, i.e., itis 1.9% of GDP cheaper.

e3 < 0, there is complementarity: higher investment (hiring)lowers hiring (investment) costs

k ,0)�g( ik , h

g( ik , h

Investment is very highly elastic with respect to the present valueof investing QK;

Hiring has much lower elasticity, lower than unitary, with respectto its present value QN .The cross elasticities are:low for investment w.r.t QN

high for hiring w.r.t QK.

Investment is very highly elastic with respect to the present valueof investing QK;Hiring has much lower elasticity, lower than unitary, with respectto its present value QN .

The cross elasticities are:low for investment w.r.t QN

Investment is very highly elastic with respect to the present valueof investing QK;Hiring has much lower elasticity, lower than unitary, with respectto its present value QN .The cross elasticities are:

low for investment w.r.t QN

Investment is very highly elastic with respect to the present valueof investing QK;Hiring has much lower elasticity, lower than unitary, with respectto its present value QN .The cross elasticities are:low for investment w.r.t QN

Correlation of�

ik , h

�or of

�QK, QN� need not be positive though

Suppose, for example, QK rises while QN declines, as in part ofthe U.S. sample period.The rise in QK will lead to higher investment and higher hiring,while the fall in QN will lead to lower investment and lowerhiring.The elasticity estimates imply that the QK movements and the QN

movements engender different responses.Therefore it is possible that investment will rise with the rise inQK while hiring falls with the fall in QN .

Correlation of�

ik , h

�or of

Suppose, for example, QK rises while QN declines, as in part ofthe U.S. sample period.

The rise in QK will lead to higher investment and higher hiring,while the fall in QN will lead to lower investment and lowerhiring.The elasticity estimates imply that the QK movements and the QN

Correlation of�

ik , h

�or of

Suppose, for example, QK rises while QN declines, as in part ofthe U.S. sample period.The rise in QK will lead to higher investment and higher hiring,while the fall in QN will lead to lower investment and lowerhiring.

The elasticity estimates imply that the QK movements and the QN

Correlation of�

ik , h

�or of

movements engender different responses.

Therefore it is possible that investment will rise with the rise inQK while hiring falls with the fall in QN .

Correlation of�

ik , h

�or of

RESULTS CO-MOVEMENT AND CYCLICAL ANALYSIS

CO-MOVEMENT AND CYCLICAL ANALYSIS

1975 1980 1985 1990 1995 2000 2005 2010

ln (h/n) levels (left axis)ln (h/n) HP filtered (right axis)

Log Hiring Rates (levels and HP filtered).

1975 1980 1985 1990 1995 2000 2005 2010

ln (i/k) levels (left axis)ln (i/k) HP filtered (right axis)

Log Investment Rates (levels and HP filtered).

Hiring ρ( htnt

, yt+i)

HP filtered (λ = 1600)lag/lead �8 �4 �1 0 1 4 8

f �0.15 �0.30 �0.34 �0.25 �0.12 0.17 0.20fn �0.13 �0.20 �0.11 �0.04 0.05 0.21 0.09fk �0.18 �0.31 �0.30 �0.19 �0.07 0.22 0.19

Investment ρ( itkt

, yt+i)

HP filtered (λ = 1600)lag/lead -8 -4 -1 0 1 4 8

f 0.10 0.50 0.84 0.79 0.63 �0.03 �0.40fn 0.10 0.62 0.63 0.50 0.29 �0.34 �0.44fk �0.06 0.60 0.84 0.75 0.55 �0.17 �0.49

Marginal costs of investment are pro-cyclical, and co-movepositively with the investment rate.

Marginal costs of hiring are counter-cyclical and co-movepositively with the hiring rate.This is true across the three cyclical measures and the two filteringmethods.

Marginal costs of investment are pro-cyclical, and co-movepositively with the investment rate.Marginal costs of hiring are counter-cyclical and co-movepositively with the hiring rate.

This is true across the three cyclical measures and the two filteringmethods.

Marginal costs of investment are pro-cyclical, and co-movepositively with the investment rate.Marginal costs of hiring are counter-cyclical and co-movepositively with the hiring rate.This is true across the three cyclical measures and the two filteringmethods.

EXPLAINING COUNTERCYLICAL HIRING RATES

ut + ot

ut+ot+ ψ

Co-Movement (contemporaneous) with Cyclical Indicators

logged, HP filtered

nthtnt

htut+ot

ut+ot+ψ

with GDP f 0.81 �0.25 0.53 �0.39 �0.82with labor productivity f

n 0.42 �0.04 0.38 �0.31 �0.46

So counter-cyclicality of ψht

ut+ot+ψ

dominates pro-cylicality of

job finding htut+ot

Co-Movement (contemporaneous) with Cyclical Indicatorslogged, HP filtered

nthtnt

htut+ot

ut+ot+ψ

n 0.42 �0.04 0.38 �0.31 �0.46

ut+ot+ψ

job finding htut+ot

nthtnt

htut+ot

ut+ot+ψ

n 0.42 �0.04 0.38 �0.31 �0.46

ut+ot+ψ

job finding htut+ot

nthtnt

htut+ot

ut+ot+ψ

n 0.42 �0.04 0.38 �0.31 �0.46

ut+ot+ψ

job finding htut+ot

RESULTS JOB VALUES ACROSS MODELS

JOB VALUES ACROSS MODELS

The standard search and matching model also posits aformulation of QN , which is the value of the job match.

QNt,search = (1� τt)c

In the current set-up the formulation is given by:

= (1� τt) ght = (1� τt)

nt)η2�1 + e3

�η3 ht

η3�1#(14)

= (1� τt) ght = (1� τt)

nt)η2�1 + e3

�η3 ht

η3�1#(14)

= (1� τt) ght = (1� τt)

nt)η2�1 + e3

�η3 ht

η3�1#(14)

= (1� τt) ght = (1� τt)

nt)η2�1 + e3

�η3 ht

η3�1#(14)

It is already clear from the comparison of (13) and (14) that

QNt,search and QN

behave differently.

The former is a positive function of vtht

and is likely to bepro-cyclical.The latter is a positive function of ht

ntand a negative function of it

given the estimates of a negative e3.It will thus be counter-cyclical, as ht

ntis counter-cyclical and it

pro-cyclical.

QNt,search and QN

behave differently.

and is likely to bepro-cyclical.

The latter is a positive function of htnt

and a negative function of itkt

,given the estimates of a negative e3.It will thus be counter-cyclical, as ht

pro-cyclical.

QNt,search and QN

behave differently.

given the estimates of a negative e3.

It will thus be counter-cyclical, as htnt

is counter-cyclical and itkt

ispro-cyclical.

QNt,search and QN

behave differently.

given the estimates of a negative e3.It will thus be counter-cyclical, as ht

pro-cyclical.

1980 1985 1990 1995 2000 2005 2010

standard S&M modelpreferredlinear hiring costs

Figure 2: Job Values (QN) across models

The reason for this difference:

The standard search model formulates vacancy costs as a functionof their duration 1

without assigning any variability to marginal costs – they arefixed at c.It ignores capital and any other variable that varies over time.Vacancy duration is pro-cyclical, hence job values are too.

The reason for this difference:The standard search model formulates vacancy costs as a functionof their duration 1

without assigning any variability to marginal costs – they arefixed at c.

It ignores capital and any other variable that varies over time.Vacancy duration is pro-cyclical, hence job values are too.

without assigning any variability to marginal costs – they arefixed at c.It ignores capital and any other variable that varies over time.

Vacancy duration is pro-cyclical, hence job values are too.

The current model captures the entire recruiting process (fromvacancy creation to the training of the hired workers) in theconvex g function

defined over the hiring rate htnt

and the investment rate itkt

.This formulation of costs follows the “tradition” of theLucas-Prescott and of the Tobin-Brainard (Q) models, wherebycosts and expected values rise with the activity in question.Importantly it is defined over the actual hiring rate.Hiring activity rises when job values rise; this means marginalcosts rise.We can infer counter-cyclical job values from counter-cyclicalhiring rates.

The current model captures the entire recruiting process (fromvacancy creation to the training of the hired workers) in theconvex g functiondefined over the hiring rate ht

ntand the investment rate it

This formulation of costs follows the “tradition” of theLucas-Prescott and of the Tobin-Brainard (Q) models, wherebycosts and expected values rise with the activity in question.Importantly it is defined over the actual hiring rate.Hiring activity rises when job values rise; this means marginalcosts rise.We can infer counter-cyclical job values from counter-cyclicalhiring rates.

This formulation of costs follows the “tradition” of theLucas-Prescott and of the Tobin-Brainard (Q) models, wherebycosts and expected values rise with the activity in question.

Importantly it is defined over the actual hiring rate.Hiring activity rises when job values rise; this means marginalcosts rise.We can infer counter-cyclical job values from counter-cyclicalhiring rates.

This formulation of costs follows the “tradition” of theLucas-Prescott and of the Tobin-Brainard (Q) models, wherebycosts and expected values rise with the activity in question.Importantly it is defined over the actual hiring rate.

Hiring activity rises when job values rise; this means marginalcosts rise.We can infer counter-cyclical job values from counter-cyclicalhiring rates.

This formulation of costs follows the “tradition” of theLucas-Prescott and of the Tobin-Brainard (Q) models, wherebycosts and expected values rise with the activity in question.Importantly it is defined over the actual hiring rate.Hiring activity rises when job values rise; this means marginalcosts rise.

We can infer counter-cyclical job values from counter-cyclicalhiring rates.

This formulation of costs follows the “tradition” of theLucas-Prescott and of the Tobin-Brainard (Q) models, wherebycosts and expected values rise with the activity in question.Importantly it is defined over the actual hiring rate.Hiring activity rises when job values rise; this means marginalcosts rise.We can infer counter-cyclical job values from counter-cyclicalhiring rates.

Evidence for counter-cyclical job values.

"ρt+1

ft+1nt+1

"(1� τt+1)

α�wt+1

ft+1nt+1

� gnt+1ft+1nt+1

!+�1� ψt+1

� QNt+1

ft+1nt+1

= Et ∑∞j=0

266666664

�∏

ji=0 ρt+1+i

� ∏

ft+i+1nt+i+1

ft+int+i

∏ji=0

�1� ψt+1+i

�� 1� τt+1+j

� α�wt+1+j

ft+1+jnt+1+j

� gnt+1+j

377777775So future

α�wt+1+j

ft+1+jnt+1+j

!plays a role

One can approximate RHS with truncated sum of actual values

Evidence for counter-cyclical job values.QN

"ρt+1

ft+1nt+1

"(1� τt+1)

α�wt+1

ft+1nt+1

� gnt+1ft+1nt+1

!+�1� ψt+1

� QNt+1

ft+1nt+1

= Et ∑∞j=0

266666664

�∏

ji=0 ρt+1+i

� ∏

ft+i+1nt+i+1

ft+int+i

∏ji=0

�1� ψt+1+i

�� 1� τt+1+j

� α�wt+1+j

ft+1+jnt+1+j

� gnt+1+j

377777775So future

α�wt+1+j

ft+1+jnt+1+j

!plays a role

"ρt+1

ft+1nt+1

"(1� τt+1)

α�wt+1

ft+1nt+1

� gnt+1ft+1nt+1

!+�1� ψt+1

� QNt+1

ft+1nt+1

= Et ∑∞j=0

266666664

�∏

ji=0 ρt+1+i

� ∏

ft+i+1nt+i+1

ft+int+i

∏ji=0

�1� ψt+1+i

�� 1� τt+1+j

� α�wt+1+j

ft+1+jnt+1+j

� gnt+1+j

377777775

So future

α�wt+1+j

ft+1+jnt+1+j

!plays a role

"ρt+1

ft+1nt+1

"(1� τt+1)

α�wt+1

ft+1nt+1

� gnt+1ft+1nt+1

!+�1� ψt+1

� QNt+1

ft+1nt+1

= Et ∑∞j=0

266666664

�∏

ji=0 ρt+1+i

� ∏

ft+i+1nt+i+1

ft+int+i

∏ji=0

�1� ψt+1+i

�� 1� τt+1+j

� α�wt+1+j

ft+1+jnt+1+j

� gnt+1+j

377777775So future

α�wt+1+j

ft+1+jnt+1+j

!plays a role

"ρt+1

ft+1nt+1

"(1� τt+1)

α�wt+1

ft+1nt+1

� gnt+1ft+1nt+1

!+�1� ψt+1

� QNt+1

ft+1nt+1

= Et ∑∞j=0

266666664

�∏

ji=0 ρt+1+i

� ∏

ft+i+1nt+i+1

ft+int+i

∏ji=0

�1� ψt+1+i

�� 1� τt+1+j

� α�wt+1+j

ft+1+jnt+1+j

� gnt+1+j

377777775So future

α�wt+1+j

ft+1+jnt+1+j

!plays a role

Co-Movement (contemporaneous) with Cyclical Indicators

logged, HP filtered

= (1� τt)ght

�̂QN

�with GDP f �0.62 �0.47

with labor productivity fn �0.42 �0.50

�̂QN

�= ∑T

266666664

�∏

ji=0 ρt+1+i

� ∏

ft+i+1nt+i+1

ft+int+i

∏ji=0

�1� ψt+1+i

�� 1� τt+1+j

� α�wt+1+j

ft+1+jnt+1+j

� gnt+1+j

377777775

= (1� τt)ght

�̂QN

�with GDP f �0.62 �0.47

�̂QN

�= ∑T

266666664

�∏

ji=0 ρt+1+i

� ∏

ft+i+1nt+i+1

ft+int+i

∏ji=0

�1� ψt+1+i

�� 1� τt+1+j

� α�wt+1+j

ft+1+jnt+1+j

� gnt+1+j

377777775

= (1� τt)ght

�̂QN

�with GDP f �0.62 �0.47

�̂QN

�= ∑T

266666664

�∏

ji=0 ρt+1+i

� ∏

ft+i+1nt+i+1

ft+int+i

∏ji=0

�1� ψt+1+i

�� 1� τt+1+j

� α�wt+1+j

ft+1+jnt+1+j

� gnt+1+j

377777775

= (1� τt)ght

�̂QN

�with GDP f �0.62 �0.47

�̂QN

�= ∑T

266666664

�∏

ji=0 ρt+1+i

� ∏

ft+i+1nt+i+1

ft+int+i

∏ji=0

�1� ψt+1+i

�� 1� τt+1+j

� α�wt+1+j

ft+1+jnt+1+j

� gnt+1+j

377777775

= (1� τt)ght

�̂QN

�with GDP f �0.62 �0.47

�̂QN

�= ∑T

266666664

�∏

ji=0 ρt+1+i

� ∏

ft+i+1nt+i+1

ft+int+i

∏ji=0

�1� ψt+1+i

�� 1� τt+1+j

� α�wt+1+j

ft+1+jnt+1+j

� gnt+1+j

377777775

How does this relate to what we know about the labor share?

Consider the dynamic cyclical behavior of wFN

, logged, HP filtered

j�wfn

�t+j

0 1 4 8 12

with GDP ft �0.39 �0.17 0.37 0.41 0.31with labor productivity ft

nt�0.58 �0.38 0.19 0.35 0.35

How does this relate to what we know about the labor share?Consider the dynamic cyclical behavior of w

j�wfn

�t+j

0 1 4 8 12

nt�0.58 �0.38 0.19 0.35 0.35

How does this relate to what we know about the labor share?Consider the dynamic cyclical behavior of w

j�wfn

�t+j

0 1 4 8 12

nt�0.58 �0.38 0.19 0.35 0.35

Contemporaneously the finding of a basic Cobb-Douglasspecification usually is of a counter-cyclical labor share

e.g., Gali, Gertler, Lopez-Salido (REStat 2007) in baseline case,though not strong 0.28Ramey and Nekarda (WP 2013) report similar findings rangingbetween 0.23 to 0.50 depending upon filtering method and wagemeasureThen when adjustments are applied – different productionfunctions, overhead labor, etc. – differences emerge w.r.t cyclicalpatterns

Contemporaneously the finding of a basic Cobb-Douglasspecification usually is of a counter-cyclical labor sharee.g., Gali, Gertler, Lopez-Salido (REStat 2007) in baseline case,though not strong 0.28

Ramey and Nekarda (WP 2013) report similar findings rangingbetween 0.23 to 0.50 depending upon filtering method and wagemeasureThen when adjustments are applied – different productionfunctions, overhead labor, etc. – differences emerge w.r.t cyclicalpatterns

Contemporaneously the finding of a basic Cobb-Douglasspecification usually is of a counter-cyclical labor sharee.g., Gali, Gertler, Lopez-Salido (REStat 2007) in baseline case,though not strong 0.28Ramey and Nekarda (WP 2013) report similar findings rangingbetween 0.23 to 0.50 depending upon filtering method and wagemeasure

Then when adjustments are applied – different productionfunctions, overhead labor, etc. – differences emerge w.r.t cyclicalpatterns

Contemporaneously the finding of a basic Cobb-Douglasspecification usually is of a counter-cyclical labor sharee.g., Gali, Gertler, Lopez-Salido (REStat 2007) in baseline case,though not strong 0.28Ramey and Nekarda (WP 2013) report similar findings rangingbetween 0.23 to 0.50 depending upon filtering method and wagemeasureThen when adjustments are applied – different productionfunctions, overhead labor, etc. – differences emerge w.r.t cyclicalpatterns

Importantly dynamic cross-correlations indicate pro-cyclicality

Rios-Rull and Santaeulalia-Llopis (JME 2010): the labor share firstfalls (rises) in a boom (recession) thereby increasing (decreasing)job profitabilityit subsequently rises for a substantial period of timeRamey and Nekarda (WP 2013) document this in their Figure 2similar numbers to those aboveThey note (fn. 8) that “These dynamic correlations provide a clueas to why Hall (NBER WP 2012) finds a procyclical labor share”

Importantly dynamic cross-correlations indicate pro-cyclicalityRios-Rull and Santaeulalia-Llopis (JME 2010): the labor share firstfalls (rises) in a boom (recession) thereby increasing (decreasing)job profitability

it subsequently rises for a substantial period of timeRamey and Nekarda (WP 2013) document this in their Figure 2similar numbers to those aboveThey note (fn. 8) that “These dynamic correlations provide a clueas to why Hall (NBER WP 2012) finds a procyclical labor share”

Importantly dynamic cross-correlations indicate pro-cyclicalityRios-Rull and Santaeulalia-Llopis (JME 2010): the labor share firstfalls (rises) in a boom (recession) thereby increasing (decreasing)job profitabilityit subsequently rises for a substantial period of time

Ramey and Nekarda (WP 2013) document this in their Figure 2similar numbers to those aboveThey note (fn. 8) that “These dynamic correlations provide a clueas to why Hall (NBER WP 2012) finds a procyclical labor share”

Importantly dynamic cross-correlations indicate pro-cyclicalityRios-Rull and Santaeulalia-Llopis (JME 2010): the labor share firstfalls (rises) in a boom (recession) thereby increasing (decreasing)job profitabilityit subsequently rises for a substantial period of timeRamey and Nekarda (WP 2013) document this in their Figure 2

similar numbers to those aboveThey note (fn. 8) that “These dynamic correlations provide a clueas to why Hall (NBER WP 2012) finds a procyclical labor share”

Importantly dynamic cross-correlations indicate pro-cyclicalityRios-Rull and Santaeulalia-Llopis (JME 2010): the labor share firstfalls (rises) in a boom (recession) thereby increasing (decreasing)job profitabilityit subsequently rises for a substantial period of timeRamey and Nekarda (WP 2013) document this in their Figure 2similar numbers to those above

They note (fn. 8) that “These dynamic correlations provide a clueas to why Hall (NBER WP 2012) finds a procyclical labor share”

Importantly dynamic cross-correlations indicate pro-cyclicalityRios-Rull and Santaeulalia-Llopis (JME 2010): the labor share firstfalls (rises) in a boom (recession) thereby increasing (decreasing)job profitabilityit subsequently rises for a substantial period of timeRamey and Nekarda (WP 2013) document this in their Figure 2similar numbers to those aboveThey note (fn. 8) that “These dynamic correlations provide a clueas to why Hall (NBER WP 2012) finds a procyclical labor share”

So the logic is that in recessionary times, firms, looking into thefuture, expect higher profitability from employing labor. Hence,they increase the rate at which they hire workers.

hiring definitions

So the logic is that in recessionary times, firms, looking into thefuture, expect higher profitability from employing labor. Hence,they increase the rate at which they hire workers.

hiring definitions

RESULTS FUTURE DETERMINANTS OF JOB AND CAPITAL VALUES

FUTURE DETERMINANTS OF JOB AND CAPITAL

VALUES

An Asset Pricing Model

Pt = Et

�R�1

t+1[Dt+1 + Pt+1]�

Campbell-Shiller (RFS 1988): using logs, this asset pricingrelationship can be approximated as:

pt � dt = k+ Et (dt+1 � dt � rt+1 + ρ(pt+1 � dt+1)) (15)

VALUES

Pt = Et

�R�1

t+1[Dt+1 + Pt+1]�

VALUES

Pt = Et

�R�1

t+1[Dt+1 + Pt+1]�

Implementing the Forecasting Model for Hiring and Investment

I cast the estimated model of hiring and investment into this assetpricing framework by defining P and D for the optimalinvestment equation and for the optimal hiring equation.

The “price” P is the value of investment or the value of hiring;The “dividend” D is the flow of net income from capital or fromlabor.Additional terms come into play here.

I cast the estimated model of hiring and investment into this assetpricing framework by defining P and D for the optimalinvestment equation and for the optimal hiring equation.The “price” P is the value of investment or the value of hiring;

The “dividend” D is the flow of net income from capital or fromlabor.Additional terms come into play here.

I cast the estimated model of hiring and investment into this assetpricing framework by defining P and D for the optimalinvestment equation and for the optimal hiring equation.The “price” P is the value of investment or the value of hiring;The “dividend” D is the flow of net income from capital or fromlabor.

Additional terms come into play here.

I cast the estimated model of hiring and investment into this assetpricing framework by defining P and D for the optimalinvestment equation and for the optimal hiring equation.The “price” P is the value of investment or the value of hiring;The “dividend” D is the flow of net income from capital or fromlabor.Additional terms come into play here.

P1t � (1� τt)

git + pI

D1t � (1� τt)

( fkt � gkt)ftkt

R1t �

G f /kt+1

�(1� δt)P1

t + D1t�

P1t�1

P2t � (1� τt) ght

� QNt

D2t � (1� τt)

α� gnt

� wtftnt

R2t �

G f /nt+1

�(1� ψt)P

2t + D2

P2t�1

Run a restricted VAR

(xt+1) = A+ Bxt + εt (22)

For capital

xt+1 =

0BBBBB@p1

G f /kt+1

�ln(1� δt+1)

1CCCCCAWith structural steady state restrictions:

e1(I � ρkB) =�(1� ρk)e2 � e3 + e4 + ρke5

�B (23)

What do we learn about the various future determinants ofinvestment and hiring values?

First, returns have the dominant role, as also found in theempirical Finance literature.

What do we learn about the various future determinants ofinvestment and hiring values?First, returns have the dominant role, as also found in theempirical Finance literature.

The coefficients are negative, implying that a rise in log prices isassociated with future declines in returns (r), for both investmentand hiring,

i.e., high prices predict low subsequent returns, as found in theFinance literature.A similar result is obtained when computing the relation betweenthe log price-dividend ratio (p� d) of investment and of hiringwith their subsequent returns.This result has been observed for stock prices and dividends andfor house prices and rents (see Cochrane (JF 2011)).

The coefficients are negative, implying that a rise in log prices isassociated with future declines in returns (r), for both investmentand hiring,i.e., high prices predict low subsequent returns, as found in theFinance literature.

A similar result is obtained when computing the relation betweenthe log price-dividend ratio (p� d) of investment and of hiringwith their subsequent returns.This result has been observed for stock prices and dividends andfor house prices and rents (see Cochrane (JF 2011)).

The coefficients are negative, implying that a rise in log prices isassociated with future declines in returns (r), for both investmentand hiring,i.e., high prices predict low subsequent returns, as found in theFinance literature.A similar result is obtained when computing the relation betweenthe log price-dividend ratio (p� d) of investment and of hiringwith their subsequent returns.

This result has been observed for stock prices and dividends andfor house prices and rents (see Cochrane (JF 2011)).

The coefficients are negative, implying that a rise in log prices isassociated with future declines in returns (r), for both investmentand hiring,i.e., high prices predict low subsequent returns, as found in theFinance literature.A similar result is obtained when computing the relation betweenthe log price-dividend ratio (p� d) of investment and of hiringwith their subsequent returns.This result has been observed for stock prices and dividends andfor house prices and rents (see Cochrane (JF 2011)).

Second, dividends play a role in the hiring case, although smallerthan returns.

In this case, higher prices are associated with subsequent higherdividends and the adjusted R2 is very high (0.95).The analysis indicates that if wages do not move closely withlabor productivity there is a meaningful effect to productivitychanges, in line with the Shimer (AER 2005) findings.Third, productivity growth, does not appear to play a role in bothcases: the VAR coefficients are not significantly different from zeroand the long run coefficients are small.This is akin to the finding in Finance that dividend growth doesnot matter much.

Second, dividends play a role in the hiring case, although smallerthan returns.In this case, higher prices are associated with subsequent higherdividends and the adjusted R2 is very high (0.95).

The analysis indicates that if wages do not move closely withlabor productivity there is a meaningful effect to productivitychanges, in line with the Shimer (AER 2005) findings.Third, productivity growth, does not appear to play a role in bothcases: the VAR coefficients are not significantly different from zeroand the long run coefficients are small.This is akin to the finding in Finance that dividend growth doesnot matter much.

Second, dividends play a role in the hiring case, although smallerthan returns.In this case, higher prices are associated with subsequent higherdividends and the adjusted R2 is very high (0.95).The analysis indicates that if wages do not move closely withlabor productivity there is a meaningful effect to productivitychanges, in line with the Shimer (AER 2005) findings.

Third, productivity growth, does not appear to play a role in bothcases: the VAR coefficients are not significantly different from zeroand the long run coefficients are small.This is akin to the finding in Finance that dividend growth doesnot matter much.

Second, dividends play a role in the hiring case, although smallerthan returns.In this case, higher prices are associated with subsequent higherdividends and the adjusted R2 is very high (0.95).The analysis indicates that if wages do not move closely withlabor productivity there is a meaningful effect to productivitychanges, in line with the Shimer (AER 2005) findings.Third, productivity growth, does not appear to play a role in bothcases: the VAR coefficients are not significantly different from zeroand the long run coefficients are small.

This is akin to the finding in Finance that dividend growth doesnot matter much.

Second, dividends play a role in the hiring case, although smallerthan returns.In this case, higher prices are associated with subsequent higherdividends and the adjusted R2 is very high (0.95).The analysis indicates that if wages do not move closely withlabor productivity there is a meaningful effect to productivitychanges, in line with the Shimer (AER 2005) findings.Third, productivity growth, does not appear to play a role in bothcases: the VAR coefficients are not significantly different from zeroand the long run coefficients are small.This is akin to the finding in Finance that dividend growth doesnot matter much.

Fourth, prices – the values of investment and hiring – arepersistent

which is consistent with the persistence of investment and hiringrates themselves.Fifth, the rates of separation and depreciation do not appear to play ameaningful role.This means that the variable that determines the length of the hiredoes not have much effect on the value of the hire, relative to theother determinants.It is the discounting of future streams which plays theoverwhelming role.

Fourth, prices – the values of investment and hiring – arepersistentwhich is consistent with the persistence of investment and hiringrates themselves.

Fifth, the rates of separation and depreciation do not appear to play ameaningful role.This means that the variable that determines the length of the hiredoes not have much effect on the value of the hire, relative to theother determinants.It is the discounting of future streams which plays theoverwhelming role.

Fourth, prices – the values of investment and hiring – arepersistentwhich is consistent with the persistence of investment and hiringrates themselves.Fifth, the rates of separation and depreciation do not appear to play ameaningful role.

This means that the variable that determines the length of the hiredoes not have much effect on the value of the hire, relative to theother determinants.It is the discounting of future streams which plays theoverwhelming role.

Fourth, prices – the values of investment and hiring – arepersistentwhich is consistent with the persistence of investment and hiringrates themselves.Fifth, the rates of separation and depreciation do not appear to play ameaningful role.This means that the variable that determines the length of the hiredoes not have much effect on the value of the hire, relative to theother determinants.

It is the discounting of future streams which plays theoverwhelming role.

Fourth, prices – the values of investment and hiring – arepersistentwhich is consistent with the persistence of investment and hiringrates themselves.Fifth, the rates of separation and depreciation do not appear to play ameaningful role.This means that the variable that determines the length of the hiredoes not have much effect on the value of the hire, relative to theother determinants.It is the discounting of future streams which plays theoverwhelming role.

RESULTS U.S. LABOR MARKET EXPERIENCE

U.S. LABOR MARKET EXPERIENCE

Matching Model

nt= µt

�σ � vt

�1�σ

qt =ht

vt= µt

��σ

g(�) =

2664e1η1( it

kt)η1

+ e2η2(λ vt

nt+ (1� λ) qtvt

nt)η2

+ e3η3

�itkt

qtvtnt

�η3

3775 f (zt, nt, kt). (25)

The steady state:

(1� τ)

qvn , i

(1� τ)gv(

vn , q, i

µ�u

�σ � vn

�1�σ= ψ+ g (28)

where g is the rate of growth of the labor force (n+ u).

Steady state equilibrium can be presented as a plot in un and v

nspace:

Vacancy creation and st. st. flows curves

26666664e2(λ

vn + (1� λ)

�µ( v

n )1�σ( u

�vn )�

λ+ (1� λ)

�µ( v

n )1�σ( u

��+e3

� ik

� � µ( vn )

1�σ( u

37777775 =QN

11� τ

µ� v

�1�σ �un

�σ= ψ+ g (30)

nspace:Vacancy creation and st. st. flows curves

26666664e2(λ

vn + (1� λ)

�µ( v

n )1�σ( u

�vn )�

λ+ (1� λ)

�µ( v

n )1�σ( u

��+e3

� ik

� � µ( vn )

1�σ( u

37777775 =QN

11� τ

µ� v

�1�σ �un

�σ= ψ+ g (30)

nspace:Vacancy creation and st. st. flows curves

26666664e2(λ

vn + (1� λ)

�µ( v

n )1�σ( u

�vn )�

λ+ (1� λ)

�µ( v

n )1�σ( u

��+e3

� ik

� � µ( vn )

1�σ( u

37777775 =QN

11� τ

µ� v

�1�σ �un

�σ= ψ+ g (30)

red–vacancy creation

purple-steady state flows

0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.100.02

red–vacancy creationpurple-steady state flows

0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.100.02

red–vacancy creationpurple-steady state flows

0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.100.02

Vacancy creation curve:

gv(vn , q, i

fn (1� τ)

slopes down as higher un means higher q so less need for v to

attain hmoves upwards ( v

n rises) as job value 1(1�τ)

for calibrated values, moves upwards as ik falls, partly because

∂gv∂i/k = e3

� ik

�q < 0

gv(vn , q, i

fn (1� τ)

∂gv∂i/k = e3

� ik

�q < 0

gv(vn , q, i

fn (1� τ)

attain h

moves upwards ( vn rises) as job value 1

(1�τ)QN

∂gv∂i/k = e3

� ik

�q < 0

gv(vn , q, i

fn (1� τ)

∂gv∂i/k = e3

� ik

�q < 0

gv(vn , q, i

fn (1� τ)

∂gv∂i/k = e3

� ik

�q < 0

Relating the Matching Model to U.S. Data

Going to the data the idea is to relate the steady state relationshipsto actual data.

The aim is to find a region in un �

vn space where these equations

seem to be a reasonable approximation of the steady state aroundwhich the data points are scattered.Hence this is a “stylized exercise” that needs to be understood assuch.

Going to the data the idea is to relate the steady state relationshipsto actual data.The aim is to find a region in u

n �vn space where these equations

seem to be a reasonable approximation of the steady state aroundwhich the data points are scattered.

Hence this is a “stylized exercise” that needs to be understood assuch.

Going to the data the idea is to relate the steady state relationshipsto actual data.The aim is to find a region in u

n �vn space where these equations

seem to be a reasonable approximation of the steady state aroundwhich the data points are scattered.Hence this is a “stylized exercise” that needs to be understood assuch.

0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.130

vu1 7691

vu2 7691

vu1 9206,

vu2 9206

vu1 0711

vu2 0711

u = official unemploymentERAN YASHIV (TEL AVIV) HIRING AND INVESTMENT JUNE 2014 55 / 71

The following interpretation of U.S. labor market developments, apartial equilibrium “story”:

Going from the 1976-1991 sub-period to the 1992/4-2006sub-period, both curves shift down.

For the vacancy creation curve: 11�τ

fn#, i

For the steady state flows curve: ψ, g # .Equilibrium unemployment and vacancy rates decline, as dohiring and separation rates.

The following interpretation of U.S. labor market developments, apartial equilibrium “story”:Going from the 1976-1991 sub-period to the 1992/4-2006sub-period, both curves shift down.

fn#, i

For the steady state flows curve: ψ, g # .

Equilibrium unemployment and vacancy rates decline, as dohiring and separation rates.

fn#, i

0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.130

vu1 7691

vu2 7691

vu1 9206,

vu2 9206

vu1 0711

vu2 0711

u = official unemploymentERAN YASHIV (TEL AVIV) HIRING AND INVESTMENT JUNE 2014 57 / 71

Going from 1992/4-2006 to 2007- 2011 both curves shift up.

For vacancy creation curve: 11�τ

fn", i

For the steady state flows curve: ψ ", despite g #Equilibrium unemployment rises (as do hiring and separationrates) while vacancy rates fall.The intuition is clear: the higher the job value, the higher isvacancy creation, and the curve for the latter moves up.The less intuitive aspect is the rise in job values in recession,discussed earlier.

fn", i

For the steady state flows curve: ψ ", despite g #

Equilibrium unemployment rises (as do hiring and separationrates) while vacancy rates fall.The intuition is clear: the higher the job value, the higher isvacancy creation, and the curve for the latter moves up.The less intuitive aspect is the rise in job values in recession,discussed earlier.

fn", i

For the steady state flows curve: ψ ", despite g #Equilibrium unemployment rises (as do hiring and separationrates) while vacancy rates fall.

The intuition is clear: the higher the job value, the higher isvacancy creation, and the curve for the latter moves up.The less intuitive aspect is the rise in job values in recession,discussed earlier.

fn", i

For the steady state flows curve: ψ ", despite g #Equilibrium unemployment rises (as do hiring and separationrates) while vacancy rates fall.The intuition is clear: the higher the job value, the higher isvacancy creation, and the curve for the latter moves up.

The less intuitive aspect is the rise in job values in recession,discussed earlier.

fn", i

Hence job values exhibited counter-cyclical behavior over thesample period, rising in recessions;

and they were dominant in the stylized explanation ofunemployment changesboth the fall, going into the 1990s and 2000s, and the subsequentrise in the Great Recession of 2007-2009.

Hence job values exhibited counter-cyclical behavior over thesample period, rising in recessions;and they were dominant in the stylized explanation ofunemployment changes

both the fall, going into the 1990s and 2000s, and the subsequentrise in the Great Recession of 2007-2009.

Hence job values exhibited counter-cyclical behavior over thesample period, rising in recessions;and they were dominant in the stylized explanation ofunemployment changesboth the fall, going into the 1990s and 2000s, and the subsequentrise in the Great Recession of 2007-2009.

CONCLUSIONS

The results indicate three sets of key implications:

One is the complementarity between hiring and investment.The hiring rate is heavily influenced by the present value ofinvestment,while the rate of investment is less influenced by the present valueof hiring.

CONCLUSIONS

The results indicate three sets of key implications:One is the complementarity between hiring and investment.

The hiring rate is heavily influenced by the present value ofinvestment,while the rate of investment is less influenced by the present valueof hiring.

CONCLUSIONS

The results indicate three sets of key implications:One is the complementarity between hiring and investment.The hiring rate is heavily influenced by the present value ofinvestment,

while the rate of investment is less influenced by the present valueof hiring.

CONCLUSIONS

The results indicate three sets of key implications:One is the complementarity between hiring and investment.The hiring rate is heavily influenced by the present value ofinvestment,while the rate of investment is less influenced by the present valueof hiring.

CONCLUSIONS

A second is that in the sample period, U.S. investment rates andtheir present value (value of capital) are pro-cyclical

while hiring and job values are counter-cyclical.Estimated job values here were shown to differ from thosederived from the standard search and matching model.The main determinant of these capital values and job values arefuture returns, in line with what has been found in the Financeliterature for asset prices.

CONCLUSIONS

A second is that in the sample period, U.S. investment rates andtheir present value (value of capital) are pro-cyclicalwhile hiring and job values are counter-cyclical.

Estimated job values here were shown to differ from thosederived from the standard search and matching model.The main determinant of these capital values and job values arefuture returns, in line with what has been found in the Financeliterature for asset prices.

CONCLUSIONS

A second is that in the sample period, U.S. investment rates andtheir present value (value of capital) are pro-cyclicalwhile hiring and job values are counter-cyclical.Estimated job values here were shown to differ from thosederived from the standard search and matching model.

The main determinant of these capital values and job values arefuture returns, in line with what has been found in the Financeliterature for asset prices.

CONCLUSIONS

A second is that in the sample period, U.S. investment rates andtheir present value (value of capital) are pro-cyclicalwhile hiring and job values are counter-cyclical.Estimated job values here were shown to differ from thosederived from the standard search and matching model.The main determinant of these capital values and job values arefuture returns, in line with what has been found in the Financeliterature for asset prices.

CONCLUSIONS

The third is that U.S. labor market experience, including the GreatRecession, can be depicted in a stylized way using the estimatedmodel.

Going from the 1970s and 1980s to the 1990s and 2000s, job valuesdeclined as did labor force growth rates.Hence there ensued a decline in vacancy and hiring rates, and,concurrently, in unemployment rates.Moving from the last period to the Great Recession, job valueswent up while labor force growth rates continued to decline,leading to a rise in unemployment and a decline in vacancy rates.

CONCLUSIONS

The third is that U.S. labor market experience, including the GreatRecession, can be depicted in a stylized way using the estimatedmodel.Going from the 1970s and 1980s to the 1990s and 2000s, job valuesdeclined as did labor force growth rates.

Hence there ensued a decline in vacancy and hiring rates, and,concurrently, in unemployment rates.Moving from the last period to the Great Recession, job valueswent up while labor force growth rates continued to decline,leading to a rise in unemployment and a decline in vacancy rates.

CONCLUSIONS

The third is that U.S. labor market experience, including the GreatRecession, can be depicted in a stylized way using the estimatedmodel.Going from the 1970s and 1980s to the 1990s and 2000s, job valuesdeclined as did labor force growth rates.Hence there ensued a decline in vacancy and hiring rates, and,concurrently, in unemployment rates.

Moving from the last period to the Great Recession, job valueswent up while labor force growth rates continued to decline,leading to a rise in unemployment and a decline in vacancy rates.

CONCLUSIONS

The third is that U.S. labor market experience, including the GreatRecession, can be depicted in a stylized way using the estimatedmodel.Going from the 1970s and 1980s to the 1990s and 2000s, job valuesdeclined as did labor force growth rates.Hence there ensued a decline in vacancy and hiring rates, and,concurrently, in unemployment rates.Moving from the last period to the Great Recession, job valueswent up while labor force growth rates continued to decline,

leading to a rise in unemployment and a decline in vacancy rates.

CONCLUSIONS

The third is that U.S. labor market experience, including the GreatRecession, can be depicted in a stylized way using the estimatedmodel.Going from the 1970s and 1980s to the 1990s and 2000s, job valuesdeclined as did labor force growth rates.Hence there ensued a decline in vacancy and hiring rates, and,concurrently, in unemployment rates.Moving from the last period to the Great Recession, job valueswent up while labor force growth rates continued to decline,leading to a rise in unemployment and a decline in vacancy rates.

CONCLUSIONS

This paper, intentionally, did not specify a full DSGE model.

This was done in order to focus on firms’ investment and hiringdecisionsand not let the analysis be affected by possible mis-specificationsor problematics in other parts of the macroeconomy.To account for firm investment and hiring behavior, one does notneed to get into issues such as optimal intertemporalconsumption and labor choices of the individual.

CONCLUSIONS

This paper, intentionally, did not specify a full DSGE model.This was done in order to focus on firms’ investment and hiringdecisions

and not let the analysis be affected by possible mis-specificationsor problematics in other parts of the macroeconomy.To account for firm investment and hiring behavior, one does notneed to get into issues such as optimal intertemporalconsumption and labor choices of the individual.

CONCLUSIONS

This paper, intentionally, did not specify a full DSGE model.This was done in order to focus on firms’ investment and hiringdecisionsand not let the analysis be affected by possible mis-specificationsor problematics in other parts of the macroeconomy.

To account for firm investment and hiring behavior, one does notneed to get into issues such as optimal intertemporalconsumption and labor choices of the individual.

CONCLUSIONS

This paper, intentionally, did not specify a full DSGE model.This was done in order to focus on firms’ investment and hiringdecisionsand not let the analysis be affected by possible mis-specificationsor problematics in other parts of the macroeconomy.To account for firm investment and hiring behavior, one does notneed to get into issues such as optimal intertemporalconsumption and labor choices of the individual.

DETOUR ON HIRING FLOWS IN U.S. DATA

Two data sources: CPS and JOLTS (since end of 2000)

Three hiring flows: U to N, O to N, N to NI use: CPS, U to N and O to N, as I am concerned with changes inaggregate NCPS and JOLTS are very different

Two data sources: CPS and JOLTS (since end of 2000)Three hiring flows: U to N, O to N, N to N

I use: CPS, U to N and O to N, as I am concerned with changes inaggregate NCPS and JOLTS are very different

Two data sources: CPS and JOLTS (since end of 2000)Three hiring flows: U to N, O to N, N to NI use: CPS, U to N and O to N, as I am concerned with changes inaggregate N

CPS and JOLTS are very different

Two data sources: CPS and JOLTS (since end of 2000)Three hiring flows: U to N, O to N, N to NI use: CPS, U to N and O to N, as I am concerned with changes inaggregate NCPS and JOLTS are very different

Total Hiring Flows (NSA, 000s)Sample: 2000 : 12� 2013 : 08

CPS JOLTSMean 8373.6 4699.8Median 8211.3 4749.7Maximum 11007.8 5776.7Minimum 6508.7 3631.0Std. Dev. 916.1 522.3Skewness 0.39 �0.18Kurtosis 2.73 1.89

The following emerges:

The CPS mean is 1.78 higher, the CPS median is 1.73 higherThe c.o.v of CPS is 0.109, very close to c.o.v for JOLTS at 0.111The correlation is 0.43The third and fourth moments are very different

For TOTAL flows – U to N + O to N + N to NLogged, HP filtered

01 02 03 04 05 06 07 08 09 10 11 12 13

JOLTS CPS

hn ,SA, including job to job flowsERAN YASHIV (TEL AVIV) HIRING AND INVESTMENT JUNE 2014 67 / 71

For CPS flows used here – U to N + O to N

1980 1985 1990 1995 2000 2005 2010

ln hn ,HP-filtered, CPS, no job to job

Faberman, Mosacrini:

JOLTS has the same scope as the CES and relates to jobs; CPS is adifferent survey and relates to workers.Thus CES/JOLTS count multiple jobs held by the same person asseparate hiresClassification error make the CPS estimates higher than what islikely the truth.The JOLTS survey and stratification causes it to undercount youngand/or volatile establishments and understate the true workerflow rates.JOLTS does not include the self-employed.

hiring definitions

Faberman, Mosacrini:JOLTS has the same scope as the CES and relates to jobs; CPS is adifferent survey and relates to workers.

Thus CES/JOLTS count multiple jobs held by the same person asseparate hiresClassification error make the CPS estimates higher than what islikely the truth.The JOLTS survey and stratification causes it to undercount youngand/or volatile establishments and understate the true workerflow rates.JOLTS does not include the self-employed.

hiring definitions

Faberman, Mosacrini:JOLTS has the same scope as the CES and relates to jobs; CPS is adifferent survey and relates to workers.Thus CES/JOLTS count multiple jobs held by the same person asseparate hires

Classification error make the CPS estimates higher than what islikely the truth.The JOLTS survey and stratification causes it to undercount youngand/or volatile establishments and understate the true workerflow rates.JOLTS does not include the self-employed.

hiring definitions

Faberman, Mosacrini:JOLTS has the same scope as the CES and relates to jobs; CPS is adifferent survey and relates to workers.Thus CES/JOLTS count multiple jobs held by the same person asseparate hiresClassification error make the CPS estimates higher than what islikely the truth.

The JOLTS survey and stratification causes it to undercount youngand/or volatile establishments and understate the true workerflow rates.JOLTS does not include the self-employed.

hiring definitions

Faberman, Mosacrini:JOLTS has the same scope as the CES and relates to jobs; CPS is adifferent survey and relates to workers.Thus CES/JOLTS count multiple jobs held by the same person asseparate hiresClassification error make the CPS estimates higher than what islikely the truth.The JOLTS survey and stratification causes it to undercount youngand/or volatile establishments and understate the true workerflow rates.

JOLTS does not include the self-employed.hiring definitions

Faberman, Mosacrini:JOLTS has the same scope as the CES and relates to jobs; CPS is adifferent survey and relates to workers.Thus CES/JOLTS count multiple jobs held by the same person asseparate hiresClassification error make the CPS estimates higher than what islikely the truth.The JOLTS survey and stratification causes it to undercount youngand/or volatile establishments and understate the true workerflow rates.JOLTS does not include the self-employed.

hiring definitions

Faberman, Mosacrini:JOLTS has the same scope as the CES and relates to jobs; CPS is adifferent survey and relates to workers.Thus CES/JOLTS count multiple jobs held by the same person asseparate hiresClassification error make the CPS estimates higher than what islikely the truth.The JOLTS survey and stratification causes it to undercount youngand/or volatile establishments and understate the true workerflow rates.JOLTS does not include the self-employed.

hiring definitions

The discount rate and the discount factor

The discount rate is based on a DSGE-type model withlogarithmic utility U(ct) = ln ct.

U0(ct) = U0(ct+1) � (1+ rt)

Hence:

ρt =ct

where c is non-durable consumption (goods and services) and 5%of durable consumption.

The discount rate and the discount factorThe discount rate is based on a DSGE-type model withlogarithmic utility U(ct) = ln ct.

U0(ct) = U0(ct+1) � (1+ rt)

Hence:

ρt =ct

U0(ct) = U0(ct+1) � (1+ rt)

Hence:

ρt =ct

U0(ct) = U0(ct+1) � (1+ rt)

Hence:

ρt =ct

U0(ct) = U0(ct+1) � (1+ rt)

Hence:

ρt =ct

U0(ct) = U0(ct+1) � (1+ rt)

Hence:

ρt =ct

Investment, capital and depreciation

based on net stock of private nonresidential fixed assets in NFCBsector,

NIPA and flow of fundsUse of investment tax credit on equipment and public utilitystructures, the present discounted value of capital depreciationallowances, and the percentage of the cost of equipment thatcannot be depreciated if the firm takes the investment tax credit.

based on net stock of private nonresidential fixed assets in NFCBsector,NIPA and flow of funds

Use of investment tax credit on equipment and public utilitystructures, the present discounted value of capital depreciationallowances, and the percentage of the cost of equipment thatcannot be depreciated if the firm takes the investment tax credit.

based on net stock of private nonresidential fixed assets in NFCBsector,NIPA and flow of fundsUse of investment tax credit on equipment and public utilitystructures, the present discounted value of capital depreciationallowances, and the percentage of the cost of equipment thatcannot be depreciated if the firm takes the investment tax credit.

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