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Royal Economic Society

Creative Destruction and Subjective Well-Being

Philippe Aghion Ufuk Akcigit Harvard UPenn Angus Deaton Alexandra Roulet Princeton Harvard April 1, 2015

Introduction (1)

Does higher (per capita) GDP or GDP growth increase happiness? − → The existing empirical literature on happiness and income looks at how various measures of subjective well-being relate to income or income growth − → e.g see Easterlin (1974), Blanchflower and Oswald (2004), Di Tella et al (2007), Deaton (2008), Wolfers and Stevenson (2013), Deaton and Stone (2013) − → However, none of these contributions looks into the determinants of growth and at how these determinants affect well-being This paper is a first attempt at filling this gap

Introduction (2)

More specifically, we look at how an important engine of growth, namely Schumpeterian creative destruction with its resulting flow

• f entry and exit of firms and jobs, affects subjective well-being

differently for different types of individuals and in different types

• f labor markets and sectors.

Introduction (3)

In the first part of the paper we develop a simple Schumpeterian model of growth and unemployment to organize our thoughts and generate predictions on the potential effects of turnover on life satisfaction − → In the model a higher rate of turnover has both direct and indirect effects on life satisfaction

Introduction (4)

Direct effects: 1) more turnover translates into a higher probability of becoming unemployed if currently employed: = ⇒ this tends to reduce life satisfaction. 2) more turnover translates into a higher probability of becoming employed if unemployed = ⇒ this tends to increase life satisfaction. Indirect effect: a higher rate of turnover implies a higher growth externality = ⇒ this enhances life satisfaction.

Introduction (5)

Main prediction of the model: the overall effect of turnover on well-being is unambiguously positive for a given unemployment rate, but ambiguous otherwise Moreover, more turnover increases life satisfaction more for more forward-looking or for less risk-averse individuals.

Introduction (6)

Empirically, the effect of turnover on subjective well-being is significantly positive when we control for unemployment, less so if we do not This finding is robust, as it holds: − → whether looking at well-being at MSA-level or at individual level; − → whether looking at the life satisfaction measure from the BRFSS or at the Cantril Ladder measures from the Gallup survey − → using two distinct databases to construct our proxy for creative destruction.

Model (1)

Model with Schumpeterian creative destruction which

generates growth

generates endogenous obsolescence of firms and jobs

Workers in obsolete firms join the unemployment pool until they are matched to a new firm.

Model (2)

The economy is populated by infinitely-lived and risk-neutral individuals of measure one, and they discount the future at rate ρ = r. The final good is produced according to: ln Yt =

• j∈J ln yjtdj

where J ⊂ [0, 1] is the set of active product lines, with measure J ∈ [0, 1] invariant in steady state Each intermediate firm produces using one unit of labor according to the following linear production function, yjt = Ajtljt, where ljt = 1 is the labor employed by the firm, and the same in all sectors

Model (3): Innovation

An innovator in sector j at date t will move productivity in sector j from Ajt−1 to Ajt = λAjt−1 The innovator is a new entrant, and entry occurs in each sector with Poisson arrival rate x which we take to be exogenous Upon entry in any sector, the previous incumbent firm becomes

• bsolete and its worker loses her job and the entering firm posts a

new vacancy Production in that sector resumes with the new technology when the firm has found a new suitable worker. Thus the measure of inactive product lines is equal to the unemployment rate ut = 1 − Jt, where u denotes the equilibrium unemployment rate.

Solving the model (4): Equilibrium life satisfaction

Our proxy for life satisfaction is the average present value of an individual employee, namely: W = uU + (1 − u)E, where: rE − ˙ E = βπY + x(U − E) rU − ˙ U = bY + (m(u, v)/u)(E − U)

Solving the model (5): Equilibrium life satisfaction

We then end up with: W = Y r − g

• βπ −

xB 1 + x

• where B ≡ βπ − b.

Solving the model (5): Equilibrium life satisfaction

We then end up with: W = Y r − g

• βπ −

xB 1 + x

• hi

1- Capitalization effect: Higher turnover increases the growth rate g which in turns acts positively on life satisfaction.

Solving the model (5): Equilibrium life satisfaction

We then end up with: W = Y r − g

• βπ −

xB 1 + x

• hi

2- Displacement effect: For given growth rate g, more turnover reduces life satisfaction because higher turnover leads to a higher probability of workers losing their current job.

Solving the model (5): Equilibrium life satisfaction

Note that W = Y r − g [βπ − uB] Thus for a given u, the effect of turnover on well-being is unambiguously positive

Main predictions

Prediction 1: A higher turnover rate increases well-being unambiguously when controlling for aggregate unemployment, less so when not controlling for aggregate unemployment. Prediction 2: A higher turnover rate increases well-being more, the more turnover is associated with growth-enhancing activities. Prediction 3: A higher turnover rate increases well-being more when unemployment benefits are more generous . Prediction 4: A higher turnover rate increases well-being more for more forward-looking individuals.

Extensions

Risk aversion Exogenous job destruction Endogenous entry Transitional dynamics

Data (1)

The data on job turnover and creative destruction − → come from the Business Dynamics Statistics, which provides, at the metropolitan (MSA) level, information on job creation and destruction rates as well as on the entry and exit rates of establishments − → job creation (destruction) rate = sum of all employment gains (losses) from expanding (contracting) establishments from year t − 1 to year t including establishment startups (shutting down), divided by average employment between t − 1 and t − → these rates are computed from the whole universe of firms as described in the Census Longitudinal Business Database

Data (2)

To proxy for subjective well-being in the Gallup Healthways data, we use the Cantril ladder of life: Imagine a ladder with steps numbered from zero at the bottom to 10 at the top; the top of the ladder represents the best possible life for you and the bottom of the ladder represents the worst possible life for you. On which step of the ladder would you say you personally feel you stand at this time? And which level of the ladder do you anticipate to achieve in five years? We refer to answers to the first question as the current ladder and to the second question as the anticipated ladder

Data (3)

To proxy for subjective well-being in the BRFSS, we use the Life satisfaction question : ”In general how satisfied are you with your life?” The possible answers are ”Very satisfied” (1), ”Satisfied” (2) ”Dissatisfied” (3), ”Very dissatisfied” (4) We recoded them so that an increase in the variable means an increase in subjective well-being

Empirical framework

MSA-level regressions of creative destruction on subjective well-being − → Across years averages to mirror the steady-state analysis of the model

Individual level regressions − → Rich set of controls for individual determinants of well-being

Robustness checks

Heterogeneity: analysis of how the effect varies with the MSA’s sectoral composition, the state-level unemployment insurance generosity and individuals’ age

Metropolitan Statistical Area (MSA) Results 1/4

MSA-level averages; Gallup data (2008-2011) - (1) (2) (3) (4) (5) VARIABLES Current ladder Unemployment rate

• 2.303***
• 2.970***
• 1.972***

(0.731) (0.730) (0.757) Job turnover rate 0.652* 1.377*** (0.365) (0.379) Job creation rate 5.889*** 4.715*** (0.945) (0.925) Job destruction rate

• 3.851***
• 1.947**

(0.843) (0.983) Observations 363 363 363 363 363 R-squared 0.097 0.015 0.158 0.163 0.211

Metropolitan Statistical Area (MSA) Results 2/4

MSA-level averages; BRFSS data (2005-2010) - (1) (2) (3) (4) (5) VARIABLES ”How satisfied are you with your life?” Unemployment rate

• 1.504***
• 1.702***
• 1.524***

(0.270) (0.247) (0.270) Job turnover rate 0.121 0.348*** (0.0868) (0.0784) Job creation rate 1.652*** 0.859*** (0.241) (0.259) Job destruction rate

• 1.622***
• 0.285

(0.259) (0.320) Observations 364 364 364 364 364 R-squared 0.257 0.007 0.311 0.133 0.323

Metropolitan Statistical Area (MSA) Results 3/4

MSA-level averages; Gallup data (2008-2011) - (1) (2) (3) (4) (5) VARIABLES Anticipated ladder Unemployment rate

• 0.560
• 1.486***
• 1.007**

(0.465) (0.461) (0.498) Job turnover rate 1.549*** 1.911*** (0.319) (0.341) Job creation rate 4.109*** 3.509*** (0.851) (0.855) Job destruction rate

• 0.653

0.320 (0.760) (0.885) Observations 363 363 363 363 363 R-squared 0.006 0.087 0.122 0.122 0.134

Metropolitan Statistical Area (MSA) Results 4/4

MSA-level averages; Gallup data (2008-2011) - (1) (2) (3) (4) (5) VARIABLES Worry Unemployment rate 0.462*** 0.382*** 0.258*** (0.0812) (0.0854) (0.0952) Job turnover rate 0.257*** 0.163*** (0.0522) (0.0565) Job creation rate

• 0.405***
• 0.251

(0.152) (0.158) Job destruction rate 0.826*** 0.576*** (0.116) (0.155) Observations 363 363 363 363 363 R-squared 0.119 0.073 0.145 0.144 0.170

Magnitude - MSA-level regressions

A one standard deviation increase in job turnover has an effect

• n the current ladder of life equivalent to a 0.7 standard deviation

decrease in the unemployment rate

• n the anticipated ladder of life equivalent to a 1.8 standard

deviation decrease in the unemployment rate

Individual Level Regressions

The specification at the individual level is: SWBi,m,t = δCDm,t + αUm,t + βXi,m,t + Tt + ǫi,s,t, Individual controls include : gender, ethnicity, detailed education and family status, age, age2 Year and Month Fixed effect Standard errors clustered at the MSA level We restrict attention to working-age individuals (18-60 years old)

Individual level results 1/4 - Life satisfaction (BRFSS)

(1) (2) (3) (4) (5) VARIABLES ”How satisfied are you with your life?” Unemployment rate

• 0.871***
• 0.954***
• 0.910***

(0.144) (0.143) (0.150) Job turnover rate 0.141** 0.212*** (0.0609) (0.0543) Job creation rate 0.384*** 0.294*** (0.0942) (0.0858) Job destruction rate

• 0.124

0.115 (0.0885) (0.0784) Year and Month F.E. x x x x x Observations 856,906 856,906 856,906 856,906 856,906 R-squared 0.064 0.063 0.064 0.063 0.064

Individual level results 2/4 - Current ladder (Gallup)

(1) (2) (3) (4) (5) VARIABLES ”Current ladder” Unemployment rate

• 2.456***
• 2.878***
• 2.704***

(0.422) (0.431) (0.437) Job turnover rate 0.254 0.752*** (0.246) (0.230) Job creation rate 1.560*** 1.224*** (0.440) (0.352) Job destruction rate

• 0.764***

0.331 (0.289) (0.267) Year and Month F.E. x x x x x Observations 502,334 502,334 502,334 502,334 502,334 R-squared 0.058 0.058 0.059 0.058 0.059

Individual level results 3/4 - Anticipated ladder

(1) (2) (3) (4) (5) VARIABLES ”Anticipated ladder” Unemployment rate 0.108

• 0.705**
• 0.677**

(0.357) (0.307) (0.307) Job turnover rate 1.319*** 1.441*** (0.154) (0.151) Job creation rate 1.602*** 1.517*** (0.275) (0.259) Job destruction rate 1.099*** 1.373*** (0.230) (0.218) Year and Month F.E. x x x x x Observations 490,086 490,086 490,086 490,086 490,086 R-squared 0.077 0.077 0.077 0.077 0.077

Individual level results 4/4 - Worry

(1) (2) (3) (4) (5) VARIABLES ”Worry” Unemployment rate 0.420*** 0.367*** 0.357*** (0.0715) (0.0759) (0.0784) Job turnover rate 0.159*** 0.0954** (0.0419) (0.0408) Job creation rate 0.0249 0.0693 (0.0747) (0.0672) Job destruction rate 0.263*** 0.119** (0.0554) (0.0569) Year and month F.E. x x x x x Observations 503,159 503,159 503,159 503,159 503,159 R-squared 0.014 0.013 0.014 0.014 0.014

Magnitude - Individual-level regressions

A one standard deviation increase in job turnover has an effect

• n the current ladder of life equivalent to a 0.4 standard deviation

decrease in the unemployment rate

• n the anticipated ladder of life equivalent to a 3.7 standard

deviation decrease in the unemployment rate

Robustness analysis

We check whether results hold when restricting attention to sub-periods

We use an alternative database to measure creative destruction

We perform a panel analysis

We construct a predicted (Bartik-type) measure of job turnover to neutralize variations of turnover driven by idiosyncratic local shocks that could have a direct effect on well-being

Robustness check 1 - Restricting to 2005-2007

MSA-level 2005-2007 averages - (1) (2) (3) (4) (5) VARIABLES ”How satisfied are you with your life?” Unemployment rate

• 1.741***
• 1.825***
• 1.602***

(0.315) (0.295) (0.267) Job turnover rate 0.0938 0.185*** (0.0826) (0.0686) Job creation rate 0.935*** 0.718*** (0.169) (0.169) Job destruction rate

• 1.116***
• 0.607***

(0.247) (0.223) Observations 364 364 364 364 364 R-squared 0.146 0.004 0.161 0.077 0.189

Robustness check 1 ct’ed -Restricting to 2008-2010

MSA-level 2008-2010 averages - (1) (2) (3) (4) (5) VARIABLES ”How satisfied are you with your life?” Unemployment rate

• 1.191***
• 1.359***
• 1.465***

(0.204) (0.203) (0.248) Job turnover rate 0.0441 0.336*** (0.120) (0.118) Job creation rate 0.780*** 0.0505 (0.274) (0.265) Job destruction rate

• 0.538**

0.602** (0.235) (0.278) Observations 364 364 364 364 364 R-squared 0.192 0.001 0.224 0.032 0.228

Panel analysis with a ”predicted” measure of creative destruction 1/2

We now construct a predicted (Bartik-type) measure of job turnover to neutralize variations of turnover driven by idiosyncratic local shocks that could have a direct effect on well-being

• CDm,t = ∑

j

ωj,m,2004 × CDj,USA,t ωj,m,2004: share of sector j in total employment of MSA m in 2004 CDj,USA,t: national measure of creative destruction in sector j

Panel analysis with a ”predicted” measure of creative destruction 2/2

(1) (2) (3) VARIABLES Current ladder (Gallup) Quarterly MSA-level averages Predicted job turnover 0.586*** 1.537*** 1.542*** (Quarterly) (0.200) (0.225) (0.516) Unemployment rate x x MSA F.E. x Year and quarter F.E. x x x Observations 5,600 5,600 5,600 R-squared 0.137 0.166 0.292 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Heterogeneity analysis

Interaction with type of sectors in the MSA

Interaction with state level UI generosity

Interaction with individuals’ age

Interaction with sectoral composition at MSA level

We check whether the effect depends on the type of sectors in the MSA : SWBi,m,t = δCDm,t + γCDm,t ∗ Abovemedianm,t + θAbovemedianm,t + αUm,t + βXi,m,t + Tt + ǫi,s,t Above median is either in terms of predicted productivity growth

• r in terms of predicted outsourcing threat using the same

Bartik-type approach as before Individual controls include : gender, ethnicity, detailed education and family status, age, age2 Year and month fixed effects Standard errors clustered at the MSA level

Measure of the type of sectors in the MSA

The measure of productivity comes from the NBER-CES Manufacturing database: for each sector, we average annual 5-factors TFP growth over 2005-2009 (the data stops in 2009)

• Productivitym = ∑

j

ωj,m × TFPgrowthj,USA Following Autor et al. (2013) we proxy outsourcing by growth of imports in a given sector between 1991 and 2007

• Outsourcingm = ∑

j

ωj,m × Importgrowthj,USA

Interaction with the type of sectors- Productivity growth

(1) (2) (3) (4) VARIABLES Life satisfaction (BRFSS) Above median * Job turnover 0.154** 0.146** (0.0711) (0.0711) Job turnover rate 0.0786 0.157*** (0.0599) (0.0604) Above median * Job destruction 0.190* 0.145 (0.107) (0.108) Job destruction rate

• 0.201**

0.0815 (0.0937) (0.0969) Above median * Job creation 0.145 0.151 (0.0986) (0.0986) Job creation rate 0.315*** 0.216** (0.0896) (0.0898) Unemployment rate x x Observations 825,298 825,298 825,298 825,298 R-squared 0.065 0.066 0.065 0.066

Interaction with the type of sectors - Outsourcing threat

(1) (2) (3) (4) VARIABLES Life satisfaction (BRFSS) Above median * Job turnover

• 0.160**
• 0.181***

(0.0657) (0.0656) Job turnover rate 0.235*** 0.316*** (0.0483) (0.0485) Above median * Job destruction

• 0.290***
• 0.323***

(0.105) (0.104) Job destruction rate 0.0725 0.332*** (0.0902) (0.0922) Above median * Job creation

• 0.0347
• 0.0554

(0.0906) (0.0906) Job creation rate 0.388*** 0.309*** (0.0737) (0.0735) Unemployment rate x x Observations 852,783 852,783 852,783 852,783 R-squared 0.074 0.074 0.074 0.074

Interaction with state level UI generosity

We check whether the effect depends on the generosity of UI : SWBm = δCDm + γCDm ∗ Abovemedianm + θAbovemedianm + αUm + ǫm Abovemedianm is a dummy equal to 1 if MSA m is located in a state above median in terms of UI generosity where UI generosity is proxied by the maximum weekly benefit amount We also split the sample of MSAs according to whether they are above median or not and run separately the baseline regression SWBm = δCDm(+αUm) + ǫm on the 2 sub-samples

Interaction with UI generosity - 1/3

VARIABLES ”Current ladder” (Gallup) Above median * Job turnover 1.411** 1.784*** (0.637) (0.680) Job turnover rate

• 0.118

0.433 (0.529) (0.512) Above median * Job destruction 3.708*** 4.526*** (1.395) (1.507) Job destruction rate

• 5.380***
• 3.524***

(0.946) (1.077) Above median * Job creation

• 1.484
• 1.734

(1.689) (1.497) Job creation rate 6.186*** 4.900*** (0.993) (1.057) Above median UI

• 0.277*
• 0.382**
• 0.256
• 0.330**

(0.166) (0.175) (0.159) (0.165) Unemployment rate x x Observations 363 363 363 363 R-squared 0.093 0.237 0.216 0.281

Interaction with UI generosity - 2/3

VARIABLES Current ladder (Gallup) Panel A: States above median in terms of UI generosity Unemployment rate

• 1.357**
• 2.390***

(0.678) (0.654) Job turnover rate 1.299*** 2.039*** (0.356) (0.410) Observations 173 173 173 R-squared 0.048 0.072 0.198 Panel B: States below median Unemployment rate

• 3.644**
• 3.915***

(1.402) (1.463) Job turnover rate

• 0.115

0.597 (0.529) (0.511) Observations 190 190 190 R-squared 0.187 0.000 0.199

Interaction with UI generosity - 3/3

VARIABLES Current ladder (Gallup) Panel A: States above median in terms of UI generosity Job creation rate 4.701*** 3.415*** (1.371) (1.303) Job destruction rate

• 1.670

0.576 (1.036) (1.328) Observations 173 173 R-squared 0.150 0.209 Panel B: States below median Job creation rate 6.203*** 4.579*** (0.985) (1.374) Job destruction rate

• 5.375***
• 3.070**

(0.934) (1.487) Observations 190 190 R-squared 0.175 0.261

Interaction with individual’s age

VARIABLES Current ladder (Gallup) Panel A: Age below median (Median age is 40) Unemployment rate

• 1.683**
• 2.358***

(0.827) (0.834) Job turnover rate 0.819** 1.394*** (0.409) (0.430) Observations 363 363 363 R-squared 0.043 0.020 0.095 Panel B: Age above median Unemployment rate

• 2.815***
• 3.374***

(0.606) (0.612) ) Job turnover rate 0.333 1.156*** (0.363) (0.370) Observations 363 363 363 R-squared 0.122 0.003 0.158

Conclusion (1): Summary

We have analyzed the relationship between turnover-driven growth and subjective well-being, using MSA level turnover data from the Longitudinal Business Database and subjective well-being data from Gallup-Healthways and from the BRFSS Our main results are consistent with a simple Schumpeterian model of growth and unemployment, namely:

The overall effect of turnover (creative destruction) on subjective well-being is unambiguously positive when we control for MSA-level unemployment, less so if we do not

Creative destruction has a more positive effect on anticipated life satisfaction than on current life satisfaction

Creative destruction increases ”worry”, but less so if control for unemployment

Creative destruction has a more positive effect on subjective well-being in MSAs dominated by sectors that are faster-growing

• r outsource less

Conclusion (2): Extensions

Compare more systematically the determinants of (per capita) GDP growth with the determinants of life satisfaction

Look at other individual and/or labor market characteristics (training systems, availability of vocational education,..) which might have an impact on the effect of turnover on subjective well-being

Solving the model (1): Equilibrium wage and profits

Logarithmic technology for final good production implies that yjt = Yt/pjt. Then equilibrium wage is wjt = β 1 + βYt = βπYt whereas equilibrium profit is πjt = pjtyjt − wjt = 1 1 + βYt = πYt with π = 1 1 + β.

Extension: Risk aversion (1)

We now consider risk averse individuals with U = ln C. Now well-being can be shown to be equal to: Wu(c)=ln c = 1 ρ

• x

1 + x ln (b) + 1 1 + x ln (βπ)

• + 1

ρ g ρ + ln Y

• Aghion (Harvard), Akcigit (UPenn), Deaton (Princeton), and Roulet (Harvard)

Extension: Risk aversion (2)

Proposition A higher turnover rate has a less positive effect on life satisfaction of agents that are risk-averse with U = ln C than on risk-neutral agents: ∂Wu(c)=ln c ∂x < 0. Moving continuously from the baseline case where individuals are risk-neutral towards the risk-averse case where individuals have log preferences, makes the effect of creative destruction on life satisfaction become increasingly less positive (or increasingly more negative)

Extension: Exogenous job destruction (1)

In our baseline model, the only source of job destruction, as well as job creation, was new entry. Now assume instead that each job can also be destroyed at the rate φ.

Upon this shock, worker joins the unemployment pool and the product line becomes idle.

When a new entrant comes into this product line at the rate x, it first posts a vacancy in which case then the same product line moves from ”idle” into ”vacant” state.

When a vacant product line finds a suitable worker, the product line enter into ”production state”. Similarly, if a new entrant enters into a actively producing line, then the worker joins the unemployment pool and the new firm posts a vacancy as in the previous model.

Extension: Exogenous job destruction (2)

A product line j ∈ [0, 1] can be in one of three states:

production µ

vacant v

idle i

We have the steady-state flow equations: production : m = µφ + µx vacant : µx + ix = m idle : µφ = ix

Extension: Exogenous job destruction (3)

For analytical tractability, assume α = 0.5. Then the unemployment rate is simply u = 1 − (Ψ + 1) −

• (Ψ + 1)2 − 4 [Ψ − Ψ2x2]

2 [Ψ − Ψ2x2] where Ψ ≡ 1 + φ/x.

Extension: Exogenous job destruction (4)

Extension: Exogenous job destruction (5)

Summary statistics - subjective well-being

Mean Standard deviation Min Max Current ladder (Gallup) 6.78 1.95 10 MSA-level averages 6.74 0.187 6.15 7.51 Anticipated ladder (Gallup) 8.05 1.99 10 MSA-level averages 7.97 0.187 7.42 8.48 Worry (Gallup) 0.35 0.48 1 MSA-level averages 0.35 0.034 0.24 0.46 Life satisfaction (BRFSS) 3.37 0.63 1 4 MSA-level averages 3.37 0.046 3.14 3.58

Summary statistics -creative destruction

(2005-2010 averages) Mean Standard deviation Min Max JJob turnover rate (BDS) 0.29 0.035 0.18 0.43 Job creation rate (BDS) 0.15 0.015 0.08 0.22 Job destruction rate (BDS) 0.14 0.017 0.09 0.22 Unemployment rate (BLS) 0.07 0.015 0.03 0.24

Unemployment and job turnover rates - 2005-2010

20 25 30 35 40 45 Job turnover rate (in %) 5 10 15 20 25 Unemployment rate (in %)

MSA-level 2005-2010 averages

Unemployment and job turnover rates

Unemployment and job turnover rates - 2005-2007

20 30 40 50 Job turnover rate (in %) 5 10 15 20 Unemployment rate (in %)

MSA-level 2005-2007 averages

Unemployment and job turnover rates

Unemployment and job turnover rates - 2008-2011

15 20 25 30 35 40 Job turnover rate (in %) 5 10 15 20 25 30 Unemployment rate (in %)

2008-2011 averages, MSA-level

Unemployment and turnover rates

Royal Economic Society

Growth through Heterogeneous Innovations1

Ufuk Akcigit University of Pennsylvania & NBER Royal Economic Society Conference - April 1st, 2015

1joint work with Willliam Kerr (Harvard University)

Introduction

Innovations come in different sizes and shapes:

internal vs external product vs process radical vs incremental

Small vs large firms have different incentives to innovate. Spillovers generated by different innovations and different-sized firms are likely to be different. How is firm size related to the innovation size? Which type of firms generate bigger spillovers? The answer is important for many reasons, particularly for policy.

This Paper:

To answer these questions, we bridge a tight link between

general equilibrium firm dynamics theory and micro data of firms, innovations and patent citations.

We proceed in 3 steps: Part 1. Theory New theory of firm dynamics and innovation where:

firms come in different sizes, firms compete in the market for leadership, firms produce different type and size innovations, hence generate different spillovers, introduce an explicit model of citations.

This Paper:

To answer these questions, we bridge a tight link between

general equilibrium firm dynamics theory and micro data of firms, innovations and patent citations.

We proceed in 3 steps: Part 2. Empirics Using Census and patent data, study the empirical link between

Firm size vs firm growth, Firm size vs innovation intensity, Firm size and innovation quality.

This Paper:

To answer these questions, we bridge a tight link between

general equilibrium firm dynamics theory and micro data of firms, innovations and patent citations.

We proceed in 3 steps: Part 3. Quantitative Analysis Using indirect inference we find:

External innovation generates larger spillovers. External innovation does not scale with firm size, = ⇒ Small firms generate larger spillovers on average.

Part 1. Model

The Model Economy

1

quality level q sector j US Economy

The Model Economy

1

quality level q sector j GDP = Sectors combined

Sector-specific Productivities

1

quality level q sector j

Example of a Firm and Firm Size Heterogeneity

1

quality level q sector j

Example of another Firm

1

quality level q sector j

Productivity Growth: Internal R&D

1

quality level q sector j internal R&D

Productivity Growth: Internal R&D

1

quality level q sector j internal R&D

Productivity Growth: External R&D

1

quality level q sector j External R&D

Productivity Growth: External R&D

1

quality level q sector j External R&D

Reallocation is Taking Place...

1

quality level q sector j External R&D

Competition Creates Selection

1

quality level q sector j External R&D

Eventually Some Firms Exit

1

quality level q sector j External R&D Exit

In the Meantime...

1

quality level q sector j

Some New Entrants Show Up

1

quality level q sector j new entrants

And New Entrants Replace Incumbents

1

quality level q sector j

R&D and Innovation

Profits in each line j is linear in quality qj: πj = πqj Innovation in product line j : qnew

j

= (1 + s) qold

j ,

s depends on R&D type Firms invest in two types of R&D:

Internal R&D (z)

External R&D (x)

External and Heterogeneous Innovations

External innovations can be of different qualities:

External and Heterogeneous Innovations

External innovations can be of different qualities:

follow-on innovation,

External and Heterogeneous Innovations

External innovations can be of different qualities:

follow-on innovation,

major innovation.

External and Heterogeneous Innovations

External innovations can be of different qualities:

follow-on innovation,

major innovation.

Follow-on innovations build on the previous technology and have declining impacts.

External and Heterogeneous Innovations

External innovations can be of different qualities:

follow-on innovation,

major innovation.

Follow-on innovations build on the previous technology and have declining impacts. After k follow-on improvements, the step size becomes s = ηαk such that: qnew

j

= (1 + ηαk)qold

j

External and Heterogeneous Innovations

External innovations can be of different qualities:

follow-on innovation,

major innovation.

Follow-on innovations build on the previous technology and have declining impacts. After k follow-on improvements, the step size becomes s = ηαk such that: qnew

j

= (1 + ηαk)qold

j

Major innovations create a new technology wave and therefore k = 0: qnew

j

= (1 + η)qold

j

Evolution of Step Size “s”

Innovation step size, s Number of times the latest technology is improved

Evolution of Innovation Quality (step size)

Evolution of Step Size “s”

Innovation step size, s Number of times the latest technology is improved

Evolution of Innovation Quality (step size)

Evolution of Step Size “s”

Innovation step size, s Number of times the latest technology is improved

Evolution of Innovation Quality (step size)

Evolution of Step Size “s”

Innovation step size, s Number of times the latest technology is improved

Evolution of Innovation Quality (step size)

Evolution of Step Size “s”

Innovation step size, s Number of times the latest technology is improved

Evolution of Innovation Quality (step size)

Major Breakthroughs Follow‐on Innovations

Internal Innovation (zj)

Internal innovations improve the quality by s = λ such that: qnew

j

= (1 + λ)qold

j

Sequence of Innovations in line j and Citations

Example: | | | η P1,f1 ηα P2,f2 ηα2 P3,f3 λ P4,f3 λ P5,f3 ηα3 P6,f4

• Tech Cluster 1

| | | η P7,f5 λ P8,f5 ηα P9,f6 ...

• Tech Cluster 2

AN EXAMPLE OF A SEQUENCE OF INNOVATIONS IN A PRODUCT LINE

Sequence of Innovations in line j and Citations

Example: | | | η P1,f1 ηα P2,f2 ηα2 P3,f3 λ P4,f3 λ P5,f3 ηα3 P6,f4

• Tech Cluster 1

| | | η P7,f5 λ P8,f5 ηα P9,f6 ...

• Tech Cluster 2

AN EXAMPLE OF A SEQUENCE OF INNOVATIONS IN A PRODUCT LINE

Cited w/p Citing Cited w/p Citing P1 : ηγ P2, P3, P4, P5, P6 P6 : ηα3γ none P2 : ηαγ P3, P4, P5, P6 P7 : ηγ P8, P9, ... P3 : ηα2γ P4, P5, P6 P8 : λγ P9, ... P4 : λγ P5, P6 P9 : ηα2γ ... P5 : λγ P6

Citation Distribution

Proposition The invariant forward citation distribution of patents with size s ∈

• λ, ηαk | k ∈ N0
• can be expressed as

Υs,n = Υs,0Ωn

s for n ∈ N0.

where Υk,0 =

θ(1−θ)kτ M[τθ+γηαk(τ(1−θ)+zξ)], Υλ,0 = zξ M[τθ+γλ(τ(1−θ)+zξ)] and

Ωk ≡

γηαk(τ(1−θ)+zξ) τθ+γηαk(τ(1−θ)+zξ).

Implication: Highly skewed citation distribution!

Part 2. Empirics

Empirics

Firm size vs firm growth: EmpGrf,t = ηi,t − 0.0351

(s.e. 0.0013) · ln(Empf,t) + ǫf,t.

Empirics

Firm size vs firm growth: EmpGrf,t = ηi,t − 0.0351

(s.e. 0.0013) · ln(Empf,t) + ǫf,t.

Firm size vs innovation intensity: Patent/Emplf,t = ηi,t − 0.1816

(s.e. 0.0058) · ln(Empf,t) + ǫf,t.

Empirics

Firm size vs firm growth: EmpGrf,t = ηi,t − 0.0351

(s.e. 0.0013) · ln(Empf,t) + ǫf,t.

Firm size vs innovation intensity: Patent/Emplf,t = ηi,t − 0.1816

(s.e. 0.0058) · ln(Empf,t) + ǫf,t.

Firm size vs innovation quality: TopPatentSharef,t = ηi,t − 0.0034

(s.e. 0.0008) · ln(Empf,t) + ǫf,t.

Part 3. Quantitative Analysis

Quantitative Analysis

Estimate the model in 3 steps:

Quantitative Analysis

Estimate the model in 3 steps:

External calibration,

Quantitative Analysis

Estimate the model in 3 steps:

External calibration,

Match the citation distribution,

Quantitative Analysis

Estimate the model in 3 steps:

External calibration,

Match the citation distribution,

Indirect inference.

Quantitative Analysis

Estimate the model in 3 steps:

External calibration,

Match the citation distribution,

Indirect inference.

External R&D technology: Xn = νRψ

x nσ,

Rx : External R&D spending n : number of product lines (proxy for knowledge stock) Implications:

Quantitative Analysis

Estimate the model in 3 steps:

External calibration,

Match the citation distribution,

Indirect inference.

External R&D technology: Xn = νRψ

x nσ,

Rx : External R&D spending n : number of product lines (proxy for knowledge stock) Implications:

ψ + σ = 1: External R&D scales up perfectly with firm size.

Quantitative Analysis

Estimate the model in 3 steps:

External calibration,

Match the citation distribution,

Indirect inference.

External R&D technology: Xn = νRψ

x nσ,

Rx : External R&D spending n : number of product lines (proxy for knowledge stock) Implications:

ψ + σ = 1: External R&D scales up perfectly with firm size. ψ + σ < 1: External R&D features diminishing returns in firm size.

Quantitative Analysis

Estimate the model in 3 steps:

External calibration,

Match the citation distribution,

Indirect inference.

External R&D technology: Xn = νRψ

x nσ,

Rx : External R&D spending n : number of product lines (proxy for knowledge stock) Implications:

ψ + σ = 1: External R&D scales up perfectly with firm size. ψ + σ < 1: External R&D features diminishing returns in firm size. ψ + σ > 1: External R&D features increasing returns in firm size.

Estimation I

Figure: Citation Distribution

Number of Citations Received

Probability

Estimation II

Table: Moments

Moment Data Model Moment Data Model profitability 0.109 0.106 entry rate 0.058 0.066 R&D intensity 0.041 0.042 average growth rate 0.010 0.010 internal/external cite 0.774 0.732 growth vs size (fact 1)

• 0.035
• 0.035

frac of inter patents 0.215 0.250 Estimated σ + ψ = 0.895.

Estimation III

Table: Robustness with Facts 1 and 2

Moment Data Model Moment Data Model profitability 0.109 0.106 entry rate 0.058 0.066 R&D intensity 0.041 0.041 average growth rate 0.010 0.010 internal/external 0.774 0.767 growth vs size (fact 1)

• 0.035
• 0.038

frac of inter patents 0.215 0.250 top innv vs size (fact 2)

• 0.0034
• 0.0034

Estimated σ + ψ = 0.895.

Estimation IV

Table: Robustness with Facts 1, 2, and 3

Moment Data Model Moment Data Model profitability 0.109 0.113 average growth rate 0.010 0.009 R&D intensity 0.041 0.049 growth vs size (fact 1)

• 0.035
• 0.057

internal/external 0.774 0.806 top innv vs size (fact 2)

• 0.0034
• 0.0061

frac of inter patents 0.215 0.272 pat/emp vs size (fact 3)

• 0.182
• 0.081

entry rate 0.058 0.059 Estimated σ + ψ = 0.907.

Quantitative Result 1: External innovation does not scale up one-to-one with firm size.

Estimation V

Table: Growth Decomposition

In Percentage Terms Internal External New Entry 19.8% 54.5% 25.7%

Estimation V

Table: Growth Decomposition

In Percentage Terms Internal External New Entry 19.8% 54.5% 25.7%

Average step size for external innovation: ¯ s = 0.07

Estimation V

Table: Growth Decomposition

In Percentage Terms Internal External New Entry 19.8% 54.5% 25.7%

Average step size for external innovation: ¯ s = 0.07 Step size for internal innovation: λ = 0.05

Estimation V

Table: Growth Decomposition

In Percentage Terms Internal External New Entry 19.8% 54.5% 25.7%

Average step size for external innovation: ¯ s = 0.07 Step size for internal innovation: λ = 0.05

Quantitative Result 2: External innovation has 40% more spillovers.

Estimation VI

Quantitative Result 1 + Quantitative Result 2 ↓↓ On average, small firms generate more spillovers per patent.

Implications

Large firms focus on their existing products and turn to more internal innovations which are more incremental in nature. Small firms explore new external ideas and try to expand into new fields. This has also implications on firm’s innovation dynamics over its life cycle. Important implications on innovation and tax policy.

Conclusion

We introduced a new model of firm and innovation dynamics. A close match between theory and data. Identified heterogeneous spillovers associated with different firms and different innovations. Very promising direction to study the role and impact of industrial policy on innovation and growth.

Royal Economic Society