Firm Heterogeneity:Firm Heterogeneity:Implications for Wage Inequality Implications for Wage Inequality

and Aggregate Growthand Aggregate Growth

Dale T. MortensenDale T. MortensenNorthwestern and Aarhus UniversityNorthwestern and Aarhus University

ISEO Summer School June 22, 2011June 22, 2011

MotivationMotivation

Matched employer-employee data Matched employer-employee data reveal that more productive firms are reveal that more productive firms are larger, pay higher wages, and are larger, pay higher wages, and are more likely to export. more likely to export.

Research Questions Research Questions 1.1.What are the quantitative implications of What are the quantitative implications of

firm productivity differences for firm productivity differences for aggregate productivity and economic aggregate productivity and economic growth?growth?

2.2.Are there large firm efficiency differences Are there large firm efficiency differences or large differences in input quality that or large differences in input quality that account for these observations?account for these observations?

Evidence from Firm Micro Evidence from Firm Micro DataData

U.S. Average total factor productivity U.S. Average total factor productivity (TFP) 90/10 ratio within (TFP) 90/10 ratio within manufacturing industries is 1.92… manufacturing industries is 1.92… Syverson (2004)Syverson (2004)

90/10 ratio across all Danish firms for 90/10 ratio across all Danish firms for labor productivity is 2.3 and firm labor productivity is 2.3 and firm wages is 1.8… Bagger et al. (2010)wages is 1.8… Bagger et al. (2010)

90/10 TFP ratios are over 5 for firms in 90/10 TFP ratios are over 5 for firms in both China and India… Hsieh & both China and India… Hsieh & Klenow (2009) Klenow (2009)

Evidence from Firm Trade Evidence from Firm Trade DataData

Few firms export and those that do are Few firms export and those that do are larger and more productive.larger and more productive.

Exporting firms pay wage premiums.Exporting firms pay wage premiums. Exporting firms are found in all Exporting firms are found in all

industries in the manufacturing sector.industries in the manufacturing sector. SourcesSources

– US: Bernard and Jensen (1995, 1999)US: Bernard and Jensen (1995, 1999)– France: Eaton et al. (2004, 2008)France: Eaton et al. (2004, 2008)– Denmark: Pedersen (2009)Denmark: Pedersen (2009)

The Danish ProjectThe Danish Project

Lentz and Mortensen (2008), "An Empirical Lentz and Mortensen (2008), "An Empirical Model of Growth Through Product Model of Growth Through Product Innovation." Innovation." EconometricaEconometrica. .

Lentz and Mortensen (2010),"Labor Lentz and Mortensen (2010),"Labor Market Models of Firm and Worker Market Models of Firm and Worker Heterogeneity." Heterogeneity." Annual Review of Annual Review of EconomicsEconomics..

Bagger, Christensen, and Mortensen Bagger, Christensen, and Mortensen (2010), "Wage and Productivity Dispersion: (2010), "Wage and Productivity Dispersion: Labor Quality or Rent Sharing?," working Labor Quality or Rent Sharing?," working paper. paper.

The Danish DataThe Danish Data IDA: Contains worker identity, earning, and IDA: Contains worker identity, earning, and

characteristics (age, gender, education, characteristics (age, gender, education, working experience, labor market histories, working experience, labor market histories, household structure) and employer IDs. household structure) and employer IDs.

Stratified rolling panel firm survey: Stratified rolling panel firm survey: Contains firm accounting information Contains firm accounting information (sales, materials purchases, investment, (sales, materials purchases, investment, capital book value, exports and imports) capital book value, exports and imports) for each year. for each year.

These are linked to create an matched These are linked to create an matched employer-employee panel which is employer-employee panel which is available for research at Aarhus University.available for research at Aarhus University.

Firm Productivity and Wage Firm Productivity and Wage Distributions: All Private Danish Distributions: All Private Danish

FirmsFirms

Firm Size vs ProductivityFirm Size vs Productivity

Growth Through Innovation IGrowth Through Innovation IGrossman and Helpman (1991)Grossman and Helpman (1991)

Klette and Kortum (2004)Klette and Kortum (2004)

Final goods and services are produced Final goods and services are produced using many differentiated intermediate using many differentiated intermediate goods and services as inputs. (Dixit-goods and services as inputs. (Dixit-Stiglitz)Stiglitz)

Intermediate products are produced with Intermediate products are produced with labor and capital. labor and capital.

More productive versions of each More productive versions of each intermediate product type are created from intermediate product type are created from time to time that replace older versions. time to time that replace older versions.

The cost of product innovation (R&D) rises The cost of product innovation (R&D) rises at the margin.at the margin.

Growth Through Innnovation Growth Through Innnovation IIII

New firms enter and continuing firms New firms enter and continuing firms grow by creating new products and grow by creating new products and shrink and exit through product shrink and exit through product destruction. destruction.

Firms differ with respect to the expected Firms differ with respect to the expected productivity of the intermediate goods productivity of the intermediate goods and services that they create.and services that they create.

The supplier of the current version of The supplier of the current version of each product sets its price.each product sets its price.

Empirical Implications I Empirical Implications I

Firms that create higher quality Firms that create higher quality intermediate products are more intermediate products are more profitable, invest more in R&D, and profitable, invest more in R&D, and supply a growing fraction of the supply a growing fraction of the products in each entry cohort.products in each entry cohort.

As new products and services displace As new products and services displace old, this process of creative-destruction old, this process of creative-destruction induces reallocate of workers from the induces reallocate of workers from the less to the more productive firms.less to the more productive firms.

Empirical Implications IIEmpirical Implications II

Aggregate growth is determined by Aggregate growth is determined by firm innovation rates and the speed firm innovation rates and the speed with which resources are reallocated with which resources are reallocated to the most innovative firms. to the most innovative firms.

Steady state firm heterogeneity in Steady state firm heterogeneity in productivity is sustained by the cost productivity is sustained by the cost of innovation, initial uncertainty of innovation, initial uncertainty about type, and the process of about type, and the process of creative-destruction.creative-destruction.

Parameter Estimation IParameter Estimation I

Create a structural model of firm Create a structural model of firm interactions that generates the interactions that generates the relationship between firm R&D relationship between firm R&D investment decisions and observables.investment decisions and observables.

Using the equilibrium steady state Using the equilibrium steady state relationships of the model, the relationships of the model, the parameters are estimated by the parameters are estimated by the method of simulated moments using method of simulated moments using observables drawn for a panel of observables drawn for a panel of Danish firms over the period 1992-Danish firms over the period 1992-1997. 1997.

Model FitModel Fit

Fit of Size vs ProductivityFit of Size vs Productivity

Fit of Productivity Fit of Productivity DistributionDistribution

Decomposing Productivity Decomposing Productivity GrowthGrowth

Growth rate in output per worker = Growth rate in output per worker =

Entry/Exit + Selection + ResidualEntry/Exit + Selection + Residual

Entry/Exit: Attributable to the fact that new Entry/Exit: Attributable to the fact that new entrants are more productive than firms entrants are more productive than firms that exist. that exist.

Selection: Attributable to the fact that more Selection: Attributable to the fact that more productive firms in each entry cohort productive firms in each entry cohort become larger over time. become larger over time.

Residual: Counterfactual contribution to Residual: Counterfactual contribution to growth of continuing firms in the absence of growth of continuing firms in the absence of selection and entry and exit.selection and entry and exit.

Model Based Productivity Model Based Productivity Growth Decomposition Growth Decomposition

Empirical Labor Productivity Empirical Labor Productivity Growth DecompositionGrowth Decomposition

References: Foster, Haltiwanger and Krizan (2001) andPatrin and Levinsohn (2004).

Theoretical ImplicationsTheoretical Implications

Changes in employment shares for Changes in employment shares for each firm type are stationary in the each firm type are stationary in the steady state.steady state.

Hence, the “between” and “cross” Hence, the “between” and “cross” terms are zero in a simple model.terms are zero in a simple model.

Hypothesis: If the economy is in a Hypothesis: If the economy is in a steady state, then none zero values in steady state, then none zero values in these terms of a FHK decomposition these terms of a FHK decomposition are “noise.”are “noise.”

Analysis of FHK Analysis of FHK DecompositionDecomposition

TFP Differences or TFP Differences or Differences in Input Quality?Differences in Input Quality?

Cobb-Douglas production functionCobb-Douglas production function lnYlnYitit = lnp = lnpjt jt + + KKlnKlnKjt jt + + LLlnLlnLjt jt + + εεitit wherewhere ppjtjt = = j j + ρp+ ρpjt-1 jt-1 + ε+ εjtjt is TFP of firm j in year t, is TFP of firm j in year t, KKjtjt is the capital input in year t, is the capital input in year t, LLjtjt=∑=∑i∈Ijti∈Ijtaaii is labor input is labor input where awhere aii is the "ability" of worker I, is the "ability" of worker I,

and Iand Ijtjt is the set of worker in firm j at is the set of worker in firm j at time t.time t.

AKM wage equation is AKM wage equation is

ln ln wwijt ijt = lna= lnait it + lnω+ lnωjtjt

The "price of ability" is determined by The "price of ability" is determined by (Stole-Zwiebel) bargaining:(Stole-Zwiebel) bargaining:

ωωjt jt = (1-β)b + = (1-β)b + LLβ/(1-β+β/(1-β+LLβ)Yβ)Yjtjt/L/Ljt jt + ν+ νjtjt

where b represents "home production” and where b represents "home production” and β denotes worker "bargaining power."β denotes worker "bargaining power."

Dispersion by IndustryDispersion by Industry

Wage-Productivity Wage-Productivity CorrelationCorrelation

Model Estimation IModel Estimation I Linked Danish manufacturing data: Linked Danish manufacturing data:

Annual observations for 1995-2005Annual observations for 1995-2005 1.1.Contains worker identity, wage, Contains worker identity, wage,

experience and employer ID in experience and employer ID in November of each year for all November of each year for all firms.firms.

2.2.Stratified rolling panel firm survey: Stratified rolling panel firm survey: Contains firm value added, wage Contains firm value added, wage bill, book value, and capital bill, book value, and capital purchases information for each purchases information for each year.year.

Model Estimation IIModel Estimation II Two Stage Procedure:Two Stage Procedure:

1.1.Use IDA data and AKM Use IDA data and AKM decomposition to estimate adecomposition to estimate aitit for for each i and t and use individual wage each i and t and use individual wage observations to identify ωobservations to identify ωjt jt and Land Ljtjt..

2.2.Under the assumption that TFP (pUnder the assumption that TFP (pjtjt) ) is an AR1 process, use firm data and is an AR1 process, use firm data and estimates of ωestimates of ωjtjt and L and Ljtjt to estimate to estimate wage bargaining and production wage bargaining and production function parameters.function parameters.

Wage and Productivity Wage and Productivity StatisticsStatistics

Structural Parameter Structural Parameter EstimatesEstimates

Individual Wage Individual Wage DecompositionDecomposition

Labor Productivity Labor Productivity DecompositionDecomposition

Policy Issues I Policy Issues I

Wage Dispersion Wage Dispersion

– Rent sharing is "unfair" in the sense that Rent sharing is "unfair" in the sense that equally qualified workers are paid equally qualified workers are paid differently.differently.

– However, wage differentials motivate However, wage differentials motivate efficient reallocation. Christensen et. al efficient reallocation. Christensen et. al (2005)(2005)

Results suggests that the efficient Results suggests that the efficient incentive effect is important. incentive effect is important.

Policy Issues IIPolicy Issues II

Efficiency: The Schumpeter tradeoffEfficiency: The Schumpeter tradeoff

– Monopoly pricing distorts input decisions.Monopoly pricing distorts input decisions. – "Business stealing” externality adversely "Business stealing” externality adversely

affects R&D investment.affects R&D investment.

Further research suggests that the latter is Further research suggests that the latter is more important. Hence, existing patent more important. Hence, existing patent and trade-mark protection may be of and trade-mark protection may be of inadequate. inadequate.