Size-dependent policies and labor substitution

IntroductionFrameworkDiscussion

Size-dependent policies and labor substitution: Thresholdeffects and missing gaps.

Carlos Ospino1

1Universidad de los Andes

Seminario IEEC.Barranquilla, Colombia.

February 12, 2016

Carlos Ospino Size-dependent policies and labor substitution 1/25


MotivationLiterature

This paper

I study theoretically and empirically how the fact that firms may substitute be-tween different types of employment changes the implications of Size-DependentPolicies (SDP) in terms of labor demand.

Literature has focused on homogeneous labor.

Introducing labor heterogeneity and potentialsubstitution reconciles model implications withempirical evidence: With substitution SDPdoes not generate a gap in the employmentdistribution at the policy threshold.

Highly policy relevant: 1-Prevalent policies onspecific types of employment (e.g. direct la-bor), 2-World-wide trend towards contract la-bor. Source: Garicano et. al., 2015




Ratio of outsourced workers to directly hired workers increased...

Source: Own calculations using Colombia’s Annual Manufacturing Survey. Dashed lines at years 2002 and 2006.

After a major labor reform in 2002.Apprenticeship compulsory quotasstarted being calculated usingdirectly hired labor (a tax on directlabor).Size Dependent: only for 15+directly hired workers.




... and the ratio of outsourced to direct labor grew particularly before the thresholdof the policy (15 workers).

Source: Own calculations using Colombia’s Annual Manufacturing Survey. 2002-2003. Vertical line at 14 directly hired workers.




Related literature I

Misallocation and productivityTheoretical size-dependent models imply that the size distribution of firms hasa spike (“bunching”) right before the threshold where SDP kick-in, and a gapat the threshold. (Guner, Ventura & Xu, 2008).

1 Some studies find bunching before threshold, but positive mass (a valley) wherea gap was expected. ((Garicano, LeLarge, & Van Reenen (2015), (Gourio &Roys (2014)).

2 These papers model distortion as combination of fixed costs, proportional taxesand measurement error to match the data.

Could this bunching and lack of a gap be explained by labor substitution?




Related literature II

Labor substitution and employment protection

Ramaswamy (2013) and Chaurey (2015) study the case of contract workersin India.

Firms substitute towards the labor type that’s not subject to size-dependentregulation at the threshold.

Marked increase in the share of contract labor in states where legislation ispro-worker.




Preview of results

Compared with models of SDP with homogeneous labor:Taxes on direct labor also reduce total labor demand both by firms at thethreshold and those above it.But labor substitution allows some firms that would bunch to keep their sizeabove the policy threshold: No gap in the employment distribution at thethreshold....even with imperfect labor substitution.Regulation induces a change in the employment composition.

Colombian manufacturing firms react to the 2002 reform according to what themodel predicts:

1 Reduced total and direct labor demand for firms above and just below thethreshold compared to those well below it.

2 Increased the ratio of outsourced to direct labor demand for firms above thethreshold compared to those well below it.



Model outline

Firm problem

max{nd ,no}

π(s,n) = s1−γ [(nd )σ(no)1−σ]γ − wdnd − wono − τ(n̂d ) (2.1)

s.t. τ(n̂d ) = 0 if nd ≤ n̂d .τ(n̂d ) = αnd if nd > n̂d .

Production function a la Guner, Ventura & Xu (2008): Lucas (1978) “Span ofcontrol” model with SDP.s: Exogenous idiosyncratic productivity.Two types of labor: Imperfect substitution.Tax on one type.



Model outline

Types of firms

DefinitionUndistorted firms are those whose direct labor demand is at most n̂d and arenot subject to the size-dependent regulation. Distorted firms are those whoselabor demand is greater than n̂d and are therefore subject to the size-dependentregulation. (Labor) Constrained firms are firms who fix the demand of direct laborat n̂d in order to avoid being subject to the regulation.



Model outline

Note: Functions simulated using a log normal distribution and the followingparameter values: γ=0.802, σ=0.65, α=0.025, Wo=0.14, Wd =0.2, n̂d =14.s−=0.160, s+=0.527

Solution to firm problem impliesthat:Profit maximization separates firmsin three groups:s−(s+) is recovered by equatingΠ(s,wi , n̂d ) = Π(s,wi(, τ)).

1 Undistorted firms: Those withs ∈ [0, s−]

2 (Labor) Constrained firms: Thosewith s ∈ [s−, s+]

3 Distorted firms: Those withs ∈ [s+,1]



Model outline

Note: Functions simulated using a log normal distribution and the following parameter val-ues: γ=0.802, σ=0.65, α=0.025, Wo=0.14, Wd =0.2, n̂d =14. s−=0.160, s+=0.527

Outsourced labor demand isincreasingly nonlinear ins ∈ [s−, s+].Demand for outsourced labor byconstrained and distorted firms fallsby less than demand for direct laborand generates a higher ratio of labortypes relative to undistortedeconomy.



Model outline

Assume wages can’t adjust

Partial Equilibrium still useful tostudy employment effects.SDP generate unemployment!SDP change the relativecomposition of employment in theeconomy (LM segmentation).The policy implications aresubstantial:

Fiscal costs: Employers avoidcontributing to social protection.Worker’s well being: Less favorablecontracts. Less incentives to investin human capital.



Model outline


nond

is:1 Same as undistorted economy for

undistorted firms.2 Increasing in productivity for

constrained firms.3 Higher than undistorted economy

for distorted firms.

At s+ there’s a jump in the ratio oflabor types.



Model outline

What about “The Gap”? I


Total demand is continuous at thethreshold (n̂d=14).A sufficient condition for the absenceof a gap at the threshold is given by:

R > 0

...which is always satisfied in thismodel because of imperfect substi-tutability of labor in the technology.



Empirical exerciseWrap up

Model predictions I

Relative to the distortion-free world, with labor substitution a size-dependentpolicy:

1 Reduces total, direct and outsourced labor demand by constrained and distortedfirms.

2 Increases the ratio of outsourced to direct labor for constrained and distortedfirms.

3 Labor demands (their ratio, Rα) increase (decreases) discontinuously at s+ forfirms subject to the regulation compared to constrained firms.




Empirical approximation I

Take advantage of exogenous variation in apprenticeship contract regulationwhich was overhauled in Dic. 2002.

Apprentices quota calculated using direct number of workers starting 2003.Up to 2002 quota used “skilled” workers. (Admin. staff).Small firms are subject to regulation starting 2003...... but only those with 15 or more direct workers.

Looks like a whole new regulation even though it’s been in effect since 1959.(e.g. Number of contracts doubled between 2002 and 2003).




Empirical approximation II

To test implication 1 and 2 I estimated (3.1) using plant-level data fromColombia’s Annual Manufacturing Survey, with and without the variables fromstructural labor demands, denoted here by X .

yit = αi + β1Tt + β2D2i ∗ Tt + β3D3i ∗ Tt + γXit + µit (3.1)

yit=Total, direct and outsourced labor demand, and ratio of labor types.D2i ≡ I(Nd = 14); D3i ≡ I(Nd ≥ 15); Tt ≡ I(Year = 2003); X=Controls,include TFP.ITT estimators. Treatment defined in 2002. Data from 2002 and 2003.X=Ratio of outsourced to direct labor, inverse share of managers in totalemployment, the average wage bill, Sector controls, and TFP.




Summary Statistics

Figure: Source: Own calculations using Colombia’s Annual Manufacturing Survey. Table shows summary statistics for firms hiring between 10and 29 directly hired workers in each year. Prices deflated using PPI 2009.




Results I




Results II




Results III




Results IV




Discussion

These policies have clear economic costs: ⇓ labor demand, misallocation, ⇓TFP, labor substitution, segmentation.They could have benefits as well: ⇑ human capital, school to work transitions,⇑ labor productivity.This paper studies the costs, which are policy relevant. But the benefitsdeserve attention as well.




Further work

Exploit other features of the regulation and data: Heterogeneous effects acrossmultiple thresholds, industries (Elasticities of substitution).Test quantitative effect of substitution channel on TFP/Output.There appears to be GE effects going on. Close the model for further intuitionabout misallocation and productivity (Another paper).The data suggests firms substitute capital as well (or may invest in labor sav-ing technology). Future research should expand the model to consider thischannel and test its relative importance.




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Economy & Finance

Size-dependent policies and labor substitution