1) The document studies how allowing firms to substitute between different types of employment, such as direct and outsourced labor, affects the implications of size-dependent policies on labor demand. 2) A theoretical model is developed where firms can substitute between direct and outsourced labor when facing taxes or regulations on direct labor. This reconciles empirical evidence that size-dependent policies do not always generate gaps in employment at thresholds. 3) The model predicts that size-dependent policies reduce total employment but increase the ratio of outsourced to direct labor for affected firms. It also finds no gap in total employment at the policy threshold due to labor substitution.

1. Introduction
Framework
Discussion
Size-dependent policies and labor substitution: Threshold
effects and missing gaps.
Carlos Ospino1
1Universidad de los Andes
Seminario IEEC.
Barranquilla, Colombia.
February 12, 2016
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2. Introduction
Framework
Discussion
Motivation
Literature
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-Dependent
Policies (SDP) in terms of labor demand.
Literature has focused on homogeneous labor.
Introducing labor heterogeneity and potential
substitution reconciles model implications with
empirical evidence: With substitution SDP
does not generate a gap in the employment
distribution at the policy threshold.
Highly policy relevant: 1-Prevalent policies on
specific types of employment (e.g. direct la-
bor), 2-World-wide trend towards contract la-
bor. Source: Garicano et. al., 2015
Carlos Ospino Size-dependent policies and labor substitution 2/25

3. Introduction
Framework
Discussion
Motivation
Literature
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 quotas
started being calculated using
directly hired labor (a tax on direct
labor).
Size Dependent: only for 15+
directly hired workers.
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4. Introduction
Framework
Discussion
Motivation
Literature
... and the ratio of outsourced to direct labor grew particularly before the threshold
of the policy (15 workers).
Source: Own calculations using Colombia’s Annual Manufacturing Survey. 2002-2003. Vertical line at 14 directly hired workers.
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5. Introduction
Framework
Discussion
Motivation
Literature
Related literature I
Misallocation and productivity
Theoretical size-dependent models imply that the size distribution of firms has
a spike (“bunching”) right before the threshold where SDP kick-in, and a gap
at the threshold. (Guner, Ventura & Xu, 2008).
1 Some studies find bunching before threshold, but positive mass (a valley) where
a gap was expected. ((Garicano, LeLarge, & Van Reenen (2015), (Gourio &
Roys (2014)).
2 These papers model distortion as combination of fixed costs, proportional taxes
and measurement error to match the data.
Could this bunching and lack of a gap be explained by labor substitution?
Carlos Ospino Size-dependent policies and labor substitution 5/25

6. Introduction
Framework
Discussion
Motivation
Literature
Related literature II
Labor substitution and employment protection
Ramaswamy (2013) and Chaurey (2015) study the case of contract workers
in India.
Firms substitute towards the labor type that’s not subject to size-dependent
regulation at the threshold.
Marked increase in the share of contract labor in states where legislation is
pro-worker.
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7. Introduction
Framework
Discussion
Motivation
Literature
Preview of results
Compared with models of SDP with homogeneous labor:
Taxes on direct labor also reduce total labor demand both by firms at the
threshold and those above it.
But labor substitution allows some firms that would bunch to keep their size
above the policy threshold: No gap in the employment distribution at the
threshold.
...even with imperfect labor substitution.
Regulation induces a change in the employment composition.
Colombian manufacturing firms react to the 2002 reform according to what the
model predicts:
1 Reduced total and direct labor demand for firms above and just below the
threshold compared to those well below it.
2 Increased the ratio of outsourced to direct labor demand for firms above the
threshold compared to those well below it.
Carlos Ospino Size-dependent policies and labor substitution 7/25

8. Introduction
Framework
Discussion
Model outline
Firm problem
max
{nd ,no}
π(s, n) = s1−γ
[(nd )σ
(no)1−σ
]γ
− wd nd − wono − τ(ˆnd ) (2.1)
s.t. τ(ˆnd ) = 0 if nd ≤ ˆnd .
τ(ˆnd ) = αnd if nd > ˆnd .
Production function a la Guner, Ventura & Xu (2008): Lucas (1978) “Span of
control” model with SDP.
s: Exogenous idiosyncratic productivity.
Two types of labor: Imperfect substitution.
Tax on one type.
Carlos Ospino Size-dependent policies and labor substitution 8/25

9. Introduction
Framework
Discussion
Model outline
Types of firms
Definition
Undistorted firms are those whose direct labor demand is at most ˆnd and are
not subject to the size-dependent regulation. Distorted firms are those whose
labor demand is greater than ˆnd and are therefore subject to the size-dependent
regulation. (Labor) Constrained firms are firms who fix the demand of direct labor
at ˆnd in order to avoid being subject to the regulation.
Carlos Ospino Size-dependent policies and labor substitution 9/25

10. Introduction
Framework
Discussion
Model outline
Note: Functions simulated using a log normal distribution and the following
parameter values: γ=0.802, σ=0.65, α=0.025, Wo=0.14, Wd =0.2, ˆnd =14.
s−
=0.160, s+
=0.527
Solution to firm problem implies
that:
Profit maximization separates firms
in three groups:
s−(s+) is recovered by equating
Π(s, wi, ˆnd ) = Π(s, wi(, τ)).
1 Undistorted firms: Those with
s ∈ [0, s−
]
2 (Labor) Constrained firms: Those
with s ∈ [s−
, s+
]
3 Distorted firms: Those with
s ∈ [s+
, 1]
Carlos Ospino Size-dependent policies and labor substitution 10/25

11. Introduction
Framework
Discussion
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, ˆnd =14. s−
=0.160, s+
=0.527
Outsourced labor demand is
increasingly nonlinear in
s ∈ [s−, s+].
Demand for outsourced labor by
constrained and distorted firms falls
by less than demand for direct labor
and generates a higher ratio of labor
types relative to undistorted
economy.
Carlos Ospino Size-dependent policies and labor substitution 11/25

12. Introduction
Framework
Discussion
Model outline
Assume wages can’t adjust
Partial Equilibrium still useful to
study employment effects.
SDP generate unemployment!
SDP change the relative
composition of employment in the
economy (LM segmentation).
The policy implications are
substantial:
Fiscal costs: Employers avoid
contributing to social protection.
Worker’s well being: Less favorable
contracts. Less incentives to invest
in human capital.
Carlos Ospino Size-dependent policies and labor substitution 12/25

13. Introduction
Framework
Discussion
Model outline
Note: Functions simulated using a log normal distribution and the following
parameter values: γ=0.802, σ=0.65, α=0.025, Wo=0.14, Wd =0.2, ˆnd =14.
s−
=0.160, s+
=0.527
no
nd
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 of
labor types.
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14. Introduction
Framework
Discussion
Model outline
What about “The Gap”? I
Note: Functions simulated using a log normal distribution and the following
parameter values: γ=0.802, σ=0.65, α=0.025, Wo=0.14, Wd =0.2, ˆnd =14.
s−
=0.160, s+
=0.527
Total demand is continuous at the
threshold (ˆnd =14).
A sufficient condition for the absence
of a gap at the threshold is given by:
R > 0
...which is always satisfied in this
model because of imperfect substi-
tutability of labor in the technology.
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15. Introduction
Framework
Discussion
Empirical exercise
Wrap up
Model predictions I
Relative to the distortion-free world, with labor substitution a size-dependent
policy:
1 Reduces total, direct and outsourced labor demand by constrained and distorted
firms.
2 Increases the ratio of outsourced to direct labor for constrained and distorted
firms.
3 Labor demands (their ratio, Rα) increase (decreases) discontinuously at s+
for
firms subject to the regulation compared to constrained firms.
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16. Introduction
Framework
Discussion
Empirical exercise
Wrap up
Empirical approximation I
Take advantage of exogenous variation in apprenticeship contract regulation
which 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).
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17. Introduction
Framework
Discussion
Empirical exercise
Wrap up
Empirical approximation II
To test implication 1 and 2 I estimated (3.1) using plant-level data from
Colombia’s Annual Manufacturing Survey, with and without the variables from
structural 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 total
employment, the average wage bill, Sector controls, and TFP.
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18. Introduction
Framework
Discussion
Empirical exercise
Wrap up
Summary Statistics
Figure: Source: Own calculations using Colombia’s Annual Manufacturing Survey. Table shows summary statistics for firms hiring between 10
and 29 directly hired workers in each year. Prices deflated using PPI 2009.
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19. Introduction
Framework
Discussion
Empirical exercise
Wrap up
Results I
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20. Introduction
Framework
Discussion
Empirical exercise
Wrap up
Results II
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21. Introduction
Framework
Discussion
Empirical exercise
Wrap up
Results III
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22. Introduction
Framework
Discussion
Empirical exercise
Wrap up
Results IV
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23. Introduction
Framework
Discussion
Empirical exercise
Wrap up
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 benefits
deserve attention as well.
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24. Introduction
Framework
Discussion
Empirical exercise
Wrap up
Further work
Exploit other features of the regulation and data: Heterogeneous effects across
multiple 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 intuition
about 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 this
channel and test its relative importance.
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25. Introduction
Framework
Discussion
Empirical exercise
Wrap up
Thank you.
cg.ospino20@uniandes.edu.co
carlos.ospino.h@gmail.com
Find latest version of the paper at:
https://sites.google.com/site/spinmetrics/
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