# How has labour market power evolved?
Comparing labour market monopsony in Peru and the United States

Jorge Davalos
Universidad del Pacifíco
Department of Management
Lima, Peru
<EMAIL_ADDRESS>Ekkehard Ernst
International Labour Organization
Research Department
Geneva, Switzerland
<EMAIL_ADDRESS>
(31 March 2021
)

###### Abstract

We document and compare the extent and evolution of labour market power by
employers on the US and Peruvian labour markets during the 2010s. Making use
of a structural estimation model of labour market dynamics, we estimate
differences in market power that workers face depending on their sector of
activity, their age, sex, location and educational level. In particular, we
show that differences in cross-sectional market power are significant and
higher than variations over the ten-year time span of our data. In contrast to
findings of labour market power in developed countries such as the US, we
document significant market power of employers in Peru vis-à-vis the tertiary
educated workforce, regardless of age and sector. In contrast, for the primary
educated workforce, market power seems to be high in (private) services and
manufacturing. For secondary educated workers, only the mining sector stands
out as moderately more monopsonistic than the rest of the labour market. We
also show that at least for the 2010s, labour market power declined in Peru.
We contrast these findings with similar estimates obtained for the United
States where we are able to show that increases in labour market power are
particularly acute in certain sectors, such as agriculture and entertainment
and recreational services, as well as in specific geographic areas where these
sectors are dominant. Moreover, we show that for the US, the labour market
power has gradually increased over the past ten years, in line with the
general rise in inequality. Importantly, we show that the pervasive gender pay
gap cannot be linked to differential market power as men face higher labour
market power than women. We also discuss possible reasons for these findings,
including for the differences of labour market power across skill levels.
Especially, we discuss the reasons for polarization of market power that are
specific to sectors and locations.

Keywords: Labour market power, monopsony, United States, Peru, structural
model

JEL codes: J2, J3, J38, J42, N30

> “That labor markets have important elements of monopsony power is becoming
> clear beyond any reasonable doubt.” (Manning, 2020)

##  1 Introduction

The rise in market power by firms has led to a concern about growing profit
mark-ups, spatial inequalities and – importantly – increases in monopsonistic
wage-setting power on labour markets (IMF, 2019). To date, however, only the
evolution of mark-ups in selected OECD countries has been documented and
analysed. In contrast, no encompassing study exist as to (i) the extent to
which monopsonistic wage-setting power has increased across a broad range of
developed and emerging countries, (ii) the extent to which such an increase
would have contributed to a rise in within-country inequalities, and (iii) the
importance this change in labour market power might have had in explaining
global trends in labour income share and inequality.

The rise of within-country inequality and the simultaneous fall in the labour
income share in a large number of (mostly) advanced economies is well
documented (Milanovic, 2016). What is less clear are the origins of this
inequality and whether common trends across countries indicate common
underlying factors. Several underlying factors have been highlighted as
potential drivers in inequality, including the rise of super-star firms in the
digital economy (Autor et al., 2020; Gutiérrez and Philippon, 2020;
Covarrubias et al., 2019), the existence of firm-specific, possibly intangible
assets (Caballero, 2007; De Ridder, 2019), globlalization (Autor et al.,
2013), changes in the tax structure (Ciminelli et al., 2019), the erosion of
labour market institutions (Jaumotte and Osorio-Buitron, 2015), a declining
degree of market competition due to rising market entry barriers (e.g. non-
compete clauses, occupational licensing111See the discussion in
https://samueldodini.com/files/Dodini_occupation_licensing_9_21_2020.pdf and
the literature cited therein, land-use regulation, see Cunningham, 2019) and
low labour market mobility (e.g. due to housing sector constraints, Ernst and
Saliba, 2018). Some but not all of these explanations would point towards
higher market power for firms also on the labour market. Others suggest that
market power might increase only for a sub-group of firms on the labour
market. For instance, the rise of super-star firms might increase labour
market power for only a small group of companies (those which are highly
attractive for workers to join) but market competition for talent might remain
the same or become even worse for the rest, leading to rising wages among the
much larger tail of the distribution of firms.

The link between inequality and rising labour market power has attracted
significant research over the past decade. Under the Obama administration, the
Council of Economic Advisors devoted an entire study on the phenomenon of
labour market monopsony.222US government discussion of labor market monopsony
To date, most studies in this area focus on the United States and on
particular parts of the labour market therein, such as the market for online
and platform work.333https://voxeu.org/article/monopsony-online-labour-markets
What is missing is a more encompassing study covering a large part of the
labour markets across different sectors, occupational groups, by gender and by
age. Also, even though a rise in income inequality is observed both in
advanced and emerging countries, only few studies exist that would look at
labour market monopsony in other, non-OECD countries.444Sokolova and Sorensen
(2021) provide a meta-study of existing estimates across a range of estimation
methods and countries. Finally, existing studies typically focus on a cross-
sectional analysis, looking at one point in time rather than the evolution
over longer periods, which makes it hard to link the rise in inequality to a
_rise_ in labour market monopsony.

In the following, we make use of a structural estimation of the labour market
to assess the degree of labour market monopsony, following a methodology
originally suggested by van den Berg and Ridder (1998) and Ridder and van den
Berg (2003). This approach allows us to provide detailed estimates of labour
market power for different groups on the US and the Peruvian labour market for
the different years from 2010 to 2020. We discuss and compare various
estimation strategies to arrive at a labour market monopsony indicator using
standard labour force survey information and analyse our preferred estimation
strategy. Our approach to estimate labour market concentration contrasts with
current ones as we make use of a structural model that allows us to
simultaneously estimate the degree of monopsony for different labour market
groups, by sector, age and educational level, providing a more detailed
overview than approaches that focus on firm-level concentration (e.g. Amodio
et al., 2020). Moreover, using the rich labour force survey information
available for the US and Peru we are able to track and compare the evolution
of labour market power for both countries.

Our estimates document significant cross-sectoral, occupational and age
differences of the degree of labour market monopsony. In particular, we show
that contrary to intuition, in the context of the Peruvian labour market it is
the high-skilled group that faces more severe labour market monopsony. Also,
labour market monopsony is higher in well-paying occupations such as
manufacturing and government services compared to agriculture. Finally, we
document that labour market monopsony has declined across the board in the
second half of the last decade in Peru but not in the United States.

The paper is structured as follows. The next section provides an overview of
the literature on labour market monopsony, which has received renewed interest
over recent years, in particular with the rise of non-standard forms of
employment via online labour platforms. We discuss and compare the estimation
strategies used by different authors and highlight that most of the recent
literature has focused on various measures of labour and product market
concentration to obtain a measure of labour market monopsony. In contrast, our
approach relies on a structural estimation of the labour market, avoiding the
porblem of identifying the relevant market, including possible cross-market
spillovers. In section 3, we discuss our data and methods, including an
overview of different estimation strategies for our structural model approach.
Section 4 summarises the main findings of our estimations and discusses the
implications. A final section concludes and discusses possible policy choices
given the heterogeneous degree of market power that we document in both
countries.

##  2 What do we know about labour market power?

The discussion on the importance of market power on labour markets has
received increased attention over the past decade. While the theoretical
concept of labour market monopsony is well known to economists, most empirical
and policy analysis of the labour market still focuses on the competitive
market assumption or – at best – on a bilateral monopoly with wage bargaining
as in the by now standard labour market search and matching model (Pissarides,
1994, 2000; Mortensen and Pissarides, 1994). As discussed by Manning (2003),
until recently most economists found it unlikely for employers to exercise
market power other than in small pockets and under specific circumstances.
Partly, this assessment was based on particular circumstances of minimum wage
adjustment an the following labour market reaction, which was not thought in
line with theoretical predictions (see, for instance, Neumark and Shirley,
2021, and the examples studied therein). Nevertheless, a substantial body of
research has developed in documenting the (country) circumstances and types of
jobs for which monopsony could be empirically established. Before presenting
our own method and results, we therefore delve into an overview of the
existing evidence in the following.

###  2.1 What is labour market monopsony and why do we care?

Labour market monopsony was first described and discussed by Joan Robinson
(1969) and refers to a situation where (a large group of) job seekers face a
single or few employers on the labour market, the latter situation also being
described as oligopsony. In practice, a single firm demanding labour might
seem to be rare but different configurations can arise – for instance when
spatial mobility is limited, few big companies collude or job seekers have
very specific profiles for which only few jobs exist – effectively limiting
competition between potential employers for workers.

In practice, any situation in which the elasticity of (labour) supply is not
infinity – and hence shifts in the labour demand curve affect the wage a
company has to pay – allows a company to excercise some power in setting the
wage rather than being a wage taker as would be the case under perfect
competition. This is true even in the case when short- and long-run
elasticities of labour supply differ and where the long-run labour supply
would be perfectly elastic (Boal and Ransom, 1997, p. 94). Such inelastic
supply can arise for several reasons, other than one single firm - or a small
number of colluding ones - offering jobs. For instance, when (geographic)
mobility is costly or (legally) restricted, hiring costs increase with wages.
The latter occurs, for instance, through occupational licensing, which - while
protection specific occupations - has adverse effects on the market power of
workers in occupations with similar skill and task profiles (Dodini, 2020).
Similarly, when skills and competencies are only imperfectly substitutable,
labour services become differentiated and workers face monopolistic
competition for their offer (Card et al., 2018). In such a situation, dubbed
“dynamic monopsony” by Ashenfelter et al. (2010) as workers cannot switch
employers costlessly to exploit wage differentials, both the separation rates
amd recruitement probabilities depend on wages and firms can exploit an
inelastic labour supply (Manning, 2003, 2020).555The dynamics here come from
the consideration of worker flows, not from any difference between long- and
short-term labour supply elasticities.  Importantly, such situations of
imperfect substitutability might arise more frequently as workers acquire more
job-specific skills that cannot easily be used elsewhere (Bachmann et al.,
2020).666“We find that workers performing mostly non-routine cognitive tasks
are exposed to a higher degree of monopsony power than workers performing
routine or non-routine manual tasks Job-specific human capital and non-
pecuniary job characteristics are the most likely explanations for this
result” Finally, jobs might not only be differentiated according to the skills
they require but also regarding the amenities and perks employers offer to
their workers and which might appeal to them differently because of preference
heterogeneity (see Manning, 2020, for a discussion and synthesis of these
different approaches).

Labour market monopsony - similar to other forms of deviations from perfectly
competitive markets - have significant implications for both efficiency and
equity considerations, some of which we will present here. First, in the
standard form of a static monopsony, firms typically tend to offer too little
employment at too low wages in comparison to perfect competition (Boal and
Ransom, 1997, p. 88; Benmelech et al., 2020). Partly, this is driven by the
lack of outside opportunities for job holders, which depresses their wages
(Bassanini et al.,
2019).777https://www.legos.dauphine.fr/fileadmin/mediatheque/recherche_et_valo/LEGOS/cv/publications/caroli_2020.pdf
A traditional answer to such inefficiencies is the introduction of a minimum
wage that allows to lift wages, thereby helping expand labour supply and
increasing employment. However, such conclusions need not hold when
considering search frictions as source of market power, and employment might
actually be inefficienctly high rather than too low, depending on the supply
elasticities of firms and workers. Most importantly, search frictions can
create thick-market effects with multiple (efficient) equilibria that can be
pareto-ranked (Manning, 2003, ch. 3). Monopsonistic competition might also
contribute to gender discrimination for which the higher propensity for women
to be hired out of inactivity might be one indication. Finally, monopsonistic
power tends to reduce firm investment in (general) training; as workers do not
receive their marginal product, they will also not have an incentive to invest
in their human capital to the (socially) optimal level, leaving the market
with less human capital than would socially be optimal.

Labour market monopsony and concentration has also adverse effect at the
macro-economic level. First, rising market concentration is associated with an
increase in wage inequality (Cortes and Tschopp, 2020) and a fall in the
labour income share (Berger et al., 2019). As increasing labour market
concentrations reduces market pressure, more inefficient firms survive in the
market for longer, depressing labour productivity (IMF, 2019; De Loecker and
Eeckhout, 2017; Banerjee and Hofmann, 2020; Jiang et al., 2017).888To the
extent that market concentration is driven by a rise in intangibles as
suggested by De Ridder (2019), such a link is more complex: An initial
increase of market concentration could follow the entry of highly innovative
companies that displace incumbents and build up market shares quickly due to
an increasing accumulation of intangibles. Once a certain market dominant
position has been reached, innovative activity will fall again and further
increases in market concentrations would be linked to a deceleration in
innovation and productivity.  Finally, with rising market concentration and
power, firms can shield themselves better against shocks, lowering the pass-
through of input prices and reducing the effectiveness of monetary policy
(Heise et al., 2020).

###  2.2 How to measure labour market concentration

Three main approaches have been used to measure the extent of monopsonistic
power by firms. A first strategy consists in measuring firm concentration, for
instance through an analysis of market share of the largest companies in a
particular country, sector or local labour market. Such an approach is
particularly useful when labour market information is scarce and does not
allow a more direct approach. Amodio et al. (2020), for instance, calculate
market concentration for 204 local labour markets in Peru and estimate a
strong negative impact of firm level concentration on wages, both for workers
in informal and formal employment. Similarly, Manning (2010) uses average
plant size estimates of local labour markets (commuting zones) to establish
the impact of firm concentration on wage premia. In particular, he finds that
higher plant sizes in agglomerations allow for labour market power to depress
wage premia in comparison to competitive wages in order to compensate for
congestion effects.

A second approach consists in estimating the elasticity of the (firm-specific)
labour supply. Indeed, when more detailed information is available, estimating
the elasticity of labour supply a firm faces allows to properly assess the
extend to which it can exercise monopsonistic power. As mentionned in the
previous section, a simple concentration of firms in a particular segment
might not be sufficient to precisely measure labour market power. Comparing
labour market concentration and labour supply elasticity Azar et al. (2019a)
confirm that both approaches - labour market concentration and labour supply
elasticity - are inversely related to each other and hence informative about
labour market power. Manning (2011, table 5) reviews the available evidence,
which refers to situations of quasi-experiments where (public) employers
document their hiring difficulties and the reaction of applicants to changes
in wages offered. Manning (2011, p. 1003) concedes, however, that the
resulting labour supply elasticities are too low to be credible, owning to the
specific circumstances of the estimates.

Instead, Manning (2003, p.44) offers a simple, alternative measure of the
degree of monopsony power using the standard search and matching framework:
Under the assumption of such a model, hiring out of non-employment rather than
through job-to-job transitions increases the power of an employer to fix
wages. While this is an appealing approach when comparing measures over time
within a given country, cross-country comparisons of such a measure will be of
limited information given the institutional differences: Employers in the
United States, for instance, tend to lay-off and re-hire workers during
downturns much more frequently than their German counter-parts who make use of
a specific instrument called “Kurzarbeit” that allows firms to suspend wage
payments during (temporary) periods of hardship without laying those workers
off.

A third approach to estimating labour market power consists in setting up a
structural model to simultaneously estimate the demand and supply curves on
relevant (local) labour markets. This is the most demanding approach of the
three in terms of data requirements. Ridder and van den Berg (2003), making
use of their estimated equilibrium search model developed in van den Berg and
Ridder (1998), derive estimates of labour market frictions for a selected
number of European countries and the United States. A key challenge of this
approach relates to the fact that tenure and worker flows might be determined
by characteristics of the job itself. For instance, they might be conditional
on a job’s wage. Often such information is not readily available, even from
micro data (we will get back to this point below). In case, only aggregate
information is available, Ridder and van den Berg (2003) also analyse the
unconditional approach, where job characteristics do not influence tenure and
worker flows.999This corresponds to the basic formulation of the search and
matching framework, where job separation rates are exogenous. The
unconditional approach despite being less demanding in terms of data is,
however, sensitive to the institutional features of the wage setting process
and might not yield robust estimates that are comparable over time or across
countries.

Finally, an indirect measure can be used by estimating the impact of a change
in the minimum wage. For instance, a high degree of monopsony has been used to
explain posive employment effects in fast-food restauration after the increase
in the New Jersey minimum wage in 1992 as documented by Card and Krüger
(1995). Alternatively, in the absence of observing an increase in employment
when minimum wages are introduced or raised, researchers have concluded that
the degree of monopsony in that specific labour market segment must be low or
absent (Neumark and Wascher, 2008; Neumark and Shirley, 2021).101010See also
the discussion here: https://voxeu.org/article/employment-effects-minimum-
wages-directions-research As noted by Manning (2003), however, the observed
relationship between the introduction of a minmum wage and changes in
employment might depend on the specific market characteristics: Under the
assumption of free entry of firms, for instance, an increase in minimum wages
can lead to both increases or decreases in employment, even in a situation of
monopsony. In other words, the competitive equilibrium and a situation with
monopsony would be observationally equivalent even if the introduction of a
minimum would still be socially efficient in the latter case.

###  2.3 What do we know about labour market concentration?

In the following we give a brief overview of some estimates of labour market
concentration, both across countries and occupations. For a meta analysis of
the available empirical analysis across more than 100 studies, we refer to
Sokolova and Sorensen (2021).

Boal and Ransom (2002) summarise historical estimates of labour market power
for selected occupations in the United States (see table 1). Even though
individual observations refer to different time periods and might, therefore,
not be comparable, the table shows significant variations across occupations.
Importantly, labour market power does not only seem to affect low-skilled
workers and depends significantly on contractual clauses as in the case of
baseball players subject to reserve clauses.

Table 1: Degree of monopsony, selected occupations, United States

Labor market |  Estimated rate of monopsonistic exploitation |  Source
---|---|---
Baseball players subject to reserve clause |  $100\%-600\%$ |  Scully (1974), Kahn (2000)
Baseball players not subject to reserve clause |  $\simeq 0$ |  Zimbalist (1992)
Teachers and nurses |  $\simeq 0$ |  Boal and Ransom (2000), Hirsch and Schumacher (1995)
University professors |  $<5\%-15\%$ |  Ransom (1993)
Coal miners in early twentieth century |  $<5\%$ |  Boal (1995)
Textile mill workers in the nineteenth century |  >0 |  Vedder, Gallaway, and Klingaman (1978), Zevin (1975)
Labor market in general |  $1\%-3\%$ |  Brown and Medoff (1989)

Source: Boal and Ransom (2002), the paper and all references cited in the
table area available at: http://eh.net/encyclopedia/monopsony-in-american-
labor-markets/

More recent approaches focus on the analysis of concentration indices and
their estimated effect on wage elasticities. For instance Azar et al. (2020a)
estimate concentration indices for local occupational labour markets, using
commuting zones as a spatial delineation for local labour markets. Using data
from online vacancy postings, they estimate concentration indices for 8000 US
local occupational labour markets and document important effects of these
concentration indices on posted wages, suggesting a significant degree of
labour market power. Using a slightly different data source for online vacancy
postings from Burning Glass, Azar et al. (2020b) also document significant
differences between labour market vs product market concentration indices,
with the former significantly lowering wages. Guest workers in the US have
been shown to experience degrees of monopsonistic power that reduces their
wages by up to 13% in comparison to a fully competitive market (Gibbons et
al., 2019). Similarly, for France, Marinescu et al. (2020) suggest to use a
Herfindahl concentration index for local (occupational) labour markets with
location identified at the 4-digit occupational breakdown. Using linked
employer-employee data, they calculate concentration indices for both firms
and workers as two separate sources of monopsony power. In order to identify
sector-specific effects of their concentration indices, they run simulations
assuming company mergers in individual sectors. In aggregate, the authors
document a significant impact of an increase in labour market concentration on
employment, but less so of product market concentration. The authors document
significant sectoral differences based on their simulation study, with effects
largest in retail trade but also building maintenance. Moreover, they
demonstrate the existence of industry-spillovers from a rise in sectoral
labour market concentration to job loss in other industries.

Using census and survey data of US manufacturers, Hershbein et al. (2019)
suggest a direct measure of labour market power by analysing the difference
between the output elasticity of (plant-level) employment and the labour share
in a firm’s total cost, i.e. a firm’s markdown. In fully competitive markets,
this ratio should be one, corresponding to the equality between the marginal
product of labour and wages. In contrast, the authors find large deviations
with workers earning on average only 65 cents for each dollar produced.
Aggregate estimates of markdowns according to this methodology declined from
the 1970s to the early 2000s before sharply rising again until 2012, above its
level observed at the beginning of the series.

With the rise of labour market platforms (online platforms, gig work),
research has focused on how this has affected labour market power. _Prima
facies_ , labour market platforms are highly competitive as on both sides of
the market, buyers and sellers of labour market services bid for the best
offer and easily switch. In reality, however, labour market intermediaries fix
the conditions besides taking a significant cut for their “intermediation”
services thanks to incomplete information (Kingsley et al., 2015). Dube et al.
(2020), running several experiments on the Amazon Mechanical Turk online
labour platform, confirm that labour supply elasticities are, indeed, low.
This applies to both recruitment elasticities - hiring workers for specific
tasks - and retention elasticities, i.e. keeping workers for additional tasks.

The introduction or (local) variation of minimum wages has also been exploited
in other countries to assess the degree of labour market monopsony. In
Germany, for instance, a minimum wage was first introduced in 2015. This
allows Bachmann and Frings (2017) to use a semi-structural estimation approach
with linked employer-employeed data to assess the degree of monopsonistic
power in different low-wage industries. They document large sectoral
differences, with accommodation and restaurants displaying high employer
labour market power whereas little employers in low-wage manufacturing (e.g.
food production) have little labour market power. Rather than studying cross-
sectoral differences, Azar et al. (2019b) focus on the retail sector
specifically, analysing local labour market concentration indices calculated
on the basis of online job postings and exploiting state-level variations in
minimum wages in the US. They document that more highly concentrated have a
significantly lower employment elasticitiy with respect to an increase in
minimum wages, with the most highly concentrated local labour markets even
having a positive employment elasticity with respect to an increase in the
minimum wage.

##  3 Data and methods

###  3.1 Data

####  3.1.1 United States

Labour force information for the United States comes from the Integrated
Public Use Microdata Series (IPUMS) of the Current Population Survey
(CPS).111111The US micro-data was gathered from IPUMS-CPS web site
https://cps.ipums.org/. Relevant for our analysis, the US CPS contains
information on labour force status, employment status, hours worked, age, sex,
education attainment, industry, wage and salary income, region (location) and
length of tenure in current job.

Detailed tenure information is essential for our analysis but is available
only ever other year. The information is collected in a supplementary survey
in January of that year. We chose to select information over the past decade
from the following years: 2010, 2012, 2014, 2016, 2018 and 2020.

To match the underlying assumptions of Ridder and van den Berg (2003), only
full-time wage workers are selected into our sample i.e. we drop the employed
labor force that worked less than 35 hours per week. Wage workers aged between
15 and 64 years are included in our sample.

####  3.1.2 Peru

For Peru, we use the Peruvian National Household Survey (Encuesta Nacional de
Hogares, ENAHO) for years 2014-2018 as our micro-data source. The ENAHO
contains information related to education, health, income, wealth, physical
assets and other social aspects of households and individuals. This survey
also includes a labor market specific module, the main source of our study. In
order to segment the labor market, we retain three key variables from the
survey: Economic sector, age (a proxy of experience) and education level. The
estimation of the monopsonistic competition index requires two additional
variables from the survey: Monthly wages (in Peruvian soles) and the elapsed
employment spell (in years). To comply with the methodological framework in
Ridder and van den Berg (2003) , we exclude self-employed individuals and
informal salaried workers from our sample.

###  3.2 Estimating labour market frictions

In this subsection we discuss our methodology of estimating labour market
power. We make use of the methodological framework developed by Ridder and van
den Berg (2003) but adapt it to the labour market information at our disposal.
In the following we discuss our preferred approach. In annex B we also present
an alternative approach that is less demanding in terms of the required input
data. In annex C we apply this approach to another country, France, and
demonstrate its short-comings.

####  3.2.1 The conditional inference estimation of labour market frictions

Our preferred approach builds on an structural model whose equilibrium
conditions depend on the distribution of offered $F\left(w\right)$ versus
observed $G\left(w\right)$ wages. Under the model assumptions two parameters
are key: The arrival rate $\lambda$ (per unit of time) at which workers
receive wage offers and the layoffs rate $\delta$ (per unit of time). Thus,
the observed wages distribution writes as:

$G\left(w\right)=\frac{F\left(w\right)}{1+k\left(1-F\left(w\right)\right)}$

where $k\equiv\lambda/\delta$ stands for the average number of job offers in a
given spell of employment. This can be interpreted as a labour market friction
index with higher values of $k$ implying less frictions. Indeed, as employees
have more opportunities to switch with more jobs being offered, the frictions
they face on the labour market decline. From the previous condition, the
following steady state relationship between the expected elapsed employment
spell (left-hand side) and the observed wages distribution arises:

$\frac{1}{\delta+\lambda\left(1-F\left(w\right)\right)}=\frac{1}{\delta\left(1+k\right)}+\frac{k}{\delta\left(1+k\right)}G\left(w\right)$
(1)

where $\delta+\lambda\left(1-F\left(w\right)\right)$ is the hazard rate of the
distribution of elapsed job durations. It is also interpreted as job exit rate
for workers earning $w$. The reciprocal provides an alternative expression to
the hazard rate of elapsed durations:

$\delta+\lambda\left(1-F\left(w\right)\right)=\frac{\delta+\lambda}{1+k\cdot
G\left(w\right)}$

####  3.2.2 Linear regression (semi-parametric) estimation

Labour market frictions are identified by the parameter $k$, which can be
estimated from the equation (1) above. Its left hand side is interpreted as
the average elapsed employment spell at a given wage level. This steady state
condition depends on the right hand side determinants and parameters where
$G\left(w\right)$ is the cumulative density function of observed wages. Thus,
adding an error term to the theoretical relationship yields uni-variate linear
model $y=\beta_{0}+\beta_{1}x+u$ such that
$y\equiv\frac{1}{\delta+\lambda\left(1-F\left(w\right)\right)}$ and $x\equiv
G\left(w\right)$ from which $k$ is easily identified without distributional
assumptions by $\beta_{1}/\beta_{0}$.

The caveat of this approach relies on its dependence on observed wage micro-
data. In the following, we illustrate this procedure with data for the
Peruvian panel of individuals in 2018, from which 12070 elapsed employment
spells were observed along with their deflated monthly wages.121212The same
approach has been used for US data and all other years. The sample is the
formal salaried labour force aged between 15 and 65 years old. The empirical
distribution of job spells and (log) wages is illustrated below:

Figure 1: Distribution of job spells and wages

Panel A: Job spells | Panel B: Monthly wages
---|---
|
Panel C.: Elapsed employment and wages

Source: ENAHO 2018, own calculations

As illustrated by the smoothing spline (blue line) in panel C in figure 1, the
relationship between elapsed employment and wages can reasonably be
approximated by a linear function. Estimating equation 1, our index of labour
market frictions $k$ can then be retrieved as the ratio of the slope and
intercept; its variance can be retrieved by the delta-method:

Table 2: Semi-parametric estimate of labour market frictions $k$ | Estimate | S.E. | 2.5% | 97.5 %
---|---|---|---|---
k | 2.4220162 | 0.1773811 | 2.0743556 | 2.7696767
$\delta$ | 0.0687030 | 0.0008862 | 0.0669661 | 0.0704398
$\lambda$ | 0.1663998 | 0.0108541 | 0.1451262 | 0.1876733

####  3.2.3 Duration estimation

Instead of using a semi-parametric approach, we also use a parametric approach
on the basis of a duration model, which is vowed to be more efficient (i.e.
displays lower variances) as it exploits information on the distribution of
employment tenure spells. Elapsed employment duration ($t_{e}$) may be
accurately represented by an exponential distribution:

$f(t_{e})=\theta_{x}\exp(-\theta_{x}\,t_{e})$

where $\theta_{x}$ represents the hazard function. Alternatively, it can be
interpreted as the expected number of job interruptions per unit of time or
the inverse of the expected elapsed employment duration. $\theta_{x}$ may be
conditioned on a set of explanatory variables ($x$). From Ridder and van den
Berg (2003)’s model, the hazard function is defined by the right hand side of
equation (2) as a function of the CDF of wages ($G(w)$):

$\theta_{x}:=\frac{\delta+\lambda}{1+kG(w)}$

Thus, the likelihood function for the non-censored i-th individual duration is
simply defined as $\ln\theta_{x}-\theta_{x}\,t_{e}$. Introducing censoring
implies that complete employment spells might not be observed for some
observations. For instance, our complete sample of Peruvian workers is
censored with respect to a complete employment spell. We could write its
likelihood from the probability of having a complete employment spell noted
$\tilde{t}_{e}$ that is longer than the observed elapsed employment duration:
$P[\tilde{t}_{e}>t_{e}]=1-F(\tilde{t}_{e})$. In practice, the latter model
parameters cannot be identified without a complementary sample of non-censored
observations. Combining the sample of censored ($C$) and non-censored
observations ($\bar{C}$) yields the log-likelihood function :

$\sum_{i\,\epsilon\,\bar{C}}[\ln\theta_{x_{i}}-\theta_{x_{i}}t_{e_{i}}]-\sum_{i\,\epsilon\,C}\theta_{x_{i}}\,t_{e_{i}}\equiv\sum_{i\,\epsilon\,\bar{C}}\ln\theta_{x_{i}}-\sum_{\forall
i}\theta_{x_{i}}t_{e_{i}}$

The structural parameters $\lambda$, $k$ and $\delta$ are implied in
$\theta_{x}$. The following table 3 provides an overview of the (maximum
likelihood) estimates of the labour market frictions index ($k$) without
censoring (0) and under three alternative (arbitrary) censoring levels (40, 20
and 10 years):

Table 3: Parametric estimates at different censoring levels | Estimate | S.E. | 2.5% | 97.5 %
---|---|---|---|---
k(0) | 2.390970 | 0.1159610 | 2.163690 | 2.618249
k(40) | 2.416392 | 0.1172191 | 2.186646 | 2.646137
k(20) | 3.679716 | 0.1732006 | 3.340250 | 4.019183
k(10) | 4.893570 | 0.2387799 | 4.425570 | 5.361570

####  3.2.4 Parametric vs semi-parametric estimation

Even though the parametric relation imposes a distributional assumption, it is
a widely accepted one i.e. durations tend to be well represented by
exponential distributions as can be seen be the kernel density presented above
(Job spell empirical distribution). This implies a gain in efficiency (higher
precision). Identification from the linear regression may also be distorted by
the non-linear slope of the empirical relationship. In an auxiliary estimation
(available upon request) that included informal workers, the parametric
estimator proved to be more robust than the semi-parametric one. Including
informal workers causes the relationship between elapsed employment and wages
to exhibit a higher slope for values of $G(w)$ greater than 0.75. Furthermore,
the parametric estimates stay plausible in the presence of informal
employment. The parametric estimation is therefore the preferred estimation
approach based on the micro-data at hand.

###  3.3 Conditional inference of labour market frictions

Returning to our conditional approach, we now implement the conditional
approach on US and Peru’s formal salaried labour force from 2014 to 2018 using
a linear regression and duration model approach respectively. As mentioned
above, the parametric approach is our preferred estimation. Nevertheless, in
this subsection we also implement the linear regression while addressing for
the potential effects of outlying observations in the data. This is done by
means of a robust (to outliers) linear regression which down-weights
observations whose residuals are too important.

####  3.3.1 Peru: 2014-2018

Figure 2 below compares the robust linear regression and parametric estimates
where error bands represent the 95% confidence intervals. As can be seen, the
parametric estimator is more stable across time; the magnitudes are coherent
with estimates by (Ridder and van den Berg, 2003) for developed countries.

Figure 2: Comparing semi-parametric and parametric estimates of labour market
frictions

(Peru: 2014-2018)

Source: ENAHO, own calculations, various years

####  3.3.2 United States: 2010-2020

Panel A in figure 3 reports the estimates of the linear model, both using a
standard linear regression (OLS) and a robust to outlying observations
regression. Panel B reports estimates using the parametric approach for
different censoring values (see discussion above). The heterogeneity between
the censored estimations suggests that shorter tenures (likely associated to
younger workers) correlate with more frequent job offers during an employment
spell. Overall, the results suggest that $k$ exhibits a slight decreasing
trend with values from the linear estimation comprised between 1.2 and 1.6.,
in line with Ridder and van den Berg (2003)’s earlier estimates for France
(1991) that stood at $k=1.4$.

Figure 3: Comparing semi-parametric estimates of labour market frictions

(United States: 2010-2020)

Panel A. Linear | Panel B. Parametric
---|---
|

Source: US CPS, own calculations

##  4 Comparing labour market power in the US and Peru

Using the conditional estimates of labour market frictions, we can now derive
a labour market monopsony indicator for the US and Peru. The advantage of this
methodology as discussed in the previous section is that is allows us to
calculate labour market power for specific segments of the labour market,
taking cross-market effects into account. In our set-up, these segments are
defined as on the assumption that labour supply is not expected to switch
between segments. Following van den Berg and Ridder (1998) we define such
segments of the labour force according to the following criteria:

  * •

For Peru: Economic sector (CIIU 1-digit, rev.4), potential experience (4 age
groups) and education level (primary or less, secondary education, technical,
and undergraduate or above);

  * •

For the United States: Industry, educational level (2 groups), region and
gender.

To avoid unreliable estimates due to the small size segments, only those with
at least 30 observation are reported (around 60 segments). From van den Berg
and Ridder (1998), the monopsonistic competition indicator for a given segment
is defined as:

$\mu=\frac{E\left(w\right)-E\left(\underline{w}\right)}{\left(1+k\right)E\left(w\right)-E\left(\underline{w}\right)}$

where $E\left(w\right)$ and $E\left(\underline{w}\right)$ are the expected
wage and wage distribution lower bound respectively. Compliance with labour
regulations for low productivity workers suggest that
$E\left(\underline{w}\right)$ should be given by the institutional minimum
wage whereas for high productivity workers $E\left(\underline{w}\right)$ may
best be described by a reservation wage that is likely to be higher than the
institutional minimum wage. Moreover, in the case of Peru, compliance with its
minimum wage legislation is likely to be low and, consequently, the threshold
provided by the (legal) minimum wage is not binding.

In their approach van den Berg and Ridder (1998) provide a structural model
that allows the estimation of $E\left(\underline{w}\right)$. However, such
estimation is vulnerable to the structure imposed to the data and data
measurement errors. For the sake of parsimony, we estimate
$E(\underline{w}_{j})$ as the wage distribution lower bound given by a boxplot
minimum estimator (lower whisker) well adapted to symmetric distributions.
This is calculated from observed wages in log scale which tend to be
symmetric. The literature of Extreme Value statistics provides alternatives
estimators that could be explored further.

The mechanisms that determine the lower bound $E\left(\underline{w}\right)$ of
the wage distribution are expected to be heterogeneous across countries
depending on labour market compliance and productivity levels. Our
implementation makes no prior assumptions regarding institutional factors that
determine certain segments minimum wages.

###  4.1 The evolution of labour market power in Peru

For the years 2014 through 2018, figure 4 displays the evolution and standard
error of our aggregate monopsony estimate, $\mu$, for Peru, showing a tendency
of market power to decline over the previous decade. This is the flipside of
the decline in market frictions (or the increase in job offers per employee)
indicated in figure 2 above.

Figure 4: Monopsonistic indicator: Peru - 2014-2018

Source: Enaho, own calculations.

Peru’s aggregate estimates of $\mu$ are well above the magnitude found by
Ridder and van den Berg (2003) for OECD countries in the late 1990s. This is
somewhat an expected result since Peru’s labour market friction index is lower
than the OECD ones reported in Ridder and van den Berg (2003), i.e. the number
of job offers per employee is much lower. Furthermore, a higher prevalence of
labour market monopsonistic power is consistent with high levels of income
inequality in Peru and other Latin-American countries.

The drop in labour market monopsony is also reflected in the aggregate
performance of the Peruvian labour market that observed a gradual decline in
its informality rate over the 2010s. At the end of the decade, Peru’s
informality rate had fallen roughly 8 percentage points since 2010, opening up
new employment opportunities and faster transition rates to formal employment
during that decade. On the other, unemployment rates have been overall very
low during the decade (less than 4%) and most likely did not play an important
role in influencing employers’ labour market power. On the other hand, the
strong macro-economic performance prior to the outbreak of the Covid pandemic
in 2020 contributed most likely to strong employment growth in the formal
economy, with knock-on effects on labour market power. Indeed, Peru performed
well above its regional neighbours during the entire decade of the 2010s (see
ILO, 2019).

At the same time, this fall in labour market monopsony hides significant
heterogeneity across different labour market groups (see figures 5 and 6).
While the general tendency to a decline in monopsony power is confirmed in all
charts across different labour market segments, it seems that younger, less
well educated (formal sector) workers in agriculture tend to experience lower
monopsonistic wage setting behaviour than graduates in services sector,
irrespective of whether services are private or public (government).

Young workers, in particular below the age of 21, seem to benefit from more
opportunities to switch jobs, which lowers employers’ market power. The same
goes for workers with less than secondary education (i.e. "primary"
education), most likely because their outside option in the informal economy
is larger than for workers with technical or university ("graduate")
education.

This finding fits well with the general characterisation of Peru’s labour
market as being "multi-segmented", a feature that it shares with many other
Latin American countries. Indeed, besides a lower segment related to
subsistence activities, many workers and companies prefer to switch to the
informal labour market in order to avoid taxation and regulation (Maloney,
2004). In such a labour market, low-skilled (and young) workers that have
opportunities in informal employment typically face low switching costs and
can command a higher share of their otherwise still meager salary.

In well paying sectors, however, such as mining or manufacturing such outside
options are typically not available. Consequently, labour market power by
employers is much higher in these sectors, regardless of age and experience
than when switching costs are low (see figure 6). Moreover, figure 6 also
demonstrates the significant barriers to (sectoral) mobility. Upward mobility
into better paying sectors such as mining or (formal) construction work is not
being observed in our sample for workers with less than secondary education
(first row). At the same time, no downward mobility is observed for workers
with tertiary education ("graduates") into (formal sector) agricultural work.
Finally the similar profile of monopsonistic market power for workers above 20
suggest that barriers to mobility are being erected early on in one’s
professional life and subject to very little variation over worker’s career
path (see figure 5, panel B).

A full decomposition of of the contribution of different labour market groups
and the historical trend to our labour market monopsony estimate is available
in table A.2 in annex A.

Figure 5: Peru: Monopsony by age and education

Panel A.: Evolution of monopsony by education

Panel B.: Evolution of monopsony by age

Note: Youth=15-20 years; Young adults=21-30; Prime adults=21-45; Older
workers=46-65. Source: ENAHO, own calculations

Figure 6: Peru: Monopsony indicator - by age, education and sector

Note: Youth=15-20 years; Young adults=21-30 years; Prime adults=21-45 years;
Older workers=46-65 years.

Source: ENAHO, own calculations

###  4.2 The evolution of labour market power in the US

Figure 7 displays the aggregate evolution of labour market power in the United
States from 2010 through 2020 as well as the confidence interval of our
estimates. As discussed, the monopsony indicator $\mu$ can only be calculated
every two years because of data limitations concerning job tenure information.
After an initial drop at the beginning of the decade - linked to the recovery
process after the Global Financial Crisis - our labour market power indicator
shows a clear upward trend, the flip side of the increase in labour market
frictions documented by our estimates in figure 3. The estimates are
relatively precise and indicate that labour market power in 2020 is
(statistically) significantly above the level at the beginning of the decade.

This evolution is inline with findings from other works, including regarding
the evolution of labour income shares (Elsby et al., 2013; Karabarbounis and
Neiman, 2014), Gini coefficients (Horowitz et al., 2020), mark-ups (De Loecker
and Eeckhout, 2017) or Herfindahl indices regarding labour market
concentration (Azar et al., 2020b) such as those presented in section 2. It
also points to the fact that the longest but also weakest recovery in post-War
US employment was accompanied by rising market power, which might have been
instrumental in the relatively slow rate of job creation. Indeed, by early
2020, the employment-to-population ratio still had not recovered to 2007
levels and the unemployment rate needed 8 years to return to pre-recession
rates, significantly longer than after previous downturns.131313See, for
instance, https://irle.berkeley.edu/the-post-recession-labor-market-an-
incomplete-recovery/

Figures 8 and 9 give some further details regarding the sources of these
developments. The left panel of figure 8, for instance, shows that the college
income and wealth gap discussed by Bartscher et al. (2020) is most likely not
related the differential developments in labour market power. Moreover, in
contrast to the situation in Peru discussed above, graduates face a much more
fluid labour market that allows them to avoid employers’ labour market power.

Figure 7: Monopsonistic indicator: United States - 2010-2020

Source: CPS, own calculations.

Figure 8: Monopsonistic indicator: United States - 2010-2020

Source: CPS, own calculations.

Figure 9: Monopsonistic indicator: United States - 2010-2020

Source: CPS, own calculations.

The right panel of figure 8 documents another interesting finding: Men seem to
face higher labour market power than women, most likely because of the
sectoral and occupational segregation that leads them to work more frequently
in labour market segments with where firms benefit from stronger labour market
power. In other words, the large gender pay gap document, for instance, in ILO
(2018) cannot be explained by differential exposure to labour market power
between men and women. Indeed, the report documents that both the raw and the
factor-adjusted monthly pay gap between men and women in the United States is
around 16%.

Figure 9 breaks down the evolution of labour market power in the US between
regions (upper panel) and sectors (lower panel).141414See figure A.1 in
appendix A for the geographical breakdown used here. The upper panel in figure
9 demonstrates persistent regional differences in the extent to which American
workers are exposed to employers’ market power. The cross-regional differences
exhibit similarities with the ones documented by (Azar et al., 2020b) although
our estimator does not permit as fine a geographical break-down as theirs.

The lower panel in 9 documents a (large) sectoral heterogeneity in the
exposure to labour market power, with some diverging trends in the second half
of the observation period. Interesting, the agricultural sector stands out as
showing faster increase in labour market power than other sectors. In contrast
to the Peruvian experience, public administration shows the lowest degree of
labour market monopsony, indicating that US employees have a much higher
degree of outside opportunities when working in public administration than
their Peruvian counter parts. Nevertheless, labour market power increases
there too and there is no sector that shows a divergence from the aggregate
trend.

Finally, and in order to better identify how and how much the various labor
market segments determine the monopsonistic index level, we decompose its
historical mean by means of a regression analysis. The explanatory variables
are the ones that define the segments themselves. Thus the coefficients are
interpreted as the specific contribution of a given category to the index
historical mean. Table A.1 in appendix A provides an overview of our
decomposition. The resulting detailed cross-segment evolution of labour market
monopsony in the US is illustrated in figure A.2 in appendix A.

###  4.3 Country comparisons

Peru and the United States show striking differences in both the evolution of
labour market power and the cross-section differences. This points to
significant differences in the way labour markets in both countries work. The
US labour market shows a high degree of fluidity with little protection of
workers on open-ended contracts. As a consequence, labour market power is felt
similarly across different levels of education - and hence skill premia are
driven by different factors - and a function of of geographical and sectoral
conditions. In contrast, Peru experiences a highly segmented labour market
with barriers to entry for informal workers. Interesting, this seems to limit
mobility options particularly for high-skilled workers who experience very few
opportunities to switch sectors or occupations.

Going back to the earlier estimates for OECD countries established by Ridder
and van den Berg (2003), reported estimates for $\mu$ typically are below
0.05. In contrast, our estimates for both the United States and Peru are well
above such magnitude. This is somewhat an expected result since its labour
market friction index is lower than the OECD ones reported in Ridder and van
den Berg (2003). Furthermore, a higher prevalence of labour market
monopsonistic power is consistent with high income inequality trends in Peru
and other Latin-American countries. Similarly, the United States experience
inequality levels well above other OECD countries, and has seen a stark
increase over the 2010s, much faster than some European competitors.

##  5 Conclusion and discussion

The paper analyses and documents trends in labour market power, estimating the
degree of monopsony on labour markets in the United States and Peru over the
decade between 2010 and 2020. It documents diverging trends between the two
countries as well as significant heterogeneity across labour market groups.
The sources of heterogeneity differ, however, between the two countries, with
large differences in labour market power depending on educational attainment
in Peru and stronger cross-sectoral differences in the United States.

A possible extension of our work would be to document similar trends in other
OECD countries, notably in Europe. Unfortunately, European labour force
surveys do not provide sufficient details on completed job spells that would
allow for stable estimates of the wage distribution for job stayers in
equation (1). This might require additional assumptions regarding their
distributional form, which would have to be validated in each specific case.

Further research could link our estimates for labour market power to a
detailed analysis of the implied wage premium. In particular, the fact that
some of the trends and cross-segment differences that we document are not well
born out in other indicators (college income gap, gender pay gap), might
require a careful analysis of the different drivers of inequality between
groups within countries. Moreover, the opposing trends observed in Peru in
comparison to the US suggest that different countries experience significantly
different forces shaping their inequality dynamics, at least as regards labour
market power. These are interesting aspects that should be taken up by follow-
up research.

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  * Sokolova and Sorensen (2021) Sokolova, A.; Sorensen, T. 2021. “Monopsony in labor markets: A meta-analysis”, in ILR Review, vol. 74, no. 1, pp. 27–55.
  * van den Berg and Ridder (1998) van den Berg, G.J.; Ridder, G. 1998. “An empirical equilibrium search model of the labor market”, in Econometrica, vol. 66, no. 5, pp. 1183–1221.

## Appendix

### A. Tables and charts

#### Decomposition of labour market power in the US

Table A.1 Predictor | Coefficient | Standard error | t | p-value
---|---|---|---|---
Intercept | 0.348 | 0.003 | 118.04 | 0.000
Dummy(year=2012) | -0.021 | 0.002 | -10.62 | 0.000
Dummy(year=2014) | 0.019 | 0.002 | 9.77 | 0.000
Dummy(year=2016) | 0.018 | 0.002 | 9.41 | 0.000
Dummy(year=2018) | 0.041 | 0.002 | 21.79 | 0.000
Dummy(year=2020) | 0.055 | 0.002 | 28.59 | 0.000
Education
University degree | 0.006 | 0.001 | 4.84 | 0.000
Demography
Gender (women) | -0.013 | 0.001 | -11.40 | 0.000
Geographic regions
East South Central Division | 0.001 | 0.003 | 0.23 | 0.820
Middle Atlantic Division | 0.001 | 0.002 | 0.41 | 0.685
Mountain Division | 0.001 | 0.002 | 0.48 | 0.633
New England Division | -0.001 | 0.002 | -0.42 | 0.671
Pacific Division | 0.011 | 0.002 | 4.85 | 0.000
South Atlantic Division | 0.009 | 0.002 | 4.24 | 0.000
West north Central Division | -0.004 | 0.002 | -1.87 | 0.062
West South Central Division | 0.003 | 0.002 | 1.38 | 0.168
Economic sectors
Business and repair services | -0.029 | 0.003 | -11.03 | 0.000
Construction | -0.030 | 0.003 | -9.01 | 0.000
Entertainment and recreation services | -0.035 | 0.005 | -6.91 | 0.000
Finance, insurance and real state | -0.034 | 0.003 | -13.04 | 0.000
Manufacturing | -0.042 | 0.003 | -15.44 | 0.000
Mining | -0.038 | 0.006 | -5.87 | 0.000
Personal services | -0.037 | 0.004 | -8.77 | 0.000
Professional and related services | -0.030 | 0.003 | -11.74 | 0.000
Public administration | -0.063 | 0.003 | -24.25 | 0.000
Trans., Comm., and other utilities | -0.041 | 0.003 | -13.81 | 0.000
Wholesale retail trade | -0.020 | 0.003 | -8.08 | 0.000

#### Decomposition of labour market power in Peru

Table A.2 Predictor | Coefficient | Standard error | t | p-value
---|---|---|---|---
Intercept | 0.0833234 | 0.0297318 | 2.802504 | 0.0062646
Trend | -0.0071257 | 0.0039693 | -1.795223 | 0.0761310
Education
Secondary education | 0.0508233 | 0.0137307 | 3.701434 | 0.0003776
Technical education | 0.0363822 | 0.0139580 | 2.606558 | 0.0107787
Graduate education | 0.0748560 | 0.0137204 | 5.455820 | 0.0000005
Demography
Age(21-30 yrs) | 0.0945188 | 0.0257751 | 3.667053 | 0.0004242
Age(31-45 yrs) | 0.1002579 | 0.0258197 | 3.883002 | 0.0002019
Age(46-65 yrs) | 0.0934590 | 0.0256420 | 3.644762 | 0.0004573
Economic sectors
Mining | 0.0667916 | 0.0155412 | 4.297704 | 0.0000453
Manufacture | 0.0469357 | 0.0145092 | 3.234900 | 0.0017276
Construction | 0.0571660 | 0.0144110 | 3.966819 | 0.0001503
Commerce | 0.0563941 | 0.0143073 | 3.941629 | 0.0001643
Government | 0.0802094 | 0.0141042 | 5.686911 | 0.0000002
Services | 0.0687932 | 0.0140284 | 4.903843 | 0.0000044

#### Regional map of the US

Figure A.1: Regional map of the US

Source: https://i.redd.it/ks05v5y5tqq41.png

#### Detailed break-down of labour market power in the US

Figure A.2: Monopsony indicator - by age, education and sector: United States

## B. The unconditional approach to estimate labour market power

Given the high demand that the conditional approach imposes on data
availability regarding information on job characteristics, van den Berg and
Ridder (1998) develop an alternative theoretical framework for the
identification of the labour friction index based on grouped data. In
particular the authors discuss the identification of _k_ from each one of the
sub-populations of the labour force:

  * E-inflow

: those who transit from unemployment to employment

  * J-inflow

: those who perform job-to-job transitions

  * E-stock

: the employed labour force

Due to the empirical identification issues associated with an econometric
estimation based on each one of the above mentioned sub-populations, the
authors recommend to ease the identification of $k$ by estimating $\delta$
(the layoff rate) from an auxiliary model, which we replicate in the
following.

As it turns out, these estimations (from $E$-inflow and $J$-inflow
populations) are highly sensitive to country-specific institutional setups and
measurement errors, although they were expected to be more efficient. van den
Berg and Ridder (1998) do not test the estimation using the E-stock. Since we
plan to apply these methods to a wider set of countries wo do not replicate
the methods to estimate the $E$-inflows and $J$-inflows and concentrate on the
third (E-stock) which was expected to be less sensitive to the measurement
errors in the data, although less efficient. Unfortunately, this approach does
not provide plausible estimates when applied to our data for Peru. Nor does it
compare favourably with previous estimates for France.

### The auxiliary model for the layoff rate

The identification of the auxiliary model relies on the observed unemployment
rate, $U$, which can be decomposed into a structural unemployment rate, $q$,
and frictional unemployment:

$U=q+\left(1-q\right)\frac{\delta}{\delta+\lambda_{0}}$

From it, we define the share of structural unemployment with respect to total
unemployment as $\pi=q/U$. Consequently, the observed distribution of elapsed
unemployment durations $\Psi\left(t_{u}\right)$ can be expressed as a mixture
of structural and frictional unemployment distributions. This leads the
survival function $\overline{\Psi}(t_{u})$ to be written as a mixture of:

  * •

1 (single mass point distribution), this is the probability of being
unemployed after $t_{u}$. This should be one since this is the structural
unemployment probability.

  * •

and $\exp\left(-\lambda_{0}t_{u}\right)$, the probability of staying
unemployed after tu for those in frictional unemployment:

$\overline{\Psi}\left(t_{u}\right)=\pi+\left(1-\pi\right)\cdot\exp\left(-\lambda_{0}t_{u}\right)$

To operationalize the identification of $\lambda_{0}$ we first aggregate our
elapsed unemployment duration microdata as follows:

Table 4: Aggregating frequencies (ex. Peru - 2018 Duration class | (0,2] | (2,5] | (5,15] | (15,Inf]
---|---|---|---|---
Frequency | 856 | 876 | 199 | 56

### Parametric estimation of the layoff rate

The likelihood function for the aggregated data shown in the table above must
be defined by the probabilities of observing $t_{u}$ between the upper and
lower class ($p_{c}$) boundaries :
$p_{c}:=\Psi(t_{u_{up}})-\Psi(t_{u_{low}})$. Thus the grouped log-likelihood
function writes :

$\mathcal{\ln
L}=n\,\ln(1-\pi)+\sum_{i=2}^{k}n_{i-1}\ln\left[e^{-\lambda_{0}t_{u_{i-1}}}-e^{-\lambda_{0}t_{u_{i}}}\right]+n_{k}\,\ln[\pi+(1-\pi)e^{-\lambda_{0}t_{u_{k}}}]$

where the $t_{u_{i}}$ is the i-th class lower bound, $n$ is the total number
of observations and $n_{j}$ is the number of observations at the j-th class.
Having an open last class yields the likelihood last term, in it, $t_{u_{k}}$
represents the lower bound of the last open class. In this particular case,
the sum operator index ranges from 2 to $k=4$ to properly calculate the class
probabilities ($p_{c}$) in our unemployment duration data.

### Grouped E-stock estimation

In RvdB, alternative estimation strategies based on grouped data are proposed.
The authors mention the posibility of focusing on the $E$-inflow, $J$-inflow
and $E$-stock populations. $E$-inflow and $J$-inflow consist of workers that
transition from unemployment to employment, and from employment to employement
(job-to-job) at a given point in time respectively. It is argued the
employment durations will be described by different probability distributions.
In $E$-inflow and $J$-inflow, the random variable is the completed job spell.
Similarly, the $E$-stock populations consists of employed workers at a given
point in time whereas the random variable is the elapsed employment spell (not
the completed one). Since aggregated (grouped) data often makes difficult to
disentangle employment spells from $J$-inflow and $E$-inflow populations, here
we develop the estimation approach based on the $E$-stock sample. It should be
noted that RvdB developed $J$-inflow and $E$-inflow illustrations given the
higher efficiency (lower variance) of the implied parametric estimator.
Nevertheless, they also verify that such estimates are often non-plausible
given the measurement errors i.e. unavailability of pure $E$-inflow or
$J$-inflow samples in grouped data.

The elapsed employment duration $t_{e}$ from a sample of employed workers at a
given point in time has density function:

$\psi\left(t_{e}\right)=\frac{\delta\left(1+k\right)}{k}\int_{\delta}^{\delta\left(1+k\right)}\frac{e^{-z\cdot
t_{e}}}{z}\cdot dz$

From this we derive the cdf:
$\Psi\left(t_{e}\right)=\int_{0}^{t_{e}}\psi\left(t_{e}\right)dt_{e}$, which
allows us to set up the grouped data log-likelihood as the probabilities
associated to each class in the grouped data:

$\ln
L=n_{1}\ln\Psi\left(c_{1}\right)+\sum_{j=2}^{J-1}n_{j}\ln\left[\Psi\left(c_{j}\right)-\Psi\left(c_{j-1}\right)\right]+n_{J}\ln\left(1-\Psi\left(c_{J}\right)\right)$

where $c_{j}$ represent the lower bound of the $j$-th class interval in our
grouped data, $J$ is the number of groups and $n_{j}$ is the frequency within
the $j$-th category. This estimator is implemented using the elapsed
employment grouped data for Peru:

Figure 10: Elapsed employment duration (in years; Peru, 2018)

Duration | (0,1] | (1,3] | (3,5] | (5,10] | (10,20] | (20,30] | (30,40] | (40,50] | (50,Inf]
---|---|---|---|---|---|---|---|---|---
Frequency | 3040 | 2155 | 1306 | 1762 | 1759 | 1283 | 692 | 73 | 0

Using these stock and flow estimates allows us to obtain alternative estimates
for our labour market friction indicator (see table 5). As can be seen, the
$k$ parameter estimation is implausible which may be explained by its
intrinsic high variance (as motivated by Ridder and van den Berg, 2003) and
measurement (recall) errors for longer spells.

Table 5: Semi-parametric estimates of Peru’s labour market frictions $k$

(grouped data E-stock approach, 2018)
Estimate S.E. 2.5% 97.5 % k 2398.1467950 6.1766725 2386.0407392 2410.2528507
$\delta$ 0.0575756 0.0001542 0.0572733 0.0578779 $\lambda$ 138.0747365
0.3695809 137.3503713 138.7991018

## C. Extension for France

The micro data required for the calculation of our labour market monopsony
index are, in principle, available for a large range of countries, including
those in the European Labour Force Survey. One drawback that this survey has,
however, is that tenure information has been discretized and is not available
as continuous information as for the United States and Peru. Typically, only
four categories of tenure brackets are available. In the following, we
illustrate the adaptation of our procedure for France.

We use France’s Enquête du Travail (French LFS) where the workers’ tenure has
been discretized into four categories has been estimated. This required an
adaptation of the previous likelihood functions to consider the grouped nature
of the microdata. Although individual wages were available, the conditional
approach does not deliver plausible results (see table LABEL:tab:France
below). The discretization of the tenure data seems to cause an information
loss that penalizes the estimators stability properties. Only 2014 has a 95%
confidence interval that allows for some plausible values. Recall that in the
original estimation by Ridder and van den Berg (2003) France’s friction index
was about 5 for 1991.

To further check the computational accuracy of our estimator we test it using
French data for 1990 and 1991 and compare it with Ridder and van den Berg
(2003)’s estimates for the same years. The comparison cannot be exact since
the authors produced their estimations using their own unreported aggregations
from microdata, while we employ OECD grouped statistics:

Table 6: France: Labour market frictions index | Estimate | SE | 2.5 % | 97.5 %
---|---|---|---|---
2010 | 0.0000091 | 0.0172834 | -0.0338658 | 0.0338839
2012 | 0.0000038 | 0.0100533 | -0.0197003 | 0.0197080
2014 | 0.2165852 | 2.0737412 | -3.8478729 | 4.2810433
2016 | 0.0000467 | 0.0774138 | -0.1516815 | 0.1517749
2018 | 0.0000308 | 0.0449509 | -0.0880715 | 0.0881330

Both the level and time variation of our labour market friction index is
substantially higher than either the index produced by Ridder and van den Berg
(2003) and our estimates for the US and Peru reported above. This indicates
that the grouped tenure data do not allow a proper application of our
estimation methodology to the publicly available French micro data.