The own-skill-group effect of emigration on source
country real wages: An analysis of Jamaican emigration
Thesis submitted in partial fulfilment of the requirements for the Degree of Master
of Science in Economics for Development at the University of Oxford
Dan Brown
Supervisor: Professor Paul Collier
Date: 01/06/12
Candidate Number: 206416
Word Count: 9,678 (Excluding title page, abstract and references: 31 pages, with
309 words on an average ‘all-text’ page (p.31) + 99 words on p.33)
Abstract
This extended essay contributes to the nascent literature investigating the ownskill-group effect of emigration on real wages in source developing countries.
After presenting a new, simple neo-classical general equilibrium theoretical
model to distinguish own-skill-group from cross-skill-group real wage effects
and their likely sign, it augments the existing empirical analysis by using a more
precise skill-group classification and more thoroughly evaluating the robustness
of estimates; considering the previously unstudied case of Jamaican emigration.
Fixed effects two-stage-least-squares estimates suggest an emigration-induced
10% reduction in the Jamaican labour force in a skill-group increases real wages
of remaining workers in that skill-group by 4.34%.
1. Introduction
Barriers to international migration perhaps constitute the largest remaining
distortion to an increasingly integrated world economy. As such, the associated
global efficiency losses are huge; Clemens claims that ‘when it comes to policies
that restrict emigration, there appear to be trillion dollar bills on the sidewalk’
(p.1 Clemens (2011)).
Clemens (2011) presents a simple diagrammatic analysis of the effects of
migration of workers from a low-wage developing to high-wage developed
country in a neo-classical two-factor (‘land’ and homogeneous ‘labour’) model.
Assuming diminishing returns to labour:
2
Figure 1: Clemens’ diagrammatic analysis:
A relaxation of international migration barriers such that emigration results in a
reduction of the developing country labour force from L1 to L2 brings a gain of
area c+b to the migrants themselves (receiving a real wage MPLH2 rather than
MPLL1), a loss of area e to developed country workers from the lower real wage
MPLH2 (from MPLH1), a gain of area e+d to owners of the fixed factor land in the
developed country, losses of a+b to developing country landowners, and gains of
area a to developing country workers through the higher real wage MPLL2 (from
MPLL1). We therefore observe net global efficiency gains of area (c+d), alongside
distributional effects between owners of different factors of production in both
the developed and developing country.
The size of the net global efficiency gains is increasingly well documented. For
example (with respect to the size of area c), Clemens, Montenegro and Pritchett
(2010) find that a 35-year-old urban male Jamaican worker with 9 years of
Jamaican education could earn between 329 and 363% of his wage by moving to
the US. The literature regarding the distributional effects of immigration for
recipient developed countries is even vaster.
3
By contrast, the part of Clemens’ diagram that remains significantly underresearched is the distributional effect of emigration across owners of factors of
production in the source developing country. It is to this end that this extended
essay is focussed. Specifically, it attempts to understand the effect of emigration
on the real wages of remaining workers of the same ‘skill-group’ (defined in
terms of a individual’s education, experience and occupation): the ‘own-skillgroup’ effect of emigration.
The sparse existing literature has considered source country real wage effects of
emigration in Mexico, Moldova, Honduras, Puerto Rico and Lithuania. As yet, the
own-skill group effect in Jamaica remains unstudied. Substantial emigration from
Jamaica, particularly to the US, UK and Canada, has resulted in a stock of
Jamaicans representing 35.77%1 of the remaining Jamaican population living
outside the country in 2000 (World Bank). This is amongst the highest emigrant
stocks in the world, and is considerably higher than in Mexico, the focus of the
existing literature (9.56%1). In this extended essay, I augment the empirical
approach taken in previous analyses and extend it to the case of Jamaican
emigration.
Section 2 summarises the existing literature on the real wage effects of
emigration in source countries. Section 3 presents my new theoretical model of
those effects, whilst section 4 presents my empirical analysis. The essay
concludes in section 5 by interpreting the economic magnitude of the estimated
own-skill-group real wage effects for poverty reduction among the wage-earning
poor who have little ownership of fixed factors of production.
2. Existing literature
The entire existing empirical literature is limited to a handful of papers. The
three earliest papers provide evidence that is at best consistent with the
existence of a positive effect of emigration on remaining workers’ wages. Lucas
(1987) estimates a system of equations exploiting variation in numbers of
1Dividing
total emigrants, 2000, in the World Bank bilateral migration database
by total population from the World Development Indicators
4
emigrants over time from Malawi and Mozambique to work in South Africa’s
mines, over the period 1946-78. He identifies a positive and significant effect of
emigration on the real wages of plantation workers in both source countries.
This allegedly played a role in the British decision to introduce quota controls on
the movement of migrants from colonial Nyasaland (modern day Malawi) to
South Africa’s mines, to protect white European plantation owners from rising
labour costs. Boyer et al. (1993) present descriptive statistics specifically
consistent with a positive own-skill-group effect of emigration. They find that
two types of unskilled real wages increased dramatically in Ireland in the
absence of industrialisation over the period 1860-1913 at the same time as mass
emigration of unskilled workers to US and Britain. Real agricultural labourer
wages doubled, bricklayers’ wages increased by a factor of 2.4, whilst the rural
population fell by 2.6 million. Finally, Hanson (2005) uses a difference in
differences estimator to demonstrate higher real wage growth 1990-2000 in
those Mexican states with ‘high’ rates of emigration in 1950.
Mishra (2007) initiated a more rigorous empirical approach to identification of
the own-skill-group effect, borrowing the ‘national approach’ first presented in
the impact of immigration literature in Borjas (2003). The national approach
uses variation in the emigrant share2 and source country wages across ‘skill
groups’, defined in terms of education and labour market experience, to identify
the effect. Every paper in the literature has identified a positive and significant
own-skill-group effect; typically of the order of magnitude of a several
percentage point increase in source country wages for a 10% increase in the
emigrant share.
In her benchmark fixed effects regressions, Mishra finds that in the case of
Mexican emigration to the US 1970-2000, a 10% increase in the emigrant share
raises real wages of workers in the same skill group by 4.4%. To deal with the
possibility of reverse causality (the fact that low domestic real wages may drive
emigration, discussed in section 4b)iv)), she uses the lagged average emigrant
share for workers of the same education group across all experience groups as
an instrument for the emigrant share. The validity of this, and other, instruments
2Emigrant
share taken as total number of emigrants divided by total labour
force in the source country.
5
employed in the literature is discussed in section 4b)iv). In her IV regressions
she unsurprisingly finds the positive and significant effect increases.
Over the period 1960-2000, Aydemir and Borjas (2006) find a 10% increase in
the emigrant share is associated with a 5.6% increase in remaining workers’ real
wages in the same skill group in Mexico, although they do not attempt to uncover
a causal effect. Borjas (2007) finds that same shock to the emigrant share relates
to a 2.1% increase in own-skill-group real wages for Puerto Rican emigration to
the US 1970-2000. He attempts to identify a causal effect using variation in US
average wages across skill groups as an instrument for the emigrant share, and
finds an economically larger effect. Gagnon (2011) also uses the US average
wages instrument in the case of Honduran emigration to the US 2001-7, and
finds a 12.8% increase in own-skill-group real wages for the 10% increase in
emigrant share. Bouton (2011) uses household survey data from Moldova for a
single cross-section 2006 to find a 4% increase in own-skill-group real wages
associated with this emigrant share shock in his male sample, but this is only a
correlation.
Finally, (again following Borjas (2003)) some papers have simulated the total
effects of emigration (incorporating both own-skill-group and cross-skill-group
effects, as explained in section 3) based on a structural model of the source
country economy calibrated with estimated elasticities of substitution between
workers of different types. Elsner (2011) claims that Lithuanian emigration
2002-6 increased the real wages of workers with less than 10 years experience
by 4.9-7%, and reduced real wages of workers with more than 30 years
experience by 1%. The Aydemir and Borjas paper does similarly, but with
conclusions vulnerable to parameter changes in the model.
3. Theoretical model
Bouton (2011) is the only of the aforementioned papers to provide an explicit
theoretical model of the effects of emigration on real wages in source countries.
However, he treats labour as a homogeneous factor input, and as such cannot
6
distinguish between own-skill-group and cross-skill-group effects. As described
above, a structural model is presented in Elsner (2011) and Aydemir and Borjas
(2006), but given its empirical purpose, to produce simulations of the overall
effects of emigration, its complexity detracts from a clearer understanding of the
intuition underlying the real wage effects of emigration. I therefore here present
my new, simple neo-classical general equilibrium model of the source country
economy, the essence of which is similar to that structural model.
i) The model:
Suppose that output, Y, is produced by a combination of capital, K (alternatively
K could represent land), and ‘aggregate’ labour, L, according to a constant
returns to scale, Cobb-Douglas production function. Hicks-neutral technology is
denoted by A, and α represents labour’s share of the value of output, where 0 < α
< 1:
𝑌𝑡 = 𝐴𝑡 𝐾𝑡1−𝛼 𝐿𝛼𝑡
(1)
Aggregate labour is in turn a composite of the two types of worker that exist in
the economy, skilled workers, S, and unskilled workers, U, according to a
constant elasticity of substitution production function; where it is assumed that
the γi > 0 (i = 1, 2). The parameter ρ = (σ – 1)/σ, where σ denotes the elasticity of
substitution between skilled and unskilled workers in the production of
aggregate labour. I restrict attention to cases where the CES production function
is convex, thus 1 ≥ ρ ≥ -∞ (where ρ = 1 gives the case where skilled and unskilled
workers are perfect substitutes, and ρ = -∞ where they are perfect
complements):
𝜌
𝜌
1
𝐿𝑡 = (𝛾1 𝑆𝑡 + 𝛾2 𝑈𝑡 )𝜌
(2)
Substituting (2) into (1) and differentiating with respect to S, I derive an
expression for the marginal product of skilled labour, which gives the real wage
of skilled workers under perfect competition:
7
𝑑𝑌𝑡
𝑑𝑆𝑡
𝜌−1
= 𝛼 𝛾1 𝑆𝑡
𝜌
𝜌
𝛼
𝐴𝑡 𝐾𝑡1−𝛼 (𝛾1 𝑆𝑡 + 𝛾2 𝑈𝑡 )𝜌
−1
(3)
ii) The own-skill-group effect:
Differentiating (3) by the stock of skilled workers, S, tells us how an emigration
induced decrease in the stock of skilled workers affects the real wages of
remaining skilled workers: the own-skill-group effect of emigration for skilled
workers (the expression for the case of unskilled workers is symmetrical).
𝑑2 𝑌𝑡
=
𝑑𝑆𝑡2
𝜌−1
[𝛼𝛾1 𝑆𝑡 𝐴𝑡 𝐾𝑡1−𝛼 ] [(𝛼
𝜌−2
[𝛼𝛾1 (𝜌 − 1)𝑆𝑡
−
𝜌−1
𝜌
𝜌)(𝛾1 𝑆𝑡 )(𝛾1 𝑆𝑡
𝜌
𝛼
+
𝜌
𝐴𝑡 𝐾𝑡1−𝛼 (𝛾1 𝑆𝑡 + 𝛾2 𝑈𝑡 )
𝜌 −2
𝛾2 𝑈𝑡 )𝜌 ] +
𝛼
−1
𝜌
(4)
]
Factorising this expression and substituting in Lt for notational clarity:
𝑑2 𝑌𝑡
𝑑𝑆𝑡2
𝜌−2 𝛼−𝜌
𝐿𝑡 ][𝛾1 (𝛼
= [𝛼𝛾1 𝐴𝑡 𝐾𝑡1−𝛼 𝑆𝑡
𝜌 −𝜌
− 𝜌)𝑆𝑡 𝐿𝑡 + (𝜌 − 1)]
(5)
Given that S, L, K and A are positive quantities by definition, and γ1 > 0, 0 < α < 1,
the term in the first set of brackets is positive. The sign of the own-skill-group
effect therefore depends on the sign of the expression in the second set of
brackets:
𝑑2 𝑌𝑡
𝑑𝑆𝑡2
𝑆
< 0 if: [𝛾1 (𝛼 − 𝜌)(𝐿𝑡 )𝜌 + (𝜌 − 1)] < 0
𝑡
𝑆
i.e. if: 𝛾1 (𝛼 − 𝜌)(𝐿𝑡 )𝜌 < (1 − 𝜌)
𝑡
Case 1: α ≥ ρ:
Firstly, suppose α ≥ ρ. In this case, (α – ρ) ≥ 0, thus:
8
𝑑2 𝑌𝑡
𝑑𝑆𝑡2
< 0, 𝑖𝑓:
𝑆
𝛾1 (𝐿𝑡 )𝜌 <
𝑡
(1−𝜌)
(𝛼−𝜌)
(6)
Since 0 < α < 1, the numerator of the right hand side of (6) exceeds the
denominator, thus the right hand side exceeds 1.
Raising (2) to the power ρ:
𝜌
𝜌
𝜌
𝐿𝑡 = (𝛾1 𝑆𝑡 + 𝛾2 𝑈𝑡 )
𝜌
Dividing both sides by 𝑆𝑡 :
𝐿𝑡
𝑈𝑡
( )𝜌 = 𝛾1 + 𝛾2 ( )𝜌
𝑆𝑡
𝑆𝑡
(7)
Thus, given γ2, Ut, St > 0:
𝐿𝑡
( )𝜌 > 𝛾1
𝑆𝑡
Thus:
𝑆𝑡
(1 − 𝜌)
𝛾1 ( )𝜌 < 1 <
𝐿𝑡
(𝛼 − 𝜌)
Therefore, inequality (6) holds.
Case 2: α < ρ:
Instead suppose that α < ρ, such that (α – ρ) < 0. In this case:
𝑑2 𝑌𝑡
< 0, 𝑖𝑓:
𝑑𝑆𝑡2
𝑆𝑡
(1 − 𝜌)
𝛾1 ( )𝜌 >
𝐿𝑡
(𝛼 − 𝜌)
(8)
9
Given that 1 ≥ ρ, the numerator is zero or positive, and the denominator
negative, and thus the right hand side of (8) is zero or negative. Thus given γ1, Ut,
St > 0, the inequality holds.
I have arrived at the unambiguous prediction that
𝑑2 𝑌𝑡
𝑑𝑆𝑡2
< 0: ceteris paribus
emigration raises the real wages of remaining workers of the same skill group.
iii) The cross-skill-group effect:
Differentiating (3) by the stock of unskilled workers, U, tells us how emigration
of unskilled workers affects the real wages of remaining skilled workers; the
cross-skill-group effect of unskilled emigration on skilled workers:
𝑑2 𝑌𝑡
𝜌−1
𝑑𝑆𝑡 𝑑𝑈𝑡
= 𝛼𝛾1 𝛾2 (𝛼 − 𝜌)𝑆𝑡
𝜌−1
𝑈𝑡
𝜌
𝜌
𝛼
𝐴𝑡 𝐾𝑡1−𝛼 (𝛾1 𝑆𝑡 + 𝛾2 𝑈𝑡 )𝜌
−2
(9)
The sign of the cross-skill-group effect therefore depends on the sign of (α – ρ). If
𝑑2 𝑌
α > ρ, 𝑑𝑆 𝑑𝑈𝑡 > 0, and thus emigration reduces the real wages of remaining
𝑡
𝑡
workers of the other skill group. By contrast if α < ρ, emigration increases the
real wages of remaining workers of the other skill group.
iv) Intuition:
Diminishing marginal returns to factor inputs drives the unambiguous own-skillgroup effect. Quite simply an emigration-induced reduction in the supply of
workers identical to you raises your marginal product, and so in perfectly
competitive markets your real wage. The cross-skill-group effect is ambiguous,
and crucially depends on the size of capital’s share of the value of output (1-α)
relative to the degree of complementarity between skilled and unskilled workers
as captured by ρ. Emigration of a worker more complementary in production to
you (lower ρ) intuitively has a more harmful effect on your marginal product,
and so increases the likelihood that α > ρ, i.e. your real wage reduces. Your real
10
wage is also more likely to reduce as capital’s share of the value of output is
lower, thus α higher. Intuitively, the lower is the relative importance of capital in
production, the less a reduction in aggregate labour (from emigration of workers
of the other skill group) will translate to an increase in the marginal product of
aggregate labour, and so in turn through to the marginal product (thus real
wages) of workers of both types.
The model provides the essential function of explicitly noting the two separate
effects of emigration. The total effect of emigration for a skill group depends on
the sum of the own-skill-group and all cross-skill-group effects on that skill
group. A failure to distinguish effects has led some authors to draw misguided
conclusions about the overall impact of emigration having only estimated an
own-skill-group effect. For example, Mishra (2007) uses her estimate of the ownskill-group effect combined with relative changes in earnings shares of different
skill-groups to ‘aggregate’ wage impacts across all skill-groups in Mexico,
claiming that emigration 1970-2000 raised the average Mexican worker’s wage
by 8%. This completely ignores the existence of cross-skill-group effects. Not
only do I refrain from making these statements, given that I only attempt to
estimate the own-skill-group effect in the next section, but the theoretical model
demonstrates the importance of controlling for cross-skill-group effects in my
regression analysis if I want to understand the true own-skill-group effect.
v) Extensions to the model:
Departure from full employment: Katseli et al. (2006) note that the effects of
emigration depend on source country labour market conditions. So far the model
has assumed full employment. However, in the presence of unemployment the
effects of emigration may operate through changes in the unemployment rate
rather than real wages. Emigration of unemployed workers from a skill group, or
emigration of employed workers who are subsequently replaced by identical
unemployed workers, may have no own or cross-skill-group effects on real
wages since relative supplies of employed factor inputs remain unchanged. This
11
may be important in the Jamaican context; Kim (2007) highlights double-digit
unemployment for much of the 1990s and 2000s.
Short run versus long run effects: The model looks at short run effects during
which time the supply of all other factor inputs as well as production methods
remain fixed. In the long run the economy may adjust to an emigration-induced
change in factor endowments through three channels other than changes in
factor prices. Dustmann and Glitz (2011) outline two of these in a HeckscherOhlin-Samuelson model. Firstly, the source country may begin to produce a
higher quantity of the good whose production is relatively intensive in those
factors that become increasingly abundant due to emigration (the Rybczynski
effect). Secondly, within the existing structure of production firms across all
sectors may begin to employ production techniques that make greater use of
those now increasingly abundant factors. Finally, lower returns to capital may
discourage capital investment.
All three effects will supress the own-skill group real wage increase from
emigration in the long run. Less capital implies the relative scarcity of those
types of labour in which there has been emigration, which drove the real wage
increase, is reduced. The Rycbzynski effect and the change in production
techniques imply a reduction in demand for the emigration-induced scarcer
workers, so again supressing their real wage increases. The long-run cross-skill
group effects can, however, differ from the short-run in either direction. For
example, suppose workers in skill-group A suffer an adverse cross-skill group
effect in the presence of strong complementarities between them and the
emigrating workers in skill-group B. That adverse effect may be worsened by the
decrease in formation of (complementary) capital. Yet the Rybczynski effect and
shift in production techniques may increase demand for workers from skillgroup A, so reducing the adverse effect on their real wages.
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4. Empirical Analysis
a) Data and methodology
i) Data sources:
Data sources and procedures applied to the raw data are summarised in Table 2
(appendix), but attention is drawn to the following. I use the IPUMS International
dataset, in which internationally comparable census data is available for selected
countries. Jamaican censuses 1982, 1991, and 2001 are used to obtain
information on annual wage income (from all types of employment) in the
source country; whilst US censuses 1980, 1990, and 2000 are used to track the
number of Jamaican emigrants to the US. Since other Jamaican migrant receiving
countries do not publish information about the exact birthplace of residents,
only Jamaican emigrants to the US can be counted. The potential implications of
this for sample selection bias are discussed in section 4ci).
ii) The pattern of Jamaican emigrant stocks 1980-2000:
Before turning to the IPUMS data, it is useful to demonstrate the broader pattern
of Jamaican emigration 1980-2000, by education and geographically. The Trade
Team at the World Bank produces a panel data set documenting changes in
emigrant numbers to six OECD countries (UK, US, Canada, Australia, France and
Germany) 1975-2000, distinguishing by education levels. Over the period 19802000 there has been a dramatic increase in high-educated (post-secondary
education completed) Jamaican emigration. The high-educated share of total
Jamaican emigrants to these six OECD countries 1980-2000 increased by
20.71%, nearly doubling its 1980 level of 22.08%. By contrast, the low-educated
share (less than upper-secondary completed) decreased by 29.42%, more than
halving its 1980 level. According to the World Bank Bilateral Migration Database,
of the stock of Jamaican emigrants in 2000, 62.17% were located in the US,
16.16% in the UK, and 12.83% in Canada.
13
iii) Methodology:
Following Mishra (2007) as described in section 2, I divide Jamaican emigrants
and the ‘remaining’ labour supply (those who stay in Jamaica) into ‘skill groups’.
Each skill group defines a type of workers who directly compete. The existing
literature has defined skill groups in terms of education and a, crude, measure of
labour market experience taken as an individual’s age minus the year they are
expected to have joined the labour force (which I take as one year after their
completed level of education, with a minimum age of 15). In all regressions four
education classifications are used: ‘less than primary education completed’,
‘primary completed’, ‘secondary completed’, and ‘university completed’. For the
four respectively, I take workers as entering the labour force aged 15, 15, 19 and
22 for the purpose of the ‘experience’ calculation. I calculate ‘experience’ as ‘age
– labour force entry age’, and then in turn use either four 10-year experience
group classifications (0-9, 10-19, 20-29, 30+), or eight 5-year classifications (0-4,
5-9, 10-14, 15-19, 20-24, 25-29, 30-34, 35+). Given women are on average more
transient in the labour force, defining experience becomes increasingly
misleading, and so throughout attention is focussed on males only.
I augment the existing literature by, for the first time, using an individual’s
‘primary occupation’ to classify workers at a level of detail beyond education and
experience. The ‘OCCISCO’ code in IPUMS defines workers into 10 primary
occupations, including, for example, ‘professionals’, and ‘plant and machine
operators and assemblers’. In my preferred regressions I therefore divide
workers into ‘education-experience-occupation’ skill groups.
For each skill group I calculate the emigrant share, defined as the total number of
emigrants divided by the remaining labour force (both employed and
unemployed individuals). I deflate the nominal wages of employed workers
according to the Jamaican CPI from the IMF International Financial Statistics to
give real wages, before taking the natural logarithm and calculating the mean
across all workers in each skill group. I have a panel of data at the skill-group
14
level over three time periods (approximately 1980, 1990 and 2000 depending on
the exact census year).
My basic regression equation is a two-way error components model of the
following form:
𝑀𝑊𝐺𝑖𝑗𝑘𝑡 = 𝜃0 + 𝜃1 𝐸𝑀𝐺𝑅𝑖𝑗𝑘𝑡 + 𝛿𝑠 𝐸𝑀𝐺𝑅𝑠𝑗𝑘𝑡 + 𝜃2 𝑇2 + 𝜃3 𝑇3 + 𝜃4 𝐸𝐷𝑖 𝑇2 + 𝜃5 𝐸𝐷𝑖 𝑇3 +
𝜃6 𝐸𝑋𝑗 𝑇2 + 𝜃7 𝐸𝑋𝑗 𝑇3 + 𝜃8 𝑂𝐶𝐶𝑘 𝑇2 + 𝜃9 𝑂𝐶𝐶𝑘 𝑇3 + 𝐸𝐷𝑖 𝐸𝑋𝑗 𝑂𝐶𝐶𝑘 + 𝑢𝑖𝑗𝑘𝑡
That is to say I regress the mean log real wage in skill-group ijk (education group
i, experience group j, occupation group k) at time t (MWGijkt) on the emigrant
share in that skill group (EMGRijkt), controlling for the emigrant share in all skill
groups of the same experience and occupation level, but different education
level, at time t (EMGRsjkt for all s ≠ i) (the cross-skill-effects I control for). Whilst I
could have controlled for emigrant shares in skill groups with different
experience or occupation but the same level of education, perhaps the strongest
complementarities in production occur between workers of different education
levels, following Mishra (2007). Mishra (2007) is the only other paper to control
for cross-skill-group effects, and even here in only one of her regressions as a
‘robustness check’.
I control for time fixed effects through dummy variables for periods 2 and 3 (T2
and T3), to capture variables that influence mean real wages and vary over time
but not across skill groups. I control for interactions between education group
and the time dummy variables (EDiTt), as well as between experience group and
occupation group and the time dummy variables, respectively (EXjTt) and
(OCCkTt). These capture all variables causing changes in mean real wages over
time by education, experience, or occupation groups.
Finally, given there are many plausible unobserved time invariant determinants
of mean real wages across skill-groups I wish to control for, I estimate my
regressions using fixed effects estimation: thus controlling for EDiEXjOCCk. A
Generalised Hausman test, augmenting random effects estimates of specification
15
[2] below with time demeaned variables (regression not reported), gave
statistical justification for the use of fixed effects: the null hypothesis that the
time demeaned variables had no significant explanatory power was rejected at
all reasonable significance levels.
The coefficient of interest is θ1, the own-skill-group effect of emigration on mean
log real wages of remaining Jamaican workers. It tells us the percentage change
in mean log real wages for a 1% decrease in the Jamaican labour supply due to
emigration. It can therefore be interpreted as a wage elasticity.
Since real wages are simultaneously determined by labour supply and demand, I
must control for all influences from labour demand to estimate the real wage
effect of the labour supply shock. The large set of fixed effects and interaction
terms imply only components of labour demand that vary over time as well as
across education-experience-occupation groups (or two of the three) could be
contained in the uijkt, and so bias the estimated coefficient of interest if correlated
with the labour supply shock.
The dependent variable is an average, calculated from a different number of
observations in each skill group depending on the number of remaining
employed Jamaican workers in that skill group. Each observation for the
dependent variable therefore contains information of varying reliability. To take
this into account, I weight all regressions using the ‘aweights’ function in Stata.
The more individual observations used to calculate the average, the lower the
variance of that averaged observation, and so the higher its weight in the
regressions. Whilst failing to weight my regressions would not lead to biased
estimates, the estimates would, in failing to take into account the information
contained in the varying reliability of observations, be inefficient.
16
b) Results
i) Descriptive statistics:
Before launching into the regression analysis, I present a scatter diagram
demonstrating the correlation between mean log real wages and emigrant
shares across skill groups across all three time periods. I use the educationexperience classification of the existing literature for visual clarity (given there
are far fewer observations by this two-way classification). The size of the points
on the scatter graph is given by the number of Jamaican remaining workers used
to calculate mean wages; thus larger points represent greater reliability of the
observation. Figure 2 plots all observations, before figure 3 ‘zooms in’ on the
cluster of observations with an emigrant share less than 0.4:
Figure 2: Scatter diagram – Mean log real Jamaican wage against emigrant share
by education-experience classification: All observations
17
Figure 3: Scatter diagram – Mean log real Jamaican wage against emigrant share
by education-experience classification: Emigrant shares < 0.4
At first glance, mean log real wages appear positively correlated with the
emigrant share. Were low mean wages driving Jamaican emigration, I might
expect a negative correlation. The descriptive statistics seem sufficiently
consistent with a positive own-skill-group effect of emigration to motivate a
more rigorous empirical analysis.
ii) Results table:
Using the specification in [1] I test for serial correlation (using the first difference
approach discussed by Wooldridge (2002)), and find that the null hypothesis of
no serial correlation is strongly rejected, p-value for the F statistic 0.0037. As
suggested in Bertrand, Duflo and Mullainathan (2004), in all the following
regressions I cluster standard errors on the skill group (i.e. allow for serial
correlation over time within skill groups).
18
Table 1: Empirical results
Variable name
[1]
Fixed
effects.
Ed-ex skill
group.
Time
invariant
weights
[2]
Fixed
effects.
Ed-ex-occ
skill group.
Time
invariant
weights
Constant
11.215***
(0.086)
0.426***
(0.061)
0.245
(0.371)
11.523***
(0.023)
0.002
(0.014)
-0.116**
(0.058)
0.514***
(0.188)
-0.126
(0.118)
0.173
(0.133)
0.434***
(0.126)
-0.145**
(0.070)
0.281***
(0.063)
-0.027
(0.050)
0.668***
(0.181)
1.384***
(0.156)
-0.274***
(0.060)
-0.377***
(0.053)
-0.059**
-0.022
(0.014)
-0.002
(0.001)
0.541***
(0.152)
1.121***
(0.205)
-0.207***
(0.032)
-0.233***
(0.045)
-6.87x10-4
0.069**
(0.033)
-1.10x10-4
(0.003)
1.103***
(0.354)
0.423
(0.301)
-0.386***
(0.100)
-0.109*
(0.065)
-0.038
-0.138***
(0.048)
-0.002
(0.005)
-0.750**
(0.369)
1.088**
(0.428)
0.256**
(0.099)
-0.243**
(0.098)
0.050
0.022
(0.023)
-7.28x10-4
(0.002)
0.799***
(0.248)
0.462*
(0.276)
-0.311***
(0.065)
-0.098*
(0.058)
-0.035
EMGRijkt
Cross-skill-group control 1
Cross-skill-group control 2
Cross-skill-group control 3
T2
T3
EDiT2
EDiT3
EXjT2
[3]
Fixed
effects-2SLS.
Ed-ex-occ
skill group.
Time
invariant
weights
[4]
First stage
of fixed
effects 2SLS
regression
[5].
[5]
Fixed
effects2SLS.
Ed-ex-occ
skill group.
Time
variant
weights
[6]
Fixed
effects. Edex skill
group. Time
invariant
weights.
Short versus
long run.
[7]
Fixed effects2SLS.
Ed-ex-occ
skill group.
Time variant
weights.
Emigrant
share
adjustment 1.
[8]
Fixed effects2SLS.
Ed-ex-occ
skill group.
Time variant
weights.
Emigrant
share
adjustment 2.
[9]
Fixed effects2SLS.
Ed-ex-occ
skill group, 8
experience
groups.
Time variant
weights.
0.256
(0.389)
0.426***
(0.123)
-0.142**
(0.069)
0.456***
(0.139)
-0.152**
(0.074)
0.461***
(0.117)
-0.064
(0.061)
0.268***
(0.063)
-0.036
(0.049)
0.669***
(0.178)
1.443***
(0.175)
-0.257***
(0.057)
-0.393***
(0.057)
-0.060**
0.022
(0.024)
-7.27x10-4
(0.002)
0.798***
(0.248)
0.468*
(0.273)
-0.308***
(0.065)
-0.099*
(0.058)
-0.034
0.034
(0.026)
-9.51x10-4
(0.003)
0.824***
(0.262)
0.370
(0.297)
-0.314***
(0.068)
-0.080
(0.062)
-0.039
0.038**
(0.018)
-3.11x10-5
(0.002)
0.955***
(0.255)
0.405
(0.267)
-0.351***
(0.066)
-0.107*
(0.062)
-0.035
11.241***
(0.083)
-
19
(0.023)
-0.004
(0.022)
EXjT3
OCCkT2
OCCkT3
(0.031)
-0.056*
(0.034)
-0.005
(0.010)
-9.93x10-4
(0.016)
BRAMWGijkt
(0.061)
0.027
(0.040)
-0.038
(0.024)
0.049**
(0.023)
-7.86x10-7
(3.38x10-6)
(0.069)
-0.140**
(0.070)
0.055**
(0.025)
-0.043*
(0.025)
4.90x10-6
(3.62x10-6)
(0.041)
-0.005
(0.033)
-0.007
(0.017)
0.044**
(0.022)
-1.88x10-6
(2.41x10-6)
SREMGRijkt
(0.024)
-0.008
(0.023)
(0.040)
0.004
(0.032)
-0.008
(0.016)
0.044**
(0.022)
-1.67x10-6
(2.43x10-6)
(0.042)
0.003
(0.034)
-0.010
(0.017)
0.049**
(0.023)
-1.85x10-6
(2.43x10-6)
(0.027)
3.40x10-4
(0.015)
-0.017
(0.016)
0.054***
(0.020)
6.70x10-8
(2.65x10-6)
-
-
-
USMWGijkt
-
-
-
5.25x10-5***
(1.35x10-5)
-
-0.337
(0.378)
0.492***
(0.085)
-
Within R2
(Not presented for 2SLS
regressions where it has little
statistical meaning)
Number of observations
Number of skill groups
0.888
0.828
-
-
-
0.891
-
-
-
96
32
331
148
297
114
297
114
297
114
96
32
297
114
297
114
413
166
Weak instruments test: Smallest
‘maximal IV size’ bias rejected
(Kleinbergen-Paap statistic)
N/A
N/A
20%
(See [5])
15%
N/A
15%
15%
10%
LREMGRijkt
Standard errors clustered on the skill-group are reported in brackets. Significance at the 10%, 5% and 1% levels are denoted by *, **, *** respectively. The
dependent variable in all but regression (4) is MWGijkt; the mean log Jamaican real wage in skill-group ijk at time t. EMGRijkt denotes emigrant share in skill-group
ijk at time t, instrumented for using mean US real wages, USMWGijkt, in all 2SLS regressions, Tt a time dummy variable for time t, EDi education group, EXPj
experience group, OCCk occupation group. The creation of cross-skill-group controls is explained in the appendix. BRAMWGijkt are Brazilian mean real wages as
discussed in section 4biv), and SREMGRijkt and LREMGRijkt are the short and long run emigrant share variables discussed in section 4bv). Regression (4) presents
the first stage fixed effects 2SLS results relating to regression (5) (thus the dependent variable is EMGRijkt).
20
iii) Benchmark fixed effects results:
Columns [1] and [2] present the benchmark fixed effects results. The first
column is included for comparison to the existing literature: skill groups are
constructed on the basis of education and experience classifications only (four
and eight groups respectively). It does, however, improve upon most papers
through the inclusion of the cross-skill group controls. Stata does not support the
use of time variant weights in fixed effects OLS regressions. As such, for both [1]
and [2] the average number of remaining Jamaican workers used to calculate the
dependent variable across all time periods for a skill group is used for the weight
in every time period (again via the ‘aweights’ function). In [1], the coefficient of
interest takes a value 0.426 and is significant at all reasonable significance levels
with a p-value, corresponding to its t-statistic, of 0.000. A 10% increase in
emigrant share is associated with a 4.26% increase in real wages of remaining
workers of the same skill group.
The own-skill-group effect however becomes insignificant both statistically and
economically when classifying individuals by occupation too, producing many
more skill groups, in [2] (note in these regressions I use four rather than eight
experience groups). As suggested in Borjas (2007), the larger the number of skill
groups used in classification, the larger measurement error is likely to be. Here I
am not discussing non-random measurement error from undercount of illegal
immigrants (discussed in section 5c)ii)), but rather measurement error that
applies even to legal immigrants from the fact that the IPUMS US census data
only captures a 5% sample of the population. Making the classical errors-invariance assumption that this type of measurement error is uncorrelated with
the true emigrant share, it will lead to an attenuation bias in my estimate of θ1.
This attenuation bias may be amplified in my fixed effects estimates if the
persistence of true emigrant shares is considerably higher than the persistence
of this measurement error. It is possible that the insignificance of θ1 in [2] stems
from attenuation bias, which is suffered less in [1].
21
iv) Understanding causality: An instrumental variables analysis:
So far I have not addressed causality. In section 4b)i), I alluded to the possibility
of reverse causation. Lower real wages, ceteris paribus, should encourage
Jamaicans to emigrate, resulting in a downward bias in my estimates of θ1.
I perform instrumental variables fixed effects regressions to try to use only
exogenous variation in the emigrant share in identification of θ1 (that fraction of
the variation in the emigrant share not caused by changes in Jamaican mean real
wages). I use US average real wages across skill groups as my instrument for the
emigrant share (USMWGijkt). If Jamaicans take into account the expected real
wage they will earn in the US in their decision to emigrate, in line with the
Harris-Todaro model, which in turn depends on the actual average real wage
earned by existing workers of their skill group in the US, I expect this instrument
to be highly relevant. This instrument was used in both Borjas (2007) and
Gagnon (2011).
Validity of the instrument:
More questionable is the validity of my instrument. If changes in US average
wages are directly correlated with changes in Jamaican average wages, over time
within skill groups, other than through its effect on Jamaican emigration, my
instrument is invalid. Part of the effect I attribute to emigration would rather
capture this direct correlation.
I control for one specific channel through which such direct correlation might
exist: the existence of global technology shocks. A worldwide improvement in
technology may increase the marginal product of labour and so real wages in
both the US and Jamaica. I have income data (total rather than wage income) for
one other country over these three time periods in the IPUMS dataset: Brazil. To
the extent that correlation between Brazilian and Jamaican average income over
time within skill groups captures those same global technology shocks that drive
direct correlation between US and Jamaican average wages, by controlling for
22
Brazilian average income across skill groups I control for this potential abuse of
my validity assumption. The fact that there is little migration between Jamaica
and Brazil implies that correlation between their incomes is not driven by direct
labour shifts between them, and so could plausibly be capturing common
technology shocks.
I should not, however, overstate the validity of my instrument. If there exist
technology shocks common to the US and Jamaica but that do not impact
Brazilian income, including the Brazilian control variable will not ensure the
validity of my instrument. Further, one could think of other channels through
which the validity assumption may be abused. An example is US import demand
for Jamaican goods. Suppose US workers from better-educated skill-groups are
those who can afford to visit Jamaica on holiday (the US Department of State
website claims that in 2010 nearly 2 million Americans travelled to Jamaica). An
increase in average wages for better-educated US workers could then translate
through to higher wages for individuals in those same better-educated skill
groups in Jamaica if they are employed in the tourist industry; leading to a direct
positive correlation between US and Jamaican average wages over time within
skill groups.
In spite of this, my instrumental variables approach improves upon that
attempted in the existing literature. Firstly, the two aforementioned papers to
use US average wages take no additional steps to support its validity, unlike as I
do. Secondly, Mishra (2007) rather uses the emigrant share across all experience
groups in that given education group lagged one period as her instrument, as
explained in section 2. In fixed effects regressions the consistency of our
estimates depends on strict exogeneity of the independent variables. If the
contemporaneous emigrant share is not strictly exogenous (due to reverse
causality) then by definition neither is its lag; thus this instrument (based in part
on the lagged emigrant share by skill group) will not be strictly exogenous either,
and so her IV estimates are inconsistent.
23
IV results:
The results for my 2SLS-FE regressions are presented in columns [3] and [5].
Other than instrumenting for the emigrant share and controlling for Brazilian
average wages (BRAMWGijkt), I use the same specification as in [2]. Even if my
instrument is both relevant and valid, IV estimates are only consistent, not
unbiased. In small samples there may still exist large biases, and so I have chosen
to use the education-experience-occupation classification as it provides me with
a larger sample of observations.
Stata supports the use of time variant weights when running fixed effects-2SLS
regressions, as it was ‘easy enough to program the feature’ (Mark Schaffer,
Statalist3). In [3] I use the same time invariant weights as in [2] for the purpose
of comparison, whilst in [5] I use the time variant weights I had originally hoped
to use in my fixed effects regressions. On this basis, the estimates in [5] are more
efficient, although the estimates of θ1 are not dissimilar in economic or statistical
significance.
In [4] I present the first stage results relating to estimates in [5]. USMWGijkt has
significant explanatory power over the emigrant share at all reasonable
significance levels; t-statistic 3.88, p-value 0.000. US mean real wages appear to
be a relevant instrument for the emigrant share, though I formally explore the
identification of θ1 using this instrument below. Space precludes the inclusion of
the other first stage results for fixed effects 2SLS regressions (with EMGRijkt as
the first stage dependent variable), but USMWGijkt was significant at beyond a
1% significance level in all cases.
In both [3] and [5] my FE-2SLS estimator of θ1 is identified. Since my errors are
not i.i.d., at least due to serial correlation over time within skill groups, I must
use the Kleinbergen-Paap rk LM test statistic to test for under-identification, a
robust alternative to the Anderson and Cragg-Donald statistics. At even the 1%
significance level in [5], I reject the null hypothesis of under-identification, given
3In
an email sent to me 05/03/12
24
a p-value 0.0011, although in [3] it can only be rejected at a 2% significance level,
p-value 0.0116.
Baum, Schaffer and Stillman (2007) note that there has not yet been developed a
test of weak instruments robust to non i.i.d. errors. However, given that the
Stock-Yogo approach to testing weak instruments employs the same test statistic
as under-identification tests (the difference being the null hypothesis tested and
the critical values they have tabulated) the former authors suggest using the
Kleinbergen-Paap rk Wald statistic (whose calculation is robust to non i.i.d.
errors), with the Stock-Yogo critical values to test for the presence of weak
instruments. Since these critical values have not been created specifically for this
test, conclusions must be drawn cautiously. In [5] using the Kleinbergen-Paap rk
Wald statistic I reject the null hypothesis that the instrument is sufficiently weak
that Wald tests of the IV estimates have a rejection rate 15% or above (as
opposed to the true rate of 5%; the ‘maximal IV size’ test), given a statistic of
15.04 compared to a Stock-Yogo 15% maximal IV size critical value of 8.96.
However, in [3] I can only reject at a 20% maximal IV size level. Nonetheless, I
tentatively conclude that my 2SLS estimates do not suffer severe problems from
weak instruments.
According to the estimate of θ1 in [5], a 10% increase in emigrant share causes a
4.34% increase in real wages of remaining workers of the same skill group. This
coefficient is statistically significant at a 1% significance level, with p-value
0.001. Not only is the estimate now statistically significant, it has also increased
significantly economically from the fixed effects estimate in [2], consistent with
the instrument removing a downward bias created by the previously described
reverse causation. Thus even if the attenuation bias suffered in [2] has not been
removed, given I have not tried to argue that my instrument is uncorrelated with
the measurement error in the emigrant share, the removal of the bias from
reverse causation is sufficient to reveal a positive and significant own-skill-group
effect.
25
The coefficient on cross-skill control 1 is negative and significant at the 5% level.
The cross-skill controls have been constructed hierarchically, cross-skill control
1 is always the emigrant share of the lowest educated of the ‘other three’
education groups controlled for (cross-skill control 3 is always the highest). The
negative sign suggests emigration of relatively low educated workers is
detrimental to others’ real wages. To explore whether a negative cross-skill
effect only operates when that emigrating worker is less educated than you I
created three dummy variables; one that takes value 1 when EMGRijkt is the
emigrant share for primary completed, one for secondary completed, and one
university completed. I interact each dummy variable with each cross-skill
control. If complementarities only exist with lower educated workers, the
interaction terms should only be significant when indicating the emigrant share
of a lower educated group. This was not the case however (results not reported).
Given this, and given the sign and significance of each cross-skill control is less
robust across specifications, I simply conclude there is suggestive evidence that
cross-skill effects do exist, so that failing to control for them would create a bias
in the estimate of θ1 were they correlated with EMGRijkt.
BRAMWGijkt is insignificant (p-value 0.436). To the extent that there exists direct
correlation between US and Jamaican average wages over time within skill
groups due to common technology shocks, those technology shocks do not seem
to have driven Brazilian income in a correlated way. Global technology shocks
and US import demand as previously described would likely drive positive
correlation between US and Jamaican average wages. If these were the main
sources of concern about the validity of the instrument, the estimate of θ1 in [5]
perhaps constitutes an upper bound, with the estimate in [2] a lower bound, for
the true effect of emigration (ignoring all other econometric problems).
v) Short run versus long run:
The analysis so far calculates the emigrant share based on the total stock of
workers in the US at that point in time. It assumes the effect of emigration is
permanent; the real wage effect on remaining workers is the same whether an
26
individual left, say, 2 or 20 years ago. For the reasons expressed in section 3v),
one might expect the effects of emigration to change over time. I discussed that
the own-skill group effect may be supressed in the long run. I therefore divide
the emigrant share into a ‘short run’ and ‘long run’ effect, similar to Mishra
(2007), although using a different definition of short and long run. I use a
variable ‘mgrate5’ from the IPUMS dataset, which expresses where an individual
resided 5 years before the census date. I separate those Jamaican emigrants who
lived ‘abroad’ five years ago from those who lived in the US. I treat the former as
capturing migrants who emigrated in the last five years, and the latter as having
moved more than 5 years ago. The measure of recent migrants is not perfect
given that it also captures individuals who left Jamaica for a country other than
the US many years ago, before moving to the US within the last five years.
Nonetheless, it presents the best approximation available using the census data.
Failing the existence of two separate instruments for the short and long run
emigrant share (simultaneously using current and lagged US mean real wages
led to under-identified models), I was forced to return to my simple fixed effects
estimates. I look to see whether the significant own skill group effect in [1]
embodies both a significant short and long run effect of emigration. By contrast
to the theory, in [6], I apparently find a significant long-run effect at all
reasonable significance levels (p-value 0.000), but the short-run effect is
insignificant, and even switches sign. However, this is perhaps to be expected
econometrically. Whilst a decrease in mean wages today may have caused an
increase in emigration from a skill group within the last five years, it will not
have caused emigration a decade or more previously. That is to say reverse
causation will bias the coefficient on the short run emigrant share downwards,
but not the long run. The absence of two or more instruments precludes further
analysis.
c) Tests of robustness
i) Sample selection bias:
27
Jamaican emigration outside of the US:
Interpreted as the own-skill group effect of Jamaican emigration to all
destination countries, my estimates may suffer from sample selection bias given
I only observe emigrants to the US. Given I estimate using fixed effects, time
invariant influences on selection to the US against other destinations will not
bias my estimates, yet unobserved time variant influences may if correlated with
the disturbance term. Since my estimates are identified from within variation in
emigrant shares, it is reassuring that according to the aforementioned World
Bank panel data set 85.6% of the total increase in Jamaican emigration to the six
OECD countries (including US, UK and Canada) 1980-90, and 91.0% of that 19902000, occurred in the US. Whilst my estimates are plausibly identified from the
majority of total within variation in emigrant shares, I should retain some
caution in interpreting results as representative of the effects of emigration
outside of the US.
Unobserved ability of emigrants:
An alternative and potentially severe sample selection bias stems from the fact
that I do not observe the inherent ‘ability’ of workers. If less able workers
emigrate from Jamaica, the average ability of remaining workers increases, and
thus the average marginal product of labour (and so real wages) will increase,
quite aside from any effect of emigration on real wages. A priori it is not possible
to sign sample selection bias, since if more able workers emigrate then by
reverse argument my estimates are downward biased. Fundamentally, the sign
of this sample selection bias depends on where in the conditional (on individual
characteristics controlled for in my regression: education, experience and
occupation) wage distribution in Jamaica emigrants have come from.
This is the same sample selection problem discussed by Clemens, Montenegro
and Pritchett (2010) (CMP). Ceteris paribus one would expect workers in the
lower tail of the Jamaican conditional wage distribution to be more likely to
emigrate (i.e. ‘less able’ individuals). However, the ability and desire to emigrate
28
may depend on a host of unobservable characteristics that also influence the
wages one obtains in the Jamaican conditional wage distribution. As an example,
CMP comment that the networks one has in the US will influence one’s ability to
emigrate there. Extending their discussion, consider the unobserved ability:
charisma. An individual who has this ability is both more likely to have a lot of
friends, and so better networks of individuals who have already migrated to the
US, but also more likely to gain promotion in their workplace and so come from
the higher tail of the Jamaican conditional wage distribution. This would imply
positive selection into emigration.
CMP provide empirical evidence to infer the likely type of selection into
emigration. The external validity of results may be limited given the barriers
(language, distance etc) workers must overcome to emigrate from one country
may be very different to another, and so the unobserved characteristics that
become important differ too. In this light perhaps the most interesting evidence
from CMP comes from emigration of workers from Costa Rica, Dominican
Republic and Haiti, countries geographically similar to Jamaica, to the US.
Comparing the conditional wage distribution of migrants’ pre-migration wage to
the conditional wage distribution of non-migrants, they estimate that the
average migrant is selected from the 50th-60th percentile of the distribution of
non-migrants, consistent with positive selection.
Whilst positive selection into emigration seems more plausible empirically, to
understand the robustness of my results I consider what degree of negative
selection would be necessary to completely eradicate the positive and significant
effect of emigration on real wages estimated in my preferred 2SLS-FE results in
[5]. This is a more desirable and transparent approach to that taken by Mishra
(2007), Gagnon (2011) and Bouton (2011). They strangely estimate the ownskill-group effect for a regional sub-sample of workers who are unlikely to
emigrate on the grounds that if virtually no one emigrates there cannot be any
sample selection bias!
29
Suppose 10% of every skill group emigrates, and the only individuals to emigrate
are of ‘low ability’. Before emigration, the average marginal product of labour, if
high ability workers have MPL = 100 and low ability have MPL = x, is:
y = (10x + (90*100))/100
After emigration, the average MPL is 100 (only high ability stay behind). The
percentage increase in the average MPL due to sample selection is therefore =
((100-y)/y)*100.
That same emigration of 10% of the initial workforce would imply in my
regressions an increase in the emigrant share variable of 10/90. From [5], the
associated
percentage
increase
in
average
real
wages
is
=
((10/90)*100)*0.43392 = 4.821%.
Therefore for the entire positive and significant effect of emigration to be
removed by sample selection bias: ((100-y)/y)*100 = 4.821. Solving for y, before
substituting back into x, gives x = 54.0.
This simple simulation exercise suggests that for the entire positive and
significant effect of emigration on real wages in my preferred estimates to be
removed, I would have to assume that, controlling for education, experience and
occupation of an individual (where 10% of the workforce emigrates and they are
exclusively the low ability workers), low ability workers on average have a
marginal product of labour only just over half that of remaining workers. An
extreme level of negative selection into emigration would be required to entirely
refute my results.
ii) Measurement error:
The main source of measurement error I must deal with is the undercount of
Jamaican emigrants due to the existence of Jamaican-born illegal immigrants
living in the US. For this form of measurement error I cannot make the classical
30
errors-in-variance assumption since the extent of the undercount of illegal
immigrants is likely correlated with the true level of emigration in a skill group.
This undercount of Jamaican emigrants is an omitted variable. Mishra (2007)
assumes that all illegal immigrants are of her lowest educated category, and that
there is an undercount of 30%. She performs regressions adjusting emigrant
shares accordingly for those skill groups.
Given that I control for all time invariant variables, perhaps a greater concern is
if there is a significant change in the extent of undercounting over time. I
suppose rather that all ‘less than primary education completed’ and ‘primary
completed’ skill groups undercount emigrants by 30% in the first period, but,
due to an improving ability of the authorities to track and deport illegal
immigrants, this undercount is only 20% and 10% in the second and third period
respectively in [7]. I then, by contrast, assume that the problem of illegal
immigration worsens, such that the undercount increases to 40% and then 50%
in the second and third periods in [8]. In all regressions I have used the 2SLS-FE
approach from my preferred regression [5]. The estimated wage elasticity
changes very little in either case, reducing to 0.426 in the former and increasing
to 0.456 in the latter.
iii) Other robustness checks:
Finally, due to the fairly arbitrary nature of the experience classification, I check
the robustness of my results in [5] to the use of the eight-group rather than the
four-group experience classification, in [9]. Again the estimated wage elasticity
changes very little, increasing to 0.461 and remaining significant at all
reasonable significance levels, p-value 0.000.
5. Conclusion
To summarise, I find significant evidence of a positive own-skill-group effect of
emigration on Jamaican real wages, plausibly robust to concerns about sample
selection and the undercount of Jamaican illegal immigrants in the US. My
31
preferred estimates suggest that over the period 1980-2000, a 10% emigrationinduced decrease in the Jamaican labour force in a skill group would cause a
4.34% increase in the real wages of remaining workers of the same skill group.
My estimates are qualitatively and quantitatively consistent with the existing
literature. Considering regressions with the most comparable sample and
specification to those in my essay, own-skill-group wage elasticities have been
estimated in the range 0.21 (Borjas (2007)) to 0.56 (Aydemir and Borjas
(2006)). These are fixed effects estimates that do not deal with causality and
classify workers in terms of education and experience only. They are most
comparable to my estimate from [1] of 0.342, which falls within the range. It is
interesting that authors across a range of developing countries find evidence of a
similar several percentage point own-skill-group effect of a 10% emigrationinduced decrease in the labour supply, in spite of the fact that determinants of
the emigration decision (and thus sample selection issues), and the level of
source country unemployment, are very context-specific.
Implications for poverty reduction and policy:
As I have stressed throughout, conclusions about the overall effects of
emigration cannot be drawn from an understanding of the own-skill-group
effects alone. Nonetheless, a brief thought experiment demonstrates the likely
implications of the economic magnitude of the estimates for poverty reduction
for the wage-earning Jamaican poor. Suppose there is emigration from a single
skill-group only, such that no cross-skill group effects influence wages in that
skill-group. Suppose 22.1% of the labour force in that skill-group emigrates (the
median decadal change in emigrant share amongst those in which the emigrant
share increased). From estimates in [5], this will produce an increase in real
wages of remaining workers by 9.6%. A relatively poor Jamaican worker earning
the equivalent of US$1,000 per annum could expect to see an increase in his real
wage to US$1,096. Abstracting from any other benefits of emigration for the
workers who stay behind (such as remittance flows), whilst emigration may pull
the emigrants themselves out of poverty (according to the estimates of CMP
32
(2010) mentioned in section 1) it appears unlikely, alone, to produce real wage
increases of an order of magnitude sufficient to pull remaining workers out of
poverty.
I do however caution against drawing policy conclusions from this analysis
alone. The own-skill-group effect estimated in this extended essay could be
combined in the future with attempts to gauge the size of cross-skill-group
effects in Jamaica to identify the remaining workers likely to suffer or gain from
the actual pattern of Jamaican emigration. Policy may then in turn aim to assist
those groups who suffer. Currently however, no such attempts exist.
33
Appendix
Table 2: Data description
Variable
name
MWGijkt
Description
Data source
Procedures applied to raw data
Mean log real
wage of
remaining
workers in
Jamaica
IPUMS
International:
Jamaica 1982,
1991, 2001; IMF
International
Financial Statistics
EMGRijkt
Emigrant
share
Cross-skill
controls (1,
2 and 3)
Cross-skill
group
emigrant
shares
IPUMS
International:
Jamaica 1982,
1991, 2001; US
1980, 1990, 2000
IPUMS
International:
Jamaica 1982,
1991, 2001; US
1980, 1990, 2000
SREMGRijkt
Short-run
emigrant
share
I converted nominal annual wage income from all
sources of employment (given by the ‘incwage’ variable
in IPUMS) into real terms using the Jamaican CPI in the
annual IFS series (dates 1982, 1991, 2001), before
taking its natural log. I then calculated the mean log real
wage across all workers for whom this variable was not
missing in the IPUMS data set in each skill group. To do
so I multiplied each log real wage by the ‘wtper’ variable
(which gives the number of workers in the population
represented by that sample point) and summed this
across all workers in the skill group (to give total wage
income in the skill group), before dividing by the
number of workers in the skill group.
I took the number of Jamaican born workers in the US
using the ‘wtper’ variable in the US census data. I then
divided this, for each skill group, by the total number of
individuals (employed or unemployed) in Jamaica in
that skill group (using the Jamaican wtper variable).
The three cross-skill control variables are simply the
emigrant share in each of the three skill groups with the
same experience and occupation but different level of
education to the skill group of the dependent variable.
Cross-skill group control 1 is always the lowest of the
‘other three’ education groups, cross-skill control 2 the
second lowest, and cross-skill 3 the highest.
Identical to EMGRijkt, but counting only those Jamaican
born workers in the US with a value ‘abroad’ for the
‘mgrate5’ variable in the US census in the numerator.
LREMGRijkt
Long-run
emigrant
share
BRAMWGijkt
Brazilian
mean real
wage
US MWGijkt
US mean real
wage (used as
the
instrument
for EMGRijkt)
IPUMS
International:
Jamaica 1982,
1991, 2001; US
1980, 1990, 2000
IPUMS
International:
Jamaica 1982,
1991, 2001; US
1980, 1990, 2000
IPUMS
International:
Brazil 1980, 1991,
2000; IMF
International
Financial Statistics
IPUMS
International: US
1980, 1990, 2000;
IMF International
Financial Statistics
Identical to EMGRijkt, but counting only those Jamaican
born workers in the US with a value not equal to
‘abroad’ for the ‘mgrate5’ variable in the US census in
the numerator.
I first converted total nominal monthly income as given
by ‘inctot’ in the Brazilian census into a single currency:
the Cruzeiro in use in Brazil in 1980 (IPUMS reports
figures in terms of the currency in use at that census
date). I then deflated nominal values using the Brazilian
CPI in the annual IFS series. Finally I took the mean
Brazilian real wage across skill groups in the same way
as for the US above.
Identical procedure to MWGijkt, deflating using annual
IFS series ‘US CPI all items city average’.
34
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