Upload
dinhthu
View
217
Download
3
Embed Size (px)
Citation preview
Essays in Macro-Labour Economics
by
Parisa Mahboubi
A Thesis
presented to
The University of Guelph
In partial fulfilment of requirements
for the degree of
Doctor of Philosophy
in
Economics
Guelph, Ontario, Canada
© Parisa Mahboubi, March, 2017
ABSTRACT
ESSAYS IN MACRO-LABOUR ECONOMICS
Parisa Mahboubi Advisor:
University of Guelph, 2017 Dr. Stephen Kosempel
This dissertation consists of three independent chapters. In the first chapter, a life cycle
model of human capital accumulation through learning-by-doing is constructed with
heterogeneity in productivity and age. The model is used to evaluate the impacts of social
security reforms on the welfare of individuals, as well as the distribution of labour supply,
consumption, and physical capital accumulation over the life cycle in the long run. In the
reference economy, retirement is mandatory with a Pay-As-You-Go (PAYG) social security
system. The following policy reforms are considered: (i) terminating the social security system
with mandatory retirement, (ii) terminating the social security system with voluntary retirement,
and (iii) introducing voluntary retirement with the social security. The results from the policy
experiments show that even low earners prefer an economy without a social security system.
Furthermore, the impacts of introducing voluntary retirement on individuals’ decisions vary by
age and productivity. The retirement decision is also affected by the presence of the social
security system, and the amount of income redistribution within the system. In particular, low-
skilled individuals (non-college graduates) decide to retire earlier while high-skilled individuals
(college graduates) remain longer in the workforce. Taxation was shown to exacerbate these
effects. However, these results do not hold if human capital is assumed to be exogenous.
In the second chapter, the impacts of investment-specific and neutral technology shocks
on individuals’ decisions are studied in a life cycle model, populated by heterogeneous
individuals with respect to age. The results show that first the aggregate fluctuations are different in a
life cycle model with an investment-specific technology shock compared to the standard infinitely
lived agent models and in a model with only neutral technology shocks. Specifically, the role of
investment-specific technology shocks as a driving source of fluctuations is weak. The results
also show that the impacts of technology shocks on labour supply, consumption, and physical
capital depend on an individual's age and the nature of shocks. Individuals’ optimal decision is to
increase their current consumption due to a positive neutral technology shock. Therefore, old
individuals work more while young individuals borrow more physical capital. However, more
accumulation of physical capital is optimal for all except the young individuals when a positive
investment-specific technology shock is introduced in to the economy. This leads to a reduction
in consumption of all individuals, and a sharp increase in the labour supply of old workers.
The third chapter studies the labour market outcomes of second generation immigrants
compared to other natives (third generation) in Canada, with an emphasis on cognitive skills and
education. By using survey data from the 2003 International Adult Literacy and Skills Survey,
this paper shows that children of immigrants are more likely to obtain a university degree.
Moreover, they obtain higher test scores in cognitive skills and thus higher earnings compared to
children of non-immigrants in Canada. Educational attainment and literacy skills are found to be
important sources of success in the labour market for second generation immigrants. The positive
association between parental education and human capital of children illustrates how the
Canadian society benefits from the immigration point system in which immigrants with higher
level of human capital are selected through an intergenerational effect.
iv
ACKNOWLEGMENTS
I would like to sincerely thank Dr. Stephen Kosempel, and Dr. Miana Plesca for being
outstanding advisors and mentors throughout my doctoral studies. This thesis and my Ph.D.
degree would have been impossible without their guidance and support.
My sincere thanks also go to Dr. Thenasis Stengos, Dr. Laurent Cellarier, and Dr. Chris
McKenna for their advice and insightful comments.
I would like to express my gratitude to all faculty members and staff in the Department of
Economics.
Finally, I would specially like to thank my beloved family, Vahid and Shayan, for their
love and support throughout my entire doctoral studies.
v
Table of Contents
1 Social Security Reforms in a Life Cycle Model with Human Capital Accumulation and
Heterogeneous Agents .................................................................................................................... 1
1.1 Introduction ...................................................................................................................... 1
1.2 The Model ........................................................................................................................ 4
1.2.1 Household’s problem ................................................................................................ 5
1.2.2 Production ................................................................................................................. 7
1.2.3 Government............................................................................................................... 7
1.2.4 Competitive equilibrium ........................................................................................... 8
1.2.5 Solution methods ...................................................................................................... 8
1.3 Model calibration ............................................................................................................. 9
1.3.1 Demographics ........................................................................................................... 9
1.3.2 Policy parameters ...................................................................................................... 9
1.3.3 Technology and preferences ................................................................................... 10
1.3.4 Human capital ......................................................................................................... 10
1.4 Results and discussions .................................................................................................. 12
1.4.1 Life cycle analysis................................................................................................... 12
1.4.2 Model evaluation .................................................................................................... 13
1.4.3 Social security reforms ........................................................................................... 14
1.5 Conclusion ...................................................................................................................... 22
2 Life Cycle Analysis of Investment-Specific and Neutral Technology Shocks ..................... 36
2.1 Introduction .................................................................................................................... 36
2.2 The Model ...................................................................................................................... 38
2.2.1 Household’s problem .............................................................................................. 38
2.2.2 Production ............................................................................................................... 40
2.2.3 Government............................................................................................................. 40
2.2.4 Competitive equilibrium ......................................................................................... 41
2.2.5 Solution methods .................................................................................................... 41
2.3 Model calibration ........................................................................................................... 42
2.3.1 Demographics ......................................................................................................... 42
vi
2.3.2 Technology and preferences ................................................................................... 43
2.3.3 The human capital profile ....................................................................................... 43
2.3.4 Stochastic parameters.............................................................................................. 44
2.4 Results and discussions .................................................................................................. 45
2.4.1 Steady States Analysis ............................................................................................ 46
2.4.2 Neutral Technology Shocks .................................................................................... 47
2.4.3 Investment-Specific Technological shocks ............................................................. 48
2.4.4 Business Cycle Statistics......................................................................................... 50
2.5 Conclusion ...................................................................................................................... 52
3 Education, Skills and Labour Market Outcomes of Canadian Second Generation Immigrants
60
3.1 Introduction .................................................................................................................... 60
3.2 Data ................................................................................................................................ 63
3.2.1 Descriptive statistics ............................................................................................... 65
3.3 Specification models ...................................................................................................... 67
3.3.1 Key independent variables ...................................................................................... 68
3.4 Estimation results ........................................................................................................... 69
3.4.1 University outcomes ............................................................................................... 69
3.4.2 Literacy outcomes ................................................................................................... 70
3.4.3 Regression results for hourly wages ....................................................................... 70
3.4.4 Regression results from income equation ............................................................... 72
3.4.5 The effect of literacy components on the labour market outcomes ........................ 73
3.5 Conclusions .................................................................................................................... 73
vii
List of Figures
Figure 1.1: Hourly Wages Profiles of College and Non College Graduates and all Individuals . 30
Figure 1.2: Calibrated Efficiency Weights, , and Productivity Sequence,
by Type and Age ........................................................................................................................... 31
Figure 1.3: Steady States Profiles for High Type and Low Type Individuals for Baseline Model
....................................................................................................................................................... 32
Figure 1.4: Ability of the Baseline Model (LBD) to Replicate the Wages, Human Capital and
Hours Worked from the US Data for High Type and Low Type Individuals .............................. 33
Figure 1.5: Impacts of Social Security Reforms on Life Cycle Profiles of Low Type Individuals
....................................................................................................................................................... 34
Figure 1.6: Impacts of Social Security Reforms on Life Cycle Profiles of High Type Individuals
....................................................................................................................................................... 35
Figure 2.1: Steady state outcomes by age ..................................................................................... 54
Figure 2.2: Hours worked comparison between model and actual data ....................................... 55
Figure 2.3: Impulse response functions for aggregate variable after a positive neutral technology
shock. ............................................................................................................................................ 56
Figure 2.4: Impulse response functions after a positive neutral technology shock by age group 57
Figure 2.5: Impulse response functions for aggregate variable after a positive IST shock .......... 58
Figure 2.6: Impulse response function after a positive IST shock by age group .......................... 59
viii
List of Tables
Table 1-1: Calibrated Baseline Model Parameters with Heterogenous Agents ............................ 25
Table 1-2: Steady States Outcomes of Policy Reforms with Endogenous Human Capital
Accumulation ................................................................................................................................ 26
Table 1.3: Average Individual Outcomes of Policy Reforms with Heterogeneous Agents for
Separate Age Groups .................................................................................................................... 27
Table 1.4: Welfare Comparison with the Benchmark Economy .................................................. 28
Table 1.5: Steady States and Welfare Effects of Policy Reforms with Exogenous Human Capital
....................................................................................................................................................... 29
Table 2.1: Calibrated model parameters ....................................................................................... 53
Table 2.2: Business cycle statistics ............................................................................................... 53
Table 3.1: Summary Statistics for the labour market characteristics by gender ........................... 75
Table 3.2: Education, parental education, region of residence, and ethnicity by gender ............. 76
Table 3.3: Marginal effects after probit for the university outcomes ........................................... 77
Table 3.4: Estimation results of the literacy equations for males ................................................. 79
Table 3.5: Estimation results of the literacy equations for females .............................................. 81
Table 3.6: Regression results of the hourly wages by gender ....................................................... 83
Table 3.7: Regression results of the income equations ................................................................. 85
Table 3.8: The effects of the literacy components on the labour market outcomes ..................... 87
Table 3.A1: Distribution of occupation ........................................................................................ 88
` 1
Chapter 1
1 Social Security Reforms in a Life Cycle Model with Human
Capital Accumulation and Heterogeneous Agents
1.1 Introduction
A pay-as-you-go (PAYG) social security system has been adopted in the United States and many
other developed countries, mainly because it guarantees sufficient retirement earnings for the
elderly through redistributing income in the economy. In this system, income is redistributed
from individuals with higher lifetime earnings to those with lower lifetime earnings. In contrast,
there have been some concerns regarding the impacts of social security systems on saving
(Feldstein, 1974; Hubbard et. al, 1995), and labour supply decisions (Diamond and Mirrless,
1978). Following Auerbuach and Kotlikoff (1987), the macroeconomic and welfare implications
of various social security reforms have been extensively analyzed in the literature to cope with
the financial challenges of an aging population on the social security system1. However, in the
existing social security literature, labour productivity is mainly assumed to be exogenous.
Furthermore, the impacts of social security reforms on low-income individuals require more
attention, as the important goal of a social security system is to protect disadvantaged groups
such as low-income retired individuals. Consequently, the assumption of heterogeneity may be
necessary to evaluate policies in a life cycle framework. Conesa and Krueger (1999) also
confirm the importance of heterogeneity to study the political impact of social security reforms,
but the previous studies, even those that considered heterogeneity among individuals, focused on
1 Including Hubbard and Judd (1987); Imrohoroglu, Imrohoroglu and Joines (1995, 1999); Huggett and Ventura
(1999); Conesa and Krueger (1999); Nishiyama and Smetters (2007); Pries (2007); Rojas and Urrutia (2008); and
Chen (2010).
` 2
aggregate outcomes. This study shows that labour supply and retirement decisions significantly
differ by the level of earnings, particularly, when voluntary retirement is an option. Figure 1.1
illustrates that non-college graduates, on average, earn less during their working period
compared to college graduates. Therefore, this study investigates how a social security reform
impacts non-college (low-skilled individuals) and college graduates (high-skilled individuals)
differently over their life cycle in order to distinguish between high and low earners.
This study also contributes to the literature by incorporating a heterogeneous human
capital accumulation mechanism. It is important to account for human capital accumulation
when a change in the economy (e.g. a change to the social security tax rate) is studied since it
impacts the labour market decisions at all ages differently (Shaw, 1986; Heckman et al., 1998;
Imai and Keane, 2004; Hansen and Imrohoroghlu, 2009). In particular, Keane (2015) shows the
assumption of endogenous human capital through learning-by-doing2 (LBD) increases the effects
of permanent tax changes over time. Peterman (2016) also shows that the LBD human capital
accumulation results in different optimal tax policy, particularly due to different response of
young individuals in the economy. Furthermore, Alvarez-Albelo (2004) studied the role of
human capital accumulation through learning-by-doing in a general equilibrium model of social
security with one type of agent to show that the capital-labour ratio and the average hours
worked differ under the model with endogenous human capital compared to a model with
exogenous efficiency units of labour. As such, Alvarez-Albelo indicated that the assumption of
exogenous efficiency units of labour may lead to imprecise results, but it is not clear how social
security reforms influence individual’s decisions differently with heterogeneous human capital
accumulation.
In this study, a life cycle model of labour supply, human capital accumulation and physical
capital accumulation with heterogeneous agents has been constructed. The model has been
developed with the intention of explaining differences in human capital accumulation and labour
supply decisions between high-skilled and low-skilled workers in response to social security
reforms. Consequently, it explains wage differentials and life cycle wage growth in a general
equilibrium setting. In this model, skill is accumulated through past work experience or LBD
2 In general, two forms of human capital accumulation have been mainly adopted in the literature: learning-by-doing
(LBD) or on-the-Job training (OJT). With OJT mechanism, individuals acquire human capital by spending time to
learn while with LBD, individuals accumulate human capital through past experience.
` 3
mechanism3. Heterogeneity derives from two channels in order to capture differences in life
cycle decisions and behavior among individuals. First, the model allows individuals to differ
within an age group as a result of differences in learning abilities and thus productivities.
Second, the model allows learning abilities to vary by age. In the reference economy, it is
assumed that there exists a PAYG social security system and mandatory retirement4. Overall, the
model provides a reasonable fit to the life cycle characteristics observed in the Panel Study of
Income Dynamics 1962-2011 in the US economy.
Furthermore, the quantitative effects of heterogeneous human capital on the evaluation of
social security reforms are investigated in four cases: (i) terminating the social security system
with mandatory retirement, (ii) terminating the social security system with voluntary retirement,
(iii) allowing voluntary retirement with the social security system where pension benefits decline
while the social security tax rate remains unchanged, and (iv) allowing voluntary retirement with
the social security system in which the tax rate rises while pension benefit stays constant.5 The
same exercises with social security reforms have also been done with exogenous human capital
to quantitatively explore how the macroeconomic outcomes are affected by this assumption. It
will be demonstrated that accounting for endogenous human capital is important for the
evaluation of social security reforms with voluntary retirement since it leads to different
outcomes. Differences between the model with endogenous human capital and exogenous human
capital derive from the differences in the price of leisure. In the model with endogenous human
capital, where work experience accumulates human capital, the opportunity cost of the leisure
equals the wage plus the marginal value of work experience. Whereas, in the model with
exogenous human capital, the opportunity cost of leisure equals only the wage.
The results from policy experiments show that distinguishing between high and low income
earners is important and this is particularly true when looking at the effects that these social
3 Hansen and Imrohoroghlu (2009) studied the effect of endogenous human capital on average hours worked by age.
They argued LBD affects labour market decisions at all ages, the assumption of endogenous human capital
accumulation is important for the life cycle analysis, if human capital is accumulated through LBD. 4 In the early 1970s, about half of Americans were covered by mandatory retirement provisions and required to leave
their jobs at a specified age such as 65. Congress amended the Age Discrimination in Employment Act to abolish
mandatory retirement in 1986. 5 Studies that focus on the extending the retirement age as part of social security reforms include Hviding and
Merette (1998) for a number of OECD countries; De Nardi et al. (1999), and Conesa and Garriga (2003) for the
U.S.; Hirte (2002) for Germany; Henin and Weitzenblum (2005) for France; Beetsma et al. (2003) for the
Netherlands; Keuschnigg and Keuschnigg (2004) for Austria; and Koka and Kosempel (2014) for Canada.
` 4
security policies have on the decision to retire. There are significant differences in the optimal
retirement dates between low types and high types in the model. The retirement decision is also
affected by (i) the presence of the social security, and (ii) the amount of income redistribution
within the system. In particular, when retirement becomes voluntary, the labour market
participation of low types declines while high types work longer. In a social security system, low
types prefer voluntary retirement and high types are better off in an economy with mandatory
retirement due to the distributional effects. This is because low types have to work for a longer
period of time with mandatory retirement to make sure a sufficient retirement earnings as high
types are not permitted to work longer and pay more pension tax under mandatory retirement.
Overall, an increase in the tax rate raises the labour force participation of high-skilled individuals
and declines the working life of low types. The welfare outcomes also show that both types of
agents are better off when social security tax is zero. By setting the tax rate to zero, the net
earnings increase which lead to more saving. Consequently, higher physical capital results in a
higher wage rate. Imrohoglue et al. (1995, 1999) and Conesa and Kruger (1999) also found
similar results in which the optimal social security tax rate is zero.
The remainder of this chapter is organized as follows. In section 1.2, the model is developed
and the solution method to obtain the steady states values is described. Calibration of the model
is discussed in section 1.3. Section 1.4 presents the results and discusses the findings of the
model with endogenous human capital accumulation. The results of the policy reform in a model
with exogenous human capital are presented in section 1.5. The conclusions of the first chapter
are provided in section 1.5.
1.2 The Model
A general equilibrium model, based on the pioneering life cycle model developed by Auerbach
and Kotlikoff (1987), is considered with endogenous human capital accumulation and
heterogeneous agents. In the model heterogeneity derives from the initial level of human capital,
ability to learn, and age. There are two types of capital in the model: physical and human.
Physical capital is accumulated during life through investment. Agents begin their life with no
` 5
physical capital and leave no intentional bequests at the end of their life. On the other hand,
agents start their life with positive human capital and human capital is accumulated only by
allocating time to work and learning by doing.
Time is discrete and each period corresponds to one year in reality. Let s denote an
individual’s age and t the time period. A new generation of equal size is born every year.
Individuals face an uncertain life span and may live for a maximum of Tmax periods. All
surviving individuals retire at age Tr. Given the conditional probability, φs, of surviving from age
s to age s + 1, the cohort shares, θs, are obtained by
, where θs= φs-1 θs-1 (1.1)
Equation (1.1) indicates that the sum of the cohort shares equals to one.
1.2.1 Household’s problem
Individuals choose optimal consumption, c, and leisure, l, to maximize their discounted life time
utility:
,
(1.2)
where γ is the disutility of non-leisure activities, η is the coefficient of relative risk aversion, and
β is the discount factor.
In each period, each individual has been provided with one unit of time. During the
working period, time can be allocated among leisure, l, and work, n. Workers receive income
from providing labour services and from renting capital assets to the production sector. Retired
agents provide no labour services and instead, receive public pensions, b, from government. The
budget constraints for working and retired agents, respectively, are as follows:
` 6
(1.3)
(1.4)
where k is physical capital, r is the real rental rate of physical capital, h is worker efficiency or
human capital, τ is the labour income tax rate, and tr is a government transfer of accidental
bequests to the surviving individuals.
The model accounts for two types of heterogeneity in the production of human capital.
First, the levels of productivity are different for individuals within the same cohort such that high
type individuals, H, can accumulate more human capital compared to low types, L, at a given
age. In the model, the fractions of high types and low types are represented by ζ and 1- ζ,
respectively. This type of heterogeneity is necessary to create a group of low and a group of high
income earners. Second, the productivity in learning is different between cohorts and declines
with age. This type of heterogeneity is essential to match the wage profiles. For both types
i , it has been assumed that human capital is accumulated through a LBD mechanism
according to the following equation,
i
sts
i
sts
i
s
i
stsh
i
sts nhhh 1,1,1,,1 )1( (1.5)
here, the parameter h is the depreciation rate of human capital, ϕ is a parameter that affects the
speed of learning by doing, and i
s is a productivity parameter which is assumed to vary by age
and type. Hansen and Imrohoroglu (2009) and Alessandrini and et.al (2015) have used a similar
function for human capital accumulation. However, Alessandrini and et.al (2015) assumed that
human capital is acquired through formal education and Hansen and Imrohoroglu (2009) did not
account for heterogeneity by type in their learning-by-doing human capital accumulation
technology. In both studies, the productivity sequences decline with age but no explanation is
provided for this exogenous decline. One possible explanation might be that for a given
technology, there may exist diminishing returns to learning (Kosempel, 2007). Kosempel
suggests that as agents age they accumulate knowledge and will approach the technology
frontier. As this happens learning will become more difficult, causing a decline in learning
productivity.
` 7
1.2.2 Production
The production sector of the model consists of competitive firms which hire efficiency units of
labour, , and rent physical capital, , to produce output, .. Letting denote the depreciation
rate of physical capital, then the net-of-capital-depreciation production function for the
representative firm is assumed to take the constant returns to scale Cobb-Douglas form:
, (1.6)
where α is the capital share of output.
1.2.3 Government
In this economy, there is a pay as you go system in which government collects labour income
taxes from workers to finance the pension payments to the retired individuals. A balanced
budget is required to be maintained in every period, and the government’s budget constraint is
given by:
maxT
Ts
stttt
r
bLw (1.7)
Furthermore, in every period t, government equally redistributes the confiscated accidental
bequests through government transfer to the survivors:
(1.8)
` 8
1.2.4 Competitive equilibrium
For a given initial distribution of human and physical capital stocks, the stationary competitive
equilibrium in the model consists of a collection of policy rules:
for each type i, and factor prices such that:
1- The policy rules solve the optimization problem of each household in equation
(1.2) subject to (1.3) and (1.5) for , and (1.4) for .
2- Production factors are compensated by their marginal products:
3- Government balances its budget constraint and transfer constraint.
4- Commodity market clears:
α
α
5- In the factor markets, individual decisions and aggregate behaviors are consistent:
1.2.5 Solution methods
The steady state of the model is solved using the computational algorithms inspired by Heer and
Maussner (2005) as follows: First, we make a guess for the initial steady state values for
aggregate physical capital and aggregate labour. Second, the factor prices and pension benefits
are computed. Third, the household optimization problem is solved separately for both types
using backward induction. Then, the new aggregate values for labour and physical capital are
computed. If these values do not match the initial guesses then they are updated and this
procedure is repeated until convergence.
` 9
1.3 Model calibration
Particular values for the parameters of the model must be assigned to obtain numerical solutions
to the model. The parameters are calibrated to match averages in the US data or set to values that
are commonly used in the macroeconomics literature. Table 1.1 summarizes the calibrated values
for the parameters of the model that will be explained in this section.
1.3.1 Demographics
It is assumed that age 1 in the model corresponds to the start of one’s working life, that is, age 18
in reality. Individuals may live up to Tmax=60 years in order to match the life expectancy at age
18 of males born in 1960 estimated by Bell and Miller (2002). The survival probabilities are also
obtained from Bell and Miller (2002). Although human capital is accumulated in the model via
LBD, it is well known that age-earnings profiles differ by education level (see Figure 1.16).
Therefore, the fraction of high types, ζ, is taken to be 0.46 to be consistent with the fraction of
individuals who pursued an education beyond high school from the Panel Study of Income
Dynamics (PSID) for the period of 1969-2011.
1.3.2 Policy parameters
In the benchmark economy, it is assumed that individuals are not allowed to continue to work
when they start collecting their pension benefits. Mandatory retirement age, Tr, is set to 48 to
target the retired to active population ratio of 21.6%. It also matches the normal (or full)
retirement age of 66 at which individuals are eligible to collect their full benefits in the US.
Furthermore, the social security payroll tax rate of 10.1 % in 19787, which implies the gross
6 Figure 1.1 shows the real average hourly earnings by age in 1969 prices from the Panel Study of Income
Dynamics (PSID) 1969-2011. 7 10.1% equals to the US Old Age and Survivors Insurance (OASI) tax rate in 1978
` 10
replacement ratios of pension benefits at 64% and 37% correspondingly for low types and high
types. These ratios are comparable to replacement rates in the data in the way that the
replacement ratio for high earners is lower than low earners. The pension benefit, b, associated
with this tax rate is 0.1935 for the benchmark model.
1.3.3 Technology and preferences
The capital share, α, of 0.36 is taken from Kydland and Prescott (1982) and the depreciation rate
of physical capital, , is set to 10% per year as in Hansen (1985). The discount factor, β, and
disutility from work, ɣ, are chosen to be 0.9747 and 1.819, respectively, to target the return to
physical capital of 6% and the average time spent working of 0.3325 in the steady state. The rate
of return to physical capital is taken from Alessandrini et al. (2015) and the average time spent
working is generated from the Panel Study of Income Dynamics 1969-2011 for individuals aged
18 to 65. In the literature, the coefficient of the risk aversion is commonly assumed to be
between 1 and 2 (e.g. Imrohoroglu and et. al, 1998). Gandelman and Hernández-Murillo (2014)
estimate a constant relative risk aversion (CRRA) function with GMM to obtain the coefficient
of risk aversion for 75 countries using data from Gallup World Poll. The value of 1.384 for the
risk aversion parameter, ɳ, is taken from their estimate for the US.
1.3.4 Human capital
The parameters associated with human capital accumulation technology are calibrated as
follows: By rewriting the human capital accumulation function, the sequence of age-specific
learning abilities,
, for each type is estimated as follows:
ϕ (1.9)
` 11
The average time spent working, and efficiency weights or exogenous human capital,
, for each age s and ability type are obtained using data on real hourly earnings and annual
work hours from the Panel Study of Income Dynamics (PSID) 1969-20118. To do this, first, male
head of households are divided into two groups based on their level of educational attainment
and six age groups (18-24, 25-34, 35-44, 45-54, 55-64 and 65-77) are defined. In particular, low
type individuals are those who achieved at most a high school diploma while high types obtained
further education above high school. Second, the average hours worked, and the real average
hourly earnings, , for each age group and type are obtained. By using the average hourly
earnings, the efficiency weights for each type and for each age group are computed following the
methodology put forward by Hansen (1993). Then, polynomial interpolation method is used to
interpolate the values of average time spent at work and efficiency weights for each age and
type. The parameter ϕ is set to be 0.029 to target the ratio of average efficiency weights between
high types and low types from PSID10
. In particular, the average hourly earnings for each age
group is divided by the average of hourly earnings obtained for all age subgroup by type. In the
model, the initial levels of human capital for low and high types are chosen to be 0.5773 and
0.5855, respectively, to match the calibrated efficiency weights at age 18 (e.g. year 1 in the
model) for each type,
and
, from the data.
Furthermore, the depreciation rate of human capital, , is assumed to be the same across all
individuals regardless of their type. In the literature, there is no consensus on the value of the
depreciation rate of human capital particularly with LBD skill accumulation. In order to select a
value for this parameter, the age-specific learning abilities series are generated with different
values for the depreciation rate of human capital within an acceptable range (e.g. 1%, 5%, 7.5%
and 10%). The wage profile from the data has a humped shape indicating that the wage declines
toward the end of the working period due to human capital deccumulation. In order to obtain
similar profiles in the model, it requires either the learning ability series take negative values or,
8 Data for years 1998, 2002, 2004 and 2008 were missing.
9 Starting with an initial guess for ϕ, the sequence of age-specific learning abilities is generated to run a simulation to
obtain a profile of human capital for each type of agent. If the ratio of average human capital between high type and
low type does not match the ratio of average efficiency weights between high type and low type from the data, the
guess for ϕ is updated until convergence. 10
For example,
.
` 12
more plausibly, a depreciation rate of human capital that is sufficiently high. By setting ,
the model is able to replicate the declines in wage profiles late in life.
Panels (a) and (b) of Figure 1.2 illustrate the estimated human capital ( ) and age-specific
abilities ( i), respectively, over the working years by type and age. The efficiency weights have
a hump shape and are increasing at the beginning of the life and declining as individuals get
older. At any given age, the values of the efficiency weights are higher for high type agents
compared to low type individuals. The calibrated age-specific abilities decline by age for both
types and are higher for high types.
1.4 Results and discussions
This section presents the simulation results of the developed model with learning-by-doing at the
steady state. The simulated life cycle profiles are compared with the observed data from the
PSID for the period of 1969 to 2011. The life cycle profiles of labour supply are illustrated for
each type of agent to evaluate the ability of these models to replicate the life cycle profiles
observed in data. Then, a number of social security policy experiments are conducted and the
impacts of each policy on the variables of interest in the steady states are discussed.
1.4.1 Life cycle analysis
Panels (a) to (d) of Figure 1.3 present the corresponding steady state values of physical capital,
consumption, human capital and hours worked for the benchmark model by age and type.
Results indicate that each type of agent makes different decisions to maximize their utility over
the life cycle. High types devote less time to work and more to leisure when they are young,
compared to low types. This is an optimal response by the high types given the rapid increase in
wages they anticipate over their life cycle. For low types, wages are more constant over the life
cycle. The simulated physical capital-age profiles illustrate that the high types start their life with
borrowing, and hold fewer assets compared to low types in the model when they are young.
` 13
However, the rate of accumulating physical capital is higher for high types so they accumulate
more physical capital at any age above 37 in the model. Capital accumulation and labour
earnings are correlated. For example, high types start their life by spending less time to work and
borrowing to cover their expenses. However, when high types start allocating more time to work,
their earnings accelerate at a higher rate compared to low types due to their higher level of
human capital accumulation and consequently they are able to accumulate more physical capital
too.
Optimal choices by both types result in increasing consumption profiles during the
working periods but consumption declines sharply at the time of retirement which is consistent
with the literature (Bernheim, Skinner, and Weinberg, 2001; Hurd and Rohwedder, 2006).
Nevertheless, the reduction in consumption upon retirement is higher for high types than low
type agents. Human capital and hours worked have hump shapes which are consistent with the
corresponding life-cycle profiles from the actual data. During the working period, high type
agents accumulate a higher level of human capital at any age and allocate more time to work
with the exception of the first few years compared to low types. This is because high types are
more productive in learning compared to low types.
1.4.2 Model evaluation
Figure 1.4 presents the ability of the model to match the empirical life-cycle profiles for both
types for hours worked, wages and human capital. Data on wages and hours worked are from
PSID (1969-2011). Wages in both the data and model have been normalized to one at age 2011
since they have different units. The overall performance of the model is satisfying. The simulated
human capital and hours worked are able to replicate the main characteristics of data from PISD.
In particular, human capital increases quickly and labour supply slowly at the beginning of the
life cycle. On the other hand, the human capital profile is flat later in life while labour supply
declines towards the end of the working period. The calibrated productivity series play important
11
Note that the normalized wages for high type should not be compared to those for low types due to variation in the
wages at age 20 across types. The wage of high type is higher than the wage of low type at age 20.
` 14
roles in the success of the model to imitate the data. Thus, the developed model is capable of
strongly replicating the human capital series and wages across all age ranges. The model is not
fully able to match the life-cycle profile of time spent working, although there is an agreement
between the observed data and model for the shape of the labour supply profile of high type
individuals. The model slightly underestimates the labour supply at the end of working periods
for both types and overestimates it for low types at the beginning of life cycle. These
inconsistencies can be probably explained by the fact that the model does not account for some
features of the data that may impact the labour supply (e.g. indivisibilities in hours worked). In
reality, there is also more heterogeneity among individuals compared to what can be considered
in the model developed here. Other sources of heterogeneity that have not been modeled may
also cause discrepancies between the data and model for life cycle labour supply. That said, the
average hours worked is 31.8% for low types and 34.5% for high types in the data. In
comparison, in the model, low type and high type agents allocate, on average, 31.4% and 35.4%
of their time to work, respectively. Overall, the model provides a reasonable fit to the life cycle
characteristics observed in the data.
1.4.3 Social security reforms
This section provides the quantitative evaluation of the impact of social security reforms on the
economy and individuals’ decisions in the long run with an emphasis on heterogeneity among
agents by age and type. Four reforms are considered to study the economic effects and welfare
implications associated with eliminating the PAYG social security system ( ) and/or
introducing voluntary retirement:
Model 1 represents an economy with mandatory retirement and no PAYG social security
system.
Model 2 characterizes an economy with voluntary retirement and no PAYG social
security system.
In the next two experiments, we introduce voluntary retirement but keep the PAYG social
security system. Note, however, that this reform affects the government revenue. When
` 15
voluntary retirement is studied, in order to satisfy the government budget constraint, it is
necessary to either raise the contribution tax rate or lower the benefit level:
Model 3 corresponds to an economy with a social security system and voluntary
retirement wherein the payroll tax matches the social security tax rate in the benchmark
(BM) economy but the pension benefit is lower.
Model 4 illustrates an economy with a social security system and voluntary retirement in
such a way that the pension benefit is the same as it is in the BM economy while the tax
rate is higher.
Note that for all model economies, we assume that individuals can not start collecting their
pension benefits until they reach the full retirement age and pension benefits are tax exempted.
We study the social security reforms by first examining the life cycle and macroeconomic
effects. Then, we examine the welfare effects.
1.4.3.1 Life cycle and macroeconomic effects
Table 1.2 compares the long run economic outcomes after each policy implementation with the steady
state outcomes of the benchmark (BM) economy in which retirement is mandatory and there
exists a social security system as described in section 1.2. Although macroeconomic outcomes of
social security reforms are well known due to the vast existing literature, the life cycle analysis
of a reform needs more attention to understand how social security reforms impact individuals
differently by age and particularly by type. Figures 5 shows the life cycle profiles for physical
capital, consumption, human capital and hours worked for low type agents in panels (a) to (d),
respectively. Figure 1.6 illustrates the same life cycle profiles for high type agents. Furthermore,
Table 1.3 presents the average individual outcomes of policy reforms for separate age groups and
by type. The life cycle analysis shows that the impact of the social security reforms on labour
supply, physical capital, and consumption depend on an individual's age and type.
In Model 1, the elimination of the social security system with mandatory retirement results
in 14.7% and 6.9% increases in aggregate physical capital and labour, correspondingly,
compared to the benchmark economy. Consequently, the capital labour ratio is higher. The
` 16
increase in the capital-labour ratio causes a 11% reduction in the rental rate of physical capital
and a 2.4% increase in the wage rate. In an economy with no social security in which the sole
source of income during retirement is capital earnings, individuals have an incentive to save
more. Consequently, they accumulate more physical capital to acquire sufficient income to
finance their expenses during the retirement period. Furthermore, elimination of the social
security tax rate coupled with a higher wage rate has a substitution effect and an income effect
on labour supply. Overall, the results indicate that the substitution effect dominates the income
effect in which the average hours worked, , increases when . The increase in hours
worked in each period not only raises the current earnings but it also boosts up human capital
and consequently the future earnings of individuals. However, the impact of the social security
tax on labour-leisure decisions is greater for low types compared to high types. This is because
low types are less productive at work compared to high types. Therefore, without a social
security system, low type individuals need to work more to increase their earnings so that they
have sufficient savings for retirement. Due to a lower interest rate in this economy, both types
accumulate less capital when they are young (high types borrow more). However, middle-aged
and old workers spend more time at work and accumulate more physical capital to guarantee a
sufficient retirement income. Although individuals consume more during their working period,
consumption drops sharply upon retirement and stays below the consumption in the BM during
the retirement period due to lower retirement incomes.
Model 2 expands on the policy experiment in model 1 by allowing for voluntary retirement
in addition to the elimination of social security. The macroeconomic effects are qualitatively
similar to Model 1 in such a way that the aggregate physical capital, labour, consumption and
human capital are higher compared to the benchmark economy. Nevertheless, the elimination of
the social security tax accompanying with higher wage rate has different impacts on each type
and age when retirement is voluntary. Although both types choose to retire later in their life
compared to Model 1, high types’ working life duration (or labour force participation) increases
considerably by 9 periods compared to low types by 2 periods. The explanation for this is that
high types are relatively more productive later in life, and they will work more if given the
opportunity. However, average labour supply during the working period declines for high types
compared to the benchmark economy and Model 1 since they have less incentive to accumulate
more physical capital for their retirement due to being able to work longer. Comparing Model 1
` 17
and Model 2 reveals that a change in the labour force participation has different impacts on
physical capital at the individual level. The accumulation of physical capital is larger under
voluntary retirement for middle-age low types as a result of a relatively higher interest rate in
Model 2 than Model 1. In contrast, middle-age and senior high types accumulate less physical
capital under voluntary retirement since they receive labour earnings for longer periods and
consequently, they have less incentive to accumulate more physical capital for the retirement
compared to Model 1. The results in Table 3 also show a reduction in physical capital for middle
age high types compared to the correspondingly age group in the BM economy.
In Model 3, voluntary retirement is introduced into an economy with a social security
system. In this economy, the social security tax rate matches the benchmark economy. It results
in a 1.5% and 2.4% increase in aggregate physical capital and labour, correspondingly, compared
to the benchmark economy. Subsequently, a relatively lower capital-labour ratio results in a 2%
increase in the rental rate of physical capital and slightly decrease in the wage rate. Given the
same tax rate as benchmark economy, the pension benefits must also decrease by 6% since the
removal of mandatory retirement is associated with early retirement of low types. Furthermore,
the average time spent working for high types declines although they work longer compared to
the benchmark economy. Low types prefer to retire earlier since they are less productive at work
and their productivities decline faster as they age compared to high types. Thus, a reduction in
the wage rate makes working less attractive and discourages low types to work longer. Instead,
their average labour supply increases by 3.5% during their working period so they can save more
due to a higher rate of return compared to the benchmark economy. The decline in low type’s
labour force participation has some impacts on their consumption profile in which young and
middle-age groups consume less compared to the benchmark economy. The consumption during
the retirement is higher for both types in Model 3 since the pension benefits and interest rate are
higher.
Model 4 is similar to Model 3 in that there exits voluntary retirement and social security.
However, in model 4 the benefit level is increased to match its value in the BM economy. The
social security tax rate must increase by about 1.1% with voluntary retirement if the pension
benefit remains unchanged compared to the benchmark economy. This is because low types
leave the labour market earlier than the time they collect pension benefits and average hours
` 18
worked over the working period of high types decline by 7% even though they retire later. In this
economy, a larger decline in aggregate physical capital than in aggregate labour causes a lower
capital-labour ratio compared to the benchmark economy. As a result, the rental rate of capital
rises by 2.7% while the wage rate drops by 0.6%. Young low types accumulate more physical
capital and young high types borrow less due to a higher interest rate. In addition, the changes in
individuals’ labour force participation coupled with an increase in the tax rate are associated with
a negative response of middle-aged individuals on their savings. In particular, low types
accumulate less physical capital due to early retirement and high types need to save less for their
retirement as they work longer given a higher return on capital.
Comparing models 3 and 4, the results show that individuals respond differently in these
economies by type. In particular, an increase in the pension benefits and consequently the tax
rate does not promote an early retirement for high types while encourages low type individuals to
retire earlier. However, higher tax rate is associated with lower aggregate human capital in the
economy. Furthermore as tax rate increases, the average labour supply of high types decline
while low types increase their average hours worked. The results suggest that distinguishing
between high and low skill individuals is important when the social security policies are studied
particularly when these policies impact the decision to retire. These findings may also have some
policy complications for policy makers who seek solutions to alleviate the negative impacts of
population aging on the social security system and labour market.
1.4.3.2 Welfare effects
Following Koka and Kosempel (2014), the welfare benefits are measured as a fixed percentage
of consumption, Δ, that is required to make individuals indifferent between living in the
benchmark economy without compensation, and the alternative economy under a policy reform
with compensation at each age:
` 19
1
0
s
j
j
(1.10)
where the expected discounted life time utilities for each type of agent born in the benchmark
economy and the alternative economy under a given policy reform are denoted by
and
, respectively. Therefore, the percentage consumption compensation for each
type of agent is computed using:
(1.11)
Furthermore, the constant percentage of consumption compensation across all types of
individuals in the economy is obtained from the weighted expected discounted life time utilities
in the economy as it is utilized in Imrohoroglu et al. (1995) to measure the average utility in each
economy, :
1
0
s
j
j
(1.12)
The computed percentage consumption compensations at equilibrium for each type of
agent and for aggregate individuals are provided in Table 4. At the aggregate level, the results
show that individuals prefer the proposed policy changes to the benchmark. For example,
individuals born in Model 1 where social security is eliminated with mandatory retirement
require 0.18% reduction in per period consumption to be indifferent with the outcomes of
benchmark economy. However, the outcomes are interesting when the compensation variation is
computed for each type of agent.
First, the results alter at the individual level by type when voluntary retirement is
introduced with a social security system as in Model 3 and 4. In particular, high types born in the
benchmark economy are better off than high types born in an economy with social security and
voluntary retirement while low types prefer voluntary retirement. In Model 3 and 4, high types
` 20
require 0.008% and 0.015% increases in per period consumption to be as well of as high types in
mandatory retirement while low type require to give up 0.011% and 0.032% of their per period
consumption correspondingly. The reason for these differences is that the redistributional effects
of social security are larger in Model 4 than in the benchmark economy since benefits are not
proportional to taxes paid. In particular, high types bear a larger tax burden compared to the
benchmark economy due to an increase in tax rate. Low types benefit from an increase in the
amount of redistribution since they work for a shorter period of time but they receive the same
annual pension benefits.
Second, low types prefer to live in an economy without social security and pension
benefits during retirement. Although the amount of consumption in each period that low types
are required to sacrifice in order to be indifferent with the outcomes of benchmark economy is
0.05% lower than high types, the magnitude of the compensation variation is still significant for
low types. This is because the social security tax generates a distortion against labour supply, and
the cost associated with this distortion is larger than benefits of income redistribution through the
social security.
Third, both types prefer mandatory retirement when social security is eliminated since the
absolute compensation variation as a percent of consumption in each period is higher for both
types in Model 1 compared to Model 2. Koka and Kosempel (2014) explain that a coordination
problem in the unconstraint economy (the voluntary retirement economy) results in a lower
utility compared to an economy with mandatory retirement. When all high types are forced to
retire early, aggregate employment falls and consequently the capital-labour ratio declines. This
change positively affects the wage rate. The higher wage rate benefits all individuals and offsets
any costs associated with a shorter working life.
Finally, in an economy with social security and voluntary retirement, low types prefer an
economy with higher benefits even though it derives a higher tax rate while high types prefer an
economy with a lower tax rate. This happens because a higher tax rate leads to a shorter working
life for low type individuals and increases their life time utility due to more leisure they obtain,
while the working periods increases for high types. Furthermore, the redistributional effects of
` 21
social security are larger in Model 4 compared to Model 3, since benefits are not proportional to
tax paid. In particular, high types bear a larger tax burden due to an increase in the tax rate since
they retire later.
1.4.3.3 Exogenous human capital
In order to show why it is important to account for endogenous human capital when social
security policies are studied, the impact of social security reforms on the economy and
individuals’ decisions are investigated in an alternative model with exogenous human capital and
heterogeneous agents. Then, the outcomes from the alternative economy are compared with the
benchmark model which is described in section 2. In this economy, the exogenous human capital
for each type is taken from the calibrated human capital series, , in section 1.3.4.
Consequently, equation (1.5) is eliminated in this model. All parameters are taken from the
benchmark model to maintain the same characteristics of individuals for comparison purposes.
Similar to section 4.3, four policy reforms are considered.
Table 1.5 compares the steady states outcomes of this alternative economy with the
outcomes of the benchmark economy in section 4 and the outcomes of all policy models (e.g.
Model A1, Model A2, Model A3 and Model A4) with exogenous human capital. As it is
expected, the aggregate physical capital and aggregate labour are higher in the benchmark
economy with endogenous human capital compared to the alternative economy. However, a
larger increase in the aggregate physical capital compared to an increase in the aggregate labour
pushes the wage rate up by 0.4% while the interest rate declines by 1.9%. The reason is that in
the alternative economy, the wage rate is taken as given and individual’s labour supply decisions
are affected only through the opportunity cost of leisure. In the BM economy, an increase in
labour supply not only raises the current earnings of individuals but it also increases their future
earnings. Consequently, the average time spent working is higher for both types in the
benchmark economy compared to the alternative economy.
Comparing Table 1.2 and Table 1.5, the results show that the assumption of exogenous
human capital not only affects the key variables of the economy, but it predicts different
` 22
outcomes for the labour market participation of individuals in some cases when retirement is
voluntary. For example, after the elimination of social security and mandatory retirement in
Model 2, both high types and low types postpone their retirement by one more period when
human capital is endogenous compared to the corresponding model with exogenous human
capital. This is because first, the increase in the wage rate following the new policy is slightly
lower in the model with exogenous human capital compared to the model with endogenous
human capital. Second, a larger increase in the average labour supply of low types or a lesser
decline in the average labour supply of high types is not associated with higher human capital
accumulation to enhance the future earnings in the alternative economy after the reform. Thus,
individuals have less incentive to provide labour services for one more period.
Furthermore, comparing Tables 1.4 and 1.5 demonstrates how the assumption of exogenous
human capital leads to contradictory outcomes in a model with a social security system and
voluntary retirement. In particular, low types prefer Model 4 to Model 3 with endogenous human
capital due to a higher level of pension benefits and lower labour market participation, while the
results alter when human capital is assumed to be exogenous. Low types prefer Model A3 to
Model A4. This is because low types’ labour force participation declines more in this setting so
they have higher ability with extra leisure. A larger response among high types for their labour
market participation declines the pension benefits at a lower rate and increases the
redistributional effects of social security in Model 3 with the exogenous human capital.
Furthermore, high types are indifferent between Model 3 and Model 4 when human capital is
exogenous while the model of endogenous human capital accumulation leads to a different
outcome for high type since they are worse off in an economy with a higher social security tax
rate when retirement is voluntary.
1.5 Conclusion
In this study, a life cycle model of labour supply and human capital with heterogeneous agents
has been constructed. In the baseline model, human capital is accumulated through learning by
doing. Agents differ in productivity and initial level of human capital. In addition, productivity
` 23
declines by age. Then, two types of social security policies have been considered in constructing
various policy reforms. In one experiment, the PAYG social security system is eliminated and
the social security payroll tax rate and pension benefits are set to be zero with mandatory
retirement. In the second experiment, the PAYG social security system and mandatory retirement
are eliminated. The third and forth experiments represent voluntary retirement policy with a
social security system where either tax rate or pension benefits, respectively, matches the
baseline economy.
The results of these experiments demonstrate that individuals respond to a social security
policy differently by age and type. In particular, the variation in labour force participation with
voluntary retirement is diverse by type. Therefore, it is necessary to account for heterogeneity in
the model to study the social security systems. In general, both types prefer an economy with no
social security and welfare effect is stronger with mandatory retirement although retirement
consumption is lower than the reference economy. In a social security system, low types prefer
voluntary retirement and high types are better off in an economy with mandatory retirement due
to the changes in the distributional effects. Overall, an increase in the tax rate raises the labour
force participation of high-skilled individuals and declines the working life of low types.
Furthermore, the same exercises with social security reforms have been done with
exogenous human capital to explore how quantitatively macroeconomic outcome are affected by
this assumption. The results imply that in addition to aggregate economy, the behavior of
individuals impacted differently when retirement is voluntary. In particular, individuals prefer to
retire earlier due to lower opportunity cost of leisure with exogenous human capital. However, a
change in the tax rate does not have any impact on high types’ decision on when to retire. In
conclusion, the assumption of endogenous human capital is important for evaluation of social
security reforms with voluntary retirement.
` 24
` 25
Table 1-1: Calibrated Baseline Model Parameters with Heterogenous Agents
Parameters set to target Value from
US data
Value from
Model
Life expectancy at age 18 58.99
Retired to active population ratio 21.60% 21.1%
Average annual interest rate 6% 6%
Average time spent working of workers ( ) 0.3325 0.3325
/
1.5079 1.5079
Social security payroll tax rate in 1978 10.1%
` 26
Table 1-2: Steady States Outcomes of Policy Reforms with Endogenous Human Capital Accumulation
BM Model 1
%Δ from
BM Model 2
%Δ from
BM Model 3
%Δ from
BM Model 4
%Δ from
BM
K 1.0011 1.1485 14.7226 1.1614 16.0094 1.0163 1.5174 0.9814 -1.9624
L 0.2829 0.3023 6.8933 0.3161 11.7471 0.2895 2.3518 0.2806 -0.8047
Ha 0.9525 0.9546 0.2138 0.9901 3.9488 0.953 0.0519 0.9360 -1.7328
r 0.0599 0.0532 -11.2039 0.0565 -5.794 0.0612 2.1149 0.0616 2.7391
w 1.0101 1.0348 2.4424 1.0226 1.2426 1.0056 -0.4431 1.0043 -0.5729
b 0.1651 0 -100 0 -100 0.1551 -6.0731 0.1651 0
τ 0.101 0 -100 0 -100 0.101 0 0.1021 1.0505
K/Y 2.2455 2.3494 4.6278 2.2999 2.4246 2.2337 -0.5225 2.2287 -0.7485
K/L 3.5393 3.7985 7.3244 3.6743 3.8142 3.5104 -0.8152 3.4980 -1.1670
C 0.3462 0.374 8.0302 0.3844 11.0226 0.3493 0.8931 0.3488 0.7500
0.2951 0.3144 6.5457 0.3211 8.813 0.2956 0.1908 0.2938 -0.4398
0.4179 0.4498 7.6309 0.4693 12.3082 0.4256 1.8362 0.4272 2.2313
0.3325 0.3537 6.3945 0.3291 -1.028 0.3308 -0.4967 0.3328 0.0907
0.3141 0.3397 8.1497 0.3226 2.6996 0.3251 3.4861 0.3361 6.9966
0.354 0.3702 4.5663 0.3366 -4.911 0.3376 -4.6454 0.3289 -7.1027
47 47
49
43
39
47 47
56
51
53
a. Aggregate level of human capital in the economy; b. The dash over the variables indicates the average; c. The average labour supply
during the working period; d. Duration of working period.
` 27
Table 1.3: Average Individual Outcomes of Policy Reforms with Heterogeneous Agents for Separate Age Groups
Age Groups* Physical Capital
Consumption
Hours Worked
Low type High type
Low type High type
Low type High type
Benchmark Economy
18-35 0.3040 -0.3432
0.2250 0.3062
0.3782 0.3603
36-64 1.7185 1.4597
0.3175 0.4635
0.2743 0.3501
64+ 0.8948 1.5822
0.3421 0.4709
0 0
Model 1
18-35 0.1911 -0.6243
0.2608 0.3590
0.3732 0.3514
36-64 1.9771 1.4748
0.3428 0.5041
0.3190 0.3818
64+ 1.6984 2.4014
0.3252 0.4542
0 0
Model 2
18-35 0.2887 -0.5362
0.2550 0.3519
0.3774 0.3542
36-64 2.1893 1.2266
0.3472 0.5131
0.3009 0.3669
64+ 1.7969 2.0433
0.3542 0.5341
0.0221 0.1411
Model 3
18-35 0.3315 -0.3140
0.2231 0.3040
0.3791 0.3615
36-64 1.7453 1.3826
0.3153 0.4669
0.2467 0.3442
64+ 1.0011 1.6384
0.3522 0.5016
0 0.0558
Model 4
18-35 0.3267 -0.3032
0.2223 0.3028
0.3782 0.3623
36-64 1.6481 1.3863
0.3106 0.4672
0.2173 0.3428
64+ 0.9657 1.5508
0.3553 0.5103
0 0.0744
* Age groups represent the actual age groups in reality.
` 28
Table 1.4: Welfare Comparison with the Benchmark Economy
Model 1 Model 2 Model 3 Model 4
% Consumption Compensation:
Δ
-0.1776 -0.1688 -0.0035 -0.0129
Δl
-0.1568 -0.1509 -0.0113 -0.0320
Δh -0.2073 -0.1944 0.0079 0.0154
29
Table 1.5: Steady States and Welfare Effects of Policy Reforms with Exogenous Human
Capital
Outcomes AL
% Δ from Alternative Economy (AL)
BM
Model
A1
Model
A2
Model
A3
Model
A4
K 0.957 4.627 12.938 17.031 1.648 -1.721
L 0.272 3.882 6.229 12.289 -1.555 -0.673
r 0.061 -1.906 -10.804 -5.609 3.157 2.625
w 1.006 0.409 2.382 1.217 -0.667 -0.556
b 0.159 3.957 -100 -100 -1.696 0
τ 0.101 0 -100 -100 0 1.187
K/Y 2.235 0.458 3.997 2.683 2.070 -0.676
K/L 3.514 0.717 6.315 4.223 3.254 -1.055
C 0.332 4.158 7.432 10.372 1.177 0.983
0.286 3.189 5.974 8.255 0.137 -0.036
0.4 4.568 7.063 11.581 2.625 2.334
* 0.321 3.482 5.603 -0.335 0.505 0.216
0.305 3.095 7.320 3.378 7.835 7.027
0.341 3.888 3.800 -4.233 -7.190 -6.932
Δ
-0.182 -0.173 -0.019 -0.016
Δl
-0.161 -0.155 -0.040 -0.034
Δh
-0.213 -0.199 0.012 0.012
Working Period Duration:
tl 47 47 47 48 38 39
th 47 47 47 55 53 53
* The dash over the variables indicates the average.
30
Figure 1.1: Hourly Wages Profiles of College and Non College Graduates and all
Individuals
22 27 32 37 42 47 52 57 52 671.5
2
2.5
3
3.5
4
4.5
5
5.5
6
Age
Av
era
ge H
ou
rly
Wag
es
Non College individuals
College individuals
All individuals
31
Figure 1.2: Calibrated Efficiency Weights, , and Productivity Sequence,
by Type and Age
0 10 20 30 40 50 600.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Age
(a) Efficiency Weights
0 10 20 30 40 50 600
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Age
(b) Productivity Sequence
Low Type
High Type
32
Figure 1.3: Steady States Profiles for High Type and Low Type Individuals for Baseline
Model
0 20 40 60-1
0
1
2
3
(a) Physical Capital
0 20 40 60
0.2
0.4
(b) Consumption
0 10 20 30 40 500.5
1
1.4
1.8
Age
(c) Human Capital
0 10 20 30 40 500
0.5
Age
(d) Hours Worked
Low type High type
0 10 20 30 40 500.5
1
1.5
2(e) Wage
0 10 20 30 40 500
0.5
(f) Earnings
33
Figure 1.4: Ability of the Baseline Model (LBD) to Replicate the Wages, Human Capital
and Hours Worked from the US Data for High Type and Low Type Individuals
0 10 20 30 40 500.5
1
1.5
Wages Low Type
0 10 20 30 40 500
0.5
1
1.5
Wages High Type
0 10 20 30 40 500.5
1
1.5
Human Capital Low Type
0 10 20 30 40 500.5
1
1.5
Human Capital High Type
0 10 20 30 40 500
0.3
0.6
Age
Hours Worked Low type
0 10 20 30 40 500
0.3
0.6
Age
Hours Worked High Type
Model
Data
34
Figure 1.5: Impacts of Social Security Reforms on Life Cycle Profiles of Low Type
Individuals
0 20 40 60
0
1
2
3
(a) Physical Capital Low Type
0 20 40 600.15
0.2
0.3
0.4
(b) Consumption Low Type
0 20 40 600.5
0.7
0.9
Age
(c) Human Capital Low Type
0 20 40 600.1
0.2
0.3
0.4
Age
(d) Hours Worked LowType
BM Model 1 Model 2 Model 3 Model 4
35
Figure 1.6: Impacts of Social Security Reforms on Life Cycle Profiles of High Type
Individuals
0 20 40 60
-1
0
1
2
3
4
5
(a) Physical Capital High Type
0 20 40 600.2
0.3
0.4
0.5
0.6
(b) Consumption High Type
0 20 40 60
0.6
0.8
1
1.2
1.4
1.6
Age
(c) Human Capital High Type
0 10 20 30 40 50 600.1
0.2
0.3
0.4
0.5
Age
(d) Hours Worked High Type
BM Model 1 Model 2 Model 3 Model 4
36
Chapter 2
2 Life Cycle Analysis of Investment-Specific and Neutral
Technology Shocks
2.1 Introduction
One of the central issues in business cycle analysis is what the driving sources of fluctuations
are. In the RBC literature pioneered by Kydland and Prescott (1982), neutral technology shocks
are determined as the main source of fluctuations.12
Whereas, Fisher (2006) and Justiniano et al.
(2010) show that the major variability of output and hours are associated with investment-
specific technology shocks as in Greenwood et al. (1988), rather than neutral technology shocks.
Fisher (2006) also suggests that it is important to account for both neutral and investment-
specific technology shocks as they together explain 40% to 60% of fluctuations in output and
hours. However, the role of investment-specific technology shocks in business cycles has not
been studied in a life cycle model, which can account for heterogeneity in responses across ages.
This study incorporates a finitely lived-agent model into a dynamic stochastic general
equilibrium framework to investigate the role of technology shocks as the source of business
cycle fluctuations. Two types of technology shocks are considered: neutral technology (NT) and
investment-specific technology shocks (IST). Greenwood et al (1997 and 2000) documented that
the correlation between relative price and quantity of new equipment is negative. This suggests
that equipment becomes less expensive due to technological improvements and consequently,
more equipment is accumulated. Therefore, the inverse of the relative price of investment has
been used to obtain a measure of IST that accounts for progress in the quality of capital. This
study also uses this measure for the realization of IST shocks. In order to identify the neutral
12
For example, see Hansen (1985), King et al. (1988), and King and Robelo (1999).
37
technology shock, it is important to separate the contributions of neutral technology shock from
other non-neutral technology (Carlaw and Kosempel, 2000; Bocola, Hagedorn, and Manovskii,
2014). In the model, fluctuations in productivity, excluding improvements in the quality of
capital, represent neutral technology shocks.
One of the main contributions of this study is to identify whether the cyclical properties at
the aggregate level are affected differently in a life cycle model when an IST shock hits the
economy compared to the infinity lived-agent models. The RBC literature shows that the
properties of the model after a NT shock remain unchanged when an overlapping generation
model is taken into the account (e.g. Rios-Rull, 1996; Krusell and Smith, 1998). The second
contribution of this study is to explore how technology shocks affect individuals differently by
age.
The results show that first the aggregate fluctuations are different in a life cycle model with
an IST shock compared to the standard infinitely lived agent models and in a model with only
NT shocks. In particular, the role of an IST shock as a driving force of fluctuations is small
where it accounts for only 10% of variation in output. In comparison, IST shocks are reported to
be responsible for about 30% and 50% of fluctuations in output in Greenwood et al. (2000) and
Justiniano et al. (2010) respectively. De Bock (2007) also shows that the importance of IST
declines from 40% to 6% when search and matching frictions are introduced in to the standard
RBC model as matching the new workers is time consuming. In this study, NT conversely
accounts for about 67% variations in output.
The outcomes are different by shock and type of model due to disparities in the nature of NT
and IST shocks and behaviour of individuals by age. The reason that the IST shocks in the life
cycle model are not as important as in the models with infinitely lived agents is that a life cycle
model accounts for differences in individuals decisions by age. Even though consumption
declines at the same rate for all individuals, labour supply and physical capital respond
differently by age with an IST shock. In particular, younger individuals even borrow more and
slightly increase their labour supply due to a reduction in the wage rate. Furthermore, differences
in the NT and IST shocks are due to differences in the nature of the shocks. In particular, a NT
shock directly impacts the production of goods through production sector in the economy and
boosts marginal returns to inputs while an IST shock affects the marginal efficiency of
investment and only triggers accumulation of physical capital directly. As a result, the wage rates
38
decline initially after the IST shocks and the response of labour supply is relatively small
particularly among younger workers. Despite the fact that individuals consume less in order to
accumulate more physical capital with IST shocks, less physical capital is accumulated in the
economy relative to the NT shocks. Therefore, NT shocks are more important than IST shocks in
the business cycle fluctuations
The remainder of the second chapter is organized as follows. In section 2.2, the model is
developed and the solution methods to obtain the steady states values and to calculate business
cycle movements are described. Calibration of the model is discussed in section 2.3. Section 2.4
presents the results and discuses the findings. The conclusions of this chapter are provided in
section 2.5.
2.2 The Model
A life cycle model is considered where time is discrete. Let s denote an individual’s age and t the
time period. It is assumed that a new generation of equal size is born every year. Individuals
begin their lives by working, retire at age Tr, and live up to Tmax periods.
Given the conditional probability, φs, of surviving from age s to age s + 1, the cohort
shares, θs, are given by
, where θs= φs-1 θs-1 (2.1)
Equation (2.1) indicates that the sum of the cohort shares equals to one.
2.2.1 Household’s problem
Individuals choose consumption, c, and leisure, l, to maximize their expected discounted life
time utility:
39
, (2.2)
where γ determines the relative importance of leisure, η is the coefficient of relative risk
aversion, and β is the discount factor.
In each period, each individual has been provided with one unit of time. During the
working period, time can be allocated among leisure, l, and work, n. Workers receive income
from providing labour services and from renting capital assets to the production sector. Retired
agents provide no labour services and instead, receive public pensions, b, from government.
Individuals begin their life with no physical capital and leave no intentional bequests at the end
of their life. Physical capital, k, is accumulated during life through investment, i, according to
(2.3)
where is the depreciation rate of physical capital, and q indicates the current state of
investment-specific technology. It is assumed that q is stationary and represents only the
stochastic component to IST. The stochastic possess for investment-specific shocks is:
(2.4)
with .
The budget constraints for working and retired agents, respectively, are as follows:
(2.5)
(2.6)
where r is the real rental rate of physical capital, h is worker’s efficiency weights or age-specific
human capital, τ is the labour income tax rate, and tr is a lump sum government transfer or tax.
In view of the fact that heterogeneity in the RBC models to some extent improves the predictions
(e.g. Alessandrini et al. 2015; Hansen and Imrohoroglu, 2009; Gomme et al., 2004; Maliar and
Maliar, 2001), age-specific human capital values are imposed.
40
It is worth mentioning that an increase in q or improvement in the quality of new capital
lowers the cost of capital. The reason is that represents the relative price of capital in terms
of consumption in the budget constraints. In other words, an individual can invest in physical
capital, in each period, by sacrificing units of consumption.
2.2.2 Production
The production sector of the model consists of competitive firms which hire efficiency units of
labour, , and rent physical capital, , to produce output, .. The production function for the
representative firm is assumed to take the constant returns to scale Cobb-Douglas form:
(2.7)
where α is the capital share of output and zt denotes the state of neutral technology which follows
the stochastic process
(2.8)
with .
2.2.3 Government
In this economy, there is a pay as you go social security system. The government collects labour
income taxes from workers and accidental bequests from those who die before Tmax. Government
revenue is used to finance pension payments to the retired individuals. A balanced budget is
required to be maintained through a lump sum transfer or tax in every period. The government’s
budget constraint is given by:
(2.9)
41
2.2.4 Competitive equilibrium
For the given initial distribution of physical capital stocks and the government instruments ( ),
the stationary competitive equilibrium in the model consists of a collection of policy rules:
,
and factor prices such that:
6- The policy rules solve the optimization problem of each household in equation
(2.2) subject to (2.5) for , and (2.6) for .
7- Production factors are compensated by their marginal productivity:
8- Government balances its budget constraint.
9- The commodity market clears:
α
α , (2.10)
where the law of motion for aggregate physical capital is:
10- In the factor markets, individual decisions and aggregate behaviors are consistent:
2.2.5 Solution methods
Inspired by Heer and Maussner (2005), the computational algorithms to solve the non-stochastic
steady state of the model are as follows: First, we make a guess for the initial steady state values
for aggregate physical capital and aggregate labour. Second, the factor prices and pension
benefits are computed. Third, the household optimization problem is solved using backward
induction. Then, the new aggregate values for labour and physical capital are computed. If these
42
values do not match the initial guesses then they are updated and this procedure is repeated until
convergence.
Next, positive neutral and investment-specific technology shocks are disjointedly introduced
in the model to study the role of each technology shock on business cycles. To do this, the first
order conditions are log-linearized around the non-stochastic steady state to compute the
transitional dynamics and business cycle statistics. A system of linear equations is numerically
solved in order to study the fluctuations. Note that the model requires being stationary at the
steady states. Then, a positive one percent shock to each type of technology is independently
introduced into the model. The impulse response functions are acquired in order to demonstrate
the time path that directs the economy toward the steady state after the shocks. Lastly, the
average business cycle statistics over 1000 runs, consisting of 100 periods, are generated for each
technology shock as well as when both shocks are combined. These statistics are compared to the
annual business cycle statistics for U.S. economy.
2.3 Model calibration
Values for the parameters of the model must be assigned in order to obtain numerical solutions to
the model. The parameters are set to match averages in the US data or set to values that are
commonly used in the macroeconomics literature. Table 2.1 summarizes the values for the
parameters of the model that will be explained in this section.
2.3.1 Demographics
It is assumed that age 1 in the model corresponds to the start of one’s working life, that is, age 18
in reality. Individuals may live up to Tmax=60 years in order to match the life expectancy at age
18 of males born in 1960 estimated by Bell and Miller (2002). The survival probabilities are also
obtained from Bell and Miller (2002). In the model, it is assumed that individuals are not allowed
to continue to work when they start collecting their pension benefits. Mandatory retirement age,
43
Tr, is set to 48 to target the retired to active population ratio of 21.6%. It also matches the normal
retirement age13
of 65 at which individuals have been eligible to collect their full benefits in the
US for many years. Furthermore, the social security payroll tax rate of 10.7% is taken from
Conesa and Krueger (1999).
2.3.2 Technology and preferences
The capital share, α, of 0.36 is taken from Kydland and Prescott (1982, 1977) to match the US
time series data. The discount factor, β, and disutility from work, ɣ, are chosen to be 0.974 and
1.817, respectively, to target the return to physical capital of 6% and the average time spent
working of 0.3325 in the steady state. The rate of return to physical capital is taken from
Alessandrini et al. (2015) and the average time spent working is generated from the Panel Study
of Income Dynamics (PSID) 1969-2011 for individuals aged 18 to 65. By setting the
depreciation rate of physical capital to 6% per year as in Alessandrini et al. (2015), the average
physical capital to labour ratio of 3 is maintained. In the literature, there is no consensus on the
coefficient of the risk aversion. It is commonly assumed to be between 1 and 2 (e.g. Imrohoroglu
and et. al, 1998). For example, Gandelman and Hernández-Murillo (2014) estimate a constant
relative risk aversion (CRRA) function with GMM to obtain the coefficient of risk aversion for
75 countries using data from Gallup World Poll. The value of 1.384 for the risk aversion
parameter, ɳ, is taken from their estimate for the US.
2.3.3 The human capital profile
The efficiency weights or human capital, , for each age s are obtained using data on real hourly
earnings from the Panel Study of Income Dynamics (PSID) 1969-201114
. To do this, first, male
head of households are divided into six age groups of 18-24, 25-34, 35-44, 45-54, 55-64 and 65-
77. Second, the real average hourly earnings, , for each age group is obtained. By using the
13
It is also known as the full retirement age. 14
Data for years 1998, 2002, 2004 and 2008 were missing.
44
real average hourly earnings, the average efficiency weights for each age group are computed
following the methodology put forward by Hansen (1993). In particular, the average hourly
earnings for each age group are divided by average hourly earnings for all subgroups. Then,
polynomial interpolation method is used to interpolate the values of human capital for each age.
Panel (a) of Figure 2.1 illustrates the calibrated efficiency weights over the working years by
age. The efficiency weights have a slight hump shape. They are increasing quickly at the
beginning of the life and then only decline slightly toward the end of the working period.
2.3.4 Stochastic parameters
The inverse of relative price of investment to consumption,
, is used to estimate the parameters
of the stochastic process for q as follows:
where,
with ) and .
To do this, yearly data on the price index of consumption is divided by the price index for
private fixed investment in structures and equipment in order to obtain the inverse of relative
price of investment to consumption. The price indexes are directly taken from the National
Income product Account (NIPA) for the sample period 1982 to 2012. The estimates for and
are 0.817 and 0.0105 respectively.
Following Greenwood and et al (1997), Fisher (2006) argue that the NIAP investment
deflator is not fully adjusted for quality, particularly, prior to 1982. Consequently, they used a
quality adjusted equipment deflator from Cummins and Violante (2002) which is an update of
Gordon’s 1990 series for the sample period 1955-2000. However, Carlaw and Kosempel (2000)
claim that the procedure for quality adjustment has been improved and the previous estimates are
revised.
45
Following Carlaw and Kosempel (2000), the neutral technology series is obtained from the
production function:
. Then, the parameters of the neutral technology shock
process are obtained as follows:
where,
with ) and .
Several steps need to be taken to generate the neutral technology series. First, the aggregate
labour is obtained using data from Bureau of Labor Statistics (1982-2012), and represents total
non-farm hours worked. Second, the physical capital series is constructed using the real domestic
private investment series from the NIPA and then, iterating over the law of motion provided in
equation (2.3). The initial value for physical capital is chosen to generate a steady state growth
rate of 4.387 for the stock of physical capital in order to match the average annual growth rate of
real domestic private investment in the NIPA data for the sample period 1982 to 2012. Lastly,
the NIPA’s output measure needs to be adjusted to remove the quality component in new capital
goods. This is because as in equation (2.10), output is measured in units of consumption and
therefore, quality improvements are not directly included. However, the components of real
output in data are not measured in units of consumption and contain the quality improvement in
investment.15
Thus, investment component of output (Real Gross Domestic product) from the
data is divided by the measure if IST, q, in order to remove the quality component of investment,
using data from NIPA (1982-2012).Therefore, the parameters and are set to be 0.895 and
0.0133 respectively.
2.4 Results and discussions
The section 2.4.1 presents the simulation results of the model at the non-stochastic steady state
where and are set to one. Then, in sections 2.4.2 and 2.4.3, the impact of neutral and
15
For more details, see Carlaw and Kosempel (2004).
46
investment-specific technology shocks on the economy and individuals’ decisions over the life
cycle are investigated.
2.4.1 Steady States Analysis
Panels (b) to (d) of Figure 2.1 present the corresponding steady state values of labour supply,
physical capital, and consumption by age. Results indicate that individuals make different
decisions to maximize their utility over the life cycle. Labour supply has a hump shape which is
consistent with the corresponding life-cycle profile from the actual data presented in Figure
2.216
. In particular, prime age workers devote more time to work and less to leisure than younger
and older workers. This is an optimal response for individuals given the rapid increase in wages
they anticipate over their midlife period. Overall, the model is more able to predict labour supply
decisions of younger and middle age worker relative to older workers who are paid the most but
work less. In particular, reduction in labour supply among older workers is larger compared to
the data. Furthermore, capital accumulation and labour earnings are correlated. The simulated
physical capital-age profiles illustrate that individuals start their life with borrowing to cover
their expenses as they initially allocate less time to work because they are initially less
productive at work.17
When they start allocating more time to work due, their earnings accelerate
at a high rate due to their higher level of productivity and consequently they are able to
accumulate more physical capital. In particular, they accumulate physical capital at any age
above 2718
. Optimal choices result in increasing consumption profiles during the working
periods but consumption declines sharply at the time of retirement due to reduction in the
earnings upon the retirement and increase in leisure which is consistent with the literature
(Bernheim, Skinner, and Weinberg, 2001; Hurd and Rohwedder, 2006).
The steady state results show how individuals’ decisions over consumption, labour
supply, and the accumulation of physical capital are age-dependent and vary over the course of
16
Data on hours worked are from PSID (1969-2011) 17
If individuals anticipate no change in their wages over time, they start their life with accumulating physical
capital. It happens when human capital is flat and age-independent. 18
It is equivalent to age 10 in the model.
47
their life. Based on this, we also expect individuals will respond differently to a shock by age.
Thus, aggregate outcomes may be different in a life cycle model compared to an infinitely-lived
agent model when a shock is introduced into the economy. Differences in individuals’ decisions
by age and their impacts on the economy by type of technology shock are investigated in the
following subsections.
2.4.2 Neutral Technology Shocks
Figure 2.3 presents the impulse response functions for the aggregate variables to a positive one
percent neutral technology shock. The percent deviations from the steady states after the shock
show that all variables are pro-cyclical. The outcomes are consistent with the typical responses in
the RBC literature and the responses are well understood (e.g. Alessandrini et al., 2015).
Innovations to neutral technology impact output directly, and lead to an increase in the marginal
products of labour and physical capital. Therefore, the boost in the returns to working and
savings, cause physical capital and labour supply to respond positively due to the NT shocks. An
increase in output also leads to a positive response for consumption since it is a normal good.
The marginal rate of transformation between physical capital and consumption goods remains
unchanged since the relative price of consumption goods to physical capital is not affected by the
NT shocks.
One of the advantages of developing a life cycle model is that we are able to provide
insight about how individuals respond differently to a shock by age. Panels (a) to (d) of Figure 4
show the impulse response functions for labour supply, net labour earnings, consumption, and
physical capital, correspondingly, after a positive neutral technology shock. Five age groups are
defined: 18-28, 29-39, 40-50, 51-64 and 65-77 years of age where the last group consists of
retired individuals. Labour supply responds positively to a positive neutral technology shock for
individuals at any age group due to a sharp increase in the wage rate which leads to a positive
response of net labour earnings. However, the increase in labour supply is stronger for senior
workers who are in the age group 51-64 compared to the younger individuals. This is due to the
fact that retirement at age of 65 is mandatory and senior workers face a shorter working horizon
48
and have a limited chance to take advantage of a rise in the wage rate. Thus, it is optimal for this
age group to substitute more leisure for consumption to maximize their discounted life time
utility. Furthermore, senior workers are relatively more productive than younger workers, but
their human capital diminishes as they age. Therefore, current leisure is more expensive than
next period leisure for this age group, whereas the opposite is true for the young.
The consumption boom is mainly driven by working individuals after a positive neutral
technology shock due to simultaneously increases in the wage rate and renal rate of physical
capital. The positive response of consumption is moderate for retired individuals since their
retirement earnings raise only through their capital earnings due to an initial positive response of
the rental rate. In regards to physical capital after a NT shock, a disparity in the behavior of
younger groups is surprisingly observed. In particular, individuals aged 18-27 who were
borrowers at the steady states need to increase their debt in order to compensate for an increase
in their consumption as an increase in their earnings is not adequate. Thus, they maximize their
life time utility by substituting future consumption for current consumption instead of more
current leisure as they are less productive at work and an increase in the wage rate is not
sufficient enough to make leisure less attractive. Conversely, individuals aged above 28
accumulate more physical capital due to a higher return to physical capital. However, physical
capital is more responsive to the NT shocks for individuals aged 28-37 since they face a
relatively longer horizon in their life.
2.4.3 Investment-Specific Technological shocks
Figure 2.5 presents the impulse response functions for the aggregate variables to a positive one
percent IST shock in the model. The adjustment of key variables towards their steady states is
slower after an IST shock compared to a neutral technology shock. The differences between the
dynamic behaviors of the aggregate economy after a neutral technology shock relative to an IST
shock derive from the differences on how the production function is affected by shocks. In
particular, the production of all goods is affected homogenously by neutral technology shocks,
whereas the cost of investment goods relative to consumption goods changes when IST shocks
49
hit the economy. Thus, a positive IST shock directly increases the investment opportunities and
impacts the production of physical capital, but the production technology for consumption goods
is not directly affected.
The percentage deviations from the steady states after an IST shock show that all
variables except wages and consumption are pro-cyclical. Initially, consumption responds
negatively to the IST shock. This is due to the fact that current consumption and leisure are more
expensive compared to future consumption. Thus, current consumption declines while labour
supply initially increases after a shock due to the substitution effects. In particular, individuals
substitute current consumption for future consumption due to the reduced cost of physical
capital. As a result, there is an investment boom. Labour supply responds positively as agents
want to work more to finance capital investment. The positive response of labour supply leads to
a reduction in the wage rate initially. As a result, the return to physical capital initially rises due
to a reduction in capital to labour ratio. Innovations to investment-specific technology results in
the accumulation of more physical capital due to a reduction in the price of investment and,
consequently, output increases. Furthermore, as physical capital is accumulated, the rental rate of
physical capital declines and the wage rate increases in the following periods. Finally,
consumption gradually rises with a fall in the rental rate of physical capital and an increase in
output.
The dynamic behavior of investment and consumption are consistent with outcomes in
Fisher (2006). In particular, investment reaches its maximum level immediately and
consumption drops first before starting to increase while Greenwood et al. (2000) found a
positive response of consumption after an IST shock. The response of output is moderate but
more persistent with IST shocks relative to NT shocks. It increases after the shock due to an
immediate response of labour supply and curves U-shaped similar to the physical capital so IST
affects output through physical capital more than through labour supply in the following periods
after the shock.
Figure 2.6 shows the impulse response functions by age group for labour supply, net
labour earnings, consumption, and physical capital after a positive IST shock in panels (a) to (d),
correspondingly. Similar to neutral technology shocks, labour supply responds positively and
strongly to IST shocks for senior workers who are in the age group 51-64 compared to the
50
younger individuals. Since older workers face a shorter horizon before their retirement, they
want to work more and invest further, so that they can boost their retirement income. However,
the response of labour supply is more moderate for all age groups after an IST shock relative to a
neutral technology shock due to the fact that an IST shock has no direct effect on output and
labour productivity. Despite a positive response of labour supply, net labour earnings respond
negatively to the shock due to negative response of wages.
After a positive IST shock, most individuals accumulate more physical capital except the
youngest individuals. The shock directly improves the production of physical capital, so physical
capital becomes cheap relative to consumption. Therefore, it is an optimal decision to
accumulate more physical capital in order to increase their future consumption after a positive
IST shock except for those young individuals who are least productive at work and have no
capital earnings. The reason is that the youngest workers start their life with no physical capital
and have to borrow as their labour earnings are not high enough to cover their consumption
expenditures due to having low productivity at work. After an IST shock, labour earnings of the
youngest workers declines due to a reduction in the wage rate and insufficient response of labour
supply so they are required to borrow more and consume less to balance their budget constraint.
This is the main difference between finite and infinite horizon models, where all ages invest
more in an infinitely lived agent model. However, similar to NT shocks, individuals aged 28-37
accumulate more physical capital. Consequently, the immediate responses of current
consumption for all individuals are negative due to a slower response of output as IST shock
impacts output indirectly through the accumulation of more physical capital. However,
consumption changes its direction and increases as the formation of new physical capital
improves future output.
2.4.4 Business Cycle Statistics
Table 2 shows the annual business cycle statistics for U.S. economy along with average business
cycle statistics over 1000 runs by different types of technology shocks. To do this, the natural
logarithms of the simulated series are obtained and then, the Hodrick-Prescott filter with the
51
smoothing parameter of 6.25 as in Rvan and Uhlig (2002) is applied to de-trend the series. The
corresponding business cycle statistics for output, investment and consumption for the US
economy are obtained using data from US Bureau of Economic Analysis (1982-2012). Output
represents the real gross domestic product adjusted by removing q as in section 3.4, and
consumption is personal nondurable and services consumption expenditure. Investment stands
for gross private domestic investment which includes investment-specific technology or quality
component in the NIPA series. Therefore, investment series from the model is multiplied by q to
make model-data comparison possible. Labour supply statistics in table 2.2 for the US economy
are obtained using data from CPS, March Supplement (1982-2012). Labour supply indicates
actual hours worked in a week before the time of survey by employed males.
Regarding U.S. data, investment fluctuates about 2.7 times as output while labour supply
and consumption volatilities are 0.3 and 0.4 of output correspondingly. In the model, the
fluctuations in investment are about 4.7 times higher than output when both shocks are
combined. It is not surprising that investment fluctuates more relative to output with IST shocks.
Furthermore, labour supply and consumption volatilities are correspondingly 0.3 and 0.5 of
output in the model. Relative to US data, labour supply and consumption fluctuate less and
investment fluctuate more in the model when both shocks are combined. Therefore, the model
underestimates the fluctuations in consumption and labour supply which is typical in the RBC
literature. Labour supply fluctuations are very low for young workers relative to data.
Overall, Output fluctuates 0.7 times as output in U.S. economy indicating technology shocks
are major sources of fluctuations in output. However, the results show that first the aggregate
fluctuations are different in a life cycle model with an IST shock compared to the standard
infinitely lived agent models. In particular, the role of an IST shock as a driving force of
fluctuations is limited where it accounts for 10% of variations in output whereas, IST shock is
reported to be responsible for about 30% and 50% of fluctuations in output in Greenwood et al.
(2000) and Justiniano et al. (2010) respectively. The reason that fluctuations in output are higher
in a model with infinitely lived agents is that those models ignore different behaviors of
individuals by age. In order to increase output significantly after an IST shock, physical capital
must respond strongly. However, the younger individuals in the model actually borrow more
after an IST shock due to a reduction in the wage rate.
52
In the model with IST shocks, consumption is counter-cyclical but combining the shocks
leads to a positive correlation between consumption and output since the counter-cyclical of
wage rate with an IST shock is offset by pro- cyclical impacts of a NT shock on the wages when
both shocks are combined.
2.5 Conclusion
In this study, a large scale overlapping generation model is constructed to study the role of
neutral and investment-specific technology shocks as driving forces of business cycles.
Furthermore, the model was used to explore the impacts of shocks on individual’s physical
capital accumulation, labour supply, and consumption and how these responses vary over the life
cycle.
The outcome of this study shows that the role of investment-specific technology shocks as a
driving source of fluctuation is not consistent with the IST literature. In particular, investment-
specific technology shocks account for about 10% of variation in output while it is 67% with
neutral technology shocks. The results also show that the impacts of technology shocks on labour
supply, consumption, and physical capital depend on an individual's age and the nature of
shocks. Differences in the response of physical capital and labour supply by age is the reason
that the IST shocks in the life cycle model are not as important as in the models with infinitely
lived agents. In particularly, younger individuals even borrow more and slightly increase their
labour supply due to a reduction in the wage rate after an IST shock. Furthermore, differences in
the NT and IST shocks are due to differences in their impacts on the production sector. In
particular, a NT shock directly impacts the production of goods through production sector in the
economy and boosts marginal returns to inputs while an IST shock affects the marginal
efficiency of investment and only triggers accumulation of physical capital directly.
53
Table 2.1: Calibrated model parameters
Parameters set to target Value from US
data
Value from
Model
Life expectancy at age 18 58.99
Retired to active population ratio 21.60% 21.1%
Average annual interest rate 6% 6%
ɣ 176 Average time spent working of workers 0.3325 0.3326
Table 2.2: Business cycle statistics
X
Corr(X,Y)
Data TFP
shock
IST
shock
Both
shock Data
TFP
shock
IST
shock
Both
shock
Y 1.57 1.05 0.15 1.07 1.00 1.00 1.00 1.00
qI 4.22 4.10 2.71 5.07 0.88 0.99 0.95 0.89
N 0.46 0.29 0.21 0.37 0.74 0.99 0.93 0.87
C 0.66 0.40 0.27 0.49 0.81 0.98 -0.87 0.73
N (18-24) 1.15 0.16 0.21 0.27 0.68 0.93 0.91 0.67
N (25-34) 0.56 0.19 0.18 0.27 0.72 0.97 0.92 0.80
N (35-44) 0.48 0.26 0.19 0.33 0.67 0.99 0.93 0.87
N (45-54) 0.42 0.42 0.29 0.51 0.69 0.99 0.94 0.89
N (55-64) 0.50 0.96 0.57 1.14 0.44 0.99 0.95 0.92
54
Figure 2.1: Steady state outcomes by age
27 37 47 57 670.4
0.6
0.8
1
1.2
1.4
(a) Human Capital
27 37 47 57 670.1
0.2
0.3
0.4
(b) Labour Supply
27 37 47 57 67 77-1
0
1
2
3
4
Age
(c) Physical Capital
27 37 47 57 67 77
0.2
0.45
0.7
Age
(d) Consumption
55
Figure 2.2: Hours worked comparison between model and actual data
22 27 32 37 42 47 52 57 62 670
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Age
Ho
urs
Wo
rked
Data
Model
56
Figure 2.3: Impulse response functions for aggregate variable after a positive neutral
technology shock.
0 10 20 30 40 500
0.5
1
Neutral Technology Shock (z)
0 10 20 30 40 500
0.7
1.5Output (Y)
0 10 20 30 40 50
0
3
6Investment (I)
0 10 20 30 40 500
0.5
1
1.5Physical Capital (K)
0 10 20 30 40 500
0.4
0.8Consumption(C)
0 10 20 30 40 500
0.5
1Wage (w)
Period0 10 20 30 40 50
-1
0
1
2Rental Rate (r)
Period
0 10 20 30 40 50
0
0.3
0.6Labour Supply (N)
57
Figure 2.4: Impulse response functions after a positive neutral technology shock by age
group
0 10 20 30 40 50
-0.2
0
0.4
0.8
(a) Labour Supply
0 10 20 30 40 50
0
0.5
1(d) Consumption
Period
0 10 20 30 40 50-10
-5
0
5(c) Physical Capital
Period
Age 18-27 Age 28-37 Age 38-47 Age 48-64 Age 65-77
0 10 20 30 40 50-0.2
0
0.4
0.8
(b) Net Labour Earnings
58
Figure 2.5: Impulse response functions for aggregate variable after a positive IST shock
0 10 20 30 40 500
0.5
1
Investment-Specific Technology Shock (q)
0 10 20 30 40 50
0
0.2
0.4
Output (Y)
0 10 20 30 40 500
1.5
3
Investment (I)
0 10 20 30 40 500
0.5
1
Physical Capital (K)
0 10 20 30 40 50
-0.3
0
0.4
Consumption(C)
0 10 20 30 40 50-0.2
0
0.4
Wage (w)
Period
0 10 20 30 40 50-1
-0.5
0
0.5Rental Rate (r)
Period
0 10 20 30 40 50-0.1
0
0.3
Labour Supply (N)
59
Figure 2.6: Impulse response function after a positive IST shock by age group
0 10 20 30-0.2
0
0.4
0.8(a) Labour Supply
0 10 20 30-0.5
-0.25
0
0.25
0.5(d) Consumption
Period
0 10 20 30-10
-5
0
5
10(c) Physical Capital
Period
Age 18-27 Age 28-37 Age 38-47 Age 48-64 Age 65-77
0 10 20 30
-0.1
-0.05
0
0.05
(b) Net Labour Earnings
60
Chapter 3
3 Education, Skills and Labour Market Outcomes of
Canadian Second Generation Immigrants
3.1 Introduction
Numerous studies have focused on the labour market outcomes of immigrants and on how
immigrants integrate into the economic and social structure of the host country (Chiswick 1978,
Baker and Benjamin, 1997; Aydemir and Skuterud, 2005; Grant 1999 and McDonald and
Worswick, 1999). The results from these studies show that immigrants suffer a wage penalty at
entry. Moreover, while older cohorts of immigrants were eventually able to catch up with the
native-born in terms of earnings, this is no longer true for more recent cohorts, for whom
assimilation can no longer happen within one generation.
A much less studied question refers to the performance of the children of these
immigrants, whom the literature refers to as “second generation immigrants”. The literature
defines immigrant generations as follows: the first generation are immigrants who were born in a
country rather than the host country, the second generation are those who were born in a country
and have at least one parent born abroad, and the third generation were born in a county from
non-immigrant parents.
The children of immigrants are expected to perform better in the labour market than
immigrants due to having achieved their education and work experience in the host country.
Given that foreign educational credentials and work experiences are often inadequately
recognized and rewarded in the labour market, we should expect that the children of immigrants
fare better than first generation immigrants. Moreover, there is a strong intergenerational
transmission of educational attainment: children of educated parents are more likely to be
61
educated themselves. In countries such as Canada and Australia, where immigrants are selected
based on education according to a points system, we should expect that children of immigrants
will be highly educated themselves. Conditional on education, second generation immigrants
should not experience any differences in the return to their human capital compared to natives,
given that they are born and educated in the host country. Investigating the human capital and
labour market outcomes of second generation immigrants is therefore very important because it
highlights an outcome of immigration policy often overlooked: the benefit to the host country
from selective immigration coming from the intergenerational transmission of human capital.
The aim of this paper is to investigate how the labour market outcomes as well as the
education and skills outcomes differ between second and third generation Canadians. Existing
literature documents that second generation Canadians are more educated than third or first
generation Canadians (e.g. Aydemir and Sweetman, 2006; Tue, 2010; Hum and Simpson, 2007).
Unconditionally, this translates into higher average earnings for second generation Canadians.
Nevertheless, the literature disagrees whether the earning premium persists, conditional on
education and socio-economic background. Using the 2001 Canadian Census, Aydemir and
Sweetman (2006) show that the positive difference in income switches to negative for Canadian
second generation immigrants when socio-economic characteristics are controlled for. They
conclude that second generation immigrants in Canada have advantages in some observed
characteristics associated with higher earnings such as education and region of residence, but the
return on those characteristics is lower than that for the third generation. However, the reason
behind the gaps in the return of return to those characteristics is not addressed. Likewise, Tue
(2010) documents a negative income gap for second generation Canadian immigrants who have
post-secondary education, while finding no significant gap for those with high school or lower
education. Ethnicity, mother tongue and city of residence are mentioned as barriers for
transferring the intellectual ability into productivity among well educated second generation
immigrants. In contrast, Hum and Simpson (2007) use the Survey of Labour and Income
Dynamics (SLID) to show that ethnic differences do not change the conclusions on the relative
performance of second generation immigrants. They find that conditional on education and other
socio-economic characteristics, second generation immigrants do not earn significantly lower
than other native counterpart. This paper contributes to the existing literature by providing
62
evidence that no wage gap exists among Canadian-born individuals based on parental birth of
place.
In terms of the effect of parental education on second generation immigrant wages, Chen
and Feng (2009) find substantial positive correlation between parental education and wages
received by immigrants’ offspring. Moreover, Borjas (1993) shows that the source countries of
immigrant parents strongly affect the earnings of second generation immigrants. Canadian
Studies also documented that parental education extensively explains educational attainment of
second generation (e.g. Bonikowska, 2005; Finnie 2008).
The studies of labour market outcomes for second generation immigrants have focused
almost exclusively only on the formal educational achievements to explain the positive labour
market outcomes of second generation immigrants compared to other natives. Nevertheless, a
very small international literature exists where differences in wage returns by immigrant
generations are examined in relation to literacy skills. While Behrenze and et al. (2007), and
Rooth and Ekberg (2003) show that second generation immigrants in Sweden experience lower
earnings compared to other natives, Nordin and Rooth (2007) apply an achievement test score to
show that it is a skill gap, rather than ethnic discrimination, that causes the income gap. They
argue that schooling is an inappropriate measure of productive skills for second generation
immigrants.19
The Canadian case may be different, because Canada applies a point system to select
educated immigrants. While these immigrants may end up working in occupations below their
education, they should transfer a high level of human capital to their Canadian born children.
Here we measure not only the relationship between parental education and labour market
outcomes of Canadian second generation immigrants, but also how literacy scores embed some
of the intergenerational transmission of human capital. To measure literacy skills, this study
uses the test scores from the Canadian component of the 2003 International Adult Literacy and
Skills Survey (IALS). IALS measures adult literacy skills in four domains: prose literacy,
document literacy, numeracy and problem solving.
19
Green and Riddell (2001) use Canadian data from the International Adult Literacy Survey (IALS) to examine the relationship between labour market success and literacy skills for first generation immigrants. Their findings indicate that literacy has a largely positive effect on immigrants’ earnings. However, they do not examine the labour market outcomes of second generation immigrants.
63
This paper shows that in the long run, Canadian society benefits from the point system in
which immigrants with higher level of human capital are selected. The children of immigrants
are likely to obtain higher educational degree. Moreover, they have higher level of cognitive
skills compared to children of non-immigrants due to higher education and parental education.
The results of the current study are comparable to the results from previous Canadian studies on
unconditional labour market outcomes for second generation immigrants in Canada. Overall,
second generation immigrants, particularly individuals whose parents are both immigrants, have
advantages in the labour market and have higher human capital indicators compared to the other
natives. The results show that education, literacy skills and a set of socio economic
characteristics explain the wage and earnings differentials for second generation immigrants
compared to other natives. In addition to examining the average literacy skills, each of the four
literacy elements were examined, separately, for their impact on labour market outcomes. Within
the elements of literacy skills, numeracy has more effect on the wage earnings potential of males
while, for females, document skills have higher effect. This study concludes that second
generation immigrant earns as well as the third generation after accounting for a set of
controlling variables and no evidence exists to imply that second generation immigrants do not
reach parity with the third generation. Furthermore, compared to other natives, second generation
immigrants not only are more likely to hold a university degree, they attain at least the same test
scores in literacy skills.
The structure of the chapter 3 is as follows: Section 3.2 presents the data and summary
statistics; Section 3.3 describes the model specifications; Section 3.4 presents the results and
discussions for the three outcomes considered in estimation: post-secondary attainment, literacy
skills, and wages; and Section 3.5 provides the conclusions.
3.2 Data
The data used in this study come from the Canadian component of the 2003 International Adult
Literacy Survey (IALS). Besides allowing us to identify the immigrant generation (first, second,
and third), very importantly, the survey provides test scores on a set of literacy skills including
prose, numeracy, document and problem solving. These test scores measure the ability of
64
individuals in implementing skills to work as well as everyday life and differences in skill levels
can be an important source of income inequality, particularly among individuals with the same
level of education. The literacy skills are defined as follows:
Prose includes the knowledge and skills needed to understand and use various kinds of
information from text including editorials, news stories, brochures and instructions
manuals.
Document contains the knowledge and skills required to locate and use information
contained in various formats including job applications, payroll forms, transportation
schedules, maps, tables and charts.
Numeracy comprises the knowledge and skills needed to effectively manage and respond
to the mathematical demands of diverse situations.
Problem solving involves goal-directed thinking and action in situations for which no
routine solution procedure is available. The problem solver has a more or less well-
defined goal, but does not immediately know how to reach it.
In this study, literacy is obtained by averaging over test scores for prose, document,
numeracy, and problem solving.
In addition, the data offers adequate information on other socio-economic information
such as age, parental education, parents’ place of birth and ethnicity. Hence, using IALS
provides an opportunity to investigate the influence of different skills on the wage differential
between second generation and third generation immigrants, while controlling for ethnical
background and parental education. It is well understood in the literature that parental education
plays an important role in educational outcome of children. Consequently, literacy skills are
strongly determined by parental education while ethnicity does not seem to play an important
role when parental education is taken into account. Furthermore, this research provides an
opportunity to benchmark the analysis for second generation immigrants by comparing the
results to the previous studies using Census or SLID data and trying to determine where the
differences come for.
Since the survey provides information on parents’ place of birth, this makes it possible to
explore the heterogeneity among second generation immigrants and to identify the effect of
immigrant parentage depending on whether one or both parents are immigrants. Thus, Canadian
65
born individuals collapse thus into four groups, including: second generation immigrants with
foreign-born father; second generation with foreign-born mother; second generation immigrants
with both parents foreign-born; and, third generation immigrants, who are natives with both
parents Canadian-born.
The sample is restricted to the individuals who have a job during the year of survey with
the age range of 25 to 65 years old for males and females, separately. The students and self-
employed are excluded from sample. Given information on wages and salaries, such as the wage
pay schedule, and the labour market hours of activities for individuals in one year, the hourly
earnings and annual earnings are constructed from the data. Wages and earnings help account for
the variation in unit earnings as well as labour supply. Taking the logarithm of earnings enforces
any observations with zero earnings to be excluded.
3.2.1 Descriptive statistics
Tables 3.1 and 3.2 summarize the descriptive overview of major labour market and human
capital characteristics, separately for each gender. Table 3.1 looks at wages and labour supply, as
well as literacy outcomes, separately by the 4 immigration generations: three categories for the
second generation, and one for the third. Table 3.2 provides educational attainment, parental
education, regions of residence, and ethnicity for each gender, for two categories of immigrants:
second and third generations20
.
The unconditional results show that, on average, second generation immigrants have
better performance in the labour market compared to Canadian individuals born from Canadian
parents. In particular, second generation immigrants with immigrant parents receive the highest
wages, despite also being younger and having fewer years of experience compared to other
groups. The difference in experience can be related to educational attainment, which is also
higher for second generation (Table 3.2), leading to lower potential experience.
20
Since data is provided by Statistic Canada, there is a restriction on the number of observations for releasing the
summary statistics. Therefore, second generation has to be reported in only one group instead of three groups in
Table 3.2 to meet disclosure requirements. It was not also possible to report summary statistics for all ethnicity
categories, but the regression analysis, subject to different disclosure requirements, controls for refined ethnicity
categories.
66
In terms of human capital, literacy score results are described in Table 3.1 and
educational attainment in Table 3.2. Both male and female second generation immigrants,
particularly those whose both parents were born abroad, have higher mean test scores in literacy
and also in its components including prose, numeracy, document and problem solving. While the
gender wage gap is not a main focus of this study, it is notable that, for all generation
immigrants, females receive lower earnings and wages than males, although they achieved
higher literacy test scores in some cases, while, on average, males have higher numeracy skill
compared to females within generation groups. We come back to this point in the regression
analysis.
The summary statistics from Table 3.1 suggest that literacy skills may have an impact on
the labour market outcomes although only education has been used as human capital to predict
the earnings in the Canadian literature. In addition, among literacy skills, numeracy seems to be a
main factor in explaining the labour market success. In order to support these findings from
Table 3.1, literacy is also taken into account in order to explain differences in the earnings
between second generation immigrants and other natives. Table 3.2 shows that second generation
immigrants in Canada are more educated that third generation immigrants. The probability of
having a high level of education, mainly having university degree is lower for third generation
immigrants compared to the second generation. On the other hand, the probability of being less
educated (at most having high school diploma) is highest for third generation immigrants.
Parental education across generations of immigrants is presented separately by the
education of mother and father. The probability of being from low educated families is higher for
third generation immigrants by about 12 to 13 percent. Consequently, second generation are
more likely to be born from educated parents. If there is any positive correlation between
parental education and earnings, second generation will likely have advantages to some extent in
the labour market compared to other natives.
The region of residence is one of the explanatory variables that have been reported to
have a significant effect on earnings. Resources, labour supply and demand vary across the
regions and hence, wages could be different from one place to another. Table 3.2 shows that
distribution of the population over the regions differs across the generation and this may give
misleading results when the region of residence is not controlled for.
67
3.3 Specification models
A probit model is estimated to study the university attainment across immigrant generation
groups. In this model, university is a binary variable that takes the value 1 if individuals obtained
a university degree and 0 otherwise. Canadian studies on education demonstrate immigrants and
their offspring are more likely to attend post-secondary education and to achieve higher levels of
education compared to the children of Canadians. We follow the literature by controlling for age,
parental education and ethnic composition, which can explain a substantial part of education
gaps (Finnie, 2008; Bonikowska, 2005; and Hansen and Kucera, 2004).
However, the skill level of the second generation immigrants compared to the third
generation immigrants, as reflected by literacy scores, has not been analyzed. We investigate the
determinants of the skill gap between second and third generation immigrants using Ordinary
Least Squares (OLS) regression for literacy, with the same controls as in the specifications for
post-secondary outcomes. The foundation for literacy score is set in the K-12 years. In these
formative years, parental education should play a crucial role in literacy outcomes, both through
a direct involvement in the education process as well as through the part of innate ability which
is transmitted genetically from parents to children. Through these mechanisms, literacy scores
for young adults measured at the end of high-school are determinants of post-secondary
enrolment as well as labour market success conditional on education. The IALS literacy skills
are measured here later on in the adult life. Besides K-12 education, ability and parental
involvement, these literacy skills also embed to some extent the outcome of post-secondary
attendance.
Finally, the Mincer earnings function is used to analyze the factors that determine the
labour market outcomes of second generation immigrants in Canada. The logarithm of hourly
wages is used as the main dependent variable for the labour market outcomes. Alternatively, the
logarithm of annual labour income of individuals before tax is also considered, as it embeds both
the productivity channel reflected in the hourly wages as well as the labour supply channel in
terms of hours of work.
68
3.3.1 Key independent variables
Indicators for generation groups based on the immigration status of parents are used in all
equations to investigate the differences in educational and labour market outcomes and skills
between generation groups: 2nd
-mother, 2nd
-father, 2nd
-both, and third generation (default base
category). A vector of the socio-economic variables is controlled for in the most models. These
explanatory variables include age, respondent’s community size (rural), dependent children
present, experience and experience2/100, region of residence, parental education, ethnicity, and
occupation. Furthermore, educational attainment and literacy skills are included as regressors in
the earnings equations. Educational attainment includes five levels of education: less than high
school, high school diploma, some post secondary, bachelor, and postgraduate (default base
category). The variable of literacy skills is the average test scores of various skills including
prose, numeracy, document and problem solving skills.
While educational attainment is known to be a strong predictor of earnings by capturing
an observable component of human capital, remaining wage gaps within a given level of
education, conditional on other observable productivity characteristics, may occur due to
differences in unobserved abilities across the individuals. Using literacy test scores provides a
measure of unobserved abilities which can alleviate to some extent the unobserved ability issues.
Therefore, direct measure of literacy skills can be an appropriate predictor to control unobserved
human capital skills. On the other hand, parental education may influence the academic
achievements and the labour market outcomes of children and it may also be a signal of innate
ability that is inherited by children. Therefore, in the present of test scores to control for skills,
and parental education to control for ability, education is no longer endogenous in the empirical
model.
In addition to above socio-economic variables, more categorical variables are used in
some equations. Region of residence is collapsed into the following categories: Atlantic, Quebec,
Ontario (default), BC, Alberta, Centre, and North. Parental education is a categorical variable
that is divided into three groups: less than high school, high school, and university education
(default) for each parent. Ethnicity is a categorical variable that is collapsed into the following
categories: English (default), French, White, Jewish, Black, Chinese, Aboriginal, and Other. The
first digit of the International Standard Classification of Occupation including 10 categories is
69
used to control for occupation in some specifications. According to table A1, the distribution of
occupation varies between second generation and third generation immigrants. Compared to
third generation, second generation immigrants are more likely to hold managerial or
professional positions, which are associated with higher earnings. This can be likely explained
by the fact that second generation Canadian tend to achieve higher level of education and literacy
skills relative to other native counterpart and consequently, they are more well-equipped to take
over professional positions.
3.4 Estimation results
3.4.1 University outcomes
Education is shown to be the important determinant in the wage regression. The unconditional
results from the summary statistics illustrate that the probability of achieving upper levels of
education is higher for second generation immigrants. In this section, the probability of holding a
university degree across the generation groups is examined.
Tables 3.3 summarizes the marginal effects of having a university degree after probit,
separately, for males and females. Without controls, the results in column (1) for males and
females show that second generation are more likely to obtain a university degree compared to
third generation counterparts21
. After controlling for age, parental education, ethnicity and
location, the statistically significant differences across generation groups disappear only for
males. Overall, the probability of holding a university degree is higher for second generation
immigrants whose parents both are immigrants. These outcomes are not surprising since the
parental backgrounds, particularly parental education, have strong effects on the educational
outcomes of children. Immigrants in Canada are selected from the highly educated applicants
and the university educated parents are more likely to have children with a university degree.
The results also show that individuals who live in the rural area are less likely to obtain a
university degree.
21
When the model is restricted to individuals who have a job, I did not find any significant difference between the
educational outcomes of second generation and third generation males.
70
3.4.2 Literacy outcomes
One could argue that the better educational outcomes for second generation immigrants are
largely the result of high parental expectation and consequently, second generation immigrants
with a university degree might be less skilled than their counterparts. In order to investigate the
differences in skills across the generation groups, literacy is used as an outcome variable in the
regression using the ordinary least square method. The estimation results are reported in Table
3.4 and 3.5, correspondingly, for males and females. In each table, the first two columns present
estimates of literacy for all individuals, respectively, without and with controls for the variables
that could be associated with the higher test scores. The sample is divided then into two
subsamples. The second two sets of results provide the corresponding estimates for those who do
not hold a university degree while last two columns present the estimates for those with a
university degree.
Second generation immigrants unconditionally achieve higher test scores in literacy skills
compared to third generation immigrants in most cases, and the results are stronger for those
without a university degree. After controlling for age, parental education, ethnicity, experience,
and location, second generation immigrants obtain at least the same test score as third generation
immigrants except for high educated second generation females whose only fathers are
immigrants. For those individuals without a university degree, the parents’ birth of place matters.
When mothers are immigrants, only sons achieve statistically significant higher score in literacy.
When fathers are immigrant, daughters attain better score. This might be associated with
differences in parental involvement in children's education by child gender.
The control variables have expected sign and magnitude. Educational attainment has
more impact on literacy than experience does and the role of parental education in achieving
higher test scores is considerable. The literacy decreases with age but the effect is smaller for
highly educated subgroup.
3.4.3 Regression results for hourly wages
71
The results of the summary statistics suggest that the unconditional labour market outcomes are
mostly in favor of second generation immigrants. These outcomes could be explained to some
degree by educational attainment and higher literacy skills since second generation immigrants
achieved higher levels of education and literacy test scores. In this section, the factors that may
explain the earning and wage differentials between second generation and third generation
immigrants will be examined.
Table 3.6 represents the regression results of the hourly wages in three columns by males
and females, separately. The unconditional wage gaps between each group of second generation
and third generation immigrants are provided in column (1) for each gender. Overall, second
generation females receive statistically significant higher hourly wages except for second
generation males whose fathers are immigrants. However, there is no significant wage gap
between second generation and third generation males.
The human capital variables, which are the educational attainment and literacy test scores
in the data, are expected to play important roles in the labour market outcomes. In order to
capture the effect of these variables on the wage gaps between second generation groups and
Canadian born individuals from Canadian parents, these variables are added to the regressions in
column (2) along with a set of basic socio economic variables for males and females, separately.
The set of basic socio-economic variables includes age, rural, dependent children, experience
and experience squared. 22
The results would be useful to investigate how well education and
literacy explain the wage gap between the generation groups because individuals in both
generations have been exposed to the same schooling system. The results indicate that the
magnitude of the positive wage gap diminishes to some extent for those whose mothers are at
least immigrants and the statistically significant positive wage differences disappear for females.
Furthermore, the negative wage gap increases but remains statistically insignificant for those
whose only fathers are immigrant23
. The results suggest that on average, the children of
immigrant do not earn significantly different than the third generation given the same level of
education and skills. Furthermore, second generation immigrants whose mothers are at least
22
Controlling for a set of basic socio-economic characteristics without education does not significantly change the
results and it only wipe out the significant positive wage gaps in favor of second generation males whose mothers
are at least immigrant while the sign of the coefficient remains the same. 23
Without control for education, literacy also captures the effect of education and the results are close to what is
reported in column (2).
72
immigrants have advantages in specific characteristics that are associated to higher wages in
contrast to third generation immigrants.
Parental education, ethnicity groups, region of residence and, occupation are used as
additional controlling variables to explain the wage gap in column (3) for males and females,
separately. Overall, conditional results show second generation immigrants do not earn
significantly less than third generation immigrants when all control variables are taken into the
account.24
The wage differentials remain positive in favor of second generation immigrants
whose mothers are immigrant for males and females, separately, although the positive wage gap
is not statistically significant. However, the results demonstrate that there is a selection bias to
ethnicity, occupation and region of residence for second generation immigrants. In addition,
parental education impacts the earnings of male individuals while has no significant effects on
females earnings.
In addition to specifications provided in Table 3.6, a comprehensive set of specifications
is considered for sensitivity analysis. The results from these specifications show that first,
positive wage gaps in favor of second generation immigrants are driven mainly through
education and literacy skills. Second, controlling for ethnicity does not have any impact on wage
differentials between second and third generation when education is taken into account, even
though some ethnicities may receive relatively higher or lower wages among males and females.
3.4.4 Regression results from income equation
Table 3.7 provides the unconditional and conditional income differentials of second generation
immigrants based on the parental immigration status compared to other natives for males and
females, separately, with an extra specification which is the number of hours of work per week.
The unconditional results from the wage regressions are not consistent with the results from the
earning estimations in all cases. Second generation immigrants whose parents are both
immigrants earn significantly higher income than natives. In addition, second generation females
24
By introducing the ethnicity as an extra control variable in the regression, the wage gap increases slightly in favor
of all second generation immigrants when compared to their native counterparts, but there exists no evidence that
ethnicity plays a significant role on the labour market outcomes of the immigrants’ offspring.
73
whose father is immigrant earn significantly more than third generation females. The sign of
coefficients for the earnings differentials is small and negative for second generation males with
immigrant mothers while it is positive for second generation immigrants whose fathers are
immigrants. These differences could be as a result of work status of individuals or the number of
hours that were contributed to work. Conditional results in column (2) for males and females,
correspondingly, indicate that second generation immigrants do not earn significantly less than
third. Second generation females whose mothers are immigrants receive higher earnings only by
2 percent. The results show that having dependent children has positive impacts on the earnings
even for females. Aging also has statistically significant negative impacts on the females’ income
while has no impact on their wages.
3.4.5 The effect of literacy components on the labour market outcomes
It has been shown that literacy is one of the explanatory variables in wage and income equations
but it is also important to determine which skill has the most important effect. For this reason,
the components of literacy including prose, document, numeracy and problem solving are
controlled in the wage and income equations, and the estimates are summarized in Table 3.8 for
males and females, independently.
The results show that numeracy has statistically significant positive effect on earnings (e.g.
wage or income) and its effect is doubled for males than for females. In addition to numeracy,
Prose skill has significant impact on the earnings for females while the only skill that has
significant positive effect on the earnings for males is numeracy. Surprisingly, problem solving
has statistically significant negative effect on the wages for females.
3.5 Conclusions
In this study, the factors that determine the cognitive skills, educational and labour market
outcomes of Canadian second generation immigrants were analyzed for males and females,
separately. Using the 2003 International Adult Literacy Survey (IALS) provides not only
important determinants of wage and income such as education and experience, but it also gives
74
an opportunity to investigate the role of literacy test scores in the labour market outcomes of
individuals. To account for the heterogeneity among second generation immigrants, they were
divided into three groups based on the immigration statues of each parent. The results confirm
that the immigration status of each parent matters in the analysis. In particular, relatively better
outcomes are observed when mother is immigrant while having only an immigrant father is
associated to a weaker or a negative gap in many cases.
The unconditional results of the summary statistics illustrate that second generation
immigrants, particularly those from foreign born parents, achieve higher earnings as well as
higher levels of schooling and skills. Conditional only on education, second generation
immigrants with post graduate degree have difficulty catching up to the earnings of third
generation immigrants who hold a postgraduate degree.
The conditional results indicate that second generation immigrants do not significantly earn
less than the third generation and second generation immigrants whose mothers are immigrants,
but the coefficients are not statistically significant. Although second generation immigrants with
both migrated parents have advantages in the labour market from unconditional results, these
advantages mostly disappear after controlling for various predictors. In conclusion, Canadian
second generation immigrants have advantages in some characteristics associated with higher
earnings. Furthermore, the impact of literacy skills is also stronger than ethnicity in explaining
the earning differentials. The ethnic differences in the labour market are small.
Furthermore, university outcomes and skill gaps between second generation and third
generation immigrants were examined. Second generation immigrants are not only more likely to
obtain a university degree, they have higher literacy skills. After controlling for the major
determinates of the university outcomes, the higher probability of holding a university degree
remains statistically significant for second generation females. Among non university degree
holders, second generation immigrants have higher literacy skills even after controlling for
parental education and ethnicity. Parental education plays an important role in explaining the
skills and educational outcomes of the individuals. In addition to examining the average literacy
skills, the impact of each skill on labour market outcomes were examined, separately. Within the
elements of literacy skills, numeracy has more effect on the wage earning potential of males
while, for females, document skills have higher effect. These results imply the gender
heterogeneity in skills.
75
Table 3.1: Summary Statistics for the labour market characteristics by gender
2nd Generation 3rd Generation
Mother Only Father Only Both Parents
Males:
Age 44.55 44.09 41.70 43.07
Yearly Income (CAD$) 51548 51619 55231 50673
Hourly Wage (CAD$) 23.69 22.69 25.16 22.87
Hours/week 42.3 43.62 43.9 42.91
Experience 23.79 23.54 20.96 22.07
Prose 297.18 290.07 304.77 282.69
Document 299.39 294.53 309.36 285.74
Numeracy 296.65 291.07 304.12 282.06
Problem solving 289.67 283.17 295.10 276.89
Literacy 295.72 289.71 303.34 281.84
Observations 140 152 158 2616
Females:
Age 43.54 44.27 40.37 42.93
Yearly Income (CAD$) 39308 39402 41059 36070
Hourly Wage (CAD$) 20.44 20.24 21.14 19.30
Hours/week 36.85 37.80 37.33 36.46
Experience 17.75 18.19 17.10 18.06
Prose 308.25 299.91 311.15 292.65
Document 303.06 294.31 304.84 285.79
Numeracy 284.99 280.79 288.36 271.02
Problem solving 297.57 288.03 294.68 280.60
Literacy 298.47 290.76 299.76 282.52
Observations 105 157 148 3149
76
Table 3.2: Education, parental education, region of residence, and ethnicity by
gender
Males
Females
2nd
generation
3rd
generation
2nd
generation
3rd
generation
Education:
Less than HS 12.83 18.43
7.07 13.62
HS 28.81 30.93
30.49 33.34
Post Secondary 30.02 27.64
26.59 27.72
Bachelor’s 23.49 18.65
31.22 21.21
Post Graduate 4.84 4.36
4.63 4.1
Mother’s Education:
Less than HS 0.48 0.58
0.51 0.6
HS 0.32 0.28
0.27 0.26
University 0.2 0.15
0.22 0.14
Father’s Education:
Less than HS 0.52 0.64
0.53 0.67
HS 0.28 0.23
0.3 0.21
University 0.19 0.12
0.17 0.12
Region of Residence:
Atlantic 11.86 21.64
9.76 22.48
Quebec 15.5 21.1
15.37 19.02
Ontario 17.19 19.65
20.24 18.77
Alberta 11.86 4.82
8.05 5.72
BC 10.9 3.71
14.15 3.97
North 15.25 13.3
17.07 12.73
Center 17.43 15.79
15.37 17.31
77
Table 3.3: Marginal effects after probit for the university outcomes
Males
Females
(1) (2)
(1) (2)
2nd _Mother 0.070*** 0.002
0.131*** 0.068**
(0.031) (0.029)
(0.031) (0.028)
2nd _Father 0.057*** 0.019
0.096*** 0.062***
(0.025) (0.024)
(0.025) (0.023)
2nd _Both parents 0.105*** 0.033
0.157*** 0.086***
(0.025) (0.025)
(0.027) (0.025)
Mother-Less than HS
-0.157***
-0.199***
(0.016)
(0.014)
Mother-HS
-0.056***
-0.091***
(0.016)
(0.014)
Father-Less than HS
-0.163***
-0.174***
(0.017)
(0.015)
Father-HS
-0.105***
-0.099***
(0.017)
(0.016)
Age
0.003***
0.000
(0.001)
(0.001)
Rural
-0.118***
-0.046***
(0.013)
(0.012)
French
0.013
0.05***
(0.018)
(0.017)
Jewish
0.252**
0.227***
(0.112)
(0.064)
Chinese
0.338***
0.251**
(0.099)
(0.128)
Black
0.016
0.178
(0.113)
(0.113)
78
White
-0.011
0.045***
(0.016)
(0.016)
Aboriginal
-0.121
-0.043**
(0.023)
(0.02)
Other
-0.041
0.057**
(0.033)
(0.029)
Region of Residence
✓
✓
Observations 4602 4602
6056 6056
pseudo R2 0.006 0.139
0.010 0.143
NOTES: Standard errors are in parentheses. Significance levels are indicated by * for 10%, ** for 5%,
and *** for 1 %. The dependent variable takes value of 1 if individuals obtained a university degree and
zero otherwise.
79
Table 3.4: Estimation results of the literacy equations for males
All`
no university degree
university degree
(1) (2)
(1) (2)
(1) (2)
2nd _Mother 21.077*** 3.968
21.459*** 9.707**
4.044 -2.188
(4.216) (3.021)
(4.713) (3.922)
(5.494) (5.274)
2nd _Father 13.126*** 2.665
11.439*** 3.405
5.084 1.758
(3.381) (2.421)
(3.739) (3.114)
(4.559) (4.326)
2nd _Both parents 27.858*** 5.287**
26.905*** 6.804*
8.738** 4.340
(3.523) (2.683)
(4.050) (3.558)
(4.282) (4.490)
Experience
1.249***
2.159***
-0.065
(0.183)
(0.224)
(0.421)
Experience2/100
-1.734***
-3.792***
-0.022
(0.386)
(0.488)
(0.753)
Age
-0.759***
-0.873***
-0.396
(0.100)
(0.122)
(0.245)
Dependent Child
3.988***
4.854***
2.666
(1.094)
(1.375)
(2.132)
Rural
-3.844***
-5.720***
-5.782*
(1.228)
(1.471)
(2.976)
Mother-Less HS
-11.725***
-17.659***
-12.270***
(1.822)
(2.408)
(3.117)
Mother-HS
-2.035
-5.198**
-0.246
(1.802)
(2.486)
(2.726)
Father-Less HS
-12.238***
-19.957***
-1.898
(1.911)
(2.664)
(2.982)
Father-HS
-4.560**
-6.723**
-4.653
(1.953)
(2.766)
(2.919)
French
-3.104*
-3.401
-1.193
80
(1.807)
(2.275)
(3.498)
Jewish
-3.706
7.661
2.575
(11.656)
(38.599)
(11.241)
Chinese
-9.051
-13.399
-7.069
(10.636)
(22.506)
(11.255)
Black
5.891
15.942
-11.528
(10.984)
(14.612)
(17.861)
White
2.741*
3.456
6.014**
(1.665)
(2.127)
(3.021)
Aboriginal
-18.483***
-21.977***
-20.223***
(2.116)
(2.605)
(5.239)
Other
-1.300
-3.943
1.014
(3.147)
(3.878)
(6.662)
Less than HS
-95.405***
(4.365)
Some HS
-56.083***
(3.342)
HS diploma
-30.413***
(3.178)
Post Secondary
-24.795***
(3.162)
Bachelor Degree
-10.412***
(3.060)
Region of Residence
✓
✓
✓
Occupation
✓
✓
✓
Observations 4602 4357
3728 3491
874 866
R-squared 0.020 0.501
0.018 0.331
0.006 0.201
NOTES: Standard errors are in parentheses. Significance levels are indicated by * for 10%, ** for 5%, and *** for 1%.
The dependent variable is literacy.
81
Table 3.5: Estimation results of the literacy equations for females
All
No University Degree
University Degree
(1) (2)
(1) (2)
(1) (2)
2nd _Mother 23.936*** 6.222**
19.253*** 4.612
11.155** 4.917
(3.976) (2.876)
(4.681) (3.853)
(4.954) (4.746)
2nd _Father 14.577*** 2.244
15.100*** 7.592**
-4.105 -6.540*
(3.113) (2.275)
(3.546) (2.981)
(4.154) (3.911)
2nd _Both parents 24.529*** -0.781
20.702*** 0.333
6.601* 1.752
(3.345) (2.556)
(4.038) (3.462)
(4.006) (4.168)
Experience
0.787***
1.284***
0.769**
(0.131)
(0.151)
(0.358)
Experience2/100
-1.370***
-2.092***
-2.797***
(0.307)
(0.351)
(0.922)
Age
-0.353***
-0.529***
-0.213
(0.064)
(0.079)
(0.141)
Dependent Child
3.509***
3.694***
3.206*
(0.960)
(1.222)
(1.867)
Rural
0.033
-0.117
-1.117
(1.055)
(1.266)
(2.322)
Mother-Less than HS
-12.268***
-15.587***
-11.098***
(1.530)
(2.090)
(2.557)
Mother-HS
-3.006*
-4.676**
-2.975
(1.542)
(2.199)
(2.324)
Father-Less than HS
-13.230***
-16.583***
-11.031***
(1.619)
(2.290)
(2.539)
Father-HS
-7.689***
-7.633***
-8.088***
(1.681)
(2.442)
(2.468)
82
French
-5.221***
-5.063***
-9.943***
(1.597)
(1.962)
(3.276)
Jewish
-7.963
-4.761
-11.904
(7.041)
(13.502)
(8.593)
Chinese
19.052
9.385
17.285
(14.898)
(35.562)
(16.371)
Black
-9.744
-7.821
-18.109
(11.024)
(15.918)
(16.393)
White
3.234**
4.981***
0.237
(1.469)
(1.833)
(2.888)
Aboriginal
-15.889***
-19.440***
-18.800***
(1.841)
(2.238)
(4.103)
Other
0.547
4.866
-13.129**
(2.775)
(3.519)
(5.158)
Less than HS
-91.908***
(4.746)
Some HS
-54.728***
(2.992)
HS diploma
-29.334***
(2.784)
Post Secondary
-23.037***
(2.739)
Bachelor Degree
-7.827***
(2.661)
Region of Residence
✓
✓
✓
Occupation
✓
✓
✓
Observations 6056 5318
4773 4072
1283 1246
R-squared 0.017 0.467
0.012 0.311
0.007 0.192
NOTES: Standard errors are in parentheses. Significance levels are indicated by * for 10%, ** for 5%, and ***
for 1 %. The dependent variable is literacy.
83
Table 3.6: Regression results of the hourly wages by gender
Males
Females
(1) (2) (3)
(1) (2) (3)
2nd_Mother 0.083 0.018 0.024
0.085* 0.018 0.008
(0.05) (0.045) (0.042)
(0.051) (0.043) (0.038)
2nd_Father -0.004 -0.053 -0.046
0.036 -0.016 -0.045
(0.042) (0.037) (0.035)
(0.044) (0.037) (0.033)
2nd_Both parents 0.071 0.003 -0.026
0.130*** 0.012 -0.009
(0.046) (0.037) (0.038)
(0.044) (0.038) (0.035)
Less than HS
-0.267*** -0.205***
-0.439*** -0.221**
(0.077) (0.074)
(0.099) (0.088)
Some HS
-0.344*** -0.249***
-0.617*** -0.358***
(0.048) (0.047)
(0.046) (0.043)
HS diploma
-0.297*** -0.208***
-0.491*** -0.261***
(0.043) (0.043)
(0.041) (0.038)
P.S. Non University
-0.202*** -0.142***
-0.329*** -0.156***
(0.043) (0.042)
(0.040) (0.037)
Bachelor Degree
-0.042 -0.002
-0.090** -0.050
(0.043) (0.040)
(0.040) (0.036)
Literacy
0.003*** 0.002***
0.003*** 0.002***
(0.000) (0.000)
(0.000) (0.000)
Experience
0.017*** 0.016***
0.017*** 0.013***
(0.003) (0.003)
(0.002) (0.002)
Experience2 /100
-0.028*** -0.024***
-0.012** -0.010**
(0.006) (0.006)
(0.005) (0.004)
Age
0.006*** 0.005***
-0.000 0.001
(0.002) (0.002)
(0.001) (0.001)
Dependent Child
0.062*** 0.052***
0.061*** 0.056***
84
(0.017) (0.016)
(0.016) (0.014)
Rural
-0.047** -0.046**
-0.041** -0.050***
(0.018) (0.018)
(0.017) (0.016)
Mother-Less than HS
-0.028
-0.025
(0.025)
(0.022)
Mother-HS
0.050**
-0.005
(0.025)
(0.022)
Father-Less than HS
0.028
-0.023
(0.026)
(0.023)
Father-HS
0.048*
0.003
(0.027)
(0.024)
French
0.051**
0.062***
(0.026)
(0.023)
Jewish
0.359*
0.010
(0.199)
(0.116)
Chinese
-0.223*
0.032
(0.135)
(0.269)
Black
-0.032
0.028
(0.162)
(0.154)
White
-0.009
0.022
(0.024)
(0.021)
Aboriginal
0.022
0.059**
(0.032)
(0.028)
Other
0.103**
-0.027
(0.048)
(0.041)
Region of Residence
✓
✓
Occupation
✓
✓
Observations 2723 2723 2722
3260 3260 3259
R-squared 0.002 0.213 0.319
0.003 0.299 0.467
NOTES: Standard errors are in parentheses. Significance levels are indicated by * for 10%, ** for 5%, and ***
for 1 %. The dependent variable is the logarithm of hourly wages.
85
Table 3.7: Regression results of the income equations
Males
Females
(1) (2)
(1) (2)
2nd_Mother -0.007 -0.073
0.093 0.020
(0.086) (0.057)
(0.065) (0.049)
2nd_Father 0.024 -0.028
0.096* -0.004
(0.050) (0.047)
(0.056) (0.042)
2nd_Both parents 0.107** -0.023
0.168*** -0.006
(0.044) (0.050)
(0.050) (0.046)
Less than HS -0.169*
-0.403***
(0.100)
(0.115)
Some HS
-0.197***
-0.435***
(0.064)
(0.056)
HS diploma -0.147**
-0.283***
(0.058)
(0.050)
post Secondary -0.107*
-0.214***
(0.057)
(0.049)
Bachelor Degree 0.018
-0.077*
(0.055)
(0.046)
Literacy
0.002***
0.002***
(0.000)
(0.000)
Experience 0.015***
0.019***
(0.004)
(0.003)
Experience2 /100 -0.020**
-0.015***
(0.008)
(0.006)
Age
0.005**
-0.004***
(0.002)
(0.001)
Dependent Child 0.075***
0.039**
(0.021)
(0.018)
Rural
-0.041*
-0.069***
86
(0.024)
(0.020)
Hour/Week 0.017***
0.026***
(0.001)
(0.001)
Mother-Less than HS 0.014
-0.016
(0.034)
(0.028)
Mother-HS 0.068**
0.013
(0.033)
(0.028)
Father-Less than HS 0.037
-0.007
(0.035)
(0.029)
Father-HS 0.052
0.012
(0.036)
(0.031)
French
0.052
0.065**
(0.035)
(0.030)
Jewish
0.368
0.045
(0.267)
(0.149)
Chinese
-0.146
0.112
(0.182)
(0.346)
Black
0.049
-0.146
(0.219)
(0.198)
White
0.015
0.000
(0.032)
(0.027)
Aboriginal
0.014
0.059*
(0.043)
(0.035)
Other
0.116*
-0.019
(0.064)
(0.053)
Region of Residence
✓
✓
Occupation
✓
✓
Observations 2740 2740
3283 3283
R-squared 0.001 0.325
0.003 0.527
NOTES: Standard errors are in parentheses. Significance levels are indicated by * for 10%, ** for 5%,
and *** for 1 %. The dependent variable is the logarithm of annual income.
87
Table 3.8: The effects of the literacy components on the labour market outcomes
Males
Females
Dependent Variable: ln(Wage) ln(Income)
ln(Wage) ln(Income)
2nd_Mother 0.034 -0.056
0.042 0.040
(0.045) (0.060)
(0.043) (0.053)
2nd_Father -0.037 -0.010
-0.017 0.021
(0.037) (0.050)
(0.037) (0.046)
2nd_Both parents 0.025 0.035
0.045 0.054
(0.039) (0.053)
(0.039) (0.049)
Prose 0.000 -0.000
0.002*** 0.002**
(0.001) (0.001)
(0.001) (0.001)
Document 0.001 0.001
0.001 0.001
(0.001) (0.001)
(0.001) (0.001)
Numeracy 0.002*** 0.002***
0.001*** 0.001**
(0.000) (0.001)
(0.000) (0.000)
Problem Solving -0.000 -0.001
-0.001** -0.001
(0.000) (0.001)
(0.000) (0.001)
Control ✓ ✓
✓ ✓
Observations 2723 2740
3260 3283
R-squared 0.230 0.239
0.316 0.429
NOTES: Standard errors are in parentheses. Significance levels are indicated by * for 10%, ** for 5%, and
*** for 1 %. Controls include Education, Parental Education, Region of Residence, Ethnicity, Rural,
Experience, and Dependent Child. Hours per Week is only controlled in Earnings equations
88
Table 3.A1: Distribution of occupation
Second generation Third generation
Managers 13.31 10.82
Professionals 20.86 16.77
Technicians and associate professionals 15.92 14.2
General support workers 13.4 13.13
Service and sales workers 12.41 14.84
Skilled agricultural, forestry and fishery workers 1.62 2.16
Craft and related trades workers 10.34 10.03
Plant and machine operators and assemblers 6.74 9.62
Elementary occupations 5.4 8.43
Total 100 100
Occupation groups are based on the first digit of the International Standard Classification of
Occupations (ISCO). The Armed forces occupations are excluded from this table.
89
References
Alessandrini, D., Kosempel, S. and Stengos, T., 2015. The Business Cycle Human Capital
Accumulation Nexus and Its Effect on Hours Worked Volatility. Journal of Economic
Dynamics and Control: 356–77.
Alvarez-Albelo C. D., 2004. Endogenous versus Exogenous Efficiency Units of Labour for the
Quantitative Study of Social Security: Two Examples. Applied Economics Letters 11:
693–97.
Auerbach, A. J. and Kotlikoff, L. J., 1987. Dynamic Fiscal Policy. Cambridge University Press,
Cambridge.
Aydemir, A. and Skuterud, M., 2005. Explaining the deteriorating entry earnings of Canada's
immigrant cohorts: 1966-2000. Canadian Journal of Economics 38:37.
Aydemir, A. and Sweetman, A., 2006. First and Second Generation Immigrant Educational
Attainment and Labor Market Outcomes: A Comparison of the United States and
Canada. Discussion Paper No. 2298, Institute for the Study of Labor (IZA).
Baker, M., and Dwayne B., 1997. The role of the family in immigrants’ labor-market activity: an
evaluation of alternative explanations. American Economic Review 87: 705–27.
Beetsma, R., Bettendorf, L., Broer, P., 2003. The budgeting and economic consequences of
aging in the Netherlands. Economic Modelling 20(5): 987–1013.
Behrenz, L., Hammarstedt, M., Mansson, J. 2007. Second-Generation Immigrants in Swedish
Labour Market. International Review of Applied Economics. Vol. 21, No. 1, 157–174,
January 2007.
Bell F. C. And Miller, M. L., 2002. Life tables for the United States social security area.
Actuarial Study, Social Security Administration, 116.
Bocola, L., Hagedorn, M., and Manovskii, L. 2014. Identifying Neutral Technology Shocks.
University of Pennsylvania.
90
Bonikowska, A. 2005. Education Attainment of Three Generation of Immigrants in Canada:
Initial Evidence from the Ethnic Diversity Survey. University of British Colombia,
Discussion Paper No.: 05-21
Borjas, G. 1996. The earnings of Mexican immigrants in the United States., Journal of
Development Economics 51: 69–98.
Borjas, George J. 1993. The Intergenerational Mobility of Immigrants. Journal of Labor
Economics, 11(1), 113–135
Borjas, G. (1993b), “Immigration policy, national origin, and immigrant skills: a comparison of
Canada and the United States”, in Small Differences that Matter (Eds) D. Card and R. B.
Freeman, University of Chicago Press, Chicago, pp. 21–43.
Boyd, Monica 2002. Educational Attainment of Immigrant Offspring: Success or Segmented
Assimilation? International Migration Review 36:1037-1060.
Carlaw, K., S. Kosempel, 2004, The sources of total factor productivity growth: Evidence from
Canadian data., Taylor & Francis in Economics of Innovation and New Technology,
2004, Vol. 13(4), June, pp. 299–309
Chen, K., 2010. A Life-Cycle Analysis of Social Security with Housing., Review of Economic
Dynamics 13: 597-615.
Chen, Y. and Feng, S., 2009. Parental Education and Wages: Evidence from China. Discussion
Paper No. 4218, Institute for the Study of Labor (IZA).
Chiswick, B. 1978. The effects of Americanization on the earnings of foreign-born men. Journal
of Political Economy, 86, 897–921.
Conesa, J. and Krueger, D., 1999. Social Security Reform with Heterogeneous Agents. Review
of Economic Dynamics 2: 757-795.
Conesa, J. and Krueger, D., 1999. Social Security Reform with Heterogeneous Agents. Review
of Economic Dynamics 2: 757-795.
Conesa, J.C., Garriga, C., 2003. Status quo problem in social security reforms. Macroeconnomic
Dynamics. 7: 691–710.
Cummins, J. and Violante, G., 2002. Investment-Specific Technical Change in the United States
(1947–2000),” Review of Economic Dynamics, Vol. 5, No. 2, pp. 243–84.
91
De Bock, R., 2007. Investment-Specific Technology Shocks and Labour Market Frictions.
National Bank of Belgium, Working Paper n108.
De Nardi, M., Imrohoroglu, S., Sargent, T.J., 1999. Projected U.S. demographics and social
security,. Review of Economic Dynamics 2: 575–615.
Diamond, P., and Mirrlees, J., 1978. A model of social insurance with variable retirement,.
Journal of Public Economics: 295-336.
Feldstein, ed., 1978. The effects of taxes on capital accumulation. Chicago: University of
Chicago Press: 7-48.
Finnie, R., 2008. Access to Post-Secondary Education Canada Among First and second
Generation Canadian Immigrants: Raw Differences and Some of the Underlying Factors.,
University of Lethbridge.
Fisher, J. D., 2006. “The Dynamic Effects of Neutral and Investment-Specific Technology
Shocks. Journal of Political Economy, 114, 413—451.
Gandelman, N. and Hernández-Murillo, R., 2014. Risk Aversion at the Country Level,
doi:Federal Reserve Bank of St. Louis, Working Paper 2014-005B.
Gomme, P., R. Rogerson, P. Rupert, and R. Wright, 2004, The Business Cycle and the Life
Cycle., Macroeconomic Annual, NBER, pp. 415–461.
Gordon, R., 1990. The Measurement of Durable Goods Prices, Chicago: University of Chicago
Press.
Grant, M., 1999, Evidence of new immigrant assimilation in Canada,. Canadian Journal of
Economics, 32, 930–55.
Green, D.A., and Riddell, W.C., 2001. Literacy, Numeracy and Labour Market Outcomes in
Canada, Ottawa: Statistics Canada.
Greenwood, J., Z. Hercowitz, and P. Krusell, 1997, Long-Run Implications of Investment-
specific Technological Change., American Economic Review, Vol 87, pp. 342–362.
Greenwood, J., Hercowitz, Z., and Krusell, P., 2000. The Role of Investment-Specific Technical
Change in the Business Cycle. European Economic Review, Vol 44, pp. 91–115.
92
Haley, W. J., 1976. Estimation of the earnings profile from optimal human capital accumulation,.
Econometrica, 44(6): 1223–1238.
Hansen, G D, 1993, “The Cyclical and Secular Behaviour of the Labour Input: Comparing
Efficiency Units and Hours Worked,” Journal of Applied Econometrics 8(1), 71-80
Hansen, G. D., and Imrohoroglu, D., 2009. Business Cycle Fluctuations and the Life Cycle: How
Important Is On-the-Job Skill Accumulation? Journal of Economic Theory 144 (6): 2293–
309.
Hansen, J., and M. Kucera. 2004. The Educational Attainment of Second Generation Immigrants
in Canada: Evidence from SLID. Montréal. Concordia University. Department of
Economics. Unpublished manuscript
Heckman, J., 1976. A life-cycle model of earnings, learning, and consumption. Journal of
Political Economy, 84(4): S11–S44.
Heckman, J., Lochner, L. and Taber, C., 1998. Explaining rising wage inequality: explanations
with a dynamic general equilibrium model of labor earnings with heterogeneous agents,.
Review of Economic Dynamics: 1–58.
Heer, B. and Maussner, A., 2009. Dynamic general equilibrium modeling,. Springer, 2ed. Berlin.
Henin, P.Y., Weitzenblum, Th., 2005. Welfare effects of alternative pension reforms: assessing
the transition costs for French socio-occupational groups,. Journal of Pension Economics
and Finance 4(3), 249 - 271
Heylen, F. and Pozzi, L., 2007. Crises and human capital accumulation,. Canadian Journal of
Economics, 40(4): 1261–1285.
Hirte, G., 2002. Welfare and macroeconomic effects of the German pension acts of 1992 and
1999: a dynamic CGE study,. German Economic Review 3 (1): 81–106.
Hubbard, R. G. and Judd, K., 1987. Social Security and Individual Welfare: Precautionary
Saving, Borrowing Constraints, and the Payroll Tax,. American Economic Review 77, 630-
646.
93
Hubbard, R. G., Skinner, J., and Zeldes, S.P., 1995. Precautionary Saving and Social Insurance,.
Journal of Political Economy: 360-99.
Huggett, M. and Ventura, G., 1999. On the distributional Effects of Social Security Reform,.
Review of Economic Dynamics 2: 498-531.
Hum, D., & Simpson, W., 2007. The legacy of immigration: Labour market performance
and education in the second generation. Applied Economics, 39 (15), 1-25.
Hviding, K., Merette, M., 1998. Macroeconomic effects of pension reforms in the context of
aging populations: OLG simulations for seven OECD countries,. OECD Working Paper, No.
201, ECO/WKP(98)14.
Imai, S. and Keane, M. P., 2004. Intertemporal labor supply and human capital accumulation,.
International Economic Review, 45(2): 601–41.
Imrohoroglu, A., Imrohoroglu, S., Joines, D., 1995. A Life Cycle Analysis of Social Security.
Economic Theory 6: 83-114.
Imrohoroglu, A., Imrohoroglu, S., Joines, D., 1999. Social Security in an Overlapping
Generations Economy with Land. Review of Economic Dynamics: 638-665.
Johnson, T. and Hebein, F. J., 1974. Investments in human capital and growth in personal
income,. The American Economic Review, 64(4):604–615.
Justiniano, A., G.E., Primiceri, A. Tambalotti, 2010, Investment Shock and Business Cycles,
Journal of Monetary Economics 57: 132-145.
Keuschnigg, C., Keuschnigg,M., 2004. Aging, labormarkets, and pension reformin Austria,.
FinanzArchiv: Public Finance Analysis 60 (3): 359–392.
King, R.G., and Rebelo, S.T., 1999. Resuscitating Real Business Cycles. in J.B. Taylor and M.
Woodford (eds.) Handbook of Macroeconomics, Vol. 1B, pp. 928–1002 (also National
Bureau of Economic Research Working Paper 7534).
Koka, K. and Kosempel, S., 2014. Life-cycle analysis of ending mandatory retirement.
Economic Modelling, 38, 57–66.
Krusell, P., and A. A Smith, 1998. Income and Wealth Heterogeneity in the Macroeconomy. The
Journal of Political Economy, Vol 106, No. 5, 867-896.
94
Kydland, F.E., and Prescott, E.C., 1982. Time to Build and Aggregate Fluctuations.
Econometrica, Vol. 50, No. 6, pp. 1345–70.
Maliar, L and S. Maliar, 2001. Heterogeneity in capital and skills in a neoclassical stochastic
growth model. Journal of Economic Dynamics and Control, 25:1367–1397.
McDonald, J. and Worswick, C. 1999, The earnings of immigrant men in Australia: assimilation,
cohort effects, and macroeconomic conditions. TheEconomic Record, 75, 49–62.
Neal, D. A., and Johnson W.R., 1996. The Role of Premarket Factors in Black-White Wage
Differences. Journal of Political Economy: 104(5), pp. 869-95.
Nishiyama, S. and Smetters, K., 2007. Does Social Security Privatization Produce Effciency
Gains?,. The Quarterly Journal of Economics 122(4): 1677-1719.
Nordin, M. and Rooth, D-O., 2007, “The Income Gap between Natives and Second Generation
Immigrants in Sweden: Is Skill the Explanation?” Paper No. 2759, Institute for the Study
of Labor (IZA).
Peterman, W.B., 2016. The Effect of Endogenous Human Capital Accumulation on Optimal
Taxation. Review of Economic Dynamics, vol. 21, pp. 46-71.
Rojas, J. A. and Urrutia, C., 2008. Social Security with Uninsurable Income Risk and
Endogenous Borrowing Constraints,. Review of Economic Dynamics 11(1): 83-103.
Rooth, D. and Ekberg, J., 2003, Unemployment and earnings for second generation Immigrants
in Sweden: Ethnic background and parent composition. Journal of Population Economics,
16 (4), pp. 787–814.
Shaw, K., 1986. Life-cycle labor supply with human capital accumulation. International
Economic Review, 30: 431–56.
Tu, J., 2010, Explaining the Labour Market Outcomes of First, Second and Third Generation
Immigrants in Canada. Paper No. 2298, Institute for the Study of Labor (IZA).