Aging Population in a Regional Economy

Abstract

This article seeks to examine the effects of the aging population in Illinois with inclusion of the household’s heterogeneity across migration status and investment in human capital. By adopting a stylized Mincer wage regression, the article shows that there are significant gaps in returns to education between migration statuses in Illinois; further, there exist significant relationships between a resident’s demographics and the probability of in- and out-migration to/from Illinois. Using a two-sector Overlapping Generations (OLG) model incorporated with the household’s heterogeneity over migration status, this article projects the economic growth of Illinois in the future. This article also shows that the effects of the government’s immigration policy that aims at replacing low-productive international immigrants with native and relatively high-productive unemployed individuals who have been unemployed, are very limited in terms of per capita income, welfare, and aggregate productivity. On the contrary, a tax and transfer policy inducing international immigrants to invest more in their education works relatively better under the demographic changes facing Illinois over the next three decades.

Keywords

aging population human capital intragenerational heterogeneity educational transfer

Introduction

In the United States, there is serious concern about the impacts of the aging population. According to the United Nation’s prospects (2010), the population cohort aged 65+ will increase from 12 percent of total population in 2005 to 20 percent in 2030, while the population cohort aged twenty to forty-nine will decrease from 43 percent to 38 percent during the same period (Figure 1). Many papers have argued that the aging population would bring a significant negative impact on the economy. For example, the aging population could lower the potential output growth mainly through a reduction in the size of the labor force while the government’s fiscal burden caused by aging population would continue to grow.

Figure 1.

Composition ratio of total population by selected age groups in the United States.

Overlapping generation (OLG) models have been used extensively to study the impacts of aging population on the economy. Included in this set are the analyses of Sadahiro and Shimasawa (2002, 2004), Park and Hewings (2009), Ludwig, Schelkle, and Vogel (2007), and Kim and Hewings (2010). In these studies, the household agents belonging to the same generation have identical parameter values and asset endowments. That is, the only heterogeneity factor in the model is the agent’s age or generation. Therefore, the solutions of household agents’ optimization problems are necessarily identical if they belong to same generation.

As a breakthrough in the development of a heterogeneous agent model in a dynamic general equilibrium context, Aiyagari (1994) proposed the model where each agent is of measure zero and lives infinitely. In his model, agents are ex-ante homogeneous but ex-post heterogeneous, depending on the sequence of realizations of uninsurable idiosyncratic earnings shock. The history of realized earning shocks naturally leads to borrowing constraints on individuals; consequent fluctuations in consumption can be mitigated only by precautionary individual savings. Since agents’ histories of earning shocks are different, the equilibrium exhibits cross-sectional distributions of wealth, saving, and consumption. Huggett (1996) adopted this ex-post heterogeneity framework within the OLG model to compare the age–wealth distribution to the corresponding distributions in the US economy. However, these papers restrict attention only to the steady state equilibrium since solving this type of model is computationally very intensive.

Alternatively, Kotlikoff, Smetters, and Walliser (2002) adopted ex-ante heterogeneity within the perfect foresight OLG framework for analyzing distributional effects of social security alternatives. Their model incorporates intragenerational heterogeneity in the form of twelve lifetime-earnings groups: each group has its own initial skill level and its own longitudinal age–skill profile. They showed that privatizing social security can generate significant long-run economic gains in the United States. This model and its methodology was adopted by various studies, that focused primarily on the effects of public pension reforms for the developed countries in which fiscal pressures on the pension system are arising due to aging population. A typical analysis would be that of Börsch-Supan et al. (2002) for Germany. In this article, members of the same generation are sorted into the categories of employment, unemployment, nonparticipating in the labor force and retirement to track the evolution of the aggregate labor supply. However, this model assumes each agent’s earning ability is an exogenous function of her age and/or type, without paying attention to the role of endogenous growth of human capital stock.

This article seeks to examine the effects of an aging population with inclusion of a household’s ex-ante intragenerational heterogeneity across migration status, extending the analysis presented in Kim and Hewings (2010). Attention to migration is very straightforward: the unique environment surrounding the US labor market is that young labor inflows coming from other countries is sizeble. Integrating these young immigrants successfully into the labor market could be critical in mitigating the negative effects of the aging population on the US economy since the immigrants could fill the deficiency in the native labor force caused by aging population in the near future.

Kim and Hewings (2010) showed that the policy measures that encourage an agent to invest more in education is very effective in mitigating the negative effect of aging population on the regional economy; but the policy that focuses on the direct redistribution of wealth cannot address the challenge of aging population in terms of per capita income, welfare and equity of income distribution.

In this present article, the analysis will focus on Illinois (IL); IL is used for illustrative purposes since it is a state with high international in-migration and significant out-migration as well as a region facing the typical challenges of an aging population. Also, the economic growth of IL is very important for the whole US economy in that IL’s economy leads the economies of twelve states in the Midwest region. According to the statistics announced by Bureau of Economic Analysis, the gross domestic product (GDP) of IL is the greatest among the twelve states in the Midwest; and ranked fifth of all of the US states and District of Columbia (Figure 2).

Figure 2.

Gross domestic product by State in 2011.

This article is organized as follows. In the second section, gaps of return to schooling are estimated across migration status with a stylized Mincer wage regression. An attempt is made to explore the relationship between an individual’s demographic profile and the probability of in- and out-migration. The third section contains a description of the model, within which the impact of aging population and effects of policy measures will be analyzed later. The fourth section describes the calibration procedure with the empirical results. The computational results will be presented in the fifth section and the final section concludes the article.

Empirical Evidence

Heterogeneity of Return to Education

Persistent efforts have been made to analyze differentials by race and migration status in the labor market performance in the field of labor economics. In particular, the return to educational investment plays a key role in labor issues such as allocation of resources, determinants of income inequality and explanation of past growth rate, and so forth. For example, Altonji and Blank (1999) adopted a Mincerian regression to show that there were ongoing and significant race differences in the labor market, even after controlling for occupational and industry location. They showed that the returns to education for blacks are actually stronger than for whites, but the returns to experience for blacks are substantially lower than those for whites. The article concluded that this sort of disadvantage for blacks significantly offsets higher returns to education for blacks. Bratsberg and Terrell (2007) examined rates of return to education of immigrant groups by country of origin, revealing the relationship between attributes of a country’s educational system and the rate of return to schooling received by US immigrants from that country.

As briefly described above, the Mincer (1958, 1974) model has been extensively adopted in empirical studies to estimate returns to schooling years and to explain the factors that generate wage gaps between interested groups. The Mincerian model can be stylized as:

log [w (s, x)] = α_{0} + ρ_{s} s + β_{0} x + β_{1} x^{2} + ϵ,

where

w (s, x)

are earnings at schooling level s and working experience x and

ρ_{s}

is the marginal effect of schooling or returns to education. In the present article, a Mincerian regression model is adopted to estimate different returns to education across migration status in IL. The sample data for this analysis (see Table 1) are obtained from the 2007 American Community Survey (ACS) implemented by U. S Census Bureau. It should be noted that all household members such as spouse, children, and parents are included in the analysis if they are more than eighteen years old. However, individuals who reported that they were not employed or not in the labor force were excluded.

Table 1.

Data Description: ACS 2007.

	United States				Illinois
	Average	SD	Min	Max	Average	SD	Min	Max
Age	39.0	23.2	0	95	38.6	23.1	0	93
Log of household income	11.1	1.2	0	16.1	11.1	1.2	1.4	16.1
Obs.	2,994,662				127,458
Sex	Male 48.6%, Female 51.4%				Male 48.4%, Female 51.6%
Race/Ethnicity	-White 77.9%, Black 9.9%, Asian 4.3%				-White 78.3%, Black 10.7%, Asian 3.7%
Race/Ethnicity	-Hispanic 12.4%				-Hispanic 10.5%
Student	-Student 25.4%				-Student 26.5%
	-No student 71.1%				-No student 70.0%
	-NA 3.5%				-NA 3.5%
Employment	-Employed 46.7%				-Employed 47.6%
	-Unemployed 2.9%				-Unemployed 3.4%
	-Not in labor force 29.8%				-Not in labor force 28.0%
	-NA 20.5%				-NA 21.0%

Source: Integrated Public Use Micro-data Series, Minnesota Population Center, University of Minnesota.

The sample was segregated into four comparison groups according to its migration status, comparing current location with residence in the prior year: individuals were grouped into (i) those who remained in IL, (ii) migrated into IL from the other states, (iii) migrated into IL from other nations, and (iv) moved out of IL.

The Mincerian regression is as follows:

l o g (a n n u a l e a r n i n g s) = β_{0} + β_{1} a g e + β_{2} {a g e}^{2} + β_{3} s c h o o l i n g y e a r + r e s i d u a l .

Here, β₃ measures returns to education.

There is a technical but important problem that needs to be addressed: measurement of schooling years. Since the Census Bureau does not provide the schooling year data but respondent’s degree or diploma based information, this has to be transformed into schooling years. One option would be to use the following tabulation between Census Bureau’s educational attainment data and schooling years (see Table 2). In this tabulation, schooling year is assigned as a mean value of each category in table 5 of Jaeger (1997) except for the categories of professional and doctorate degrees.²

Table 2.

Tabulation between Census’ Educational Attainment and Schooling Years.

Census’ educational attainment categories	Schooling years
No school completed	1.30
Nursery school to 4th grade	3.92
5th to 6th grade	6.22
7th to 8th grade	7.84
9th grade	9.08
10th grade	9.90
11th grade	10.81
12th grade, no diploma	11.38
High school graduate, or GED	12.00
Some college, less than 1 year	13.35
One or more years of college but no degree	13.87
Associate degree	14.29
Bachelor’s degree	16.04
Master’s degree	17.57
Professional degree	18.57
Doctorate degree	20.57

Source: Jaeger (1997) except for the cases of professional degree and doctorate degree.

Note: School years of professional degree = school years of master’s degree + 1. School years of doctorate degree = school years of master’s degree + 3.

The estimation results imply that there exist significant gaps in the returns to education over the migration status (second to fourth columns in Table 3). The coefficients of schooling years were 0.190 (domestic in-migrants) > 0.129 (natives) > 0.109 (international immigrants). However, one should be very cautious in interpreting these estimation results. The overall distribution of earnings across schooling years for domestic in-migrants might be lower than natives even though the returns to schooling for domestic in-migrant is higher than natives. To explore this issue, the following alternative regressions were run with the dummy variables of migration status:

Table 3.

Mincerian Regression Results: Different Migration Status.

	I. Natives in IL	II. Domestic in-migrants to IL	III. Inter’l immigrants to IL	Current residents in IL (I + II + III)	Emigrants from IL
Constant	4.196 (0.039)	2.195 (0.324)	4.270 (0.751)	4.172 (0.039)	2.875 (0.255)
Age	0.191 (0.002)	0.250 (0.016)	0.168 (0.041)	0.192 (0.002)	0.233 (0.013)
Age²	−0.002 (0.000)	−0.003 (0.000)	−0.002 (0.001)	−0.002 (0.000)	−0.002 (0.000)
Schooling year	0.129 (0.002)	0.190 (0.014)	0.109 (0.030)	0.130 (0.002)	0.159 (0.012)
d _int’l				−0.485 (0.065)
d_dom				−0.121 (0.031)
obs.	66,104	1,262	280	67,646	1,626
R ²	.2587	.3296	.1990	.2611	.3484

Note: Standard errors are denoted inside the parentheses.

\begin{aligned} l o g (a n n u a l e a r n i n g s) = {c o n s t a n t + β}_{1} {a g e + β}_{2} {a g e}^{2} + β_{3} s c h o o l i n g y e a r \\ + β_{4} {d_i n t^{'} ‘ 1 + β}_{5} d_d o m e s t i c . \end{aligned}

where d_int’l and d_domestic respectively represent an individual who lived outside the United States and an individual who migrated into IL from the other states in the previous year.

Note that there exist notable negative effects from the dummy variables on earnings in IL (fifth column in Tables 3). For example, the coefficients for the dummy variables, representing domestic and international immigrants, were −0.121 and −0.485, respectively. These results, in particular, verify that the overall distribution of earnings over ages of domestic in-migrants is notably lower than natives even though the returns to education for domestic in-migrants are very high. The most important result from the estimation above is that the earnings distribution over ages and returns to schooling of the international immigrants are the lowest among three migration status groups in IL.

Migration and Demographics

Immigration: From Rest of the United States (ROUS) to IL

Within the literature that has evaluated the migration associated with demographic issues, Frey (1995) analyzed in- and out-migration patterns of California from 1990 Census data. This paper discovered that California’s out-migration consists of two different systems: first, the exporting of lower-income and less-educated residents to near-by states, and second, the redistribution of better-educated and higher-income migrants across the ROUS. Meyer and Speare (1985) showed that mobility behavior is associated with sociodemographic characteristics, using a longitudinal data set of Rhode Island from the Census. For example, younger, married, and more affluent elderly are more likely to select out-of-state migration. In case of recent analysis on IL, Yu (2009) describes the migration patterns of IL such as the average household income of in- and out- migrants of IL, using the Internal Revenue Service data for 1992 through 2006. It revealed that there is a notable discrepancy in the income levels of domestic and international in- and out-migrants of IL; further, she noted that, on average, $1.682 billion of personal income drains out of IL per year. The literature reveals that migration is deeply affected by resident’s demographic and skill factors including age, schooling years and household income.

To explore the issue further, a binary logit regression model, whose dependent variable is whether the individual selected IL or not, was estimated, where move-in (=1) and no move-in (=0). The analyzed sample is composed of individuals who did not live in IL one year ago and have the experience of moving between states for the previous one year. Individuals younger than eighteen years were excluded. Attention was directed to estimating the probability of mobility with demographic and skill factors, which are related to age, income, and schooling years. In the next section, the empirical results of this section will be used in the calibration of the dynamic OLG model.

The regression specification is as follows:

\begin{aligned} l o g i t (p r o b . o f m o v e i n t o I L) \\ = c o n s t a n t + γ_{1} {a g e + γ}_{2} l o g (h o u s e h o l d i n c o m e) \\ + γ_{3} {s c h o o l i n g y e a r s + γ}_{4} d_i n t ’ 1 + r e s i d u a l, \end{aligned}

where d_int’l represents an individual who lived outside the United States in the previous year.

The estimation results imply that the probability of moving into IL from ROUS is inversely related to age and household income, but positively related to years of schooling. Further, international immigrants have a higher probability of choosing IL as their destination than US domestic residents (Table 4).

Table 4.

Result of Binary Logit Regression: ROUS → Illinois.

	Coefficient (SE)
Constant	−3.2992 (0.2016)
Age	−0.0083 (0.0015)
Log of household income	−0.0604 (0.0125)
Schooling year	0.0612 (0.0084)
d_int’l	0.1186 (0.0567)
Obs.	61,463
R ²	.0064

Note: Standard errors are denoted inside the parentheses.

Now, to check the expected probability of moving into IL, the other explanatory variables are set equal to their mean values except the age and dummy variables. Figure 3 plots the expected probability of moving into IL according to an individual’s age. For example, the results reveal that a domestic resident who is forty years old, who is going to move between states, chooses IL as a destination with the probability around 3 percent. However, the expected probability declines gradually as the individual ages.

Figure 3.

Expected probability of selecting move into IL from ROUS.

Out-migration: From IL to ROUS

A similar binary logit regression model was created to explore out-migration, whose dependent variable is whether the individual moves out of IL: move-out (=1) and no move-out (=0). The sample is restricted to individuals who lived in IL the previous year and has moved within and between states for the previous year. The binary logit regression is specified as follows:

\begin{aligned} l o g i t (p r o b . o f m o v e o u t f r o m I L) = c o n s t a n t + γ_{1} {a g e + γ}_{2} {a g e}^{2} \\ + γ_{3} l o g (h o u s e h o l d i n c o m e) \\ + γ_{4} s c h o o l i n g y e a r s + r e s i d u a l . \end{aligned}

The estimation result reveals that there exist a slight quadratic relationship between age and probability of emigrating from IL (Table 5).¹ Note that the sign of the coefficient of logged household income is positive. This positive sign should be compared with the result of in-migration analysis (case of ROUS → IL) in the previous section, where the coefficient of logged household income was negative. This result implies that there is a reverse effect of household income level on in- and out-migration to IL. Lower-income residents outside IL have a higher probability of migrating into IL than higher-income residents. On the contrary, higher-income residents in IL are more likely to migrate out of IL than lower-income residents. These results confirm the findings of Yu (2009).

Table 5.

Result of Binary Logit Regression: IL → ROUS.

	Coefficient (SE)
Constant	−3.7680 (0.2492)
Age	−0.0164 (0.0069)
Age²	0.0002 (0.0001)
Log(household income)	0.0841 (0.0115)
Schooling year	0.1189 (0.0099)
Obs.	11,562
R ²	.0185

Again, to check the expected probability of moving out of IL, the other explanatory variables are set equal to their mean values except age. The expected probability declines until the individual is about fifty years and then increases afterward² (see Figure 4). However, the overall shape of this expected probability seems to be partially counterintuitive: the probability of migrating out of IL peaks for the cohort aged eighty years and more. This odd shape of expected probability comes from the fact that the magnitude of the explanatory variable age³ in the binary logit model accelerates rapidly as the age approaches to eighty and older; this inflated magnitude of covariate age² and its positive coefficient dominates the effects from the other explanatory variables. Note that the size of the sample of those eighty and older is relatively small; thus, the regression result itself was not affected significantly by the data whose individual’s age is eighty and older. An alternative binary response model was adopted to deal with this problem in the expected probability as follows:

Figure 4.

Expected probability of selecting moving out of IL to ROUS.

\begin{aligned} l o g i t (p r o b . o f m o v e o u t f r o m I L) = c o n s t a n t + d_a g e_c o h o r t^{'} β \\ + γ_{1} l o g (h o u s e h o l d i n c o m e) \\ + γ_{2} s c h o o l i n g y e a r s + r e s i d u a l, \end{aligned}

where d_age_cohort is composed of dummy variables representing the age-cohort group such as below 30, 30–40, 40–50, 50–60, 60–70, 70–80, and 80+. The results imply that there still exits the quadratic relationship between age and out-migration probability until age seventy; but the probability of out-migration drops substantially after age seventy (Table 6). Note that the sign and magnitude of logged household income and schooling years are largely consistent with the former binary regression. Figure 5 shows the expected probability over the age-cohort groups by using this binary regression results. The high expected out-migration probability between 60 and 80 could be interpreted as the high frequency of retirement migration to the other states from IL.

Table 6.

Result of Binary Logit Regression with the Dummy Variables: IL → ROUS.

	Coefficient (SE)
Constant	−4.1589 (0.2034)
d_age3040	−0.1327 (0.0653)
d_age4050	−0.2071 (0.0799)
d_age5060	−0.1124 (0.0874)
d_age6070	0.6488 (0.0997)
d_age7080	0.3392 (0.1292)
d_age80	−0.4997 (0.1612)
Log(household income)	0.0954 (0.0114)
Schooling year	0.1169 (0.0098)
Obs. R ²	11,562 0.0251

Note: d_age3040 represents the group of people who are ≥30 and <40; and d_age80 represents the people who are ≥80.

Figure 5.

Expected probability of selecting moving out of IL to ROUS (alternative).

The empirical results presented in this section reveal that there are statistically significant gaps in the returns to education between the agents belonging to different migration groups in IL. This empirical evidence will be incorporated into the intragenerational heterogeneous OLG model, whose specification will be described in the next section. Also, the results indicated that there are linear and quadratic relationships between age and probability of in- and out-migration in IL. These results will be used for projecting the composition of residents of IL in terms of migration status.

Model Descriptions

There are three types of agents in the baseline model: households, firms, and government. The households maximize utility, subject to the usual budget constraint. Household agents participating in the labor market at age 1 (i.e., age category 1) would continue to participate in the market until retirement age and nonparticipating agents would continue to remain outside the market. Hence, it is assumed that there is no change in labor market status over a lifetime. We assume that there are no unemployed individuals if they participate in the labor market. Firms hire labor and rent physical capital to produce physical goods in a competitive market. The Government levies a social security tax on the workers and operates the social pension system of a “pay-as-you-go” type with the tax revenue. There are two sectors in the economy: physical goods and human capital sectors. The target period is 2001 through 2050, a period during which the aging phenomenon is expected to assume greater importance in IL as well as in the United States. There exist J generations in every single year: the generations are overlapped every sample period. For a parsimonious description of modeling, only fundamental equations will be presented in this section.⁴

Households

We suppose that households are heterogeneous in their returns to education. This intragenerational heterogeneity depends on their migration status even though they belong to same age cohort. It is assumed that the individual enters into labor market at age 1 and retires at age j*. Every agent is supposed to live until age J.⁵ At the beginning of age 1, each agent, who will continue to participate in labor market, makes a decision on allocating resources between consumption and savings as well as splitting the endowment time between schooling and work for a whole lifetime to maximize his or her lifetime welfare. The instantaneous utility function has two arguments, consumption and investment in human capital:⁶

u (c_{t, j}, e_{t, j}) = \frac{c_{t, j}^{1 - γ} + θ e_{t, j}^{1 - γ}}{1 - γ} γ > 1, 0 < θ < 1,

where

c_{t, j}

is consumption and

e_{t, j}

is time fraction of investment in human capital⁷ at time t and age j while θ is the parameter of the degree of educational investment motive and γ is the parameter of inverse of the intertemporal elasticity of substitution.

Human Capital

We follow the human capital production function of Sadahiro and Shimasawa (2002):

h_{j + 1, t + 1}^{q} = (1 - δ_{h}) h_{{j,}_{t}}^{q} + B^{q} (m k_{t})^{ϕ} (h_{j, t}^{q} e_{j, t}^{q})^{1 - ϕ},

where k_t is the physical capital/labor ratio while B^q is the parameter for accumulation efficiency of human capital applied to group q, m is the portion of physical capital stock that is allocated for producing the human capital stock, δ _h is the parameter for the depreciation rate of human capital stock and φ is the parameter of the elasticity of the human capital formation function. Therefore, we assume that some portion of physical capital is needed for accumulating the human capital, in addition to the schooling investment. The next step involves developing a rule of assigning a human capital stock for age 1 generation of each year. Following Sadahiro and Shimasawa (2002), it is assumed that the new generation is born with a portion of human capital stock of previous generations according to the following scheme:

h_{t, 1}^{q} = π^{h c, q} ((\sum_{j = 1}^{j *} h_{{t -}_{1, j}}^{q} (v^{q} N_{{t -}_{1, j}}^{q})) / \sum_{j = 1}^{j *} (v^{q} N_{{t -}_{1, j}}^{q})),

where

π^{h c, q}

is the parameter of efficiency of human capital transmission applied to group q;

N_{{t,}_{j}}^{q}

denotes population size of age-cohort j in time t; and v^q denotes labor-market participating rate of group q.

Firms

Each firm produces a composite good by renting physical capital and effective labor in order to maximize its profit each year. A Cobb–Douglas production function is adopted that has the following specification:

Y_{t} = A (K_{t}^{d})^{α} (L_{t}^{e d})^{1 - α},

where

K_{t}^{d}

the demand of physical capital and

L_{t}^{e d}

is the demand of effective labor at time t while A is the parameter of total factor productivity and α is the parameter of the physical capital income share.

Government

The government operates the social security system: government levies a social security tax on labor income and transfers the pension benefit to retirees. The government’s budget is assumed to be balanced every period:

τ_{t}^{p} (\sum_{q} \sum_{j = 1}^{j *} (v^{q} N_{{t,}_{j}}^{q}) ((1 - e_{{t,}_{j}}^{q}) w_{t} h_{{t,}_{j}}^{q})) = \sum_{q} \sum_{j = j * + 1}^{J} (v^{q} N_{{t,}_{j}}^{q}) {p e n}_{{t,}_{j}}^{q},

where

τ_{t}^{p}

is the social security tax rate at time t; and pen _t,j is the level of pension benefit at time t and age j.

The magnitude of the annual pension benefit of each retiree is dependent on his or her average yearly (gross) labor income before retirement. The Government transfers a pension benefit to a retiree which amounts to his or her yearly average labor income multiplied by replacement ratio (ξ).

Calibration

This article uses the same parameter values as Kim and Hewings (2010) except for the parameters of return to education (B) and degree of efficiency in transmitting human capital stock from generation to generation ( $π^{h c}$ ) as well as the initial human capital stock distributions.

Given the age-cohort population structure and death rate of each age for the initial year of the model, the size of the population belonging to each age cohort in the future could be estimated simply using a modified cohort survival model. That is, for example, the number of population of age-1 cohort in 2010 multiplied by (1-death rate) is same as the number of population in age-2 cohort in 2011. This projection result provides the basic population structure of IL. However, the population structure will be affected by migration so that the actual age–population structure might be significantly different from the basic population structure. The following procedure is used to forecast the age–population structure:

\begin{aligned} # o f p o p u l a t i o n b e l o n g i n g t o a g e j i n t i m e t i n I L \\ = (1 - d e a t h r a t e o f a g e j - 1) \times # o f p o p u l a t i o n b e l o n g i n g t o a g e j - 1 i n \\ t i m e t - 1 i n I L \\ + # o f d o m e s t i c i n - m i g r a n t s o f a g e j i n t i m e t t o I L \\ + # o f i n t e r n a t i o n a l i m m i g r a n t s o f a g e j i n t i m e t t o I L \\ - # o f o u t - m i g r a n t s o f a g e j i n t i m e t f r o m I L . \end{aligned}

The expected number of domestic and international in-migrants to IL and out-migrants from IL can be estimated by using the empirical result of the second section. For example, the following projection strategy could be adopted for estimating the number of domestic in-migrants in the future. First, the projections of the national age-cohort population structure in the future are available from the US Census Bureau. By using ACS (2007) data, it is possible to compute the nation’s yearly ratio of individuals per age cohort who move between states from among the total individuals in each state. Now, the number of potential in-migrants into IL and their distribution across ages are known. Next, the estimation results summarized in Table 4 and Figure 3 are used to compute the expected number of domestic in-migrants into IL per age cohort in the future. Similar methods are used to estimate the number of international in-migrants and out-migrants⁸ per age cohort for every year in the future. Table 7 shows the example of calibration of the population structure related to migration status. The calibration procedure regarding the population of migrants is largely consistent with the actual population structure of ACS (2007).

Table 7.

Ratio of Migrants: Calibration versus Survey Data.

	Ratio of residents who migrated domestically into IL for one year (%)	Ratio of residents who migrated internationally into IL for one year (%)	Ratio of residents who migrated out of IL for one year (%)
Calibration in case of 2007	1.66	0.47	2.24
ACS 2007	1.58	0.43	2.01

Note: Based on the people who age ≥20.

Figure 6 presents the growth rate of the retirees. From this figure, it is possible to conjecture that the aging phenomenon of IL will accelerate until the mid-2020s and then decelerate substantially. In addition, it is assumed that a domestic in-migrant’s status lasts only one year: that is, the heterogeneity across domestic in-migrants and native residents will disappear in one year as the in-migrant takes on the characteristics of the existing residents. However, the characteristics as an international in-migrant are not assumed to disappear permanently; for example, prior experience with migration may make a household less risk adverse to migrating again in contrast with a household that has only remained in the same state.

Figure 6.

Growth rate of the retirees.

The returns to education parameter value should be given to natives, domestic in-migrants, and international in-migrants consistently with the result of the second section. For this, it is assumed that the labor earnings per a unit of working time reflect labor productivity of the corresponding worker perfectly. The value of the parameter B of each migration group should be consistent with the exponentials of coefficients of schooling year from Table 3 (second and fourth columns). Therefore, the values were assigned from Table 8. The value of B in Kim and Hewings (2010) was 0.28; thus, the assignment of the parameter values is made so that the average of parameter value weighted by each migration group’s composition ratio is 0.28.

Table 8.

Parameter Value of B: Efficiency of Human Capital Accumulation.

	Coefficient of schooling year	Exp (Coef.)	Value assignment to B
Continual residents	0.129	1.1377	0.2796
Domestic in-migrants	0.190	1.2092	0.2972
International immigrants	0.109	1.1152	0.2741

In the second section, it was noted that the migration effect of being an international immigrant on earnings is the lowest among the three migration categories. This could be a consequence of notable gaps in the average human capital stocks belonging to young generations of each race. To calibrate this interpretation into the model, different values for the parameter $π^{h c}$ are assigned across migration status (Table 9). Note that this parameter determines the level of transmission of human capital stock from proceeding generation to the new generation. Again, the weighted average of this parameter value is set equal to the values in Kim and Hewings (2010) (=1.0). Also, the initial human capital stock distribution over ages was assumed to be heterogeneous between migration status; but their average values should be same as that in Kim and Hewings (2010).⁹

Table 9.

Parameter Value of $π^{h c}$ : Efficiency of Human Capital Transmission.

	Coefficient multiplied by dummy variable	Value assignment to $π^{h c}$
Continual residents	0	1.0087
Domestic in-migrants	−0.121	0.8867
International immigrants	−0.485	0.5195

Computational Results

The computational results show that per capita output will increase by 46.4 percent from 2001 to 2050. Growth of per capita output will decrease until the mid-2020s and then will recover thereafter (Figure 7). The computational results imply that the gaps of human capital levels between continuing residents (native) and international immigrants will be maintained in the future.¹⁰ International immigrants’ human capital level is 58.0 percent smaller in 2001 and will be still 46.4 percent smaller than natives in 2050 (Figure 8).

Figure 7

Per capita output and its growth rate.

Figure 8.

Average human capital stock per worker.

Policy makers could consider two alternative policies because there are significant productivity gaps between migration statuses. Those policies are called international immigration restriction and educational transfer policy in this article. First, international immigration restriction policy strengthens the criteria for employment of international immigrants; therefore, natives’ unemployment rate will decrease. This policy stems from the belief in the crowding out notion that immigrants displace native residents in the job market; alternatively, immigration policy could target specific occupational needs to maximize matching immigrants with unmet job demands thus minimizing the competition with native residents. In the simulation, newly immigrated international individuals’ labor market participation rate is set to be zero. Instead, these international individuals are replaced with native individuals who have been unemployed but have higher productivity than international immigrants. Second, we experiment with the educational transfer policy regime, which was explored in Kim and Hewings (2010). When the government operates the educational transfer system, it levies an educational tax on household’s income that is reimbursed proportionally to his or her opportunity cost stemming from time spent on educational investment. In this experiment, the government’s educational transfer policy targets the individuals with relatively low productivity, namely international immigrants. For illustration, the reimbursement rate is set to .20, but it is assumed that the government reimburses part of opportunity cost of schooling investment of only international immigrant workers.

This educational transfer policy for international immigrants could be supported by the following information. According to the facts revealed by Capps et al. (2003), 18 percent of all foreign-born workers attained less than ninth grade; on the contrary, only 1 percent of native workers attained less than ninth grade. Even in a same group of low-wage workers, defined as workers earning less than 200 percent of the state minimum wage, the gaps of formal schooling between the international immigrant and native workers are obvious: 28 percent of foreign-born workers finished less than ninth grade while only 2 percent of native workers attained less than ninth grade. Also, 46 percent of all foreign-born workers have limited English proficiency. Without fiscal incentives, the lack of formal schooling and English proficiency would continue to play as a barrier to international immigrant workers’ participation in schooling and thus accumulation of human capital with the result that it would have a deleterious impact on their current income and their capacity to accumulate assets for retirement.

For simulation, we assume that government’s social security system and educational transfer system are operated independently from each other. Also we continue to assume that the government’s budget is balanced every period. Therefore, the budget constraint corresponding to the educational transfer system is like following while the constraint of social security system is same as equation (11):

\begin{aligned} τ_{t}^{e} ((\sum_{q} \sum_{j = 1}^{j *} v^{q} N_{{t,}_{j}}^{q} ((1 - e_{{t,}_{j}}^{q}) w_{t} h_{{t,}_{j}}^{q})) + (\sum_{q} \sum_{j = 1}^{J} v^{q} N_{{t,}_{j}}^{q} (r_{t} a_{{t,}_{j}}^{q}))) \\ = μ \sum_{j = 1}^{j *} v^{int} N_{{t,}_{j}}^{int} (e_{{t,}_{j}}^{int} w_{t} h_{{t,}_{j}}^{int}), \end{aligned}

where superscript int denotes international immigrants.

Computational results show that educational policy focused on improving human capital of low-productive workers is preferable in terms of improving aggregate productivity in contrast to the immigration restriction policy that restricts the international immigrants’ employment. When governments restrict newly arrived international immigrants’ employment even completely and replaces those workers with relatively high productive native residents, the positive effects on per capita output is close to constant in term of deviation from the baseline economy. However, if the government tries to improve international immigrant worker’s productivity in a way that the policy encourages immigrant people to spend more time in education, the effect on per capita output will accumulate and grow gradually (Figure 9).

Figure 9.

Deviation of per capita output from baseline economy.

This is mainly because aggregate human capital stock is more positively affected by educational policy (Table 10). In 2050, aggregate human capital stock under the educational transfer policy regime would be 4.27 percent higher than the baseline economy where no government policy is involved. On the contrary, human capital under the restrictive immigration policy is barely (0.66 percent) higher than the baseline economy. It should be noted that the educational transfer policy, which is focused on improving international immigrants’ human capital stock, also improves the human capital stock of native workers by 4.16 percent while the restrictive immigration policy has no such impact. This could be interpreted to imply that there exist the positive spillover effects between native and international immigrant’s human capital stock. Further, as Park and Hewings (2009) have documented, under an aging population with no immigration, welfare effects are likely to deteriorate as the shrinking of the labor force raises not only the dependency ratio but also bids up wages that may reduce the region’s competitiveness as well as reducing gross product and gross product per capita. However, the findings in this article suggest that absent a proactive program to enhance immigrants’ human capital, continued immigration may result in deterioration in income inequality.¹¹

Table 10.

Comparison of Human Capital Stock of Each Group in 2050.

	Baseline economy (A)	Under restrictive immigration policy (B)	Under educational transfer policy (C)	(B−A)/A	(C−A)/A
Whole workers	2.7599	2.7782	2.8778	0.66%	4.27%
Native workers	2.7842	2.7827	2.9000	−0.05%	4.16%

Another available option to counteract the negative effects caused by the aging population would be for the government to encourage firms to extend the retirement age of their employees. Extending the retirement age would prevent the abrupt shrinkage of labor force by utilizing the elderly population, while it would mitigate government’s fiscal burden by increasing the tax revenue and decreasing the fiscal spending (especially for social security). For simulating this option, the retirement age parameter (j*) is increased by one to three years. The computational outcome implies that the effect of extending the retirement age could be more desirable than the educational policy in the short run (Figure 10). Under the scenario of extending the retirement age by one to three years, the international immigrants’ human capital stock would be persistently less than under the scenario where the educational policy was implemented. In the case of extending the retirement age by three years, the international immigrants’ average human capital stock would shrink by about 15 percent, compared to the human capital stock under the educational policy scenario in 2050.

Figure 10

Effects of extending the retirement age by three years. Note: ¹Ratio of human capital stock under the scenario of extending retirement age to the scenario of implementing educational policy.

Nevertheless, in the short run, the effect of extending the retirement age on economic growth is not trivial. Overall, taking the fiscal advantage as well as this immediate and obvious effect on the economic growth, extending the retirement age could be considered an alternative policy measure. For example, a mixed policy measure of educational policy and extending the retirement age presents the advantage of boosting economic growth and sustaining fiscal prudence. The fiscal funds necessary for implementing the educational policy could be raised partially by the fiscal surplus generated by extending the retirement age.

Conclusion

In this article, we have developed a two-sector OLG model with intragenerational heterogeneity over individual’s migration status in the region of the United States. With this model, we examined the impact of aging population on the regional economy and examined the effect of three alternative government policy measures on the economy. To accomplish this, we set up an empirical model to investigate the implication of heterogeneity over migration status. We found out that there are significant gaps of return to education between migration status: there are overall noteworthy negative effects for international immigrants on their earnings.

Using a two-sector OLG model, we drew some implications for policy makers. The positive effects of a policy that restricts employment of the international immigrants turn out to be limited in terms of per capita income, welfare, and aggregate productivity. On the contrary, a tax and transfer policy that induces international in-migrants to invest more in their education works much better. Even though the regime’s direct beneficiary is an international immigrant, the natives’ human capital stock also improves significantly because of positive spillover effects.¹² The government’s policy to encourage firms to extend employee’s retirement age would be significant in the short run; however, the computational results revealed that its long-run effect would be limited. More rigorous research should be carried on the effects of extending the retirement age on the government’s fiscal status and its endogenous relationship with the regional economy.

Overall, with the limited fiscal budget constraint, government policies should be focused on facilitating the growth of the human capital of the disadvantaged groups (such as international immigrants in this article) to maintain the sustainable growth in the future, taking the fact into considerations that today’s skilled workforce are rapidly approaching to retirement age.

Finally, two comments on further research topics will be presented. First, the subject this article explored could be examined further by adopting the approaches of Aiyagari (1994) and Huggett (1996). In our article, even though we incorporated the heterogeneity between migration status, the heterogeneity inside the same migration status group was not captured in our model. Therefore, further study could assume that the individuals are exposed to the uninsured idiosyncratic productivity shock over their lifetime. The transition specification of risks including a Markov chain of the shocks could be calibrated from the empirics including the results in the second section. This kind of article would present a more detailed and robust picture of transition path of economic variables such as income distribution and welfare.

Second, as Yoon and Hewings(2006) revealed, the heterogeneity of consumption bundles among different age cohort groups as an empirical fact, our one-composite-commodity general equilibrium model could be extended to trace the interactions between the change of demographics and development of consumption structure and growth of the economy. As a starting point, Foellmi (2005)’s growth model could be adopted into our OLG framework. It accepted the non-homotheticity but proposed a hierarchical preference structure, whose property eventually enables individual’s consumption composition to exhibit different patterns according to the development of an individual’s income level. Hence, heterogeneity in consumption presents an important challenge since it will have important impacts on what goods and services are produced and consumed, potentially changing income generation with important welfare impacts over time.

Footnotes

Appendix A

Appendix B

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes

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