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Can guest workers solve Japan's fiscal problems?

I. INTRODUCTION

The population in Japan has already started to decline. According to recent forecasts of fertility and longevity, the population is expected to decrease from its recent high of 127.4 million in 2010 to about 50 million by 2100. In addition, the working-age population is declining even faster. Due to this rapid aging, public expenditures for pensions and health are projected to require sizeable new revenues when the tax base is already shrinking. If Japan wants to avoid massive spending cuts or tax increases, it may need to "manufacture" workers in order to minimize the impact of this secular demographic change.

One way to increase the size of the work force is to introduce a foreign worker policy. Indeed, the Japanese government announced early in 2014 that it would consider a guest worker program that would bring 200,000 foreign workers annually to Japan for a period of 10 years, eventually accumulating a stock of about 2 million guest workers. Can such a guest worker program solve Japan's fiscal problems? This paper investigates the effects of guest worker programs on fiscal sustainability in Japan and the welfare effects on the native Japanese individuals.

Japan has followed insular policies for centuries and relied on native-born workers for their economic growth. Their post-World War II growth and "catching up" in the 1960s through 1980s have turned into the lost decades since 1990. While a large wave of globalization and capital deepening has propelled most of the Asian economies, in particular China, into faster economic growth, Japan has lost significant ground. Meanwhile, Japan is fast approaching crossroads as it seeks to find more workers to mitigate the projected decline in the working-age population. Additional workers would produce additional goods and services and pay more taxes to help achieve fiscal sustainability. With a male labor force participation rate among the highest in the world across age groups, additional labor supply in Japan can only come from (1) increases in the fertility rate to produce younger native-born workers, (2) increases in the female participation rates and/or increases in labor in efficiency units, and, (3) foreign-born workers.

The fertility rate has been far below the level necessary for a stationary population and the population has been declining already. The total fertility rate in Japan was 1.46 in 2015, much lower than 2.0 in the United States and well below the replacement rate that would keep the population constant. Unfortunately for Japan, the fertility rate is projected to stay significantly below 2 over the next few decades. (1)

Another potential source of additional labor supply is the pool of Japanese females. The female labor force participation (FLFP) rate has been rising over the last two decades in Japan and it is now 65.1% within the 15-64 age group, very close to the 66.1 % in the United States. It is true, however, that when older working ages are considered (65+) Japan's FLFP rate. 49%, is lower than those in France (51 %), Germany (54%), and especially the United States (57%), according to the World Bank data over 2010-2013. So, it may be possible to raise the FLFP rate in Japan further. In addition, many females are on irregular or part-time jobs that pay much less than regular jobs. Raising their human capital and hence income may make a more important contribution to solving Japan's fiscal imbalance. (2)

The third source of additional workers is to introduce a major guest worker program. Several European countries, most notably Germany, benefited immensely from significant immigration in the 1960s and 1970s. The United States has received a large in-flow for more than a century and the current law specifies an annual flow of legal permanent immigration at 675.000, although there is an additional unreported or illegal flow of immigrants. The skill distribution is bimodal; there is a significant group of highly skilled immigrants in research and development, academia, and at consulting, finance, and insurance services industries, as well as a larger group of low-skilled workers in agriculture and hospitality service industries. In 2014. the share of foreign-born workers in total employment in the United States was 16.4%.

In this study, we develop a quantitative general equilibrium (GE) model of native workers, assess the impact of various guest worker programs on the Japanese economy, and evaluate the welfare effects of these programs on the native Japanese. We build a large overlapping generation model populated with native-born individuals between 20 and 110 years old, who face longevity risk and make optimal consumption and saving decisions over the life cycle. Labor is exogenous and therefore labor income taxes are not distortionary. (3)

There is a stand-in firm which maximizes its profits. The government taxes consumption and income from capital, labor, and government bonds, to finance exogenous government purchases, transfer payments, and its debt.

We present results that assume that the productivity of guest workers is either 50% or 100% of that of the native workers. A key assumption in our setup is that the guest workers leave after working for 10 years and therefore they do not receive pensions or significant public health transfer payments. To the best of our knowledge, the existing models of immigration including those we mention below assume that foreign-born workers become identical to native-born workers after one period in the model. To make contact with this literature, we also present an extended version of the model in which the foreign-born workers eventually become permanent residents after a work life of 30 years.

The model is calibrated to Japanese data; in particular, we calibrate the native individuals' life-cycle earnings to our estimates from micro data. We assume that the debt to gross domestic product (GDP) ratio is maintained forever at its 2013 level of 130%. The baseline experiment computes the equilibrium transition from 2014 toward a final steady state in the far distant future and produces an endogenous path for the consumption tax rate that satisfies the government's budget in each period in the face of increases in public expenditures due to aging. Similar to the findings in the literature (see below) we find consumption tax rates above 35% for several decades; there is a very high cost, in terms of unprecedentedly high tax rates, of loading all of the fiscal burden on a single fiscal instrument.

When we initiate a guest worker program in which 200,000 foreign-born workers are introduced into the workforce every year to leave after a 10-year tenure on the job, the consumption tax rate rises 2-3% less than that in the baseline case. The fiscal gains are small but there are large welfare gains for native-born workers.

If Japan adopts a larger-scale U.S.-style guest worker program which builds a stock of foreign-born workers equal to 16.4% of employment and maintains this ratio, then the gains in consumption tax reduction can be as large as 10%. This experiment demonstrates how a guest worker program could contribute to achieve fiscal sustainability in Japan.

These quantitative results depend on two forces that go in the same direction and necessitate very large fiscal adjustments in Japan. The first is aging-related; the combination of a shrinking tax base and increased public pension and health expenditures. This is essentially the result of the increase in the old-age dependency ratio. In addition, there is a second mechanism, present in GE models, and, this second force is the increase in the equilibrium wage rate arising from the increase in the time path of the capital-labor ratio. The labor supply is falling monotonically from 2014 through post-2100. The capital stock, on the other hand, rises for a while as the extended retirement years motivate individuals to raise their private saving. The reduction in the number of savers eventually puts an end to this process and the capital stock eventually falls along the transition. As a result, the capital labor ratio in Japan rises significantly until about 2050, and then falls, but it converges to a level still much higher than that in 2014. With the wage rate following a similar path, and pensions tied partially to wages, this mechanism delivers added expenditures that the Japanese government must finance.

In our partial equilibrium (PE) exercise, we turn off this second mechanism and even without guest workers or immigration, the consumption tax rate needed to achieve fiscal sustainability is around today's levels in Scandinavian countries such as Denmark, Finland, Norway, and Sweden, at 25%. In other words, if Japan could implement policies that mitigate the run-up in wages over the next few decades produced by the predicted increase in the capital labor ratio, then the fiscal adjustments needed to finance aging-related public expenditures would be much more manageable.

Of course, any immigration or guest worker policy program faces political, societal, and technological challenges, some of which are specific to Japan. An immigration policy, as opposed to a guest worker program, requires planning for and financing of additional old age pensions and public health expenditures. Clearly this would raise the overall fiscal burden and possibly outweigh the contributions to the tax base during working ages over the life cycle. A guest worker program, on the other hand, introduces difficulties in the termination of the finite working age to stay in Japan, requiring assurances and controls to keep the "guest" feature of the program in place. We do not wish to minimize the practical, technological, linguistic, and societal challenges posed by immigration or guest worker programs. Instead, this paper focuses on the opportunities that a guest worker policy can provide for Japan. A strong foreign-born worker policy may help Japan achieve fiscal sustainability.

The article is organized as follows. Section II presents a brief literature review relevant to our work. Section III describes our economic model, Section IV provides the details of our calibration strategy, Section V presents our quantitative findings, Section VI presents some additional exercises, and Section VII gives our concluding remarks.

II. RELATED LITERATURE

This study builds on and contributes to two strands of literature. First, there is a large literature on measuring the size of adjustments Japan needs to make in order to bring about fiscal sustainability as it faces the projected aging-related public expenditures. Doi. Hoshi, and Okimoto (2011) estimate the tax revenue as a fraction of GDP required to sustain the debt at the 2010 level; they find that revenue has to go up by 7-14% of GDP, from 33% in 2010. Hansen and imrohoroglu (2016) use a one-sector neoclassical growth model and measure the needed consumption tax rate that achieves fiscal sustainability to be about 50%, unless there is a significant spending cut. Braun and Joines (2015) and Kitao (2015a) employ large-scale overlapping generations models and calculate tax rate increases of similar size. Reforms of health insurance copay for the retirees or extensions of the normal retirement age appear to contain the required increases in tax rates. (4)

Second, we are contributing to the literature on immigration and its impact on public finances. An earlier study by Storesletten (2000) uses a GE model with overlapping generations, calibrated to the U.S. economy and argues that a large immigration policy (about 1.6 million annual flow starting in 2000) of high- and medium-skilled immigrants could resolve the fiscal problems. Auerbach and Oreopoulos (1999) and Lee and Miller (2000) also find large gains from immigration for the United States. Storesletten (2003) uses an accounting model for Sweden and calculates the net public gain of a new immigrant as the discounted value of future tax payments minus transfers and additional government consumption, and finds the potential gains to be large, about $20,000 per new immigrant. (5)

Among the immigration studies for Japan, however, Fehr, Jokisch, and Kotlikoff (2004) are less enthusiastic. Fehr, Jokisch, and Kotlikoff (2004) develop a three-region overlapping generations model for United States, Japan, and European Union in which immigrants (1) broaden the tax base but lower the real wage (dampening the initial beneficial effect), (2) accumulate the capital they arrive with, raising wages, and, (3) require public expenditures like natives as they become identical to natives after one period. Their baseline experiment calls for an annual flow of 54,000 immigrants (with the same amount of capital and children as their native-born counterparts), and an alternative of 108,000 of only high-skilled immigrants. (6) Their overall conclusion is that there are small welfare effects and that the impact is "too little too late."

Shimasawa and Oguro (2010) use a 16country/region overlapping generations model in which immigrants cannot be distinguished from natives upon entry. Like Fehr, Jokisch, and Kotlikoff (2004) and other studies, this assumption makes their productivity the same as their native counterparts subject to being in the same skill category, and makes them eligible for pensions and public health insurances. (7) Their baseline immigration policy brings in an annual flow of 150,000 immigrants and the foreign-born population eventually reaches 37% of the Japanese population by 2100. (8) Despite this large immigrant population, there are little gains on the fiscal front. The debt to GDP ratio by 2050 is 699% compared to the baseline case of zero immigration value of 719%. When a consumption tax rate is raised and set at 30% (in their Scenario 8) under this high immigration assumption, the gains are much larger and the debt to GDP ratio declines to 234% in 2050. Overall, Shimasawa and Oguro (2010) conclude that immigration alone cannot alleviate the fiscal burden.

III. MODEL

In order to discipline the behavior and calibration of our model for the native individuals, we will develop a dynamic GE model which consists of overlapping generations of finitely lived individuals. We denote time with t and the age of an individual with j. We will first describe our benchmark model without foreign workers and introduce them in the model in Section V, where we discuss guest worker policies.

A. Demographics

Individuals enter the economy at age j = 1 and can live up to J years. Lifetime is uncertain and agents of age j at time t face a conditional probability of [S.sub.j,t] to survive to age j + 1 at time t + 1. [S.sub.j,t] = 0 for all t. The size of a new cohort entering the economy grows at rate y,. We denote by [n.sub.j,t] the number of individuals of age j at time t.

B. Endowment, Skills, and Earnings

Labor supply is exogenously determined in the model and we denote by [[for all].sub.j,t][member of] [0,1], the employment rate of age j individuals at time t. Earnings of working individuals at age j < [j.sup.R] at time t are given as [y.sub.j,t] = [[eta].sub.j][W.sub.t].[[eta].sub.j] denotes age-specific productivity which evolves deterministically and [w.sub.t] is the market wage at time t. Average earnings of an age j individual net of labor income taxes at [[tau].sub.i,t] (and payroll taxes at [[tau].sub.p,t] are denoted as

[[??].sub.l,t] = (1 - [[tau].sub.l,t] - [[tau].sub.p,l])[y.sub.j,t][[for all].sub.j,t].

C. Individuals ' Problem

The lifetime utility function of an individual who enters the economy at age j = 1 as an adult is given by

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [C.sub.j,t+j-1], is consumption at age j and time t + j - 1, [S.sub.j,t+J-1] denotes unconditional probability that an individual born in at time t survives j - 1 periods up to age j at time t +j - I. That is, S.sub.j,t+J-1] = [[product].sub.j-1k=1], S.sub.k,t+k-1]. The subjective discount factor is denoted by [beta] and the coefficient of relative risk aversion is given by [theta].

The budget constraint of an individual in each period is given as

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where R, is the after-tax gross return factor on individuals' savings defined in Section III.E, and [[tau].sub.ct] is the consumption tax rate. Individuals can buy and accumulate one-period riskless assets which consist of a combination of investment in physical capital and holdings of government bonds. We assume that there are annuity markets to cover the event of early death with the actuarially fair price The assets of the deceased are distributed equally to individuals of the same cohort. (9) The individuals receive nonpension net, lump-sum transfer payments [t.sub.rt] from the government (net of lump sum taxes) and also collect pension benefits [P.sub.jt] after retirement j [greater than or equal to] [j.sup.R].

D. Technology

Firms produce output Yt using aggregate capital [K.sub.t], labor supply Lt, and productive technology [Z.sub.t] according to a constant returns to scale technology

[Y.sub.t] = [Z.sub.t] [K.sup.[alpha].sub.t] [L.sup.1-[alpha].sub.t].

[alpha] is capital's share of output and capital depreciates at constant rate [delta] [member of](0,1). The total factor productivity (TFP) Z, grows at rate [[lambda].sub.t]. The rental price of capital [r.sub.k,t] and wage rate [w.sub.t] are determined competitively and equated to the marginal product of each factor and defined as follows:

(3) [r.sub.k,t] = [alpha][Z.sub.t]([K.sub.t]/[[L.sub.t]).sup.[alpha]-1] - [delta],

(4) Wt = (1 - [alpha])[Z.sub.t]([K.sub.t]/[[L.sub.t]).sup.[alpha]].

E. Government and Fiscal Policies

The government raises revenues through taxation and issuance of one-period real debt to finance public consumption, transfers to individuals, as well as debt repayment and interest payments on outstanding debt. The government also runs the public pension scheme and provides pension benefits to retirees.

Government Budget. In each period, the government finances its total expenditures [G.sub.t], total net (nonpension) transfers to individuals T[R.sub.t], total pension benefits to retirees [P.sub.t] and the cost of debt servicing through taxation [T.sub.t] and issuance of new debt Bt+]. The government budget constraint is given as follows:

(5) [B.sub.1+1] = (1 + [r.sub.b,t])[B.sub.t] + [G.sub.t] + [P.sub.t] + T[R.sub.t] - [T.sub.t].

Here (1 + [r.sub.b,t])[B.sub.t] is the principal and interest payments on the stock of government debt. We assume that the government issues one-period bonds at real interest rate [r.sub.b,t].

We distinguish between [r.sub.b,t] the interest rate paid on the government debt, and [r.sub.k,t], return to physical capital rented to firms. This allows us to capture the level of interest rate paid by the government and approximate the total interest expenses of the government. As in Braun and Joines (2015) and Kitao (2015a), we assume that individuals allocate an exogenous fraction [[phi].sub.t], of their saving to government debt and a fraction (1 - [[phi].sub.t]) to firms' physical capital. (10) After-tax gross return factor on individuals' asset holdings is given as [R.sub.t] = 1 + (1 - [[tau].sub.k,t])[r.sub.k,t]) + (1 - [[phi].sub.t]) + (1 - [[tau].sub.b,t])[r.sub.b,t][[phi].sub.t].

The government revenues and spendings are defined as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[T.sub.t] represents taxes on three sources of revenues; consumption at the proportional rate ([[tau].sub.c,t] income from asset holdings at a combination of [[tau].sub.k,t] and [[tau].sub.b,t], and labor income at [[tau].sub.l,t] (and [[tau].sub.p,t] [g.sub.j,t], denotes exogenous per-capita government purchases for individuals of age j at time t. [P.sub.j,t] is per-capita pension payments to retirees at age j at time t, and [tr.sub.t] is per-capita, age-independent, net, nonpension transfers at time t.

Pension Benefits. Pension benefits [P.sub.j,t] mimic the current Japanese public pension system in which the benefit depends on past earnings and are given by the formula

[P.sub.j,t] = [[kappa].sub.t] [W.sub.j,t]/[j.sup.R] - 1.

Cumulated past gross earnings W, are computed recursively using

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [j.sup.R] is the normal retirement age at which individuals start to receive public pensions. [[kappa].sub.t] represents the replacement rate, which is time-dependent to calibrate recent public pension reforms.

F. Definition of Equilibrium

Given a sequence of exogenous demographic parameters {[[gamma].sub.t],[S.sub.j,t], [n.sub.j,t]}, government policy variables {[g.sub.j,t],[P.sub.j,t],[t.sub.r,t] [[tau].sub.k,t],[[tau].sub.p,t]}, and interest rates on the government debt and asset allocation rule {[r.sub.b,t]([[phi].sub.t])}, a competitive equilibrium consists of sequences of individuals' consumption and asset holding choices {[C.sub.j,t][a.sub.j]+ 1,t + 1}, factor prices {[r.sub.k,t], [w.sub.t]}, and consumption tax rates {[[tau].sub.c,t]} that satisfy the following conditions:

1. Individuals' allocations {[C.sub.j,t][a.sub.j]+ 1,t + 1} maximize the objective function (Equation (1)) subject to a sequence of budget constraints (Equation (2)).

2. Factor prices are determined competitively as in Equations (3) and (4).

3. The capital, bond, and labor markets clear:

[K.sub.t] = 0 - [[phi].sub.t]) [summation over (j)][a.sub.j,t] [n.sub.j,t],

[B.sub.t] = [[phi].sub.t] [summation over (j)][a.sub.j,t] [n.sub.j,t],

[L.sub.t] [summation over (j)][[eta].sub.j,][[LAMBDA].sub.j,t] [n.sub.j,t].

4. The goods market clears:

[C.sub.t] + [K.sub.t+l] + [G.sub.t] = [Y.sub.t] + (1 - [delta])[K.sub.t], where [C.sub.t] = [[SIGMA].sub.j] [C.sub.j,t][n.sub.j,t] is aggregate consumption.

5. The consumption tax rates {[[tau].sub.c,t]} satisfy the government budget constraint (Equation (5)).

IV. CALIBRATION

The frequency of the model is annual. We calibrate parameters of the model in two steps. The first set of parameters is calibrated based on the data and set independently from the model's equilibrium. The second set of the parameters is determined within the model so that it matches a target moment for each parameter in equilibrium.

As we discuss more in Section V, we first compute what we call "the initial steady state" which represents features of the Japanese economy prior to 2014. Starting in 2014, we compute the transition dynamics to a final steady state, in which the economy follows a balanced growth path under the demographics that are projected for the long run. Note that since the demographics in 2014 are far from stationary, we use the actual age-distribution of the population in 2014 in computing aggregate statistics and the government budget for 201 4.

Table 1 summarizes the calibrated parameters.

A. Demographics, Preferences, and Earnings

We assume that age-specific survival rates [S.sub.j,t] follow the projection of the National Institute of Population and Social Security Research in Japan (IPSS) from 2014 to 2060, the last year for which official projections are available. They are assumed to stay constant after 2060. The growth rate of a new cohort [[gamma].sub.t] is based on the fertility projection of the IPSS, which implies the average annual cohort growth rate of - 1.24% over the period of 2014 to 2080. Thereafter we assume that the growth rate will gradually increase and converge to 0% by 2150.

Risk aversion parameter [theta] is set at 2.0. Subjective discount factor [beta] is set so that the model matches the capital-output ratio of 2.5 as estimated by Hansen and imrohoroglu (2016).

For the age-specific productivity [[eta].sub.j], we use estimates of life-cycle earnings of male workers in the Statistical Survey of Actual Status for Salary in Private Sector (SSPS) as it covers a wide range of employed workers. (11) Participation rates are estimated from the Labor Force Survey (LFS) to be consistent with the earnings profile. In particular, as the SSPS covers employees including part-time job workers, nonregular workers, and contract job workers, we include them in the labor force participation.

B. Technology

The growth rate of TFP is set at 1.5%. The level of initial productivity [Z.sub.0] is set for normalization so that the average earnings (age 20-64) is 1.0 in the initial steady state of the model. The depreciation rate 5 is set at 0.0821, computed following the methodology of Hayashi and Prescott (2002), using the data between 1981 and 2013. The capital share is set at 0.3794, based on the aggregate data (System of National Accounts [SNA]) during the same period.

C. Government

In order to satisfy the period budget constraint (Equation (5)), at least one of the policy parameters must be determined in the model's equilibrium. As we discuss below, we calibrate all the parameters to the data in the initial steady state except for the lump-sum transfer, which is determined in equilibrium. When we compute the transition dynamics, we assume that the lump-sum transfer will remain constant, only adjusted for the growth of the economy and use the consumption tax [[tau].sub.c,t] t to satisfy the budget constraint each period.

Labor income tax x, is set at 18%, based on the estimates of the effective labor income tax rate by Gunji and Miyazaki (2011) at 33% in 2007 net of pension premium 15% in the same year. The premium for the employment based pension (kosei nenkin) is 17.12% of earnings in 2014, rising 0.353% annually to 18.3% in 2019. We set the payroll tax [[tau].sub.p] at 18% throughout the transition. Capital income tax [[tau].sub.p] is set at 35%, based on the method of Hayashi and Prescott (2002) as updated by Hansen and imrohoroglu (2016). The interest paid on government debt is taxed at rate [[tau].sub.b], 20%.

Consumption tax [[tau].sub.b] is set at 8% in the initial steady state. As discussed above, the tax rate is determined endogenously during the transition to achieve the government budget balance and used as an indicator to represent the cost of demographic transition, fiscal cost or benefit of alternative policies that will be discussed in Section V.

Per-capita government purchases [g.sub.j,t], are age-dependent and represent the sum of age-independent component [[??].sub.t], and medical expenditures [m.sub.j,t] covered by the government for an individual of age j at time t. Therefore we have [g.sub.j,t] = [m.sub.j,t] + [[??].sub.t]. For the medical component [m.sub.j,t] we use the gross medical expenditure data of the Ministry of Health, Labour and Welfare (MHLW) for health-care and long-term care and the age-dependent copy rates for each type of care to compute the payment made by the government. (12) The age-independent government purchases per capita [[??].sub.t] are calibrated in the initial steady state so that the model matches the ratio G/K = 0.18 in 2013 and remains constant during the transition.

Total expenditures for pension benefits represent 10.6% of GDP in 2013. We set the replacement rate [[kappa].sub.t] to match this ratio in the initial steady state. The pension reform signed into law in 2004 will reduce the replacement rate of public pension benefits over the next few decades through the adjustment according to the "macroeconomic slide" if successfully implemented. According to the official projections (zaisei kensho) of 2014, the replacement rate will decline by approximately 20% when the adjustment is completed in 30 years. We embed the reduction in benefits that is expected in the coming decades by reducing the replacement rate [[kappa].sub.t] by 20% from the initial level over the first 30 years of the transition. The replacement rate remains constant thereafter.

The net government debt to GDP ratio was 130% in 2013 and we set the level of the debt [B.sub.t] to match the ratio each year. The interest rate on the government debt is set at 1 %, the average real interest rate on the Japanese government debt. (13)

V. NUMERICAL RESULTS AND POLICY EXPERIMENTS

Our baseline case is an economy without guest workers and the government uses the consumption tax rate [[tau].sub.c,t] to satisfy its budget. In other words, the consumption tax rate is endogenously calculated each year while the population ages, public expenditures rise, and the debt to GDP ratio stays at 130%.

Against this baseline transition, we introduce guest worker programs that differ along certain dimensions such as the number of guest workers and their relative productivities, and evaluate how alternative policies affect the path of the Japanese economy. In particular, the fiscal impact of guest workers is reflected in the change in equilibrium consumption tax rates, which are used as a measure of the benefits from the temporary inclusion of foreign-born workers in the economy. Finally, we measure the welfare effects of guest worker programs on the native Japanese workers, both alive at the time of the policy change and future generations. The Appendix provides details of the computation method.

A. Guest Worker Programs

We add an accounting model of foreign-born workers to the dynamic GE model for native-born workers described above. We assume that foreign workers in our model are hand-to-mouth individuals. The main reason for this assumption is the lack of reliable data on the earnings and consumption of foreign-born workers in Japan that we could use as calibration targets. Therefore, we treat foreign-born workers as accounting units as a first pass or logical step at quantifying their impact on the Japanese fiscal sustainability issue. (14)

We need to specify three aspects of our guest worker programs: (1) the number of guest workers, (2) their age distribution, and (3) their productivities relative to the native-born workers.

Scant data on foreign-born workers in Japan along the last two dimensions appear to suggest a typical foreign worker at age 40 with a productivity at 50% of that of his native counterpart. (15) Therefore, we assume that foreign workers enter at age 35, work for 10 years and leave before reaching 45, and that their productivity is 50% of that for native workers. In order to check the sensitivity of our findings on the assumed productivity of foreigners, we also consider cases in which guest workers are just as productive as the native workers.

We consider three values for the number of foreign workers. First, we assume an inflow of 100,000 or 200,000 workers per year. The 200,000 annual flow and a 10-year stay are broadly consistent with the early 2014 announcement by the Japanese government about the number and duration of their initial exploration for a guest worker program. We also consider a smaller scale entry at 100,000 foreign-born workers per year. Second, we consider a larger-scale U.S.-style guest worker program which gradually builds a stock of foreign-born workers to the level seen in the U.S. economy in 2014.

In all the economies with guest workers, we assume the following:

* Guest workers pay [[tau].sub.l] personal income tax on earnings and [[tau].sub.c] on consumption, at the same rates as the native Japanese.

* Guest workers do not pay the pension premium [[tau].sub.p] and they do not receive pension benefits.

* Guest workers consume 50% of their earnings (net of the consumption tax), a propensity to consume in line with the native workers. (16)

* Guest workers do not save domestically and instead send their net earnings that are not consumed back to their home economies (or simply hold them until they return to their countries), and therefore are not invested in the capital stock in Japan.

* The government incurs medical expenditures [g.sup.*.sub.j,t] for each guest worker of age j, that are paid for by general taxes collected from all workers.

* We assume [g.sup.*.sub.j,t] consists of 50% of medical expenditures [m.sub.j,t] incurred for each native person of age j.

We consider six guest worker programs using combinations of two parameters, the number and productivity of workers. Experiments 1 and 3 assume an annual in-flow of 100,000 guest workers whereas Experiments 2 and 4 allow for 200,000 guest workers. In addition. Experiments 1, 2, and 5 assume that the productivity of guest workers is 50% of that of native-born workers, and, Experiments 3, 4, and 6 assume that guest workers are just as productive as the average native-born workers. In Experiments 5 and 6, we assume an annual inflow of foreign-born guest workers such that the share of guest workers in total employment rises to and is maintained at 16.4%, the same percentage as the 2014 share of foreign-born workers in the United States.

We would like to emphasize that foreign-born workers are quite distinct from their native-born Japanese counterparts in key dimensions. In particular, guest workers are not eligible for pensions and they do not stay long enough to require significant public health expenditures. The key elements of the experiments are summarized below in Table 2.

In Figure 1, we show the time paths for the stock of foreign-born workers in the economy as well as the ratio of guest workers to total employment (including the guest workers).

According to the first frame in Figure 1, the stock of guest workers is built in 10 years to 1 million, 2 million, and 16.4% of total employment (which is declining over time as the labor force shrinks), respectively. The second frame displays the foreign workers' share of employment. By 2100, these are 4.4%, 8.8%, and 16.4%, respectively. In the steady state, the shares are 7.4%, 14.8%, and 16.4%, respectively. Note that the two-way "revolving door" nature of our guest worker experiments keeps the share of foreign-born workers relatively low despite very large flows in Experiments 2, 4, 5, and 6. In contrast, existing studies we are aware of assume that guest workers become exactly like native workers upon entry into the native economy and therefore even moderately small annual flows accumulate into significant shares for foreign-born workers. For example, the main experiment (Scenario 2) in Shimasawa and Oguro (2010) allows for an annual flow of 150,000 foreign-born workers and the share of foreign-born workers in total population rises to 37% in 2100. Nevertheless, flow and eventual stock of guest workers in Experiments 5 and 6 are especially very large, given the current levels of immigration in Japan. We provide the quantitative results of these cases as a point of comparison with current levels of immigration in the United States.

At the outset, it should be mentioned that there are significant barriers to entry into the Japanese labor market. In particular, the language requirements to successfully participate in the labor market, either as care givers or factory workers, are severe. In addition, there are potential cultural and historical reasons for why it may be very difficult for guest workers to provide labor services close to those of native workers. Given the difficulty of modeling these barriers to entry, the current paper has chosen instead to quantify only the fiscal benefits and costs of guest workers. The reader is invited to take into account the benefits and costs outside of the economic and fiscal considerations outlined in this paper.

The First Four Guest Worker Programs. First, we will describe the findings from Experiments 1-4 because these appear to be fairly close to those under discussion in the public sphere. Later, we will turn our attention to Experiments 5 and 6 which are designed to highlight the two key components of a successful guest worker program.

Experiments 1 and 2: guest workers at 50% productivity of native workers. In our baseline simulations, the size of the economy and the tax base shrink over time as working-age population declines due to the retirement of baby boom generations and low fertility rates. In addition, the age-related public expenditures such as pensions and health expenditures rise, which requires significant increases in the consumption tax rate to finance the spending driven by the demographic shift (as will be shown in Figure 4). Implementing a guest worker program mitigates the decline in the total labor input and slows down the fall in the tax base. As a result, a smaller increase in the consumption tax rate is now sufficient to finance age-related public spending. Our model provides a quantitative assessment of how a guest worker policy can help Japan achieve fiscal sustainability in the next few decades.

We begin by describing the impact of guest workers on selected macroeconomic indicators. The left panels of Figure 2 display the time paths of detrended capital, labor, and output from 2014 toward the steady state for the baseline economy. The right panels are the paths under Experiments 1 and 2, expressed as ratios to the baseline counterparts. The labor input declines monotonically in the baseline simulations because of the decline in the working-age population. This decline is mitigated under Experiments 1 and 2 thanks to the inflow of guest workers and their labor supply.

The capital stock rises for the first few decades as individuals live longer and need to save more for a longer period of retirement. The decline in the population offsets the increase in aggregate capital as it reduces the number of savers and this effect starts to dominate in the 2030s in the baseline model. In economies with guest workers, the return to capital is higher than that in the baseline economy as discussed below and the capital stock is higher. The difference, however, is quantitatively small, about 1.5% of the baseline level in the long run under Experiment 2 with a larger number of guest workers.

Output is mostly flat in the first 2-3 decades as the increase in the capital stock counteracts the decline in the labor input but then falls rapidly as both inputs decline over time. (17) Output differences caused by the guest worker programs are small in the beginning, less than 1% during the initial 10 years in both experiments, but rising to about 2.8% and 5.5%, respectively, in the long run.

As the aggregate capital rises and labor supply falls during the initial decades, the capital labor ratio rises rapidly early on. As shown in Figure 3, the interest rate will fall and the wage rate will rise during this period. Thereafter, the decline in capital dominates the fall in labor supply and the interest rate will rise and wage will decline gradually. (18) Under the guest worker policies, the wage rate will always be lower than that in the baseline transition as labor is less scarce with more workers. The magnitude of the difference, however, is very small in the two experiments.

Figure 4 shows the time paths of the consumption tax rate under the baseline transition and Experiments 1 and 2. The differences across the three transitions are fairly small, especially in the first few decades, indicating the relatively small contribution from the implementation of the guest worker programs. After 2050, the difference increases somewhat and remains between 2 and 3 percentage points in Experiment 2. Overall, these results suggest that a guest worker program which targets low-skilled guest workers is unlikely to contribute to solving Japan's fiscal sustainability problem.

Experiments 3 and 4: more productive guest workers. Now we discuss the impact of the two guest worker programs in which the productivities of foreign-born workers are identical to those of native Japanese workers. In the previous calculations above, we assumed that foreign-born workers were half as productive as their native counterparts. (19) In the experiments below, we assume that guest workers are identical to the Japanese workers in productivity over their working lives in Japan. Perhaps this can be interpreted as choosing a more high-skill biased guest worker program.

Figure 5 displays the effects on the economy from these skill-biased guest worker programs, expressed as the ratio to the level of variables in the baseline model with only native workers. The effects are similar to those under Experiments 1 and 2 examined above, but the magnitudes of the effects are significantly larger, especially in the long run. For example, output is more than 10% higher in the long run with the addition of guest workers that are twice as productive as those in Experiment 2, where the effect was about 5.5%.

The change in the capital labor ratio is more pronounced and this can be seen as larger effects on factor prices in Figure 6. Note that the labor input in the production function is in efficiency units and with foreign-born workers twice as productive in Experiments 3 and 4 relative to those in Experiments 1 and 2, the paths of the capital labor ratio are visibly lower than that under the baseline economy. This results in higher returns to capital and lower wage rates with larger and skill-biased guest worker programs compared to those in Experiments 1 and 2.

The effects on the consumption tax rate in Experiments 3 and 4 are larger due to our assumption that the productivity of guest workers is higher than that in Experiments 1 and 2 and the same as that of native-born workers at each age. This leads to more significant broadening of the tax base and therefore allows the government to limit the increase in the consumption tax to maintain fiscal sustainability. Figure 7 indicates a significant reduction in the consumption tax required to finance the increasing public expenditures. The impact of a larger tax base, either through a bigger guest worker program, or targeting more productive guest workers, is summarized in Table 3.

As shown in Table 3, Experiment 4 provides the largest relief on the government budget, producing a consumption tax rate that is lower than that in the baseline case by two percentage points in 2040 and by 5.5 percentage points in 2100.

The difference remains above 5 percentage points throughout the transition after 2100.

The fact that the consumption tax rises less than that in the baseline under the guest worker program described by Experiment 4 implies that the taxes are less distortionary on the saving decisions of individuals. In a model with endogenous labor supply, the gain from this particular policy is likely to be even larger because the consumption tax would distort work decisions less in that case.

In the long run, the consumption tax rate falls to 11.73% in the baseline case, and much lower in the guest worker experiments, due to our assumption that demographics become stationary eventually at an old age dependency ratio which is much lower than that in 2100 but still higher than that in 2014. In the steady state, Experiment 4 delivers a consumption tax rate which is more than 5 percentage points lower than that in the baseline case and lower than the actual consumption tax rate in 2014. According to the results of Experiment 4, a relatively large annual inflow of 200,000 guest workers with a level of productivity or skill equal to the average native worker produces a lower than otherwise consumption tax rate in dealing with the looming public spending. The relief, however, is not very large, only about 2-3 percentage points for several decades in the medium term. A guest worker program alone will not solve Japan's fiscal problem.

Turning American: A U.S.-Style Guest Worker Program. In this subsection, we conduct an experiment modeled after the current U.S. immigration environment. According to the Bureau of Labor Statistics "Foreign-Born Workers: Labor Force Characteristics--2013" (published on May 22, 2014), there are 25.3 million foreign-born workers in the United States that constitute about 16% of the labor force. They include naturalized citizens, legal permanent residents, temporary migrants (including H-1B workers and students), refugees, asylum seekers, and unauthorized immigrants (to the extent that they are counted in the CPS).

The exercises we conduct in this section take the current (as of the end of 2014) employment of 64 million in Japan and gradually add a flow of foreign-born workers who remain and work in Japan for 10 years so that the eventual stock of foreign-born workers is at 16.4% which would be 10.5 million in 2014. (20) This would require an annual flow of about 1 million workers, five times as large as what the Abe government announced in early 2014. However, given the projected decline in the working-age population and employment in Japan, we gradually reduce the annual flow of guest workers to keep the share of foreign-born workers at 16.4% of the total employment in steady state. The productivities of the guest workers will be assumed to be 50% or 100% of those of the native workers.

Clearly, this would broaden the tax base significantly more than the guest worker programs presented above. How much would it improve the fiscal balance? Figure 8 shows the time path of the consumption tax rate under these two U.S.-style guest worker programs and the benchmark path with no guest workers.

Even with the productivities of guest workers at 50% of those of the Japanese workers, the large influx of workers raises the tax base significantly and allows for a smaller increase in the consumption tax rate. This is especially true under the assumption that the foreignborn workers have the same productivity as the native-born workers. In this case, the resulting consumption tax rate is much lower than that in the benchmark case and temporarily rises to levels similar to those in some European economies (about 25%) before declining to a level lower than the current 8% consumption tax rate. In other words, a guest worker program alone can nearly solve Japan's fiscal problems if the program is large and the guest workers are sufficiently skilled.

Table 4 displays a few snapshots of the tax rate over time for experiments with U.S.-style guest workers. Even if we assume guest workers' productivities are 50% of the Japanese, the increase in the consumption tax rate is significantly more subdued relative to the baseline case. With the assumption of 100% productivity, the tax rate is lower by more than 10 percentage points at the peak. It suggests that a policy to bring foreign workers for a limited duration could significantly mitigate the fiscal cost of the demographic transition, depending on the size and productivity of guest workers.

B. Welfare Analysis

In this subsection, we study welfare effects of the guest worker programs on the Japanese individuals that belong to different cohorts. First, in order to assess the welfare effects on current generations that are already economically active (above age 20) in 2014. the first year of the transition, we compute the consumption equivalent variation (CEV) for individuals at each age. It represents a percentage change in consumption for the remainder of each individual's life which will make him indifferent between the baseline economy and the alternative economy under a particular guest worker policy. The CEV of 1%, for example, implies that individuals are better off if a guest worker program is introduced and his lifetime utility for the remaining years of his life would be the same in the baseline economy if his consumption in each period were raised by 1%. For the generations that will enter the economy after 2014, we compute the CEV in a similar way, as a percentage increase in consumption that is needed to equalize the lifetime utility between the baseline and an experiment, evaluated at the time of his entry to the economy.

Figure 9A shows the welfare effects in CEV from the first four guest worker programs on the generations alive in 2014 and Figure 9B shows the CEV for future generations by the "birth" year of their entry to the economy at the age of 20. The welfare effects are determined by changes in the paths of three factors relative to the baseline simulations, (1) consumption taxes, (2) return to labor supply (wage), and (3) return to savings (interest rate). The net gain on each individual is determined by the combination of the changes in the three factors that they will face at different stages of their life cycle.

As shown in Figure 9A, all four guest worker programs yield welfare gains for the native-born workers at all ages. Wages are lower by the introduction of guest workers as labor becomes less scarce, but working-age individuals experience welfare gains as the negative effects are offset by benefits of lower consumption taxes and higher interest rate. The gains are smaller for old individuals at the time of the reform. Although they benefit from higher return on their savings and lower consumption taxes, the effects are much smaller during the initial decades of the transition as we saw above and many of them will not survive until when the difference grows more significantly.

Welfare gains are larger for future generations that will enter the economy later in the century, as shown in Figure 9B, as they will fully enjoy the large decline in consumption taxes when the economy has a larger number of guest workers in stock. The largest welfare gain is achieved under Experiment 4, in which working-age individuals in 2014 will experience about 2% of welfare gains in consumption equivalence and future generations will enjoy 2-4% of gains. Experiments 2 and 3 generate almost identical welfare benefits for Japanese workers because they lead to nearly identical expansions in the tax base and similar paths of factor prices.

Figure 10A shows the welfare gains from the U.S.-style guest worker programs on the cohorts alive in 2014. In these experiments, the movement of factor prices is more significant and younger individuals will have lower welfare gains than those at around age 60 who are close to retirement, since they will experience a large drop in wages during the transition. The gains, however, are larger in magnitude compared to the other four experiments, where age-20 individuals had a welfare gain of less than 2% of consumption. In Experiments 5 and 6, age-20 individuals experience a welfare gain of 2.2% and 4.4% in CEV, respectively. Future generations will gain more because the decline in the wage rate will eventually stabilize and the consumption tax will be much lower than in the baseline economy, as shown in Figure 10B.

VI. EXTENSIONS

In this section, we present two additional exercises. In the first, we will simulate the model under the assumption that factor prices remain the same as in the initial year. The exercise is to isolate and understand the effects of endogenous transitions of interest rate and wage rate. In the second, we simulate a policy in which the Japanese government allow guest workers to stay much longer than the 10 years that we assumed above, a policy to treat foreign workers more like permanent residents or immigrants.

A. PE Analysis: Effects of Factor Price Adjustments

In our baseline GE model, factor prices are determined endogenously in each period according to their marginal productivities. The time paths of these prices depend on the time path of the capital-labor ratio. The wage rate follows a time path similar to that of the capital-labor ratio whereas the return to capital follows an opposite path. According to Figure 3C, the wage rate rises by about 23% from 2015 to 2050 and then falls to a level above its 2014 level, which is exactly what the capital-labor ratio does. The main reason for the rise in the capital-labor ratio is the exogenous decline in the labor input driven by the shrinking labor force and the increase in the lifecycle saving motive as the life expectancy rises. After 2050, the capital stock starts to fall as the fraction of nonsaving elderly increases significantly and the decline in the labor force continues. The return to capital falls from about 7% in 2014 to about 2.5% in 2050 and then rises eventually to about 5%. The increase in the wage rate from 2015 to 2050 raises the tax base along the way but it also increases the pensions to be paid out post-2050. After 2050, the tax base starts to shrink but the higher pension payments persist for a while, requiring a high consumption tax rate to achieve fiscal sustainability, as shown in Table 3.

In order to isolate the effects associated with price adjustments, we now consider a scenario in which prices are fixed at the levels of the initial year, 2014. throughout the transition. In particular, we assume a small open economy, where the return to capital is determined at an exogenous level and the level of domestic capital is determined to be consistent with the "world" interest rate. Put differently, we allow for capital inflows and outflows consistent with time-invariant factor prices in a small open economy, which we label as our PE model.

Table 5 summarizes the path of consumption taxes under the baseline model (both GE and PE variants) without guest workers and the four scenarios of introducing guest workers as studied above, but this time under PE. The equilibrium consumption tax rates are significantly lower in the baseline model PE where prices are fixed. Since wages are kept lower than those in the GE model, wages and therefore pension expenditures are lower, which mitigates the need to raise consumption taxes. Higher interest rates under the PE assumption imply a lower level of capital stock and output in our model. Since we assumed and set the government debt as a fixed percentage of GDP, it also reduces the level of the debt and the cost of servicing it, contributing to a lower consumption tax to finance the demographic transition.

It is important to emphasize that the looming fiscal adjustments arise from two sources. First, the exogenous demographics of a rapidly aging society lead to an economy in which there are "too few" workers to pay for the pensions and health expenses of "too many" retirees. In addition, there is a second, endogenous force in GE. This mechanism is the increase in the wage rate in response to the predicted increase in the capital-labor ratio in Japan, until about 2050. The labor supply is projected to decline monotonically post-2100. The capital stock, however, is predicted to have an inverted-U shape, rising for 10-20 years with the stronger life-cycle saving motive on the part of the workers facing extended retirement lives. But as the dependency ratio keeps rising, the capital stock eventually starts to fall with the diminished number of savers as opposed to dissavers. The combination of movements in the capital stock and labor supply leads to an inverted-U shape in the capital-labor ratio that tops out around 2050 and converges to a level still much higher than that in 2014.

To be more concrete, the capital-labor ratio rises 73% from 2014 to 2050 and then falls after 2050 but it is still 56% higher in 2100 than its level in 2014. The impact on the wage rate is an increase of 23% by 2050 and the leveling off results in a wage still 18% higher in 2100 than its level in 2014. Since pensions are partially tied to wages, this GE effect adds significantly to the fiscal burden already created by the "numbers game" of an older society. Our PE exercise turns this second channel off and our results suggest that this effect is quantitatively quite large.

Although the level of consumption taxes is significantly lower for these reasons, the effects of the guest worker policies are qualitatively the same. The effects are also similar quantitatively, though the fiscal savings through the introduction of guest workers are somewhat smaller since the tax contributions of guest workers are smaller with a lower market wage rate under PE.

Another way to measure the economic contribution of guest workers is to compute the additional output produced by a typical guest worker in an experiment relative to the equilibrium path in the baseline case. By 2024, the annual gains per guest worker are between $20,000 (under GE and with guest workers only 50% as productive as native-born workers) and $66,000 (under PE and with guest workers as productive as Japanese workers).

B. An Extended Guest Worker Program: "Immigration "

In the guest worker experiments studied above, we assume that foreigners arriving in Japan are required to return in 10 years. In this section, we run the experiments assuming that the Japanese government allows foreigners to stay much longer and they eventually become permanent residents. We continue to let foreign-born workers arrive in Japan at the age of 35. Instead of having them leave in 10 years, we assume that they do not return to their home countries and live in Japan up to the male life-expectancy, which we set to 70. (21) We assume that they will follow the same pattern of labor force participation by age as the Japanese natives for the remainder of their life.

We maintain the assumption that they pay the labor income and consumption taxes, but do not pay the pension premia nor receive benefits. The government pays 50% of the medical expenditures incurred for each native person. As before, we abstract from the effects of children of foreign workers. (22) The paths of the consumption taxes are summarized in Table 6. Compared to the consumption tax rates under the 10-year guest worker programs presented in Table 3, the tax rates are not very different during the initial few decades. Once, however, the initial waves of guest workers reach the 10th anniversary and stay in Japan beyond 10 years, the difference becomes larger since the stock of foreigner-born workers continues to rise and they contribute to the budget through the payment of labor income and consumption taxes. By 2100, the consumption tax rates would be lower by 3-10 percentage points compared to the 10-year guest worker programs. We note, however, that we abstracted from the children of those foreigners and that they could potentially raise the required consumption taxes in the long run if they become entitled to public transfers in their adulthood including pensions and health insurance benefits. In addition, this policy may face other political and social issues that have to be overcome to a greater degree than the fixed-duration guest worker programs. Nevertheless, the results presented in this extended analysis demonstrate the significant fiscal gains that would be realized through a more aggressive immigration program.

VII. CONCLUSION

The Japanese economy is seen as struggling, due to little growth since 1990, and diminishing, because the working-age population has started to decline rapidly. Projections of future fertility rates and survival probabilities indicate a severe reduction in both total and working-age population. Among the options to mitigate the effects of this demographic transition in Japan is a new immigration policy. In this study, we construct a GE model and evaluate various guest worker programs. The two key aspects of a successful program that helps achieve fiscal sustainability are (1) the size of the guest worker or immigration program as this directly increases the tax base and (2) the skill level of the guest workers and immigrants.

A guest worker program that brings 200.000 foreign-born and unskilled workers to Japan for 10 years allows a smaller increase in the consumption tax rate, by 3 percentage points, than that in the baseline case. If the program targets skilled guest workers so that their mean earnings equal those of native-born workers, then the gains can be more than 5 percentage points in consumption taxes. Although these do not significantly address Japan's fiscal sustainability problem, there are significant welfare gains for all native-born workers, about 2% of consumption each year for working-age workers but smaller gains for retirees in the case of high-skilled guest worker policy. Welfare gains are larger for future generations, exceeding 4% in CEV in the long run, because of the smaller consumption tax rate increases needed to finance rising public expenditures due to demographic aging. A larger-scale U.S.-style guest worker program brings the foreign-born workers' share in total employ ment to 16.4% in 10 years and maintains this ratio forever. The benefits are huge: the consumption tax is now significantly lower by 5-10 percentage points, relative to baseline transition. The welfare gains are even larger: 2-9% in consumption equivalence. Finally, if the Japanese government manages to prevent the increase in the capital-labor ratio between now and 2050 (as in our PE case) and thereby prevents the buildup of pension payments, or it starts a larger immigration program (as in the extended immigration case), then the needed increase in the consumption tax rate to achieve fiscal sustainability is very small. There are clear and substantial economic benefits from a guest worker or immigration program, especially one that targets high-skilled workers.

The political economy of a guest worker or immigration program, however, is less clear and often a sensitive topic to be discussed. Historically, Japan has been insular concerning immigration, at least in part due to real and significant technological (linguistic) barriers to entry into the local Japanese labor market. Given the projected increases in public expenditures caused by aging, our quantitative results suggest that a guest worker program may be one of the policy options on the table that is worth more open discussion, although a complete solution would involve other policies such as tax reform, pension and health care reform, and initiatives that concern family economics and the female labor supply.

APPENDIX: COMPUTATION OF EQUILIBRIUM

Denote the net-of-taxes gross interest rate as [R.sub.t].

From the FOC with respect to asset holdings next period, we obtain

[c.sub.j+1,t+1]/[c.sub.j,t] = [[[beta] 1 + [[tau].sub.c,t]/1 + [[tau].sub.c,t+1][R.sub.t+1]].sup.1/[theta]] [equivalent to] [g.sub.t+1],

which is the optimal growth rate of consumption between any age j and j + 1 and between time I and f+ 1. Iterating on Equation (A1). we obtain:

(A2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The discounted present value of the total (gross of taxes) lifetime consumption of an individual of age 1 at time t can be expressed as:

(A3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Denote by [[??].sub.j,t] earnings of an individual of age j at time t net of transfers, lump-sum taxes, and pensions, that is,

[[??].sub.j,t] = [[??].sub.j,t] + t[r.sub.t] + [p.sub.j,t].

The discounted present value of the total (net of taxes) lifetime earnings of an age - 1 individual at time t is

(A4)[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Since individual optimization requires [[bar.c].sub.1,t] = [[bar.x].sub.1,t], from Equations (A3) and (A4),

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The path of the individual's consumption [{[c.sub.j,t+1]}.sup.J.sub.j=1] is computed from Equation (A2) and the assets at each age are computed recursively by the flow budget constraint (Equation (2)).

ABBREVIATIONS

BSWS: Basic Survey on Wage Structure

CEV: Consumption Equivalent Variation

CPS: Current Population Survey

FLFP: Female Labor Force Participation

GDP: Gross Domestic Product

GE: General Equilibrium

IPSS: National Institute of Population and Social Security Research in Japan

LFS: Labor Force Survey

MHLW: Ministry of Health, Labour and Welfare

PE: Partial Equilibrium

SNA: System of National Accounts

SSPS: Statistical Survey of Actual Status for Salary in Private Sector

TFP: Total Factor Productivity

doi: 10.1111/ecin.12439

SELAHATTIN IMROHOROGLU, SAGIRI KITAO and TOMOAKI YAMADA *

* We are grateful to Masahiro Hori for suggestions on earnings profiles, and seminar participants at the Federal Reserve Bank of Philadelphia and 2015 SAET conference in Cambridge for very useful comments. Kitao acknowledges the support from Tokyo Center for Economic Research (TCER) and from Research Institute of Economy, Trade and Industry (RIETI). Yamada thanks the Ministry of Education. Science, Sports, and Culture, Grant-in-Aid for Specially Promoted Research 15H05692 for their financial support.

Imrohoroglu: Professor, Marshall School of Business, University of Southern California, Los Angeles, CA 90089. Phone +1 213-740-6546, Fax +1 213-740-6650, E-mail selo@marshall.usc.edu

Kitao: Professor, Faculty of Economics, Keio University, Tokyo, 102-0085, Japan. Phone +81-35427-1574, Fax +81-35427-1578, E-mail sagiri.kitao@gmail.com

Yamada: Professor, School of Commerce, Meiji University, Tokyo. 101-8301, Japan. Phone +81-33296-2274, Fax +81-33296-2274, E-mail tyamada@meiji.ac.jp

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(1.) In addition, even if fertility unexpectedly rises significantly in the future, it may not help with the fiscal imbalance. Indeed, tmrohoroglu. Kitao, and Yamada (2016) conduct an experiment in which future fertility rates are 1.68 but this leaves the fiscal imbalance nearly unchanged. The reason is that these additional native-born workers broaden the tax base during their working ages but raise public expenditures during their retirement years with extra pension and health expenditures to be financed.

(2.) In the United States, nearly 60% of recent university graduates are females. In some OECD countries this ratio is two-thirds. Japan is one of a few OECD countries where female graduates make up less than 509c of total university graduates, less than those in South Korea and Turkey. In addition, there is an "M-curve" of FLFP over the life cycle. A typical Japanese female withdraws from the labor force upon having a child and despite rejoining the labor force later in the life cycle, the new job is typically an "irregular" job that pays less than a regular job. Depreciation of skills and a lack of accumulating further human capital (by learning by doing or on the job training) combine to yield a much higher fraction of irregular jobs held by females than males. Another finding in imrohoroglu. Kitao. and Yamada (2016) is that an increase in the FLFP rate without an increase in the fraction of regular jobs does not broaden the tax base significantly to solve Japan's fiscal imbalance. We leave the FLFP rate and the role of human capital in producing a gender gap in regular versus irregular jobs for future research.

(3.) This makes the benefits of a guest worker program conservative since such a program would lead to reductions in the required tax increases with the broadening of the tax base. As a result, the labor supply would be distorted less under a guest worker program. By shutting this mechanism down, our results can be viewed as a lower bound on the benefits of immigration.

(4.) Earlier and other contributors to this literature are Broda and Weinstein (2005), Doi (2008). imrohoroglu and Sudo (201 la), imrohoroglu and Sudo (201 lb), Hoshi and Ito (2014), Hsu and Yamada (2015), and Kitao (2015b).

(5.) A recent survey by Preston (2014) reviews various approaches to measuring the impact of immigration, evaluating the mechanisms in accounting models, or static or dynamic behavioral economic models.

(6.) Fehr, Jokisch. and Kotlikoff (2004) maintain a consumption tax rate of 5%, use a normal retirement age of 60. which has since been changed to 65. and include a strong bequest motive.

(7.) In addition. Lagakos et al. (2016) document that returns to potential experience among U.S. immigrants are higher on average for workers coming from rich countries than for those coming from poor countries, making it unlikely that foreign-born workers would become like native workers soon after they enter the host country.

(8.) In contrast, our guest worker policies keep the foreignborn share of employment at 4% to 16.4%, depending on the particular experiment. In Section VI.B, we simulate an extended guest worker program, in which guest workers stay longer and constitute a larger fraction of the workforce comparable to that of Shimasawa and Oguro (2010).

(9.) As in Attanasio, Kitao, and Violante (2007), we assume an annuity market rather than unintended or accidental bequests. This assumption eliminates accidental bequests from the model and simplifies the computation of equilibrium transitions.

(10.) This amounts to assuming that government bonds crowd out private investment. In particular, a $1 allocation of assets into government bonds reduces private investment by [phi]/(1 - [phi]).

(11.) We also examined the earnings profile using the Basic Survey on Wage Structure (BSWS) and it was slightly higher than the estimates by the SSPS because the BSWS drops all employees working in small establishments with less than five persons.

(12.) See Kitao (2015a) for more details of the two insurance programs.

(13.) The average number of years to maturity of existing Japanese bonds is 7 years and the interest rate on 7-year government debt is 1%.

(14.) An alternative approach in modeling the guest workers is to assume that they are imperfect substitutes in the production function. For example, we could introduce skill heterogeneity and have skilled and unskilled workers aggregate up to total labor input. Then, various skill distributions for guest workers could be analyzed. This approach would have implications on the aggregate wage as well as the skill premium. However, this also requires reliable data on the skill and earnings distributions of guest workers. This important extension is left for future research.

(15.) See, for example, "The Survey on the Way of Working among Foreigners" (in Japanese) by the Japan Institute for Labour Policy and Training (2011). In order to put this assumption in the current Japanese context, consider that the natives' average annual earnings figure in the SSPS data used in calibration is about 4 million yen. Given an average annual hours worked of 1,730 and the current minimum wage of 823 yen per hour in Japan, a worker that works 1,730 hours at the minimum wage makes about 1.4 million yen. Therefore, our productivity assumption on guest workers is still above what a full-time Japanese individual that works a minimum wage job makes.

(16.) In the benchmark economy, the natives' average marginal propensity to consume is about 45%.

(17.) Note that when the TFP growth rate is used to produce the level of output, it grows slightly over time as the assumed TFP growth rate consistent with a balanced growth rate of 1.5% is slightly greater than the average decline of about 1.4% in the labor input.

(18.) We assume that the decline in the wage rate is not sufficient to entice the guest workers to return to their home economies.

(19.) In the United States, the ratio of median weekly earnings of foreign-born workers to that of native-born workers is 80%, according to the Current Population Survey (CPS) in 2014.

(20.) The ratio is obtained as the number of employed immigrants in 2013 to the total employment during the same year in the United States.

(21.) We set the life expectancy to 70, taking into account the range of male life expectancies of major countries that have foreign workers in Japan, such as China (74), Brazil (70), and the Philippines (65).

(22.) If we allow for the possibility of foreigners having children and assume that their offsprings are identical to the native Japanese economically, then it is equivalent to increasing fertility rates. The effects of such experiments are studied in more detail in the study by tmrohoroglu, Kitao, and Yamada (2014).

Caption: FIGURE 1 Foreign-Born Workers: Number and Share

Caption: FIGURE 2 Capital, Labor, and Output

Caption: FIGURE 3 Factor Prices

Caption: FIGURE 4 Consumption Tax Rate

Caption: FIGURE 5 Capital, Labor, and Output in Experiments 3 and 4

Caption: FIGURE 6 Factor Prices in Experiments 3 and 4

Caption: FIGURE 7 Consumption Tax Rate (Experiments 3 and 4)

Caption: FIGURE 8 Consumption Tax Rate (Experiments 5 and 6)

Caption: FIGURE 9 Welfare Effects of Experiments 1-4 (% in CEV)

Caption: FIGURE 10 Welfare Effects of Experiments 5 and 6
TABLE 1
Parameters of the Model

Parameter             Description             Values/Source

Demographic
  [{[s.sub.j,t]}.     Conditional survival    IPSS (2012)
  sup.J.sub.j=1]      probabilities

  [[gamma].sub.t]     Cohort growth rate      IPSS (2012)

  J                   Maximum age             91 (110 years old)

Preferences
  [beta]              Subjective discount     1.0162 (K/Y = 2.5)
                      factor

  [theta]             Risk aversion           2.0

Labor market
  [{[LAMBDA]}.sup.    Participation rates     LFS
  J.sub.j=1]

  [{[[eta].sub.j,     Productivity            SSPS
  t]}.sub.j=1]

Technology
  [Z.sub.t]           TFP level               Normalization

  [[lambda].sub.t]    TFP growth rate         1.5%

  [alpha]             Capital share           0.3794

  [delta]             Capital depreciation    0.0821
                      rate

Government
  [[tau.].sub.l]      Labor income tax        18%

  [[tau].sub.p]       Payroll tax             18%

  [[tau].sub.c]       Consumption tax         8% (in 2013)

  [[tau].sub.a]       Capital income tax      35%

  [[tau].sub.b]       Tax on gov. bond        20%
                      return

  [tr.sub.t]          Net transfers           See text

  [{[m.sub.j,t]}.     Medical expenditures    See text
  sup.J.sub.j=1]

  [{[g.sub.j,t]}.     Government              See text
  sup.J.sub.j=1]      purchases               (G/F = 0.18)

  [[kappa].sub.t]     Pension replacement     0.476 (in 2013,
                      rate                    P/Y = 0.106)

  [B.sub.t]/          Net debt to GDP ratio   130% (2013)
  [Y.sub.t]

  [r.sub.b]           Int. on government      1.0%
                      bond

TABLE 2
Six Alternative Guest Worker Policies

                    Annual Flow of
                     Foreign-Born        Their Relative
                       Workers           Skill Level (%)

Experiment 1           100,000                 50
Experiment 2           200,000                 50
Experiment 3           100,000                 100
Experiment 4           200,000                 100
Experiment 5    s.t. 16.4% are foreign         50
Experiment 6    s.t. 16.4% are foreign         100

TABLE 3
Consumption Tax Rate under Alternative Guest
Worker Policies

              Baseline   Exp 1   Exp 2   Exp 3   Exp 4

2015            8.17     8.05    7.92    7.92    7.67
2020           10.24     9.97    9.70    9.69    9.15
2030           13.95     13.63   13.32   13.30   12.68
2040           21.88     21.40   20.93   20.92   19.99
2050           28.94     28.26   27.60   27.57   26.29
2060           34.20     33.32   32.47   32.45   30.82
2070           36.41     35.35   34.33   34.30   32.37
2080           35.75     34.55   33.40   33.37   31.20
2100           35.98     34.43   32.98   32.93   30.23
[infinity]     11.73     10.27   8.92    8.86    6.39

TABLE 4
Consumption Tax Rate under U.S.-Style Guest
Worker Programs

              Baseline   Exp 5   Exp 6

2015            8.17     6.84    5.55
2020           10.24     7.56    5.09
2030           13.95     11.18   8.68
2040           21.88     18.20   14.99
2050           28.94     24.42   20.58
2060           34.20     29.00   24.65
2070           36.41     30.80   26.15
2080           35.75     30.08   25.40
2100           35.98     30.25   25.50
[infinity]     11.73     8.65    5.92

TABLE 5
Consumption Tax Rate under PE

              Baseline        PE Experiments

               GE      PE     Exp 1   Exp 2   Exp 3   Exp 4

2015          8.17    11.35   11.10   10.86   10.86   10.38
2020          10.24   12.96   12.56   12.17   12.16   11.38
2030          13.95   14.93   14.63   14.34   14.32   13.74
2040          21.88   19.76   19.41   19.06   19.04   18.34
2050          28.94   22.71   22.29   21.89   21.87   21.06
2060          34.20   24.83   24.36   23.90   23.88   22.96
2070          36.41   25.55   25.01   24.48   24.45   23.41
2080          35.75   24.65   24.04   23.45   23.42   22.27
2100          35.98   24.69   23.91   23.16   23.13   21.67
[infinity]    11.73   9.15    8.16    7.23    7.17    5.41

TABLE 6
Consumption Tax Rate under Extended Guest
Worker (Immigration) Program

              Baseline   Exp 1   Exp 2   Exp 3   Exp 4

2015            8.17     8.07    7.96    7.96    7.75
2020           10.24     10.01   9.77    9.77    9.29
2030           13.95     13.31   12.68   12.66   11.45
2040           21.88     20.61   19.41   19.35   17.10
2050           28.94     27.12   25.45   25.29   22.20
2060           34.20     31.82   29.68   29.50   25.62
2070           36.41     33.52   30.97   30.75   26.22
2080           35.75     32.46   29.59   29.35   24.36
2100           35.98     31.77   28.23   27.93   22.00
[infinity]     11.73     7.91    4.84    4.43    -0.53
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Author:Imrohoroglu, Selahattin; Kitao, Sagiri; Yamada, Tomoaki
Publication:Economic Inquiry
Article Type:Abstract
Geographic Code:9JAPA
Date:Jul 1, 2017
Words:13272
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