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Discussion Paper Series

Faculty of Economics

Hiroshima University

Discussion Paper Series No.2012-02

Capital market integration and optimal

employment protection policies

Keisuke Kawata

Capital market integration and optimal employment protection

policies

Keisuke Kawata

Graduate School of Social Science, Hiroshima University

Abstract

This study analyzes the e¤ect of capital market integration on labor market policies. To do so, this paper builds a tax competition model with an imperfect labor market. There are two types of households, types 1 and 2, who are risk-averse. While each type of households is endowed with one unit of worker, a type-2 household owns a lager capital stock than a type-1 household. The government can choose the following policies: unemployment bene…ts, layo¤, payroll, and capital subsidies or taxes. When the capital market is integrated, households can invest their capital stock in capital markets in foreign countries. Integration of capital markets leads to ine¢cient policies under which labor productivity is high; however, income inequality within a country and the frequency of job destruction are also high. As a result, the social welfare of each country in integrated capital markets is lower than in non-integrated capital markets.

1 Introduction

The e¤ect of global capital market integration on labor markets has provoked a great deal of debate among economists, politicians, and commentators. For example: what impact does capital market integration have on the unemployment rate and wages? Does capital market integration trigger labor market deregulation? To answer these questions, this paper incorporates a model of an imperfect labor market proposed by Blanchard and Tirole (2008) in a footloose capital model with multiple countries and analyzes the impact of capital market integration on the labor market through policy reform.

Zodrow and Mieszkowski (1986) argued that when capital markets are integrated, governments reduce capital tax rates to attract capital and the provision of local public goods is too low; this is called tax competition. Previous studies analyzed the impact of tax competition on a single labor market policy.¹ However, Blanchard and Tirole (2008) and Algan and Cahuc (2009) pointed out that the interactions of the various labor market policies are important. This paper …rst considers these interactions in the literature on tax competition.

In this paper, there are two types of households, types 1 and 2; who are risk-averse. Each type of household is endowed with one unit of worker, and a type-2 household owns larger capital stock than a type-1 household. Firms in the …nal goods sector produce tradable consumption goods using two types of intermediate goods. One type of intermediate goods is produced using only capital; another type is produced using only workers. While capital and intermediate goods markets are perfectly competitive, the labor market is imperfect, as in Blanchard and Tirole (2008), in which …rms post a wage contract before revealing their productivity. By this assumption, a …rm with low productivity may …re an employed worker, and she or he becomes an unemployed worker.

I consider the following policy instruments: unemployment bene…ts, layo¤, payroll, and capital subsidies or taxes. Following the literature on tax competition, the government of each country chooses these policies to maximize its social welfare. Since households are risk averse, the government wants to redistribute income among households using unemployment bene…ts, payroll subsidies, and capital taxes. Additionally, the gov- ernment chooses layo¤ tax rates to lead …rms to internalize the cost of unemployment and make an e¢cient layo¤ decision. Assuming the utility costs of unemployment, layo¤ tax rates are chosen to balance the trade-o¤ between worker productivity and job security.

I especially thank Ryousuke Okazawa, Daishin Yasui, the Osaka Workshop on Economics of Institutions and Organizations, and Kyoto Macroeconomics Workshop for their helpful comments and suggestions.

yE-mail address: keisuke@hiroshima-u.ac.jp

1See for example, unemployment bene…ts in Lejour and Verbon (1994), the minimum wage in Gabszewicz and van Ypersele (1996), and bargaining power of trade unions in Boulhol (2009).

1

In non-integrated capital markets, households cannot move their capital stock to foreign countries. In this case, the government chooses very high capital tax rates and relatively high layo¤ tax rates and redistributes these tax revenues to households through payroll subsidies and unemployment bene…ts. Under these policies, households are perfectly insured against the risk of income ‡uctuations caused by changes in employment status, income inequality between type-1 and 2 households is eliminated, and the layo¤ tax provides moderate employment protection.

In integrated capital markets, households can move their capital stock to foreign countries. In this case, the government chooses low capital tax rates to attract capital, which leads to the income inequality within the country. Additionally, the capital market integration decreases layo¤ tax rates because the shadow price of

…nal goods increases with income inequality within a country, and the government has an incentive to improve worker productivity. The capital market integration also decreases payroll subsidy rates because of declining tax revenue from capital and layo¤ taxes. However, the impacts of capital market integration on unemployment bene…ts are ambiguous because there are positive and negative e¤ects: declining tax revenues from capital and layo¤ and reducing expenditure for payroll subsidies. These results are consistent with an empirical fact such as Potrafke (2010), who argued that globalization has a negative impact on protection of regular employment workers’ contracts but no signi…cant impact on unemployment bene…ts.

Under equilibrium policies in integrated capital markets, labor productivity is high; however, income in- equality within a country and the frequency of job destruction are also high. To maximize a country’s social welfare, government should choose the same policies as in a non-integrated market; this implies that capital market integration reduces social welfare of each country through policy reform.

This paper’s basic framework of the labor market based on Blanchard and Tirole (2008), who characterized the optimal layo¤ and payroll subsidies or taxes, and unemployment bene…ts in a closed economy. This paper introduces mobile capital and capital taxes into their model. With this extension, I can analyze the e¤ect of capital market integration on the labor market.

Some papers analyzed the tax competition in an imperfect labor market². These papers analyzed the impact of tax competition on capital or corporate tax rates; in contrast, this paper analyzes its impact not only on capital tax rates, but also on labor market policies.

This paper is structured as follows. Section 2 introduces the basic structure of the model. Section 3 demonstrates the properties of an equilibrium under non-integrated capital markets. In section 4, I characterize an equilibrium under integrated capital markets. Finally, section 5 presents the study conclusions.

2 Setting

There are many symmetric small countries, in each of which there are two types of households indexed by i 2 f1; 2g. The mass of type i households is ni; and they are endowed with ki units of capital (assuming k2> k1) and a single worker who can be either employed or unemployed.

Both types of household are risk-averse, and their utility from consuming …nal goods is given by u (x) (u⁰ >0; u⁰⁰<0; and u⁰⁰⁰ >0), where x is the consumption level of …nal goods. Additionally, following to Blanchard and Tirole (2008), a household with an unemployed worker pays the utility cost of being unemployed, B. Some empirical evidence suggests that the utility cost of becoming unemployed is high (see, for example, Winkelmann and Winkelmann (1998) in economics and Darity and Goldsmith (1996) and Hallock (2009) in social psychology).

Producing …nal goods requires two intermediate goods, and the production technology of …nal goods features constant returns to scale technology and continuously diminishing marginal products. I denote the technology by f (x1; x2), where x1 and x2 denote, respectively, the inputs of intermediate goods 1 and 2.

Firms in sector 1 produce intermediate goods 1 using only workers under perfect competition. Following Blanchard and Tirole (2008), if a …rm enters the labor market, a worker is hired, and the productivity of the match is then revealed. Productivity is given by y and is drawn from cumulative distribution function G(y), with density g (y) on ( 1; 1). The one important assumption of this model is that the wage contract posted by …rms cannot depend on the productivity of the match. This assumption implies that …rms with low productivity may want to …re workers, and that these workers may then become unemployed. Note that when

2See, for example, the fair wage model by Egger and Seidel (2011), the job search models by Konrad (2011) and Sato (2008), the monopolistic labor supply (trade union) model by Ogawa, Sato, and the Tamai (2011), and the …xed wage models by Ogawa and Sato (2006) and Piga (2010).

the productivity of a …rm is too low, such a worker should be unemployed to maximize social welfare³. Firms in sector 2 produce intermediate goods 2 using only capital under constant returns and perfect competition. The marginal productivity of capital is constant and is the same between …rms in sector 2 because …rms can hire capital after revealing their own productivity if the capital market is ‡exible. Then, only the …rms with the highest productivity can hire capital in equilibrium. For simplicity, the equilibrium marginal productivity of capital is normalized to one.

To maximize social welfare, each government can choose the following policies: (i) layo¤ subsidies or taxes for …rms in sector 1 that layo¤ a worker, f , (ii) unemployment bene…ts for unemployed workers, b, (iii) payroll subsidies or taxes for employed workers, te, and (iv) capital subsidies or taxes for capital income, tk.

To summarize, the timing of events in the model is as follows: Step 1: Each government simultaneously chooses its policies.

Step 2: Both the labor and capital markets are opened, and in each of which wages w and the rental price of capital r are determined.

Step 3: Firms in sector 1 observe their productivity, and afterward, the …rms decide whether to …re workers. Step 4: The market of intermediate goods is opened and …nal goods production occurs.

Under non-integrated capital markets, capital cannot move across countries, and capital supply is then exogenously determined. In contrast, under integrated capital markets, capital can be mobile between countries with zero moving costs in step 2, and capital supply is then endogenously determined using the arbitrage condition (as shown later).

In the integrated capital markets case, a household is supposed to spend capital income in the home country regardless of where the capital is employed⁴. Additionally, I assume that while both intermediate goods are not tradable, the …nal goods are freely tradable. Therefore, the ‡ows of capital income o¤set …nal goods trade imbalances, thereby ensuring the balance of payments equilibrium. Note that in the non-integrated capital markets case, international trade does not occur if the goods market is internationally integrated.

3 Equilibrium in non-integrated capital markets

First, I consider an equilibrium in a non-integrated market where capital cannot move across national borders. This implies that the amount of capital in a country is K^N = k1n1+ k2n2:

The equilibrium concept in this model is the sub-game perfect Nash equilibrium (SPNE), which is charac- terized using the backward induction method.

3.1 Equilibrium in step 4

First, I derive the equilibrium in step 4. Using the production function of …nal goods, the pro…t of a …rm in the …nal goods sector, x; is

x= f (x1; x2) p1x1 p2x2;

where p1 is the price of x1, p2 is the price of x2; and the price of …nal goods is normalized to one. A …rm in the …nal goods sector determines the input level of xi to maximize x:The optimal conditions of this …rm are then,

p1= ^{@f(x1; x2)}

@x1

; p2=^{@f(x1; x2)}

@x2

: (1)

Since the production function is continuously diminishing marginal products, equation (1) implies that

@p1=@x1; @p2=@x2<0:

3Similar to Algan and Cahuc (2009), it is an important assumption for this model that the productivity of a …rm may be negative. An alternative assumption is that the minimum value of y is non-negative, but unemployed workers can produce intermediate goods 1 in home production.

4This is called the footloose capital model, which was proposed by Martin and Rogers (1995).

3

3.2 Equilibrium in step 3

Next, I characterize the decision marking by …rms in sector 1 on whether to …re a worker. When a …rm with productivity y keeps an employed worker, the ex-post pro…ts of this …rm 1are given by p1y w;which implies that ex-post pro…ts equal revenue p1y minus wages w. On the other hand, when the …rm lays o¤ the worker, ex-post pro…ts are f;which is the layo¤ taxes payment.

Let y be the threshold productivity below which workers are laid o¤. Then, the threshold is given by

|{z}f

lay o¤ the worker

= p1y w

| {z }

continue to em ploy the worker

() y= ^{w f}

p1

: (2)

(2) shows that y decreases with layo¤ tax levels f and the price of intermediate goods 1 p1 and increases with wages w. Moreover, the number of unemployed workers is equal to the number of workers who are …red, G(y) N; which is decreasing in f and p1 but increasing in w.

3.3 Equilibrium in step 2

In this subsection, I characterize wages w rental prices r and the price of goods i pi: The marginal pro…t of capital in sector 2 is p2 t2 r: Under perfect competition, marginal pro…t is zero, and the rental prices are then

r= p2 tk: (3)

Naturally, rental prices increase with p2and decrease with tk:

Next, I derive equilibrium wages. The ex-ante expected marginal pro…ts of …rms in sector 1 (E 1) are given by

E 1= Z

y

(p1y w) dG (y) G(y) f;

where the …rst term in the right-hand side of above equation represents the expected pro…ts when the job is not terminated, and the second term is the expected tax bill when the job is terminated.

Similarly, using the zero pro…t condition of …rms in sector 1 (E 1= 0), wages are

w=^p1 R

y^{ydG(y) G(y) f}

1 G(y) ^{: (4)}

The wage increases with p1 and decreases with layo¤ tax rates f . Note that there would be a trade-o¤ for workers between the job security and wages because equations (2) and (4) show that both wages and the probability of …ring decrease with layo¤ tax rates.

Next, I characterize the total output of intermediate goods. Using the de…nition of y, the total output of x1is given by

x1= Z

y

ydG(y) N: (5)

The right hand side of above equation is the total output in sector 1.

In a non-integrated market, the total output of x2 is very simple because the total amount of capital is exogenously determined. The total output of x2 is given by

x2= K^N: (6)

The equilibrium prices of x1 and x2 are determined by substituting equations (5) and (6) into equation (1) : Given the policies, the market equilibrium in the non-integrated market is then de…ned by equations (1) through (6).

Finally, I de…ne the market-clearing condition of …nal goods to analyze the optimal policies. While the income for a type-i household with an employed worker is the sum of capital income rki and labor income ce= w te(which is wages minus payroll taxes); the income for a household with an unemployed worker is the

sum of capital income rkiand labor income cu= b (which is unemployment bene…ts): Thus, the market-clearing condition of …nal goods x can be de…ned as follows:

f(x1; x2) = [(1 G(y)) ce+ G (y) cu] N + rK^N: (7) The …rst term on the right-hand side is aggregate labor income, and the second is aggregate capital income. Thus, the right-hand side represents the total demand for x, and the left-hand side is the total output of x.

Given a constant returns to scale production function, using equations (5) and (6) ; equation (7) can be rewritten as

f Z

y

ydG(y) ; ~k^N = (1 G(y)) ce+ G (y) cu+ r~k^N; (8) where ~k^N = K^N=N. The left-hand side of the above equation is output per household, and the right-hand side is the expected income for a household.

Note that in this model, the unemployment rate at step 4 is G (y) because all workers are employed at step 2, and a worker becomes unemployed if her or his productivity is less than y at step 3:

3.4 Equilibrium in step 1

Finally, I characterize government policy in non-integrated capital markets. The balanced budget constraint of the government is given by

tkK^N + [(1 G(y)) te+ G (y) f ] N = G (y) bN

() tk^~k^N + (1 G(y)) te+ G (y) f = G (y) b (9) where the left hand side of (9) is the average revenue from capital, payroll and layo¤ taxes, and the right hand side is the average expenditure for unemployment bene…ts.

The government chooses capital taxes tk; payroll taxes te;unemployment bene…ts b; and layo¤ taxes f to maximize social welfare S such that

S=^X

i

[(1 G(y)) u (ce+ rki) + G (y) (u (cu+ rki) B)] ni

Then, the above social welfare S is the aggregate utility of each type of household. Note that the government considers not only the utility from …nal goods consumption but also the utility cost of unemployment B:

The optimal problem of the government is given by

tkmax;te;b;f^S;s.t. (1) ; (2) ; (3) ; (4) ; (8) ; and (9) :

It is useful to rewrite this program as a choice problem of labor income for a household with an employed worker ce; an unemployed worker cu; capital income r; and threshold productivity y subject to the market-clearing condition of …nal goods (8) as

ce;imax;cu:i;y

X

i

[(1 G(y)) u (ce+ rki) + G (y) (u (cu+ rki) B)] ni; s.t. (8) :

After that, a government chooses policies to implement optimal ce;i; cu;i; r;and y.

The equilibrium values determined by a government are indicated by superscript N: I have shown this in the following proposition.

Proposition 1 The optimal capital incomer^N is such that

r^N = 0; (10)

labor incomec^N is

c^N = ce= cu; (11)

where

c^N = f Z

^ y^N

ydG(y) ; ~k^N : (12)

5

The threshold productivity y^N is

y^N = ^BN_N

p^N₁ ^{; (13)}

where

N _{= u}0 _cN _N:

Proof. See Appendix A.

(11) is the insurance condition. It implies that households should be insured against unemployment risks such as cA= ce= cu because households are risk-averse. (10) is the redistribution condition, and implies that income inequality between type-1 and 2 households should be eliminated and that capital income should be zero, r^N = 0: The consumption level of each household is determined by (12) ; which is the average output per household.

(13) is the threshold condition. It implies that the optimal threshold productivity y^N is negative if the utility costs of unemployment B are positive: To maximize the total output of …nal goods, outputs in sector 1 should be maximized, and y should then be zero, which is called the production-e¢cient threshold productivity in Blanchard and Tirole (2008): However, there would be a trade-o¤ between production-e¢ciency and the utility costs of unemployment, and lower threshold productivity would be required to balance this trade- o¤. It is straightforward to show that the optimal threshold productivity decreases with the utility costs of unemployment:

Threshold productivity increases with an increase in the price of intermediate goods 1 p^N₁ and the shadow price of …nal goods ^N:This is because when p^N₁ or ^N is high, the social value of intermediate goods 1 is also high. Thus, a government should reduce the gap between production-e¢cient threshold productivity and y to improve productivity in sector 1:

A government chooses policies to implement optimal conditions as characterized by Proposition 1. Proposition 2 Equilibrium policies are as follows:

f^N = p^N₁ Z

y^N

y y^NdG(y) ; (14)

t^N_k = p^N₂; (15)

b^N = p^N₁ Z

y^N

ydG(y) + p^N₂ ^{^}k^N; (16)

t^N_e = G y^N p^N₁ y^N p^N₂^{^}k^N: (17)

Proof. See Appendix B.

In non-integrated capital markets, the government chooses very high capital tax rates and positive layo¤ tax rates, it then redistributes revenue from these taxes toward households through payroll subsidies and unemployment bene…ts. These policies lead to an attainment of the …rst-best social welfare, in which there is no income inequality between type 1 and 2 households, and households are perfectly insured against the risk of income ‡uctuations because of changes in employment status and are moderately protected against unemployment risk.

Finally, from comparative statics, I obtain the following proposition for the layo¤ tax rate. Proposition 3 The layo¤ tax rate f^N decreases with threshold productivityy^N:

Proof. See Appendix C.

Combining this with Proposition 1, the layo¤ tax rate increases with the utility costs of unemployment B and decreases with the shadow value of …nal goods ^N and the price of intermediate goods 1 p^N₁ through a decrease in threshold productivity y^N:Note that in the non-integrated capital market case, there is obviously no policy interaction among governments.

4 Equilibrium in integrated capital markets

Similar to the previous section, I characterize the market equilibrium in integrated capital markets using the backward induction method. By assumption of a small open economy, no single government can a¤ect the world rental price ^r; which is determined by an aggregate of the policies of all governments. The sub-game equilibrium in steps 3 and 4 is the same as the equilibrium in the non-integrated market (Section 3), and (1) and (2) are the prices of intermediate goods and the threshold productivity in integrated capital markets, respectively.

4.1 Equilibrium in step 2

In step 2, equilibrium wages and capital supply in a country are characterized. Equilibrium wages are deter- mined by the free entry condition just as in non-integrated capital markets, and the wages are then (4) :

Let K^I denote capital supply in a country. It is endogenously determined by factor price equalization as follows:

^

r= r = p2 tk: (18)

(18) implies that the domestic rental price r must be equal to the world rental price ^r. Since the world rental price ^ris given, (18) implies that tk can be connected to the capital supply in country K^I:

Proposition 4

@K^I

@tk

= ^@

2_f(x 1; x2)

@x²₂

1

: (19)

Proof. Total di¤erentiation of (18) yields

@p2

@K^I

@K^I

@tk

= 1: Using (1) and (6) ;

@p2

@K^{I =}

@²f(x1; x2)

@x²₂ ^: Combination of the above two equations gives (19) :

Since ^@2f(x_@x¹2^;x2)

2 ^<0; (19) de…nes the negative relationship between the capital tax rate of a country and its capital supply, which is an additional constraint of the government’s problem in step 1.

Finally, I de…ne the market clearing condition in integrated capital markets as follows: f

Z

y^

ydG(y) N; K^I = [(1 G(y)) ce+ G (y) cu] N + ^rK^I:

The left-hand side of the above equation represents the aggregate output of …nal goods, which is an increasing function of K^I:The second term in the right hand side is labor share, and the …nal term is capital share which may include the capital income of households in foreign countries.

From the assumption of a constant returns to scale production function, the market clearing condition can be rewritten as

f Z

y^

ydG(y) ; k^I = (1 G(y)) ce+ G (y) cu+ ^rk^I; (20) where ^k^I =^K_N^I:

4.2 Equilibrium in step 1

In step 1, given the world rental price ^r, each government simultaneously chooses capital, payroll, and layo¤ subsidy or tax rates and unemployment bene…ts to maximize social welfare S of its country. As in the non- integrated capital markets case, each government’s optimization problem is rewritten as a choice problem of labor income of employed and unemployed workers and the threshold productivity. However, there is a signi…cant di¤erence in the non-integrated capital markets case, as the governments cannot choose their capital income, which is determined by the world rental price ^rby (18). Thus, I de…ne the optimization problem in which governments choose their capital tax rates in addition to labor incomes and threshold productivity under

7

the arbitrage condition (19) and the market clearing condition (20) : More formally, the optimization problem of a government is given by

ce;cmaxu;tk;y

X

i

[(1 G(y)) u (ce+ ^rki) + G (y) (u (cu+ ^rki) B)] ni

s.t. (19) and (20) :

The above optimization problem implies an important e¤ect of capital market integration. Capital tax rates do not directly impact social welfare, but have an impact on the market-clearing condition. This is because that a government cannot choose capital income, which is determined by the world rental price. A decrease in the capital tax rate attracts capital stock from other countries (see (19)), increasing not only the total output of

…nal goods but also the exports of …nal goods to o¤set the ‡ow of capital income. As a result, the government’s choice problem of capital tax rates is equivalent to the maximization problem of total income of households in its country using capital tax rates.

Recall that in the non-integrated capital markets case, a government chooses the capital tax rate to com- pletely eliminate income inequality. In integrated capital markets, the degree of income inequality depends only on the world rental price, and no governments can eliminate income inequality. Instead, capital supply depends on capital tax rates, and each government then chooses its capital tax rate to maximize the income of households in its country.

The equilibrium values in non-integrated capital markets are indicated by superscript N: I consider the symmetric equilibrium in which all governments choose the same capital tax rates t^I_k; labor income of an employed worker c^I_e;labor income of an unemployed worker c^I_u;and threshold productivity y^I:In the symmetric equilibrium, capital does not move across borders, and K^I = K^N because all governments choose the same capital tax rates, and the rental price is the same among all countries.

Formally, I summarize the results in Proposition 5. Proposition 5 The optimal capital income is

r^I = p^I₂ (21)

and labor income is

ce= cu= c^I; (22)

where

c^I = f Z

y^I

ydG(y) ; k^I p^I₂k^I: The optimal threshold productivity is

y^I = ^BN_I

p^I₁^{; (23)}

where

I ₌^X

i

u⁰ c^I+ r^Iki ni:

Proof. See Appendix D.

From the comparison of Propositions 1 and 5, I can show that capital market integration has several impacts on the optimal condition of a government. Comparing (10) and (21) suggests that capital market integration increases capital income in each country because tax competition arises between countries. Intuitively, a decrease in capital tax rates increases both the total output of …nal goods and the export of …nal goods (which is the cost of attracting capital stock). To maximize the income of households in the country, the government chooses a capital tax rate under which p^I₂= ^r because, while the marginal …nal goods output of capital is p^I₂; the marginal cost of attracting capital is ^r: Using the symmetric equilibrium condition of ^r= r^I;the optimal condition of tk is given by p^I₂= ^r:

Moreover, in this model, capital market integration leads to income inequality within a country, as type-2 households can obtain higher income than type-1 households. This is because that type-2 households can obtain a large share of aggregate capital income in a country.

(13) and (23) imply that the optimal threshold productivity in integrated capital markets is higher than in non-integrated capital markets (see Appendix E for a formal proof). Intuitively, an increase in income inequality increases the shadow value of …nal goods ^I:As a result, each government would like to increase its

Proposition 6 Equilibrium policies are as follows: f^I = p^I₁ Z

y^I

y y^IdG(y) ; (24)

t^I_k = 0; (25)

b^I = p^I₁ Z

y^I

ydG(y) ; (26)

t^I_e = G y^I p^I₁y^I: (27)

Proof. See Appendix F.

The comparison of Proposition 2 and 6 highlight the main results of this paper. (15) and (25) imply that capital market integration decreases capital tax rates because of tax competition pressures. This is a standard result in the literature of tax competition.

From (24) ; equilibrium layo¤ tax rates have the same functional form as (14) : From Proposition 3, the equilibrium layo¤ tax rates in integrated capital markets are lower than in non-integrated capital markets because the equilibrium threshold productivity in integrated capital markets is higher than in non-integrated capital markets. In other words, capital market integration triggers deregulation of …ring restrictions.

A decrease in the capital and layo¤ tax rates imply that government revenue from these taxes also decreases. Through this channel, capital market integration a¤ects payroll subsidies and unemployment bene…ts. Capital market integration decreases payroll subsidies from (17) and (27) and has an ambiguous e¤ect on unemployment bene…ts from (16) and (26) : This is because that capital market integration decreases not only revenue from capital and layo¤ taxes but also expenditure for payroll subsidies.

Finally, I analyze the e¤ect of capital market integration on social welfare of each country. Obviously, when all countries are symmetric, the global optimal policies by which social welfare of each country is maximized are same as the policies in the non-integrated market. Then, I obtain following the proposition.

Proposition 7 Capital market integration reduces social welfare of each country.

Integration of capital markets leads to an ine¢cient economy in which labor productivity is high, and the aggregate consumption level of …nal goods is then also high. However, income inequality within a country and frequency of job destruction are high because capital and layo¤ tax rates are low. As a result, social welfare of each country in integrated capital markets is lower than welfare in non-integrated capital markets.

5 Conclusion

This paper considered the impacts of capital market liberalization on the labor market through changing labor market policies. The government of each country tries to redistribute income between households and leads to the optimal layo¤ decision. Capital tax competition between countries arises as a result of capital market integration, which reduces capital tax rates and leads to income inequality within a country. Capital market integration also has impacts on labor market policies, by which each government reduces layo¤ tax rates to increase productivity. To maximize social welfare of each country, the capital and layo¤ tax rates in integrated markets may become too low, and capital market integration then has negative impacts on social welfare of each country through policy reform.

Appendix A

The Lagrangian of the government program, L; is given by

L = ^X

i

[(1 G(y)) u (ce+ rki) + G (y) (u (cu+ rki) B)] ni

+ ^N f Z

y

ydG(y) ; ~k^N (1 G(y)) ce G(y) cu r~k^N ;

9

where ^N is the Lagrangian multiplier. The …rst-order conditions read,

@L

@ce;i

= 0 () ^X

i

u⁰(ce+ rki) ni= ; (A1)

@L

@cu;i

= 0 () ^X

i

u⁰(cu;i+ rki) ni= ; (A2)

@L

@r ^{= 0 ()}

X

i

[(1 G(y)) u⁰(ce+ rki) + G (y) u⁰(cu+ rki)] kini= ~k^N (A3)

and

@L

@y ^{= 0 ()} X

i

[ u (ce+ rki) + u (cu+ rki) B] ni+ ^{@f(x1; x2)}

@x1

y ^X( ce+ cu) : (A4)

(A1) and (A2) together imply c^N = ce= cu;under which (A3) can be rewritten as X

i

u⁰ c^N + rki kini = ^~k^N

= ^X

i

u⁰ c^N + rki ni^~k^N:

This condition implies that r^N = 0: Using the redistribution condition r^N = 0; and the insurance condition c^N = ce= cu;the market-clearing condition of …nal goods (7) can be rewritten as

c^N = f Z

^ y

ydG(y) ; ~k^N : (A4) can thus be rewritten as

BN = ^{N@f(x1; x2)}

@x1 ^y N_:

() y^N = ^BN_N p^N₁ ^: Using (A1), c^N = ce;and r^N = 0; I obtain

N _{= u0 c}N _N:

Appendix B

To implement (10) ; from (3) ; capital tax rates t^N_k must be equal to the price of intermediate goods 2; p2: To implement (13), from (2) and (4), the layo¤ tax rate f^N must satisfy the following condition:

f^N = p^N₁y^N +^p

N1

R

y^{NydG(y) G yN fN}

1 G(y^N)

= p^N₁ Z

y^N

y y^N dG(y) :

To implement (10) and (11) ; unemployment bene…ts, payroll subsidy rates, and capital tax rates must satisfy the following conditions:

w^N t^N_e = b^N; (B1)

t^N_k = p^N₂:

Finally, I characterize the optimal payroll subsidy rate t^N_e and unemployment bene…ts b^N. From (2) ; (13) can be rewritten as

B = w^N f^N

using (B1);

b^N+ t^N_e = f^{N B}

u⁰(c^N)^{: (B2)}

Now, the budget constraints of government (9) can be rewritten as

1 G y^N t^N_e = G y^N b^N f^N p^N₂k^{^N}: (B3)

Combining (B2) and (B3); unemployment bene…ts b are b^N = f^N 1 G y^{N B}

u⁰(c^N)^{+ p}

N2 ^{^kN:}

Using (13) and (14) ; the above equation can be rewritten as b^N = p^N₁

Z

y^N

ydG(y) + p^N₂ ^{^}k^N:

The optimal payroll subsidy rate ^N_e can be obtained by substituting the above equation into (B2) or (B3). For example:

t^N_e = G y^N p^N₁ y^N p^N₂^{^}k^N:

Appendix C

The total di¤erentiation of (14) is

@f^N

@y^{N =}

@p^N₁

@x^N₁

@x^N₁

@y^N Z

y^N

y y^N dG(y) p^N₁ (1 G(y)) :

@p₁

@x₁ ^{<0; and}

@x₁

@y ^>0 if 0 > y^N:From (13) ; y^N <0; and thus ^@f_@y^NN <0:

Appendix D

The Lagrangian of a government program is

L = ^X

i

[(1 G(y)) u (ce+ ^rki) + G (y) (u (cu+ ^rki) B)] ni

+ ^I f Z

y

ydG(y) ; ^k^I [(1 G(y)) ce+ G (y) cu] r^^k^I ;

where ^k^I is determined by (18) and ^I is the Lagrangian multiplier. Using (19) ; the …rst-order condition with respect to the capital tax rates is

@L

@tk

= 0 () ^{@f(x1; x2)}

@x2

^ r ^{@^k}

I

@tk

= 0

Since all countries are symmetric, all governments choose the same capital tax rates, and thus ^r= r:

The …rst order conditions with respect to the labor income of an employed worker and an unemployed worker are, respectively,

@L

@ce

= 0 () ^X

i

u⁰(ce+ ^rki) ni = 0;

@L

@cu

= 0 () ^X

i

u⁰(cu+ ^rki) ni = 0:

Because u⁰⁰<0; this condition holds if and only if ce= cu= c^I;where c^I = f

Z

y^I

ydG(y) ; ^k^I p^I₂^{^}k^I: 11

The …rst order condition with respect to the threshold productivity level ^@L_@y = 0 is

0 = ^X

i

[u (ce+ ^rki) u(cu+ ^rki) + B] ni+ ^{@f(x1; x2)}

@x1

y+ ce cu

+ ^{@f(x1; x2)}

@x2

^ r ^{@^k}

I

@y ^:

Using the …rst order conditions with respect to the capital tax rate and the consumption level of households, the above condition can be rewritten as

BN = ^{@f(x1; x2)}

@x1

y^I () y^I = ^BN_I

p^I₁^; where

I ₌^X i

u⁰ c^I+ ^rki ni:

Appendix E

To show y^I > y^A; we proceed by contradiction. Suppose that y^I y^A: From y^I; y^A < 0; x^I₁ x^A₁, which implies that p^I₁ p^A₁ and f ^R_y^IydG(y) ; ~k^I f ^R_y^NydG(y) ; ~k^N : The market-clearing condition implies

that _X

i

c^I+ ^rki

ni

N ^c

N_:

Since u⁰⁰<0; u⁰⁰⁰>0; using Jensen’s inequality, X

i

u⁰ c^I+ ^rki

ni

N ^{> u}

0 _cN _:

Combining p^I₁ p^N₁ gives

P B

i^{u0(cI+ ^rki) nipI}1

> ^B

u⁰(c^N) N p^N₁ ^: Using (13) and (23) ; the above inequality can be rewritten as

y^I > y^N; which contradicts y^I y^N:

Appendix F

To implement (21), the capital tax rate must satisfy t^I_k= 0:

To implement (13), from (2) and (4), …ring tax rates must satisfy the following condition:

f^I = p^I₁y^I+^p

I1

R

^

y^{IydG(y) G yI fI}

1 G(^y)

= p^I₁ Z

y^I

y y^I dG(y) :

Next, I characterize the optimal payroll subsidy rate t^I_eand unemployment bene…ts b^I. To implement (22) ; unemployment bene…ts and the payroll tax rate must satisfy the following condition

w^I t^I_e= b^I: (F1)

From (2) ; (23) can be rewritten as P BN

i^{u0(cI+ ^rIki) ni}

= w^I f^I: Using (F1);

b^I + t^I_e= f^I P ^BN

i^{u0(cI+ ^rIki) ni}

: (F2)

Now, the budget constraints of government (9) can be rewritten as

1 G y^I t^I_e= G y^I b^I f^I : (F3)

Combining (F2) and (F3); the unemployment bene…ts b^I are b^I = f^I 1 G y^{I B}

u⁰(c^I)^: Using (23) and (24) ; the above equation can be rewritten as

b^I = p^I₁ Z

y^I

ydG(y) :

By substituting the above equation into (F2) or (F3), the optimal payroll subsidy rate t^N_e can be obtained as t^I_e= G y^I p^I₁y^I:

13

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