This paper investigates the relationship between the unemployment gap be- tween the United States and Europe that widened dramatically in the mid-.
European unemployment gap and capital mobility
Allen Head* Shouyong Shi† Karlis Smits*
May, 2002 Preliminary and incomplete Do not quote
Abstract This paper investigates the relationship between the unemployment gap between the United States and Europe that widened dramatically in the mid1980’s and the opening of international capital markets. This time period was also characterized by substantial increases in international capital flows - a significant share of which were flows from Europe to the US. We consider the implications of capital mobility for unemployment levels and current accounts in a multi-country dynamic general equilibrium model with incomplete international capital markets and national labor markets characterized by search and matching. The economy also features unemployment insurance consisting of a benefit equal to a replacement rate times the market wage and financed by distorting taxes. It is shown that given differences in the generosity of unemployment benefits lead to a substantially differences in unemployment rates across countries when there is international capital mobility than in autarky. Moreover, when capital markets are opened, high benefit countries experience both an increase in the unemployment rate and an outflow of capital, and low benefit countries experience both a reduction in the unemployment rate and an inflow of capital.
* Department of Economics at Queen’s University in Kingston, Ontario † Department of Economics at Indiana University in Bloomington, Indiana 1
1. Introduction During the first decades after the second world war unemployemnt rates in Western European countries were equal to or less than those of other developed economies, but in the 1970’s the situation started to change and European countries suffered large increases in unemployment relative to other industrial countries. Three important characteristics of the European unemployment gap are focus of extensive research. Firstly, unemployment rates in Europe have been persistently higher than ones in other OECD countries for over last two decades. Secondly, there is clear pattern of divergence in unemployment rates across individual countries. Thirdly, there is an increase in duration of unemployment in countries of high unemployment rate. In general, previous studies can be summarized into two main categories. Firstly, so called shock-based theories focus on how various economic turbulences effect labor markets. Clearly, the start of the unemployment gap coincides with significant changes in the global economy such as increased competition and globalization. Blanchard and Wolfens (1999) are more specific in identifying particular adverse events that have had negative effects on the unemployment rates in Europe. Among other things, total factor productivity decline experienced in Western Europe during the 1980’s have had negative effect on employment. Productivity slowdown combined with higher real interest rates have lead to higher cost of capital that have resulted in lower capital accumulation and subsequently decrease in employment. Alternatively, Ljungqvist and Sargent (1998) focus on dynamic responses of economic shocks to a welfare states. They suggest that the real explanation for persistently higher European unemployment level is to be found in inability of high welfare economies to adjust to continuously changing economic environment. Secondly, significant proportion of studies focus on analyzing differences in institutional aspects of labor markets in industrialized countries. This literature is also referred to as labor demand side approach. A range of researchers attribute strict regulations of European labor markets and other structural market rigidities as a source of the unemployment gap. Blanchard and Summers (1986) and Lindbeck and Snower (1988) have developed insider-outsider theory that focuses on conflicts between employed and unem2
ployed workers that arise in highly unionized economies of Europe. One can find a close link between labor market rigidities and external shocks. As clearly showed by Ljungqvist and Sargent (1998) labor market rigidness can extend the transition path from the external economic turbulence. Generous unemployment benefits combined with various restrictions of hiring and firing have led to rigid economies vulnerable to big external shocks. Interestingly, the opening of unemployment gap has coincided with significant movements in capital among industrialized countries. The increase of capital flows in 1970ies is attributed to technological evolution in the financial industry, petrodollar recycling, removal of many restrictions on capital movements, adoption of floating currency exchange rates. Although high unemployment rates in Europe coincide with significant capital outflows from the region, impact of capital flows on unemployment has been largely overlooked in literature. Azariadis and Pissarides (2000) study the responses of domestic unemployment rates to total factor productivity shock for countries with high capital mobility and low labor mobility. They show that capital mobility has important impact on the transition path adjusting from the total factor productivity shock. Countries with high capital mobility experience higher fluctuations in unemployment rates. This result is consistent with observation that variability of employment has increased in industrialized countries during the last decade. Several other studies have looked at a role of capital flows and have analyzed a relationship between employment and current account. However, the focus of these studies was to analyze effects of various trade barriers (tariffs) on employment. Two notable studies include Shi (1997) and van Wiljnbergen (1987). The purpose of this paper is to investigate the role of international capital movements on labor market in a multi-country dynamic general equilibrium model with incomplete international capital markets and national labor markets characterized by search and matching. The paper is structured as follows. Section 2 describes the unemployment and capital movement dynamics for the last decades in the United States and Western Europe. Section 3 describes the model. Section 4 describes the functional forms and parameter values for 3
calibration. Discussion and concluding remarks in Section 5. 2. Evidence 2.1: Employment and Unemployment Dynamics As a result of robust post war economic expansion in Europe, Japan and North America during the 1950’s and 1960’s unemployment rates in the OECD countries were relatively low. In the 1970’s the OECD economies experience two major oil price shocks (1973-1974 and 1979-1980) followed by changes in economic environment in terms of increasing global competition and rapid technological advances. These events trigger a notable productivity downturn resulting in a large increase in the number of unemployed across industrialized countries, however, the rising trend in the unemployment is uneven across countries. Figure 2.1. Standardized Unemployment Rate dynamics 12
10
%
8
6
4
2
USA
OECD Europe
2000Q2
1999Q1
1997Q4
1996Q3
1995Q2
1994Q1
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1986Q3
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0
E15 (European Union)
Note: Seasonally adjusted quarterly standardized unemployment rates. Standardized unemployment rates for European Union available from 1998. Source: Quarterly Labour Force Statistics, OECD
Although during the 1960’s unemployment rates in the United States are slightly higher than the OECD average (including Western Europe), since early 1970’s there has been only a moderate trend increase in unemployment rates in the United States. Nevertheless, we observe large fluctuations in the unemployment rates with peaks in mid 1970’s, 4
early 1980’s, and early 1990’s (see Figure 2.1). These fluctuations suggest, that labor market in the United States was quick to recover after exposures to the oil shocks and economic downturns. This recovery is much faster than in other OECD countries (especially Western Europe). Fluctuations in European unemployment rates follow a similar pattern observed in the United States, however, average unemployment rates in Europe have risen sharply since mid 1970’s (see Figure 2.1). In particular, the European unemployment rates are more rigid in terms of adjusting to normal levels after economic downturns. This suggests a presence of so called adjustment gap when economies are slow in adopting to changing economic environment (OECD(1994)). As a result, since mid-1970 the unemployment rates in Europe are persistently higher than those in other developed countries, especially the United States (see Figure 2.2). Persistent nature of the European unemployment gap during 1980’s and 1990’s is well documented empirical fact and focus of extensive research. There exist significant disproportions in shares of long-term unemployment among the OECD countries. In particular, European countries tend to have proportionally larger shares of long-term unemployment. While long term unemployment shares had risen sharply in Europe during the recession of early 1980’s with only a moderate decline during mid 1980’s, in the United States there was only a moderate increase with prompt decline by mid-1980s1 . The structure of long-term unemployment suggests that inflow rates into the unemployment pool are lower (lower separation rates) in Europe comparing to ones in the United States. Once unemployed, workers in the United States have greater chances of returning to employment quickly.
1
In 1983 proportion of workers unemployed for 1 year and over as percentage of unemployment accounted for 13.3 percent in the United States. By 1986 the share of long term unemployment declined to 8.7%. For comparison, in 1983 a share of long term unemployment accounted to 58.2% in Italy, 42.2% in France, 41.6% in Germany. Source: Labour Force Statistics 1980-2000, OECD
5
Figure 2.2 The European and Canadian Unemployment Gap with the United States 8
6
4
%
2
2000Q2
1999Q1
1997Q4
1996Q3
1995Q2
1994Q1
1992Q4
1991Q3
1990Q2
1989Q1
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1979Q1
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1972Q4
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1970Q2
1969Q1
1967Q4
1966Q3
1965Q2
1964Q1
0
-2
-4
-6 European Unemployment Gap
Canadian Unemployment Gap
Note: Seasonally adjusted quarterly standardized unemployment rates. Source: Quarterly Labour Force Statistics, OECD
During the 1980’s European countries lagged the United States in terms of employment growth. In Western Europe countries the employment increased only by 7% comparing to 19% in the United States for the same time period. Europe has suffered several concomitants of high unemployment, namely, reduced labor force participation and involuntary reductions in working hours. 6
Table 2.1 Net Unemployment Benefit Replacement Rates in 1994 for single-earner Households Single
1st Yr Belgium France Germany Netherlands Spain Sweden United Kingdom United States
79 79 66 79 69 81 64 34
With Dependent
2nd and 4th and 3rd Yrs 5th Yrs 55 63 63 78 54 76 64 9
55 61 63 73 32 75 64 9
1st Yr
2nd and 3rd Yrs
4th and 5th Yrs
70 80 74 90 70 81 75 38
64 62 72 88 55 100 74 14
64 60 72 85 39 101 74 14
Note: Benefit replacement rates are benefit entitlements on a net-of-tax and housing benefit basis as a percentage of net-of-tax earnings. Data for Sweden and the United Kingdom pertain to 1995. Source: Martin (1996), table 2
Traditionally, differences in institutional framework of labor market policies are considered to be a leading cause for observed differences in the unemployment rates among the OECD countries, including the European unemployment gap. Various labor market protection mechanisms distort incentives of economic agents (workers, firms) resulting in inability to meet demands of changing economic environment. Unemployment replacement rates are one of the most studied labor market policy tool widely used after the second world war in developed countries. Although significant differences are observed among individual countries, the unemployment benefit rates relative to average earnings (replacement rates) are generally higher in Europe than in other OECD countries, especially the United States (OECD (1994)). In addition, during the 1970’s and 1980’s several countries have increased their unemployment benefit rates (Blanchard and Wolfens (1999)). This increase is especially significant in several small European countries (Denmark, Norway, Finland, Portugal, Spain, Ireland, Sweden, and Switzerland). Some European countries such as Germany and UK have resisted the rise, however, the rates remain higher than ones observed in the United States. Table 2.1 provides an example of average replacement rates for a typical 40 year old worker with previous job experience in mid-1990’s. 7
1.2: Capital flows The first post war decades (1950’s, 1960’s) are marked by remarkable economic expansion in the OECD countries. Nevertheless, post war Bretton-Woods financial system is characterized by presence of various restrictions on international capital mobility. Initially, these controls are designed as a mechanism to prevent currency crises and runs in presence of fixed exchange rate system. The collapse of the Bretton-Woods system and subsequent introduction of floating exchange rates in the 1970’s allowed governments to ease various restrictions on capital movements. Combined with technological evolution in the financial industry, and petrodollar recycling industrial economies have experienced significant increases in international capital movements reflected by their current account fluctuations. During the 1980’s and 1990’s globalization of business environment combined with closer economic integration of the OECD countries has fostered the importance of international capital movements. By late 1990’s the world capital movements have surpassed levels observed before the first world war (Obstfeld and Taylor (2002)).
Figure 2.3 The United States Current Account Balances (% of GDP) 0.02
0.01
%
-0.01
-0.02
-0.03
-0.04
-0.05
Source: Bureau of Economic Activity
8
2000
1998
1996
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A steady increase in capital movements coincides with reversing direction of the flows in early 1980’s. Although most of the capital flows still occur among the developed nations, the United States from being a net lender becomes a net recipient of capital. Since early 1980’s the United States began accumulating negative trade balance that resulted in sharp increase in the current account deficit (capital account surplus) (see Figure 2.3). With brief exceptions in early 1990’s, the United States has persistently maintained negative current account balances for the last two decades with a sharp increase in late 1990’s. The United States continues to maintain significant current account deficit both in nominal and real terms. Analyzing current account dynamics of each European country separately, it is difficult to see a clear pattern in the direction of flows between Europe and the United States. This is due to the fact that majority of transactions of individual European are among other European countries. On the other hand, if we focus on aggregate capital flows between Europe and the United States a clear pattern emerges.
Figure 2.4 Total asset inflows/outflows between Western Europe and United States as a percentage of the US GDP 0.08
0.06
0.04
% of GDP
0.02
2000
1998
1996
1994
1992
1990
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-0.02
-0.04
-0.06 U.S.-owned assets in Western Europe
Western European owned assets in US
Source: Bureau of Economic Activity
Focusing on just the flows of capital between the United States and Europe (inflow 9
of European-owned assets in the United States and the U.S. owned assets in Europe) we see a steady increase in the flows during the last decades, with significant increases in the second part of 1990’s (see Figure 2.4). This is not surprising, as the United States remained the prime destination of majority of capital outflows from Europe and Japan. Dynamics of the flows show slight volatility, especially at the beginning of 1990’s (partly due to unification of Germany), however, it is clear that the United States emerges as a net borrower of capital from Europe during the last decades.
Figure 2.5 Cumulated FDI stock in select OECD countries (mln USD) 250000
200000
150000
100000
50000
0
1970s na
-50000
Ca
da
Fr
ce
an
er G
an m
y
ly
UK
Ita
US
A
1980s 1990s
-100000
-150000
-200000
-250000
-300000
Source: International Direct Investment Statistics Yearbook, OECD figure includes statistics up to 1998
Furthermore, similar patter arises when flows of foreign direct investments (FDI) are considered. The United States has managed to accumulate significant cumulative direct investment capital stock during the 1980’s, while other major OECD countries experienced outflows (see Figure 2.5). Situation in the 1980’s is different to one in the 1970’s, when direct investment flows were still relatively small and the United States had a negative cumulated FDI stock. During the 1990’s FDI flows in the OECD countries have increased significantly resulting in significant FDI outflows in the UK, and Germany. 10
The opening of the European unemployment gap coincides with significant changes in international capital flows, in particular, an increase in European unemployment rates coincides with significant outflow of capital from the region. It is evident that these structural changes in unemployment and capital flow dynamics start in the 1970’s as a result of significant external shocks and changes in economic environment. This suggests that the outflow of capital from Europe, that continued throughout 1980’s and 1990’s might have contributed to the unemployment growth in the Western Europe. 3. The Economy 3.1: The Environment The world is comprised of two symmetric countries of equal size. There is no uncertainty and time is discrete. Each country is populated by a large number of identical households, with each of these households comprised of a unit measure of members. In each period, measure n of these members is employed (i.e. supplying labor to a firm), measure s are searching for employment, and the remaining members (measure 1 − n − s) are idle. The allocation of members to particular activities is determined by household choices. All members care only about overall household utility; they do not have independent objectives and make no independent decisions. There is a single consumption good available in each period. A household derives utility from consumption of this good and from leisure, where the quantity of leisure consumed in a given period is proportional to the measure of household members that are idle in that period. Households have preferences that order infinite horizon consumptionleisure plans. Let ψjt denote the time t value of the utility to a country j, j = 1, 2, household from a given consumption-leisure plan that runs from time t on. We assume that ψjt can be written recursively as, ψjt = u(cjt , `jt ) + β(cjt , `jt )ψjt+1
j = 1, 2
∀t,
(3.1)
where `jt ≡ 1 − njt − sjt , u(·) denotes the household’s period utility, and the function β(·) governs the rate at which the household discounts future utility. Let u(·) be strictly increasing in both arguments and strictly concave. We consider two ¯ utility is specifications for the discount factor function β(·): First, with β(·) a constant, β, 11
time separable. Alternatively, β(·), may be decreasing and strictly concave, thus exhibiting increasing marginal impatience. For these cases we restrict attention to specifications in which preferences exhibit weak separability in the sense of Shi (1994), which requires β` βc = . uc u`
(3.2)
Weak separability in this sense may be interpreted as the requirement that the marginal rate of substitution between consumption and leisure depend on the levels of c and ` in the future, but not in the past. In each country the single consumption good is produced by means of a constant returns to scale technology. This good is produced by a competitive industry consisting of a large number of identical firms. Let yjt denote the output of a representative country j firm1 in period t, where yjt = F (kjt , njt )
j = 1, 2.
(3.3)
Here kjt and njt denote the capital and labor employed by this firm. The production function F (·) is strictly increasing and concave in both arguments with lim kj →0 Fk = ∞ and limnj →0 Fn = ∞. Physical capital is produced by each household in each country using a standard intertemporal technology. The law of motion for a country j household’s capital stock is kjt+1 = (1 − δ)kjt + ijt
δ ∈ (0, 1)
j = 1, 2.
(3.4)
Here δ denotes the one-period depreciation rate for capital and ijt is household investment in country j at time t in units of time t consumption good. Country j households are endowed with one unit of time per period, equal shares of ownership in the initial aggregate country j capital stock, Ki0 ; and equal shares in all country j firms. Markets for goods and capital are competitive. The labor market, however, is not Walrasian but rather is characterized by search and random matching of workers with 1
Throughout, lower case letters will be used to denote per capita or per firm quantities, and upper case letters to denote aggregates.
12
firms. Wages are determined by bargaining once a match is made. Let N jt denote the aggregate measure of country j household members that are matched with firms in period t. Then the number of workers matched with a firm at time t + 1 will depend on the share of the previously matched workers who remain with their firms and the number of new matches that are formed during period t. These new matches will be determined by the number of vacancies posted by country j firms at time t, Vjt , and the measure of country j household members who search for employment in period t, Sjt , according to the matching function, Mjt = M (Vjt , Sjt )
j = 1, 2.
(3.5)
M (·) exhibits constant returns to scale and is strictly increasing and concave in both arguments with limVj →0 M1 = ∞ and limSj →0 M2 = ∞ j = 1, 2. We may then introduce notation for the average rates at which unemployed (i.e. searching) workers and unfilled vacancies are matched, respectively: m(V, S) =
M = Xα S
µ(V, S) =
M = X α−1 , V
(3.6)
where X ≡ V /S will be referred to as labor market tightness. The aggregate number of active matches (i.e. employment) in country j then evolves over time according to Njt+1 = (1 − θ)Njt + M (Vjt , Sjt )
j = 1, 2.
(3.7)
In each country there is a government which consumes, collects lump-sum taxes, and pays subsidies to households in proportion to the measure of household members who are searching for employment. The government has no explicit objective, but must satisfy the following budget constraint, Tjt + Gjt + τj wjt Sjt = 0,
j = 1, 2,
∀t.
(3.8)
In period t, Tjt is the lump-sum tax, Gjt is government consumption, and τj ∈ (0, 1) determines the subsidy paid to searching workers as a fraction of the current wage. The aggregate state of the economy may then be summarized by Γt = K1t , K2t , N1t , N2t , G1t , G2t , B1t , 13
(3.9)
where B1t denotes claims held by households in country 1 to units of the time t consumption - investment good owned by country 2 households. With regard to these claims, we restrict attention to two different regimes for international capital markets. In the first regime international borrowing and lending are prohibited. Because there is only one consumption - investment good and labor is assumed to be internationally immobile, this is sufficient to force the two countries into autarky. In this case, B1t = 0 for all t. In the second regime international borrowing and lending is limited to trade in one-period non-contingent bonds, of which the net supply is zero. 3.2: Optimization Consider first optimization by firms. Since firms in the two countries are entirely symmetric, the subscript j will be suppressed. Also, to simplify exposition, the subscript “
t
” will be dropped from current period variables and a superscript “ 0 ” will be used to
denote the value of a variable in the next period. A representative firm chooses a quantity of capital to rent, kf , and a number of vacancies, v to post as functions of its individual state in each period in order to maximize the present value of its dividends. Let H(n f , Γ) denote the value of a firm with nf workers in the current period when the current aggregate state is Γ. Given (3.6), the law of motion for the individual firm’s matches with workers is given by n0f = (1 − θ)nf + µ(V, S)v,
(3.10)
Let π denote the firm’s current profits. Then, π(nf , Γ) = F (kf , nf ) − r(Γ)kf − w(Γ)nf − pv,
(3.11)
where r(Γ) and w(Γ) denote the rental rate of capital and wage as functions of Γ, respectively and p is the marginal cost of posting an additional vacancy. We then have 1 0 H (1 − θ)nf + µ(Γ)v, Γ , H nf , Γ = max π(Γ) + kf ,v 1 + R(Γ0 )
(3.12)
where R(Γ) and µ(Γ) are the interest rate and matching rate for vacancies as functions of the aggregate state, Γ. The first-order conditions satisfied by the optimal choices for k f and v give rise to Fk = r(Γ) 14
(3.13)
µ(Γ) p(1 − θ) 0 0 p= F − w(Γ ) + . 1 + r(Γ0 ) n µ(Γ0 )
(3.14)
We now turn to optimization on the part of households. The state of a household is determined the number of its members who are currently matched with firms, n, and its holdings of physical capital, k, and foreign bonds, b, in addition to Γ. Given (3.6), the measure of household members matched with firms evolves according to n0 = (1 − θ)n + m(V, S)s,
(3.15)
Using the law of motion for household capital, (3.4), the household’s budget can be written,
c + k 0 + b0 = [r(Γ) + 1 − δ]k + w(Γ)n + τ w(Γ)s + π(Γ) + [1 + R(Γ)]b − T.
(3.16)
Let J(k, b, n, Γ) denote the value of future utility to a household in state (k, b, n, Γ). Then, 0 0 0 0 J(k, b, n, Γ) = max u(c, 1 − n − s) + β(c, 1 − n − s)J(k , b , n , Γ ) 0 0 s,k ,b
(3.17)
subject to (3.15) and (3.16). Defining Ψ(c, `, k 0 , b0 , n0 , Γ0 ) = u(c, `) + β(c, `)ψ(k 0 , b0 , n0 , Γ0 ),
(3.18)
the first-order conditions for optimal choices of k 0 , b0 , and s then imply Ψc = β(c, `)[1 + R0 ] Ψ0c 1 1−θ 0 [Ψ` − τ w0 Ψ0c ] − [Ψ0` − w0 Ψ0c ]. [Ψ` − wτ Ψc ] = β(c, `)m m0
(3.19)
(3.20)
¯ then utility is time-separable with Ψc = uc and Note that if β(c, `) is a constant, β, Ψ` = u` . 3.4: Wage Determination 15
Wages are determined by Nash bargaining between a matched worker and firm. In such a match, the surplus accruing to the worker’s household can be written wΨ c − Ψ` . The surplus accruing to the firm can be written Fn − w. We assume that the wage solves the following maximization problem, max[wΨc − Ψ` ]λ [Fn − w]1−λ , w
(3.21)
where λ ∈ [0, 1] determines the relative bargaining power of the workers in the negotiation. Solving (3.21) we obtain: w = λFn + (1 − λ)
Ψ` . Ψc
(3.22)
As is standard in matching models, the wage is a weighted average of the marginal value product of labor, Fn , and the household’s reservation wage, Ψ` /Ψc . 3.5: A Recursive Equilibrium We assume that the time paths of the government expenditures, {Gjt }∞ t=0 , and the subsidy rates, τj , j = 1, 2 are exogenously given. For an economy with these characteristics, a recursive equilibrium is a collection (for each country) of policy functions, k 0 (k, b, n, Γ), s(k, b, n, Γ), b0 (k, b, n, Γ), v(n, Γ), and kf (n, Γ); value functions for households and firms, J(k, b, n, Γ) and H(nf , Γ), respectively; pricing functions, r(Γ) and w(Γ); an interest rate R(Γ); and sequence of transfers, {Tjt }∞ t=0 , such that: 1. taking the pricing functions, interest rate, and matching rate, m(·), as given, J(k, b, n, Γ) satisfies the household Bellman equation, (3.17), with k 0 , s, and b0 the associated policy functions. 2. taking the pricing functions, interest rate, and matching rate, µ(·) as given, H(n f , Γ) satisfies the firm Bellman equation, (3.12), with kf and v the associated policy functions. 3. All markets clear. This requires that k = kf = K, n = nf = N , v = V , s = S, b = B. In addition, it requires that the market for international bonds clears: B1 + B 2 = 0 16
(3.23)
and so does the world-wide market for the consumption-investment good: 2 X
[Kj0
+ Cj + G j ] =
j=1
2 X j=1
[1 + R(Γ)]Kj + Fn (Kj , Nj )Nj − pVj .
(3.24)
4. Given the sequences of government expenditures {Gjt }∞ t=0 and search subsidy rates τj , j = 1, 2, the transfers, {Tjt }∞ t=0 , satisfy the two countries’ government budget constraints. 4. Quantitative analysis of the model 4.1: Parametrization The functional form of instantaneous individual utility function for each household in country j is represented by:
u(c, l) =
(1 − l)ρ cσ −ϕ σ ρ
(4.1)
Individual risk aversion parameter σ is set to -2, which give a relative risk aversion 3 that is consistent with estimations in Hansen and Singleton (1993). The base value of ρ is set to 3.5 to obtain a labor supply elasticity = 1/(ρ − 1) = 0.4, which falls in the range in Killingsworth (1983). The value of ϕ is found by matching the steady state of labor force participation, n ¯ + s¯, with the realistic value of around 0.68. As indicated previously, we restrict our attention to a case in which preferences exhibit weak separability in the sense of Shi (1994). Generally there are three cases when the condition (3.2) of weak separability is satisfied: (i) constant rate of time preference, βc = βl = 0; (ii) Epstein-Hynes specification, u constant, uc = ul = 0; (iii) original Uzawa (1968) specification, β = β(u). For calibration purposes we consider Uzawa (1968) type preferences. The functional form of endogenous time preference parameter in country j is given by:
β(c, l) = β(u(c, l)) =
1 1 + ζ u(c, l) + expu(c,l) 17
(4.2)
The parameter value for the time preference coefficient ζ is chosen to match the steady state annual interest rate of approximately 4%. Each firm uses labor and capital as inputs in Cobb-Douglas production function:
y = F (k, n) = Ak γ n1−γ
(4.3)
The capital share, γ, in the production function is set to 0.33. Depreciation is set to 0.025, a widely used value in RBC literature Hansen (1985). Technology parameter, A, is set to 1. Government spending, G, is chosen to be approximately 20% of a steady state output. Parameters related to labor search are selected as follows. First, quarterly rate of transition from employment to unemployment, θ, is set to 0.05 as in Shi and Wen (1999). This value implies that the steady state duration of unemployment of around 1/m(¯ x) = 1.27, which roughly matches the average quarterly unemployment duration in the postwar U.S. data (Layard et al 1991). Second, the unit cost of vacancy posting, p, is chosen to match a steady state unemployment rate s¯/(¯ s+n ¯ ) with the realistic value of approximately 0.05. Third, the base value of elasticity of job vacancies, α, is 0.6 as indicated by Blanchard and Diamond (1989) and the base value for λ is 0.4 as used by Shi and Wen (1999) 1 . The parameter values are summarized in Table 4.1.
1
In the model the number of job matches per search, m, depends on search effort s, and the number of job matches per job vacancy µ, depends on job vacancies v . In household and firm optimization problems this dependency is not taken into account. In general the search equilibrium will not deliver efficient allocations unless these labor market externalities are internalized with specific matching functions and wage bargaining rules. With the Cobb-Douglas matching function these conditions are internalized by a single condition: λ = 1 − α
18
Table 4.1 Base values of parameters Household σ relative risk aversion coefficient ρ elasticity of substitution ζ time preference coefficient ϕ constant term
-2 3.5 -0.14 3.8
A γ δ
Firm Technology parameter 1 Capital share in production function 0.33 Depreciation rate of capital 0.025
θ α λ v
Labor market Labor separation rate Elasticity in job vacancy Nash bargaining power of workers price of a vacancy posting
0.05 0.6 0.4 1.1
4.2: Effects of Unemployment Subsidy in a steady state First, we look at a closed economy that has no access to international bond markets. Table 4.2 summarizes steady state values for employment, search, interest rates, capital and output for different levels of unemployment subsidy τ . Table 4.2 Role of unemployment subsidy in a closed economy Variable n ¯ s¯ s¯/(¯ s+n ¯) ¯ k x ¯ = v¯/¯ s r¯ ¯b y¯ w ¯ rw ¯
employment search unemployment rate capital stock tightness of labor market interest rate foreign bond holdings output wage rate reservation wage
τ = 0.45
τ =0
τ = 0.25
τ = 0.75
.6310 .0331 .0498 6.5922 .9254 .0447 0 1.3794 1.3563 1.2890
.6379 .0238 .0359 6.1163 1.6308 .0489 0 1.3552 1.2841 1.1959
.6356 .0280 .0422 6.2473 1.2348 .0476 0 1.3614 1.3300 1.2570
.6110 .0481 .0730 8.7411 .4689 .0316 0 1.4833 1.5521 1.5079
An increase in unemployment replacement rates increases labor search intensity and decreases employment rate resulting in a steady increase in unemployment rate (tightening 19
of labor market). An increase in search intensity is directly linked to the condition that unemployment benefits are paid only to ones who are actively engaged in labor search. Subsequently, it results in an increase in individual reservation wages. As wages are set by Generalized Nash bargaining between workers and firms, an increase is reservation wage (rw) leads to an increase in wages (here Fn > w > rw). Higher wages, in turn, result in increasing numbers of household members who substitute employment for leisure (fall in n). Furthermore, an increase in wages and unemployment transfers results in higher levels of capital accumulation which stimulates an increase in output (in a closed economy the only savings mechanism for households is investing in domestic capital k). Next we consider what would happen if a closed economy described above opens its capital markets. The calculations for the open economy case are conducted as follows. We consider two identical countries with unemployment benefit rates being the only parameter different between the countries. Two cases are considered: (i) a country (home) with τ h = .45 opens its capital market to a country (foreign) with higher unemployment replacement rate τf = .75 and (ii) home country opens capital markets with a country having lower replacement rate τf = .25. Results are summarized in Table 4.3. Table 4.3 Role of unemployment subsidy in an open economy Variable
Autarky τc = 0.45
n ¯ s¯ s¯/(¯ s+n ¯) ¯ k x ¯ = v¯/¯ s r¯ ¯b y¯ w ¯ rw ¯
.6310 .0331 .0498 6.5922 .9254 .0447 0 1.3794 1.3563 1.2890
Home Foreign Home τh = 0.45 τf = 0.25 τh = 0.45 .6316 .0334 .0502 6.4023 .9128 .0462 .0486 1.3670 1.3408 1.2728
.6349 .0277 .0419 6.4352 1.2520 .0462 -.0486 1.3740 1.3270 1.2499
.6279 .0315 .0478 8.1961 .9942 .0376 -.3322 1.4487 1.4421 1.3780
Foreign τf = 0.75 .6131 .0503 .0758 7.5316 .4378 .0376 .3322 1.4146 1.4690 1.4228
A key difference between open and closed economy is the fact that in an open economy households can buy or sell foreign bonds b. As described previously, high unemployment 20
replacement rates results in higher wages and unemployment transfers. In an open economy, households will channel their savings to buying foreign bonds and domestic capital stock. Therefore, we observe that a country with higher unemployment replacement rates becomes a net buyer of foreign bonds. The amount of foreign bond holdings increase as the difference between unemployment replacement rates increases. The described outflow of capital is a key difference with the autarky case described previously. For a country with high search subsidy, the capital outflow is reflected by a decrease in domestic capital stock k, that has a direct effect on total output. Similarly, changes in domestic labor market in home country depend on the search subsidy in the foreign country after opening of capital markets. Firstly, if a foreign country has lower unemployment replacement rate, employment level and search intensity increases leading to an increase in unemployment rate (comparing to a case when capital is immobile across countries). Thus, in presence of capital movements among two countries the differences in unemployment rates will be more significant than in a case of closed economies. Table 4.4 compares unemployment gaps between the two countries for various levels of τ j . Table 4.4 Unemployment Gap Closed Economies Replacement rates τ1 = .25, τ2 = .45 τ1 = .45, τ2 = .75 τ1 = .25, τ2 = .75
Unemployment rates un1 = .0422, un2 = .0498 un1 = .0498, un2 = .0730 un1 = .0422, un2 = .0730
un1 − un2 -.7576 % -2.3241 % -3.0817 %
Unemployment rates un1 = .0419, un2 = .0502 un1 = .0478, un2 = .0758 un1 = .0401, un2 = .0764
un1 − un2 -.8299 % -2.8067 % -3.6235 %
Open Economies Replacement rates τ1 = .25, τ2 = .45 τ1 = .45, τ2 = .75 τ1 = .25, τ2 = .75
Firstly, it is clear that unemployment gap between two countries increases as differences in unemployment replacement rates become larger. Secondly, the unemployment gap increases as economies open their capital markets. For example, in case one country has τ1 = 0.25 and other one τ2 = 0.75, the gap increases from 3.08% to 3.62%. Thus, we show 21
that even when labor is immobile between the countries, opening of capital markets can affect the labor market structure in two countries. In particular, unemployment rates in two countries that have different unemployment replacement rates diverge after opening of capital markets. 5. Conclusions This paper focused on effects of unemployment replacement rates in an open economy in presence of incomplete capital markets. It is shown that presence of international capital mobility contributes to increase in the unemployment gap arising due to differences in unemployment benefit replacement rates. Moreover, when capital markets are opened, high benefit countries experience both an increase in the unemployment rate and an outflow of capital, and low benefit countries experience both a reduction in the unemployment rate and an inflow of capital. Therefore, it is argued that capital outflows from Europe to the United States throughout the 1980ies have contributed to the persistence in the unemployment gap.
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