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6. On unemployment and real wages in the long-run In this chapter, we would like to address two questions. Firstly, how is the unemployment rate determined in the long-run? The long-run rate of unemployment is often called the natural rate of unemployment. Secondly, how is the determination of real wages related to the natural rate of unemployment? For the second question, neo-classical and Keynesian macroeconomists prepare completely opposite answers. The former claims that real wages are increasing in the natural rate of unemployment, while the latter asserts that they are decreasing. An answer for the second question also forms a basis for the aggregate supply relation.

6.1. Unemployment rates and the flows of workers Let us begin with the definition of the unemployment rate. The potential candidates for workers may be the population of age 15 or older. It is divided into those in the labor force and those out of the labor force. The latter includes full-time students, houseworkers, and retirees. The labor force, denoted by L , is further divided into those employed ( E ) and those unemployed ( U ). The unemployment rate, denoted by u , is defined as the ratio of those unemployed to those in the labor force, or = u

U U . = L U +E

A difficult part is the definition of the unemployment status. Its definition differs substantially among countries. According to the Labor Force Survey in Japan, those who are employed on either day of the last week of each month (the survey week) are classified as ‘employed’. On the other hand, those who are unemployed on any day of the survey week and are looking for a job are classified as ‘unemployed’. A job search activity is verified by at least once-a-month visit to either of the public placement offices. In the U.S., those who are unemployed at the time of the interview, and have been looking for a job in the last four weeks are classified as ‘unemployed’. Given this definition, a person who do not have a job at the time of the interview, and stopped job search two months ago is classified as ‘out of the labor force’. Let us move to take a careful look at the labor market statistics of the

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Japanese economy. In March 2016, as reported below, the size of the population of age 15 or older amounted to 108.4 million. Out of 108.4 million, 63.8 million participated in labor markets as the labor force. Out of 63.8 million, 61.7 million were employed, but 2.1 million were unemployed. Thus, the unemployment rate was 3.3% (= 2.1/63.8) as of March 2016. ---------------------------------------------------------------------------------Those 15 years old or older: 108.44 million The labor force: 63.80 million Those employed (including self- or family-employed): 61.70 million Those employed (excluding self- or family-employed): 55.37 million Those unemployed: 2.10 million Those out of the labor force: 44.58 million School attending 6.59 million Housework 15.41 million Others 22.58 million Unclassified 0.06 million --------------------------------------------------------------------------------As shown in Figure 6-1, the unemployment rate of March 2016, 3.3% is relatively low in the recent trend, but is still high in the long-run trend. The unemployment rate decreased from well above 2% to 1% in the 1950s and

3 Figure 6-2: Average monthly flows of workers in U.S. from 1994 to 2011 (unit: million)

Employment 132.4

1.8 (1.36%)

3.3 (4.50%) 3.6 (2.72%)

2.1 (25.0%)

Unemployment 8.4

1.8 (2.46%)

1.9 (22.62%)

Out of the labor force 73.3

1960s, but it increased from 1% to just below 3% by the mid-1980s. After a mild decline in the latter half of the 1980s, the unemployment rate resumed increasing from 2% to 5% by the early 2000s. Since then, it fell sharply, rose noticeably, and fell fast again. Behind such a heavy movement of the unemployment rate, there have been large flows of workers among the employment statuses, employed, unemployed, and out of the labor force. The labor market statistics record the constant flows of workers in detail month by month. Figure 6-2 (6-3) Figure 6-3: Average monthly flows of workers in Japan from 2000 to 2015 (unit: million)

Employment 62.367

0.347 (0.56%)

0.820 (1.91%)

0.340 (11.58%)

Unemployment 2.937

0.287 (0.67%)

0.327 (11.14%)

0.874 (1.40%)

Out of the labor force 42.94

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reports the monthly average flows of workers among the three pools, employment, unemployment, and out of the labor force, for the period from 1994 to 2011 (from 2000 to 2015) in the U.S. (Japan). Before comparing between the U.S. and Japan, I would like to propose one convenient way to interpret those figures. A part of those in one of the three pools move to either of the other two pools. Using the Japan’s case, out of 2.937 million in the unemployment pool, 0.340 million moved to the employment pool, and 0.327 million to the out of the labor force pool. Accordingly, 22.72% ((0.340+0.327)/2.937) of those unemployed moved to either of the other pools. Suppose that one quarter (25%) of the unemployment pool moved to either the employment pool or the out of the labor force pool. I here claim that an inverse of 25% or four months corresponds to the average duration of the unemployment pool. You may want to think it as follows. In the first month, one quarter move out of the unemployment pool. Then, another quarter in the second month, another one quarter in the third month, and the final quarter eventually move out of it in the fourth month. That is, the entire employment pool has now been replaced completely in four months. In this way, if the ratio is 10% instead of 25%, the average duration is an inverse of 10% or 10 months, 5 months for 20%, and 2 months for 50%. Given the above interpretation, the average duration of the employment pool was 24.5 months in the U.S. and 51.0 months in Japan, that of the unemployment pool was 2.1 months and 4.4 months, and that of the out of the labor force pool was 14.4 months and 38.8 months respectively. For either of the three pools, the average duration was shorter in the U.S. than in Japan. It suggests that in comparison with the U.S., Japanese workers move less actively among the three pools, and tend to stay longer in either pool.

6.2. A simple model of workers’ flows Let us model the large flows of workers under three simplifying assumptions. Firstly, we pay attention to only the flows of workers between the employment and the unemployment pools. Secondly, the size of the labor force ( L ) is assumed to be constant, while the size of either of the two pools ( E or U ) may vary over time.

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L = Et + U t The third assumption concerns constancy of the job separation rate s and the job finding rate f . The job separation rate represents the proportion of unemployed workers who find a job each month, while the job finding rate represents the proportion of workers who are separated from their current jobs each month. We begin with finding the long run rate of unemployment in the sense that the rate never changes any more. The rate is often called the natural rate of unemployment u * . At the natural rate of unemployment, the labor flow from the employment to the unemployment pools is exactly equal to the * opposite flow. That is, fU * = sE * or fU = s ( L − U * ) . Using the definition of

the unemployment rate u * =

U* and the constant labor force E *= L − U * , we L

obtain:

 U*  U* f = s 1 −  L L  

* or fu= s (1 − u * )

(6-1)

Thus, solving equation (6-1) for u * leads to the natural rate of unemployment as follows. u* =

s s+ f

(6-2)

Now, we move to consider the dynamic process in which the unemployment rate converges to the natural rate. A change in the size of unemployment is characterized as

∆U t +1 = U t +1 − U t = sEt − fU t . Using the

definition of the unemployment rate, it is rewritten as ∆ut +1 =− s ut ( s + f )  s  = − ut  (s + f ) s+ f 

(6-3)

= ( s + f ) ( u* − ut )

As equation (6-3) implies, if ut < u * , then ut goes up toward u * , otherwise it goes down to u * . Thus, the unemployment rate ut eventually reaches the natural rate u * . Let us interpret real world data along equation (6-3). A marked departure from a standard model like equation (6-3) is that the separation

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rate and the finding rate are no longer constant. As shown in Figure 6-4, both rates change noticeably for the period from 2000 to 2015 in the Japanese labor markets; in this figure, the one-year moving averages of both rates are adopted to remove seasonal components. The data are not available for the period from March to August 2011 due to the Great East Japan Earthquake.

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Using these one-year moving averages of the separation and the finding rates, we compute the natural rate of unemployment by a modified version of equation (6-2) or ut* =

st . Figure 6-5 depicts the actual rate and the st + ft

natural rate of unemployment. There are four periods when both rates differed substantially. For the early 2000s, the actual rate of unemployment was quite high, but it was still much lower than the natural rate. It implies that there was a strong upward pressure on the unemployment rate. In the early 2000s, the Japanese labor market was indeed subject most severely to too weak demand and too much supply. In 2006 and 2007, on the other hand, the actual rate was quite low, and it was even lower than the natural rate. In 2009, on the contrary, the actual rate rose sharply, and it was even beyond the natural rate. In 2014, the actual rate was again below the natural rate. A contrast between 2006/2007 and 2009, and the behavior of 2014 indicate that the actual rate swung more than the natural rate did.

6.3. Vacancies and unemployment Another frequently cited measure of labor markets is the vacancy rate, which is as important as the unemployment rate. The rate v is defined by the ratio of the number of job openings or vacancies (unfilled jobs) V to the size of the labor force L ( v =

V ). The ratio of the vacancy rate to the L

unemployment rate is called the opening-to-application rate or the O/A rate ( o / a=

v V L V ). Precisely, the number of those unemployed differs from = = u U L U

that of job applicants because a definition is different from each other. Figure 6-6 depicts the time series of the O/A rate for the period from 1963 to 2015. By construction, as the unemployment rate is low, the O/A rate is high. However, the relative ratio between the vacancy rate and the unemployment rate tells a little more about labor market performance. If the O/A rate is greater than one, then the number of vacancies exceeds the number of applicants, and labor demand is particularly strong. The O/A ratio

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was above one from the late 1960s to the early 1970s, from the late 1980s to the early 1990s, in the mid-2000s, and in the mid-2010s. The job finding rate f is obviously increasing in the O/A rate. Let us formulate the finding rate by

η

v f = ε   , where ε > 0 and 0 < η < 1 . Both u

parameters, ε and η , represents the efficiency of job matching between vacancies and applicants. Using equation (6-2), the natural rate of unemployment can be written as follows. u* =

s η

 v  s +ε  *  u 

(6-4)

The job separation rate s is still treated as constant. ∂u * From equation (6-4), it is easy to prove < 0 . That is, the natural rate ∂v of unemployment is decreasing in the vacancy rate. This theoretical result is quite intuitive; more unemployed workers can find jobs with more vacancies. Another important implication of equation (6-4), given an improvement of the job matching efficiency (an increase in either unemployment rate is lowered.

ε

or

η ), the

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According to the above implications, on the space of the unemployment rate as a vertical axis and the vacancy rate as a horizontal axis, we have a downward relation, the so-called UV curve or the Beveridge curve which is taken after an English economist William Beveridge. In addition, the downward sloping UV curve moves toward (away from) the origin as the job matching efficiency improves (deteriorates). As shown in Figure 6-7, we can observe the above implications for the Japanese labor market between 1970 and 2015. For the period from 1970 to 1995, the downward sloping UV curve indeed emerges. In the latter half of the 1990s, the UV curve moves upward; the matching efficiency might have deteriorated during the corresponding period. The UV curve is again downward sloping in the 2000s and the 2010s.

6.4. Real wages and unemployment: Neo-classical versus Keynesian 6.4.1. A neo-classical model We have so far discussed how the unemployment rate is determined in the long-run. We will now explore how the determination of real wages is related to the long-run or natural rate of unemployment. There have been quite contrasting views on this issue in a history of macroeconomic thought.

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At a debate between two groups, neo-classical economists claim that real wages are increasing in the natural rate of unemployment, while Keynesians argue that they are not increasing, but decreasing in the actual unemployment rate. Let us begin with a neo-classical case. A production function is

Y = F ( N ) , where Y is real GDP, and N is labor input. The marginal productivity of labor F ′ ( N ) is diminishing; that is, F ′ ( N ) > 0 and F ′′ ( N ) < 0 . In a competitive market, labor demand is determined by a typical condition, or equality between the marginal productivity of labor and real wages

w , where w is nominal wages and p is a price level. p w = F′( N ) p

(6-5)

On the other hand, labor supply is determined by the labor force minus the natural level of unemployment. As shown in Figure 6-8, given a downward sloping labor demand F ′ ( N ) , real wages are increasing in the natural level of unemployment. This result also indicates that real wages are Figure 6-8: Real wage determination: A neo-classical case Real wage (

)

Natural unemployment (

)

Employment ( N ) Labor force ( L )

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counter-cyclical; they are high in recessions (high unemployment rates) and low in booms (low unemployment rates). In this way, the diminishing marginal productivity of labor is responsible for counter-cyclical movements of real wages.

6.4.2. A Keynesian model: A counter-cyclical markup Based on one empirical finding that real wages are not counter-cyclical, but pro-cyclical, Keynesians have been against the above proposition made by neo-classical macroeconomists. They also have paid serious attention to another empirical finding that the markup is counter-cyclical. In a monopolistic goods market, a firm charges a margin over the marginal nominal cost of producing one unit of goods, thereby setting the

nominal price of her own goods p . Here, the markup m is defined as the price over the cost. Let us compute the marginal nominal cost of producing one unit of goods. In our setup, the cost consists only of labor input. By definition, the marginal productivity of labor F ′ ( N ) is the number of units of goods produced by

Figure 6-9: Real wage determination: A Keynesian case (1) Real wage (

)

Natural unemployment Employment ( N ) Labor force ( L )

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another unit of labor input. Thus, its inverse

1 represents how many F′( N )

units of labor are required to produce another unit of goods. Thus, the marginal nominal cost of labor is the required units of labor times nominal wages, or

w . F′( N )

Then, a monopolistic firm sets the price higher than the marginal cost by the markup m as follows:

= p

w (1 + m ) F′( N )

(6-6)

Equation (6-6) can be rearranged as

w F′( N ) = p 1+ m

(6-7)

As implied by equation (6-7), if the markup is zero, then real wages reduce to those determined in a competitive market. Given the positive markup, labor demand shifts downward as shown in Figure 6-9. For the moment, the neo-classical implication still survives; real wages are increasing in the natural unemployment rate. Now we introduce the counter-cyclical markup; the markup is high in recessions and low in booms. For this purpose, we assume that the markup Figure 6-10: Real wage determination: A Keynesian case (2) Real wage (

)

Unemployment Employment ( N ) Labor force ( L )

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is zero at the full employment level, and that the markup is decreasing in employment and increasing in unemployment.

m ( L) = 0

(6-8)

m′ ( N )= m′ ( L − U ) < 0

(6-9)

Given the above varying markup, labor demand is switched to

F′( N ) w = . If the markup is counter-cyclical enough, and a tiny increase in p 1 + m( N ) unemployment leads to a considerable increase in the markup, then real wages are discounted more heavily from F ′ ( N ) by m ( L − U ) . The higher unemployment is, the heavier discounting is. As shown in Figure 6-10, accordingly labor demand is not downward, but upward sloping if unemployment exceeds a certain level. Thus, real wages are decreasing in the unemployment rate except for the neighborhood of full employment (zero unemployment). In this way, the effect of the diminishing marginal productivity of labor is cancelled out by that of the counter-cyclical markup; then, we have pro-cyclical real wages.

6.4.3. A Keynesian model: A pro-cyclical wage bargaining Keynesians propose an alternative story for pro-cyclical real wages. For simplicity, suppose that real GDP is linear in labor input. The marginal productivity of labor is constant at α . (6-10)

Y =αN

Given the constant markup, a monopolistic firm sets the price of her own goods according to = p

w

α

(1 + m )

as a special case of equation (6-6). Then, real

wages should be determined by w α . = p 1+ m

(6-11)

Let us introduce as another element the wage bargaining process. That is, real wages are determined as a consequence of bargaining between

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Figure 6-11: Real wage determination: A Keynesian case (3) Real wage (

)

Natural unemployment Employment ( N ) Labor force ( L )

employers and employees. More specifically, as the unemployment rate increases, the bargaining power shift from employees to employers, and real wages are determined at a lower level. Conversely, as the unemployment rate decreases, more bargaining power on the side of employees results in higher real wages. Thus, the wage determination function is characterized as w = G (= N ) G ( L − U ) , where G′ ( N ) > 0 . p

(6-12)

At a full-employment level ( U = 0 or N = L ), real wages reduce to a competitive market level or the constant marginal productivity of labor α .

G ( L) = α

(6-13)

In the above setup, real wages and the natural rate of unemployment are jointly determined such that equations (6-11) and (6-12) may be satisfied simultaneously. As shown in Figure 6-11, real wages are again decreasing in the natural rate of unemployment in the above case. Another important aspect of the above model is that a monopolistic behavior on the firms’ side is responsible for the positive natural rate of unemployment. As the markup, which indicates the degree of monopolistic power, goes up, long-run real wages go down and the natural rate of unemployment goes up.

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At this moment, we would like to draw a clear distinction between the potential output Yp and the full-employment output Y f , both of which are often confused as equivalent to each other. A full-employment output is the output which is achieved when the entire labor force is employed or N = L . That is, Y f = α L . A potential output is, on the other hand, the output which is attained when unemployment is natural ( U = U n ) or employment is potential ( N= N p= L − U n ). Thus, Yp = α N n . Given the positive natural unemployment, the potential output is lower than the full-employment output, or Yp =α ( L − U n ) =Y f − αU n < Y f .

6.5. Real wages and unemployment: Two kinds of empirical findings… Let us take a casual look at the Japanese labor market statistics. Figure 6-12 depicts the time series of the real wage index of manufacturing sectors and the actual rate of unemployment rate. Up to 2011, real wages seem procyclical; real wages and the unemployment rate tended to move in opposite directions. However, real wages look counter-cyclical from 2012; real wages tended to decrease with the unemployment rate. As shown in Figure 6-13, when the real wage index is scattered against the unemployment rate for the period between 2002 and 2011, there emerges

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a pro-cyclical pattern; real wages are high with low unemployment rates. As shown in Figure 6-14, on the other hand, when the same graph is constructed for the period from 2012 to 2016, there emerges a counter-cyclical pattern; real wages are high with high unemployment rates. Though the above empirical examination is not necessarily rigorous, both neo-classical and Keynesian cases may be embodied in the Japanese labor market.