Foundations of Modern Macroeconomics B. J. Heijdra & F. van der Ploeg Chapter 7: A Closer Look at the Labour Market

Transcription

1 Foundations of Modern Macroeconomics: Chapter 7 1 Foundations of Modern Macroeconomics B. J. Heijdra & F. van der Ploeg Chapter 7: A Closer Look at the Labour Market

2 Foundations of Modern Macroeconomics: Chapter 7 2 Aims of this lecture To discuss some of the most important stylized facts about the labour market To demonstrate what the standard models are able to explain To look for the direction(s) in which we should look for plausible explanations NOTE: Every serious student of the labour market(s) should consult the book by Layard, Nickell, and Jackman (1991), Unemployment: Macroeconomic Performance and the Labour Market.

3 Foundations of Modern Macroeconomics: Chapter 7 3 Some stylized facts SF1 Unemployment fluctuates over time. See Figures SF2 Unemployment fluctuates more between business cycles than within business cycles. See Figures for long date series for the UK and the US. There is a lot of persistence in the data: Û t = U t 1, (UK, ) (0.039) Û t = U t 1, (US, ) (0.051) SF3 The rise in European unemployment coincides with an enormous increase of long-term unemployment. See Tables In Europe the high unemployment level is not due to an increased probability of losing one s job but rather to a decreased probability of finding a job when unemployed!! (see Chapter 9)

4 Foundations of Modern Macroeconomics: Chapter European Community United States Figure 7.1: Unemployment in the EC and the US

5 Foundations of Modern Macroeconomics: Chapter Sweden 6 4 Japan Figure 7.2: Unemployment in Japan and Sweden

6 Foundations of Modern Macroeconomics: Chapter United Kingdom 4 2 Netherlands Figure 7.3: Unemployment in the UK and The Netherlands

7 Foundations of Modern Macroeconomics: Chapter Figure 7.4: Unemployment in the United Kingdom,

8 Foundations of Modern Macroeconomics: Chapter Figure 7.5: Unemployment in the United States,

9 Foundations of Modern Macroeconomics: Chapter 7 9 Table 7.1. The nature of unemployment Annual Annual Long-term Inflows a Outflows a Unemployment b European Community United States Japan Non-EC Europe c Notes: a: Percentage of source population b: Percentage of total unemployment c: Nordic countries only Source: Bean (1994)

10 Foundations of Modern Macroeconomics: Chapter 7 10 Table 7.2. Unemployment duration by country All Under Over All Under Over 1 year 1 year 1 year 1 year Belgium Denmark France Germany Ireland Italy Netherlands Portugal Spain United Kingdom Australia New Zealand Canada United States Japan Austria Finland Norway Sweden Switzerland Source: Layard, Nickell, and Jackman (1991, p. 6)

11 Foundations of Modern Macroeconomics: Chapter 7 11 SF4 In the very long run unemployment shows no trend. Take the time series representation for unemployment: where U t = α 0 + α 1 U t 1 Ū = α 0 1 α 1, Ū is the long-run unemployment rate [6.21% for the UK]. We can derive the transition speed as follows: U 1 = α 0 + α 1 U 0, U 2 = α 0 + α 1 U 1 = α 0 + α 1 [α 0 + α 1 U 0 ]. U t. = α 0 [ 1 + α1 + α α t 1 1 ] + α t 1 U 0,

12 Foundations of Modern Macroeconomics: Chapter 7 12 we thus find: U t Ū = [ U 0 Ū] α t 1, where U 0 is the unemployment rate in some base year. Experiment: Suppose that the unemployment rate is currently U 0 and the long-run unemployment rate is Ū. How many periods (t H) does it take, for example, before half of the difference (U 0 Ū ) is eliminated? We can use t H (the half life ) as the indicator for the adjustment speed in the system: [ UtH Ū] [ U 0 Ū] α t H 1 = 1 2 α t H 1 = 1 2 [ U0 Ū] t H log α 1 = log 2 t H = log 2 log α 1. For the UK the half life of the adjustment is years!

13 Foundations of Modern Macroeconomics: Chapter 7 13 SF5 Unemployment differs a lot between countries. See Table 7.2 SF6 Few unemployed have chosen themselves to become unemployed SF7 Unemployment differs a lot between age groups, occupations, regions, races and sexes. See Tables So we have quite a lot to explain!!

14 Foundations of Modern Macroeconomics: Chapter 7 14 Table 7.3. Sex and age composition of unemployment Over 25 Under 25 All Men Women Men Women Belgium Denmark France Germany Greece Ireland Italy Netherlands Portugal Spain United Kingdom Australia New Zealand Canada United States Japan Austria Finland Norway Sweden Switzerland 2.4 Source: Layard, Nickell, and Jackman (1991, p. 7)

15 Foundations of Modern Macroeconomics: Chapter 7 15 Table 7.4. The skill composition of unemployment Blue Collar White Collar Australia Canada United Kingdom United States Source: OECD (1994, p. 15)

16 Foundations of Modern Macroeconomics: Chapter 7 16 Some standard models A. Can we explain the difference in unemployment of skill groups? Skilled and unskilled labour in the production function: Y = G(N U,N S, K) = G(N U,N S, 1) F(N U +,N S + ), with F U F/ N U > 0, F S F/ N S > 0, F UU 2 F/ NU 2 F SS 2 F/ NS 2 < 0 < 0, and Representative firm chooses two types of labour: max Π PF(N U,N S ) W U N U W S N S, {N U,N S } where the respective wage rates are W U and W S.

17 Foundations of Modern Macroeconomics: Chapter 7 17 The usual marginal productivity conditions are obtained: F U (N U,N S ) = W U P w U F S (N U,N S ) = W S P w S With our usual trick we find the demands for the two types of labour: dn S dn U = ( 1 F SS F UU F 2 SU ) F UU F SU F SU F SS dw S dw U

18 we find: Foundations of Modern Macroeconomics: Chapter 7 18 N D S N D U = N D S (w S,w U? ) = N D U (w S?,w U ) If F SU < 0 then the cross effects are positive [skilled and unskilled labour gross substitutes] Supply curves of the two types of labour are both assumed to be inelastic: N S S = N S N S U = N U

19 Foundations of Modern Macroeconomics: Chapter 7 19 See Figure 7.6 for a graphical representation. Punchlines: with flexible wages, both types are fully employed [equilibrium skill premium, (w S /w U ) ] with a binding, skill-independent, minimum wage w the unskilled will experience unemployment [not unlike Classical unemployment discussed in Chapter 5]. How to cure it? abolish minimum wage [incomes distribution problems] subsidize unskilled work [ Melkert jobs ] let government hire unskilled workers [ dead end jobs ] train unskilled workers to become skilled [investment in human capital may pay for itself] So this standard model has sensible predictions.

20 Foundations of Modern Macroeconomics: Chapter 7 20 w S w S 1 w S *! E 1 S! E 0 S w - w -!! A - N S D N S (w S,w) - D N S (w S,w* U ) N S w U w U * E 1 U E 0 U!! - N U B D 1 N U (w S,w U ) D * N U (w S,w U ) N U Figure 7.6: Skilled and Unskilled Labour

21 Foundations of Modern Macroeconomics: Chapter 7 21 B. Can changes in the tax system explain the difference in unemployment [over time and across countries]? Single type of labour (as in Chapter 1) Short-run (capital constant) Representative firm chooses employment (and thus output): Π PF(N, K) W(1 + t E )N, where t E is the payroll tax [a tax on the use of labour levied on employers, e.g. employer s contribution to social security]

22 Foundations of Modern Macroeconomics: Chapter 7 22 The first-order condition, F N (N D, K) = w(1 + t E ) can be loglinearized: [ ] Ñ D = ǫ D w + t E, w W/P is the gross real wage, ǫ D F N /(NF NN ) is the absolute value of the labour demand elasticity, Ñ D dn D /N D, t E dt E /(1 + t E ), and w dw/w The representative household chooses consumption and leisure just as in Chapter 1 but faces some extra taxes. The utility function and budget equation are: U = U(C, 1 N S ), P(1 + t C )C = WN S T(WN S ) (1 t A )WN S, where T(WN S ) is the tax function and t A T(WN S )/(WN S ) is the average tax rate

23 Foundations of Modern Macroeconomics: Chapter 7 23 The tax system is progressive, i.e. the average tax rises with income and the marginal tax rate is denoted by: t M dt(wns ) d (WN S ) = T Note: t M is either constant (if T = 0) or increasing (if T > 0). The household takes the tax progressivity into account when deciding on consumption and labour supply. The Lagrangian is: L U(C, 1 N S ) + λ [ (1 t A )WN S P(1 + t C )C ], the first-order conditions: L C = U C λp(1 + t C ) = 0 [ ( L N = U S 1 N + λw (1 t A ) N S dta dn S )] = 0

24 Foundations of Modern Macroeconomics: Chapter 7 24 Simplifying the first-order conditions we obtain: U C λ = P(1 + t C ) = U 1 N W(1 t M ) ( ) U 1 N 1 tm = w U C 1 + t C (A) The marginal rate of substitution between consumption and leisure is affected the marginal tax rate t M on labour income [not the average tax rate] The tax on consumption affects the MRS just as if it was a tax on labour income Eq. (A) and the household budget constraint, P(1 + t E )C = (1 t A )WN S, together determine C and N S. In loglinearized form we get for labour supply [see Ch. 7 for further details]:

25 Foundations of Modern Macroeconomics: Chapter 7 25 Ñ S = (1 N S ) [ (σ CM 1) w σ CM ( t M + t C ) + t A + t C ] = ǫ SW [ w t M t C ] + ǫsi [ t A + t C w ] = ǫ SW [ w t C ] ǫsw t M + ǫ SI t A, where ÑS dn S /N S, t C dt C /(1 + t C ), t M dt M /(1 t M ), and t A dt A /(1 t A ). We now have quantitative handles: (a) ǫ SW σ CM (1 N S ) 0 is the compensated wage elasticity [corresponds to the substitution effect and is always non-negative] (b) ǫ SI (1 N S ) < 0 is the income elasticity [corresponds to the income effect and is always negative] (c) ǫ SW ǫ SW ǫ SI = (σ CM 1)(1 N S ) is the uncompensated wage elasticity [the total effect of a change in the gross wage]. Total effect of a wage change is positive (zero, negative) if σ CM > 1 (= 1,< 1)

26 Foundations of Modern Macroeconomics: Chapter 7 26 Summary of out labour market model with tax effects: Ñ D = ǫ D [ w + t E ] (labour demand) Ñ S = ǫ SW [ w t C ] ǫsw t M + ǫ SI t A (labour supply) we can complete [or close ] the model in two ways: (a) Equilibrium interpretation, N = N D = N S, or: Ñ = ÑD = ÑS (flexible wage) (b) Disequilibrium interpretation, N = MIN[N D,N S ] = N D, say because the consumer wage [w C w(1 t A )/(1 + t C )] is inflexible

27 Foundations of Modern Macroeconomics: Chapter 7 27 (a) Taxes and the labour market: flexible wages See Figure 7.7 for the graphical illustration [Table 7.5 contains the analytical results] More progressive tax system [ t M > 0 only]: shifts labour supply to the left [pure substitution effect], so that w and N Higher average tax rate [ t A > 0 only]: shifts labour supply to the right [income effect], so that w and N Higher payroll tax [ t E > 0 only]: shifts labour demand to the left, so that w and (provided ǫ SW > 0) N [Try to draw opposite case also!] Higher consumption tax: [ t C > 0 only]: shifts labour supply to the left if ǫ SW > 0, so that w and N [Try to draw opposite case also!]

28 Foundations of Modern Macroeconomics: Chapter 7 28 w N 1 S N 0 S E 1! N 2 S B! E 0!! A D!! E 2 C! N D N Figure 7.7: Taxes and a Clearing Labour Market

29 Foundations of Modern Macroeconomics: Chapter 7 29 Table 7.5. Taxes and the competitive labour market (a) Flexible wage (b) Fixed consumer wage w Ñ du w Ñ du t M ǫ SW ǫ SW +ǫ D ǫ D ǫ SW ǫ SW +ǫ D ǫ SW t A ǫ SI ǫ SW +ǫ D ǫ D ǫ SI ǫ SW +ǫ D 0 1 ǫ D ǫ SW + ǫ D t M = t A ǫ SW ǫ SW +ǫ D ǫ Dǫ SW ǫ SW +ǫ D 0 1 ǫ D ǫ D t E ǫ D ǫ SW +ǫ D ǫ Dǫ SW ǫ SW +ǫ D 0 0 ǫ D ǫ D t C ǫ SW ǫ SW +ǫ D ǫ Dǫ SW ǫ SW +ǫ D 0 1 ǫ D ǫ D w C 1 ǫ D ǫ SW + ǫ D

30 Foundations of Modern Macroeconomics: Chapter 7 30 (b) Taxes and the labour market: rigid consumer wage Suppose that workers have an aversion against reductions in their real consumer wage, i.e. w C w(1 t A )/(1 + t C ), is inflexible downward! In loglinearized form we have: w C w t A t C (A) Substituting (A) into the demand and supply functions yields: Ñ D = ǫ D [ wc + t A + t E + t C ] Ñ S = ǫ SW w C + ǫ SW [ t A t M ] we have approximately that the change in the unemployment rate is: du = ÑS ÑD

31 Foundations of Modern Macroeconomics: Chapter 7 31 ( ) NOTE: U NS N D = 1 ND N log S N S N S N D so that du = ÑS ÑD. Workings of the disequilibrium model are illustrated in Figure 7.8. [Table 7.5 contains the analytical results]. We see that taxes work differently now. More progressive tax system [ t M > 0 only]: shifts labour supply to the left [pure substitution effect], so that w C and N constant but unemployment down Higher average tax rate [ t A > 0 only]: shifts labour supply to the right [income effect] and shifts labour demand to the left. Hence, w C constant but N Higher payroll tax [ t E > 0 only]: shifts labour demand to the left; w C constant but N (regardless of sign of ǫ SW ) Higher consumption tax: [ t C > 0 only]: shifts labour demand to the left; w C constant but N (regardless of sign of ǫ SW )

32 Foundations of Modern Macroeconomics: Chapter 7 32 w C N 1 S N 0 S - w C E 0 B!!! A N D N Figure 7.8: Taxes and a Fixed Consumer Wage

33 Foundations of Modern Macroeconomics: Chapter 7 33 Conclusion based on Standard models Models with flexible wage(s) hard to bring in line with the real world (e.g. empirical studies suggest that σ CM 1 to that ǫ SW 0: almost vertical uncompensated labour supply curve). The facts suggest that the macroeconomic wage equation is almost horizontal (even though the microeconomic labour supply is almost vertical). See Figure 7.9 Hence, we desperately need a theory of real wage rigidity [one of the Holy Grails of modern macroeconomics]

34 Foundations of Modern Macroeconomics: Chapter 7 34 w N S macro wage equation + _ N D N Figure 7.9: The Macroeconomic Wage Equation

35 Foundations of Modern Macroeconomics: Chapter 7 35 The Theory of Efficiency Wages Basic idea: worker productivity depends positively on the wage that he/she receives Possible reasons for this effect are: link between productivity and nutrition labour turnover and training costs high wage to attract the best workers high wage to limit shirking fair wage hypothesis The effort exerted by a worker may be S-shaped as in Figure 7.10

36 Foundations of Modern Macroeconomics: Chapter 7 36 E i E 0! B! E i =e(w i,w R ) A! W i A W i * W i B W i Figure 7.10: Efficiency Wages

37 Foundations of Modern Macroeconomics: Chapter 7 37 A simple model of efficiency wages Effort function: E i e(w i,w R ), e W > 0, e WR < 0, + where E i is the effort of a worker in firm i, W i is the wage paid by firm i to its workers, and W R is the reservation wage [the wage that can be obtained elsewhere in the economy] Profit of firm i is defined as: Π i P i AF(E i N i }{{} L i ) W i N i, (1) where P i is the price of firm i, A is a general productivity index, and L i represents the effective labour units employed in firm i [dimension: bodies effort per body]

38 Foundations of Modern Macroeconomics: Chapter 7 38 Firm chooses N i and W i [the latter to control effort]. First-order conditions: Π i N i = P i AE i F L (E i N i ) W i = 0 (#) Π i W i = P i AN i F L (E i N i )e W (W i,w R ) N i = 0 By combining these conditions we get the Solow condition: W i e W (W i,w R ) e(w i,w R ) = 1 (*) Hence, the firm picks the wage W i for which the elasticity of the effort function equals unity. In terms of Figure 7.10, points A and B are no good but point E 0 is just right Once W i and thus via the effort function E i are known, equation (#) determines the number of workers, N i

39 Foundations of Modern Macroeconomics: Chapter 7 39 Major result already: The firm chooses (W i,e i,n i ) but there is no reason to believe that all firms taken together will demand enough labour to employ all workers! The wage does not clear the market but instead is a motivating device. Unemployment will probably exist!!! We close the model with an expression for the reservation wage: W R = (1 U) W + UB = W [1 U + βu], where U is the unemployment rate, W is the average wage paid in the economy, and β B/ W is the unemployment benefit expressed as a proportion of the average wage paid in the economy (the so-called replacement rate).

40 Foundations of Modern Macroeconomics: Chapter 7 40 Finally, we adopt a specific effort function to keep things simple: E i = (W i W R ) ǫ, 0 < ǫ < 1, where ǫ measures the strength of the productivity-enhancing effects of high wages, which we call the leap-frogging effect. For this effort function we can apply the Solow condition: W i E i E i W ( ) i Wi W R W i = 1 = ǫ W i = W R 1 ǫ. Hence, the firm pays a markup 1 1 ε times the reservation wage!!

41 Foundations of Modern Macroeconomics: Chapter 7 41 But all firms are assumed to be the same so that they all set the same wage so that W i = W. This implies: W i = W = W R 1 ǫ = W(1 U + βu) 1 ǫ U ǫ = 1 β. Hence, there is indeed a positive equilibrium unemployment as we thought there would be. U is higher the higher is ǫ and the higher is β. The intuition can be understood with Figure 7.11 W i W W i W = 1 (1 β)u 1 ǫ (RW curve) = 1 (EE curve) The RW curve slopes down because, as U is high there is a strong threat of unemployment. This means there is less reason to pay high wages.

42 Foundations of Modern Macroeconomics: Chapter 7 42 W i /W -! E 0 E 1!! EE RW 1 RW 0 U Figure 7.11: Relative Wages and Unemployment

43 Foundations of Modern Macroeconomics: Chapter 7 43 **** Self test **** Study the effects of taxation on unemployment and wages for the efficiency wage model. One interesting result is that increasing the progressivity of the tax system leads to a reduction of the equilibrium unemployment rate! There is less scope for leap frogging by firms. Wages fall and employment rises. ****

44 Punchlines Foundations of Modern Macroeconomics: Chapter 7 44 We have stated some stylized facts about the labour market Standard models can explain a lot There is a tension between micro- and macroeconomic evidence regarding the labour supply elasticity The efficiency wage theory has some very attractive features in removing this tension Taxes affect the labour market no matter what theory you use [the direction of the effects depends on the details]