Intermediate Macroeconomics

Transcription

1 Intermediate Macroeconomics Lecture 6 - Capital Utilisation and Unemployment Zsófia L. Bárány Sciences Po 2011 October 12

2 Preview of today s lecture Last week: baseline business cycle model in response to a temporary increase in A demand for capital and labour increases capital fixed real rental rate increases both labour input and real wages increase mild pro-cyclical movement in consumption and large pro-cyclical movement in investment This week: extend the business cycle model more realistic treatment of resource markets 1. allow for a variable capacity utilisation of capital 2. allow for frictions in the labour market introduce unemployment

3 Variable capital utilisation until now: assume that 100% of capital is used at all times now: extend microeconomic foundations allow for a variable capital utilisation variable supply of capital services what does variable capital utilisation mean? the stock of capital, for example number of machines, is fixed full capacity utilisation means that all these machines are used, say 8 hours a day, 5 days a week, 52 weeks a year, so 2080 hours per year in practice: use of machines varies, sometimes there might be two 8 hour shifts, so the machine is used 16 hours a day, or there might just be a 6 hour shift

4 K - stock of capital κ - represents the capital utilisation rate κk is the flow of capital services final output is Y = A F (κk, L) if κ increases, then Y increases for a given technology level, A, capital stock K, and labour input, L

5 Demand for capital services I. Firms maximise profits by choosing how much capital and labour to hire: π P = A F ((κk)d, L d ) w P Ld R P (κk)d optimum: the demand for capital services, (κk) d such that: MPK = R P if A increases at a given real rental rate, the demand for capital services increases before: capital supply K s is fixed the rental rate has to increase now: capital supply is flexible

6 Demand for capital services II.

7 Demand for capital services III.

8 Supply of capital services I. the owners of the capital stock might decide to supply more or less capital services by year by varying κ why would anyone wish to supply less than the maximum they can? increases in κ tend to increase the depreciation rate 1. more intensive use leads to the capital wearing off faster 2. as κ rises, there is less time left for maintenance the depreciation rate is an increasing function of κ: δ = δ(κ)

9 Supply of capital services II. the owners of the capital stock maximise their net real income from renting capital services by choosing κ, while taking the rental price, R P, as given R P κk δ(κ)k = K[R P κ δ(κ)] their net rate of return on capital is then: R P κ δ(κ) the net real rental price is maximised where R P = δ (κ) if the function δ( ) is well behaved (increasing, convex, differentiable)

10 Supply of capital services III.

11 Supply of capital services IV.

12 Supply of capital services V. an increase in A increases the real rental price of capital which raises the capital utilization rate, since the higher real rental price makes it worthwhile to raise κ despite the resulting increase in the depreciation rate, δ(κ) the technology level A does not have a direct impact on the supply of capital services the supply of capital services is an upward sloping function of the real rental rate

13 Clearing of the capital market I.

14 Clearing of the capital market II. when the technology level rises to A the demand curve for capital services shifts to the right while the supply curve does not shift the market clears at the higher real rental price, R P, and the larger quantity of capital services, κ the interest rate is still given by : i = R P κ δ(κ) the increase in the technology level, A, raises the rate of return from owning capital, the interest rate, i, increases the interest rate is still pro-cyclical in the model

15 Effect on the GDP A change in A affects the GDP through three channels: 1. a high or low technology level, A, causes real GDP to be correspondingly high or low 2. a high or low A causes the labour input L to be correspondingly high or low 3. a high or low A causes the capital utilization rate, κ, and, thereby, the quantity of capital services, κk, to be correspondingly high or low

16 The cyclical behaviour of capacity utilisation in the data

17 The labour force, employment and unemployment in the data the labour input is strongly pro-cyclical: when measured as total hours worked the correlation of the cyclical part with the cyclical part of GDP is 0.88 last week we allowed for a variable labour supply: economic booms lead to higher real wage rates people reacted by supplying more labour however, we did not specify whether the increased labour input is a result of 1. an increase in the labour force 2. an increase in the employment rate 3. an increase in hours worked per worker

18 Market clearing... in the model the real wage rate adjust to equate the quantity of labour supplied to the quantity of labour demanded the market clearing employment, L, equals the labour supplied, L s, and the market clearing employment, L, equals the labour demanded, L d... in the real world the labour force is always greater than employment, the difference is the number of people unemployed the number of jobs the employers want filled is always greater than employment, the difference is the number of job vacancies

19 Some basic concepts unemployment rate u = number of unemployed labour force = labour force - number of employed labour force = 1 number of employed labour force = 1 v employment rate v = number of employed labour force = labour force - number of unemployed labour force = 1 vacancy rate number of unemployed labour force = 1 u number of vacancies number of jobs the employers want occupied

20 Cyclical behaviour of US real GDP and labour force

21 Cyclical behaviour of US real GDP and employment rate

22 Cyclical behaviour of US real GDP and average weekly hours

23 Why extend the baseline model? the equilibrium business cycle model is probably satisfactory for understanding fluctuations in the labour force and hours worked per worker the real wage rate, w P, adjusts to equate the quantity of labour supplied, L s, to the quantity demanded, L d however, this approach leaves unexplained one of the most important factors: the fluctuations in the employment rate or, equivalently, in the unemployment rate to understand unemployment and vacancies we have to introduce some friction into the workings of the labour market why does it take people some time to find a job? why does it take business some time to fill vacancies?

24 A model of job finding I. think about a person looking for a job applies to firms, the firms interview her and potentially offer a job with a wage w P assume, for simplicity, that jobs only differ in the wage rate, which is based on what the firm thinks her marginal product is the person then decides 1. take the job and earn w P 2. remain unemployed, receive an unemployment benefit (ω) and continue searching rejecting the job offer is only worth it, if it is likely that a higher wage offer will come along when making this decision, one has to think about the distribution of likely wage offers

25 Distribution of real wage offers

26 A model of job finding I. distribution of wage offers for each real wage rate, w P, on the horizontal axis, the value on the vertical axis shows the probability of receiving that offer ω is the effective real income received while unemployed key decision: whether to accept a real wage, w P clearly only accept wage offers where w P > ω for wage offers above ω benefit of rejecting: potentially a better offer might come along cost of rejecting: the individual forgoes income while not working the optimal is a reservation wage rule

27 Reservation wage rule Denote the reservation wage by w P wage offers with w P < w P will be rejected wage offers with w P w P will be accepted How does the value of the reservation wage affect the time spent looking for a job and the expected wage? if w P is low: expected duration of unemployment short expected wage rate low if w P is high: expected duration of unemployment long expected wage rate high some job offers are unacceptable there will always be some unemployment

28 Comparative statics I. ω increases for a given distribution of wage offers an increase in ω increases the reservation wage w P it is more likely that w P < w P will apply job offers will be rejected more often job searchers tend to take longer to find a position the job-finding rate decreases the expected duration of unemployment increases

29 Comparative statics II. an improvement in the entire distribution of wage offers if the reservation wage w P stays the same it is more likely that w P w P will apply job offers will be accepted more often the job-finding rate increases the expected duration of unemployment decreases

30 Comparative statics III. an improvement in the entire distribution of wage offers might increase the reservation wage the previous argument goes through if the reservation wage increases by less than how much the distribution of wage offers shifts this might be because the increase in workers MPL is not fully permanent future wage offers increase by less even if it is fully permanent if ω deos not rise, then w P will rise proportionately less than the distribution of wage offers Overall, an improvement in the wage offers increases the job-finding rate reduces the expected duration of unemployment

31 Job separations I. workers and firms evaluate their match as precisely as possible they might find out later that they made a mistake (worker less productive, job more boring than anticipated) when a match quality looks much worse than initially separation ex: firm get adverse shock, decline in the demand for a firm s product, change in worker s family status, location, etc. tendency of a job match to break up is higher if the job match was borderline some jobs are temporary at the outset job separations take place

32 Job separations II. higher job separation rate for inexperienced workers - hard to evaluate young people - more likely change in family status in industries that are subject to frequent technology and demand shocks without job separations, with no new people entering the labour force and no new jobs, the search process would eventually eliminate unemployment due to job separations, new job seekers, and new positions the finding of jobs is continually offset by the creation of new unemployment and vacancies

33 Movements between employment and unemployment I.

34 Movements from employment to unemployment the Bureau of Labor Statistics estimates the job separation rate for the entire non-farm economy using the Job Openings and Labor Turnover Survey (JOLTS) average between December 2000 and February 2006: 3.1% per month, 4.32 million people did not vary much: between 2.8% and 3.5% per month suggests that the job separation rate may not have a strong association with recessions and booms not everyone becomes unemployed, some people immediately find a job, others exit the labour force

35 Job separation and unemployment rate

36 Movements from unemployment to employment we ignore people moving out of the labour force for example the discouraged workers the ratio of job hirings compared to civilian employment averaged at 3.2% per month, 4.45 million people job finding rate = number of hires pre month unemployment 0.58 this is an over-statement: does not distinguish between people who changed jobs (and were never unemployed) who found a job from outside the labour force (and were not counted as unemployed) this is a problem for levels, but the changes in the job finding rate are probably accurate its movement mirrors the movement of the unemployment rate

37 Job finding and unemployment rate

38 The natural rate of unemployment is the unemployment rate that the economy tends towards, given the rates at which people lose and find jobs the change in the number of persons employed over a month, L is given by L = ψu }{{} job findings σl }{{} job separations the long-run level of L and U are constant ( L = U = 0) ψu = σl = σ(u + L U) (ψ + σ)u = σ(u + L) u n = U L + U = σ ψ + σ this is the equation of the natural rate of unemployment

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40 Important aspects of the unemployment rate even if u eventually settles at its natural rate, there is a large amount of job turnover about 4 million people lose and find jobs each month these large flows in and out of jobs is part of the operation of the labour market keys to the dynamics of employment are the rates of job separation and job finding: key equation of the natural rate of unemployment again: if σ u n if ψ u n u n = σ ψ + σ

41 Economic fluctuations, employment and unemployment I. a negative shock hits the technology level, A the marginal product of labor for the typical worker and job drop the job-finding rate, ψ, falls since market opportunities become poorer compared to ω we assume (as the data suggests) that σ stays the same

42 Economic fluctuations, employment and unemployment II.

43 Economic fluctuations, employment and unemployment III. the build-up of a recession involves a period of gradually falling employment and rising unemployment even after the economic recovery begins, it takes a while for employment and unemployment to return to their pre-recession levels even during the recession a large number of jobs is created each month, they are just outnumbered by the jobs lost

44 Vacancies the number of vacancies a firm posts is not constant over time: an increase in MPL, raises the number of job openings an increase in w P required to get workers to accept jobs lowers the number of job openings a reduction in the costs of posting jobs and processing applications raises the number of job openings an increase in the technology, A, increases MPL, and if the real wage does not change (or only to a smaller extent), then firms will increase their vacancies in booms prediction: vacancies are pro-cyclical in the data when A is high, unemployment is low, and vacancies are high when A is low, unemployment is high, and vacancies are low

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47 Summary We extended the baseline real business cycle model with 1. Variable capital utilisation prediction: capital-utilisation will be pro-cyclical data on capacity utilisation is in line with this 2. Search frictions 3 sources for variation in total hours worked (in order of importance): 1. employment rate 2. average hours worked 3. size of labour force model of search explains why the unemployment rate is positive prediction: pro-cyclical employment rate and vacancies