Tax Wedge and Job Distribution in a Directed Search Model

Transcription

1 Tax Wedge and Job Distribution in a Directed Search Model Ryoichi Imai Kyushu University March 8, 2018 Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

2 Tax Wedge More Economists agree on that a high tax wedge reduces job creation and output - Prescott (2002, 2004) International Comparison - OECD Tax Wedge is de ned by Ψ P = 1 + t P 1 t where t P, P = G, B, is the payroll tax rate, and t is the income tax rate. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

3 Tax Reform In policy discussion, it is often argued that payroll tax should be replaced by income tax or consumption tax. However, economists usually say that replacement of payroll tax with income tax is irrelevant. That is, it does not change employment or output, because the tax wedge is the same. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

4 This Paper Two Sectors: Good (high productivity) sector and Bad (low productivity) sector, following Acemoglu (2001). The labor market is frictional. Search is directed. There is on-the-job-search from bad to good jobs. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

5 Results Cinsider a balanced budget switch from payroll tax to income tax. 1 If both the sectors are taxed at an uniform rate, the policy is irrelevant for the distribution of good jobs and bad jobs, or the welfare distribution between workers and rms. 2 If the bad sector is taxed at a lower pyaroll tax rate, and the payroll tax is gradually replaced by the income tax in the good sector, 1 the policy only slightly reduces the tax wedge in the good sector, while it considerably raises it in the bad sector. 2 however, the policy does not a ect the distribution of jobs by so much. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

6 Environments There are identical works, of which the population is normalized to one. Unemployed workers enter the labor market and search for jobs. There are two types of jobs: Good and Bad according to Accemoglu (2001). Job search is directed. There is on-the-job search, with which workers switch from the bad job to the good job. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

7 Agents u G : mass of unemployed workers searching for the good job. u B : mass of unemployed workers searching for the bad job. e G : mass of workers employed at the good job e B : mass of workers employed at the good job R: mass of retired workers, out of the market, die at Poisson rate φ. u G + u B + e G + e B = 1. At each instant, workers retire at Poisson rate δ, and are replaced by new ones, of which a fraction p goes to u G. (exogenous education) Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

8 Transition Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

9 Policy and Institution Unemployed workers receive bene t b. Retired workers receive pension h. Firms pay wage w i, i = G, B, to their employees, and pay payroll tax t i w i to the govenment Workers receive pre-tax income w i, i = G, B, and pay income tax tw i. The government budget constrint: bu + hr = (t G + t)w G e G + (t B + t)w B e B, where u = u G + u B. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

10 Search There are three labor markest, Good, Bad, and On-the-Job Search from Bad to Good jobs. Search is directed. θ i, i = G, B, S, is the labor market tightness, which is equal to the ratio of the mass of vacancies to the mass of job searchers. α(θ) is the standard matching function. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

11 Workers ru G = b e + θ G α(θ G )[W G U G ru B = b e + θ B α(θ B )[W B U B ] rw G = (1 t)w G + σ G (U G W G ) rw B = (1 t)w B e + θ S α(θ S )[W G W B ] + σ B (U B W B ) b is the unemployment bene t. e is the job search cost. The discount rate r = ρ + δ: ρ is the time preference rate. δ is the retirement rate. A worker employed at a good job receives wages (1 the income tax rate t)w G where t is A good (bad) job is destroyed by an exogenous shock that comes at Poisson rate σ G (σ B ). θ i α(θ i ), i = G, B, S, is the rate at which a worker is employed. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

12 Workers 1 The value U G for an unemployed worker searching for a good job is written as ru G = b e + θ G α(θ G )[W G U G ] where W G is the value for a worker to work at a good job. b is the unemployment bene t. e is the job search cost. The discount rate r = ρ + δ: ρ is the time preference rate. δ is the retirement rate. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

13 Workers 2 The value U B for an unemployed worker searching for a bad job is written as ru B = b e + θ B α(θ B )[W B U B ] Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

14 Workers 3 Once a worker is employed at a good job, his value W G is written as rw G = (1 t)w G + σ G (U G W G ). A worker employed at a good job receives wages (1 t)w G where t is the income tax rate and w G is the pre-tax wage. A good job is destroyed by an exogenous shock that comes at Poisson rate σ G. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

15 Workers 4 The value W B for an on-the-job searcher searching for a good job is written as rw B = (1 t)w B e + θ S α(θ S )[W G W B ] + σ B (U B W B ) where w B is the pre-tax wage of the bad job, which is destroyed by an exogenous shock that comes at Poisson rate σ B, as well as by the employee s job search at rate θ S α(θ S ). Note that θ G 6= θ S since job search is directed and then the good job market for unmployed workers is separated from the good job market for on-the-job searchers. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

16 Firms rv G = f + α(θ G )[J G V G ] rv S = f + α(θ S )[J G V S ] rv B = f + α(θ B )[J B V B ] rj G = y G (1 + t G )w G + σ G (V G J G ) rj B = y B (1 + t B )w B + σ B (V B J B ) Firms can create a vacancy of the good job by paying cost k, while they can create a vacancy of the bad job for free. f is the cost to hold a vacancy. t G and t B are the payroll tax rates for the good and bad jobs, respectively. (Assumption for simpli cation) An exogenous shock occurs at Poisson rate δ to force a rm to close its business. Additionally, for a lled job, that shock occurs at the same timing as the employee suddenly retires. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

17 Firms 1 Firms enter the labor market by carrying a vacancy of the good job or the bad job. The instant product of the good job is higher than that of the bad job, in other words, y G > y B. Firms can create a vacancy of the good job by paying cost k, while they can create a vacancy of the bad job for free. The value V G for a rm carrying a good job vacancy for unemployed workers is written as rv G = f + α(θ G )[J G V G ] where J G denotes the value of a rm holding a lled good job. f is the cost to hold a vacancy. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

18 Firms 2 Other good rms targets at employees at the bad job. The value V S for a rm carrying a good job vacancy for workers on the bad job is written as rv S = f + α(θ S )[J G V S ]. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

19 Firms 3 Other rms provides vacancies of the bad job. Its value V B is written as rv B = f + α(θ B )[J B V B ]. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

20 Firms 4 The value functions of rms with lled jobs, J G and J B, are written as follows. rj G = y G (1 + t G )w G + σ G (V G J G ) rj B = y B (1 + t B )w B + σ B (V B J B ) where t G and t B are the payroll tax rates for the good and bad jobs, respectively. (Assumption for simpli cation) An exogenous shock occurs at Poisson rate δ to force a rm to close its business. For a lled job, that shock occurs at the same timing as the employee suddenly retires. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

21 Entry The three labor market tightness (θ G, θ B, θ S ) are determined as follows. First, good rms enter the market until their values equals the invesment cost k. V G = V S = k. (1) Second, bad rms enter the labor market until their value to create the bad job reaches zero: V B = 0 (2) Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

22 Wages Since there are three markets, there could be three wages, which are determined by directed search. However, we assume that the good rms recruiting employees at the bad jobs will pay the same wage as the good rms recruiting unemployed workers. Firms carrying a good vacancy attract unemployed workers by committing to pay the highest wage they can pay subject to the constraint that V G = k. This strategy is represented by the tangency condition of the indi erent curves of rms and unemployed workers. U G / θ G U G / w G = V G / θ G V G / w G. (3) Similarly, rms carrying a bad job post a wage such that (3) and (4) are solved for (w G, w B ). U B / θ B U B / w B = V B / θ B V B / w B. (4) Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

23 Aggregate Welfare The linear utility implies that the social welfare is equivalent to the sum of the output net of the costs. Ω = y G e G + y B e B e(u G + u B ) f (v G + v B + v S ) where v G = σ G e G α(θ G ), v B = σ B e B α(θ B ), v S = σ G e G α(θ S ) Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

24 Welfare Distribution Analysis of welfare distribution across workers and rms is more subtle, if pro ts are not redistributed from rms to workers. We restrict our attention to the ow welfare again. The average welfare accrued to workers is de ned as Ω W = (b e)(u G + u B ) + (1 t)w G e G + ((1 t)w B e)e B + hr The average welfare accrued to rms is de ned as Ω F = f (v G + v B + v S ) + [y G (1 + t G )w G ]e G + [y B (1 + t B )w B ]e B Note that Ω = Ω W + Ω F. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

25 Excercises Replace payroll tax with income tax such that 1 (Both sectors are equally taxed) Reduce t G = t B and raise t to keep unemployment bene t b and pension bene t h. 2 (bad jobs are lower taxed than good jobs) Set t B =.1 and reduce t G >.1 and raise t to keep unemployment bene t b and pension bene t h. Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

26 Parameters (no structural estimation) r =.05, δ =.024, φ =.04, p =.3, a = 2, c =.4, σ G =.1, σ B = σ S =.2, y G = 40, y B = 20, b = 8, h = 20, e = 1, f = 3, q = 4, k = 15 Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

27 Both sectors are equally taxed 1 t G payroll tax # t B payroll tax # t income tax " w G no big change w B no big change θ G no change θ B no change θ S no change u no change u G no change u B no change e G no change e B no change R no change Table: Both Sectors are equally taxed 1 Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

28 Both sectors are equally taxed 2 t G payroll tax # t B payroll tax # t income tax " w G no big change w B no big change θ G no change θ B no change θ S no change Ω no change Ω G no change Ω B no change Ψ G matches OECD data Ψ B matches OECD data Table: Both Sectors are equally taxed 2 Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

29 Bad jobs are taxed at a low rate 1 t G payroll tax # t B payroll tax constant t income tax " w G gradually rises w B no big change θ G no big change θ B no big change θ S no big change u no change u G no change u B no change e G no change e B no change R no change Table: Bad jobs are taxed at a low rate 1 Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

30 Bad jobs are taxed at a low rate 2 t G payroll tax # t B payroll tax constant t income tax " w G gradually rises w B no big change θ G no big change θ B no big change θ S no big change Ω slightly rises Ω W slightly rises Ω F slightly rises Ψ G slightly declines Ψ B rises Table: Bad jobs are taxed at a low rate 2 Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

31 Results (Summary) 1 If both sectors are equally taxed, replacing payroll tax with income tax under the contant transfer policy is neutral in the sense that it does not a ect the job distribution (T1) or the tax wedge (T2). 2 If the bad sector is taxed at a lower rate, reducing the payroll tax rate and raising the income tax rate in the good sector, 1 slightly reduces the tax wedge in the good sector, and considerably increases the tax wedge in the bad sector (T3), 2 while it does not a ect by so much the job distribution or the labor market tightness (T4). Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

32 Discussion 1 There might be multiple equilibria. 2 In this model, the replacement of payroll tax with income tax changes the tax wedges, while it does not a ect the job distribution by so much, Are there any evidences? 3 Employment protection should be considered simultaneously as in Blanchard and Tirole (2005). Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

33 References Accemoglu, Daron [2001], Good Jobs versus Bad Jobs, Journal of Labor Economics 19(1), Blanchard, Olivier and Jean Tirole [2005], Journal of European Economic Association. Goerke, Laszlo [2005], Tax Liability and Tax Evasion in a Competitive Labor Market, Journal of Public Economic Theory, 7 (2), Hosios, Arthur J. [1990], On the E ciency of Matching and Related Models of Search and Unemployment, Review of Economic Studies 57, Koskelaa, Erkki, and Ronnie Schobb [1999], Does the composition of wage and payroll taxes matter under Nash bargaining?, Economics Letters 64, Manning, Alan [2001], Labour supply, search and taxes, Journal of Public Economics 80, Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34

34 McDonald, Ian M., and Robert M. Solow [1981], Wage Bargaining and Employment, American Economic Review 71(5), McDonald, Ian M., and Robert M. Solow [1985], Wages and Employment in a Segmented Labor Market, Quarterly Journal of Economics 100(4), Picard. Pierre M., and Eric Toulemonde [2001], On the Equivalence of Taxes Paid by Employers and Employees, Scottish Journal of Political Economy 48(4), Prescott, Edward [2002], Prosperity and Depressions, American Economic Review 92, Prescott, Edward [2004], Why Do Americans Work So Much More Than Europeans?, Federal Reserve Bank of Minneapolis Quarterly Review 28, Ryoichi Imai (Kyushu University ) Tax Wedge and Job Distribution in a Directed Search Model March 8, / 34