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									 Optimal Labor Income Tax and
Transfer Programs for Individuals
          and Families

         Mike Brewer, IFS
     Emmanuel Saez, UC Berkeley
       Andrew Shephard, IFS



          September 2006
INTRODUCTION

Goals of Project:

1. Analyze lessons from optimal tax theory for the design of
   taxes and transfers for individuals and families

2. Apply those lessons to the UK:

•   Describe current tax/transfers in the UK

•   Simulate optimal tax/transfers in the UK

3. Identify issues that are debated among policy makers not
   well explored in the literature
OUTLINE

I)    The current tax/transfer system in the UK
•     Describing current marginal and average taxes
•     Key issues in the policy debate

II)   The standard Mirrlees optimal tax model
•     Simple theoretical derivation
•     Simulations applied to the UK

III) Adding labor force participation effects

IV)   Other topics
•     Migration issues and taxation
•     Treatment of the family
•     Framing and understanding transfers/taxes?
I. CURRENT UK TAX AND TRANSFER SYSTEM

Budget constraint is c=z-T(z)

Two key concepts:

1. Intensive Margin: Marginal Tax Rate = T’(z)

2. Extensive Margin: Participation Tax Rate = [T(z)-T(0)]/z

In the UK:

+ Income Support creates high MTR, PTR at the very bottom
+ In-work tax credits reduces PTR for low income workers (16+
    hours/week)
+ Payroll + income tax no longer very progressive from middle
    to top
                         Fig 1. Budget Constraint in the UK in 2004 (one earner, 2 kids)
                    £30,000

                    £25,000
Annual Net Income




                    £20,000

                    £15,000

                    £10,000

                     £5,000

                         £0
                                             £10,000


                                                       £15,000


                                                                 £20,000


                                                                           £25,000


                                                                                     £30,000


                                                                                               £35,000


                                                                                                         £40,000
                                    £5,000
                              £0




                              Annual Gross Earnings (1 earner, 2 kids, 8 Pounds/hour)
                   Fig 2. Participation and Marginal Tax Rates in the UK in 2004
            100%
            90%
                                                                 PTR                  MTR
            80%
            70%
Tax Rates




            60%
            50%
            40%
            30%
            20%
            10%
             0%
                                   £10,000


                                             £15,000


                                                       £20,000


                                                                  £25,000


                                                                            £30,000


                                                                                        £35,000


                                                                                                  £40,000
                          £5,000
                   £0




                   Annual Gross Earnings (1 earner, 2 kids, 8 Pounds/hour)
I.   MAIN DEBATE ISSUES IN THE UK SYSTEM

1.   Structure of Marginal Tax Rates for Lone Parents

     Provide support vs. incentives to work

2.   Taxation of Couples

     UK has moved to individual income taxation but in-work
     tax credits are family based

3.   Administration and Delivery of Tax Credits

     Difficulty of integrating transfers (family monthly based) to
     individual annual income tax
II. OPTIMAL INCOME TAXATION IN MIRRLEES MODEL

Budget constraint is c=z-T(z)

Intensive Response of earnings only captured by e = elasticity
    of earnings wrt to net-of-tax rate 1-T’.

Distribution of earnings H(z), density h(z)

Social welfare weight: G(z) = average social marginal value of
   c for those earning more than z. G(z) decreasing. G(0)=1.

Optimal tax rate (assuming no income effects):

       T’(z)/[1-T’(z)] = (1/e) * [1-H(z)]/[z h(z)] * [1-G(z)]

Optimal top rate:      T’=1 / (1 + a*e) where a=2 Pareto param.
II. UK APPLICATION

1. Elasticity e
   + Many studies on e at the bottom and middle

   + Little work estimating e at the top:
   Look at evolution of top incomes following large top MTR
   cuts in the 1970s and 1980s

2. Distribution parameter [1-H(z)]/[z h(z)]

   As in the US, it is U-shaped in the UK

3. 1-G(z) increasing

With constant e, this generates an optimal U-shape pattern of
   MTRs in the UK
                                 A. Top 1% Income Share and MTR, 1962-2003
                    80%                                                                                  16%

                    70%
                                                                                                         14%
                    60%
Marginal Tax Rate




                                                                                                         12%




                                                                                                               Income Share
                    50%                 Top 1% MTR
                                        Top 1% income share
                    40%                                                                                  10%

                    30%
                                                                                                         8%
                    20%
                                                                                                         6%
                    10%

                    0%                                                                                   4%
                          1962

                                 1966

                                          1970

                                                 1974

                                                        1978

                                                               1982

                                                                      1986

                                                                             1990

                                                                                    1994

                                                                                           1998

                                                                                                  2002
II. ESTIMATING TOP INCOME ELASTICITY

1. Feldstein-Lindsey method from 1978 to 2003:

   Top 1% income share increases from 6% to 12%
   Net-of-tax rate increases from 20% to 60%

   Elasticity e = (12/6)/(60/20)=2/3, T’max=43%

2. Identification Issues: Is relative growth in top 1% due only to
   tax cuts?

   Estimation sensitive to comparison years

   Control group (next 4%)
                                   B. Top 5-1% Income and MTR, 1962-2003
                    80%                                                                                16%

                    70%
                                                                                                       14%
                    60%
Marginal Tax Rate




                                                                                                       12%




                                                                                                             Income Share
                    50%


                    40%                                                                                10%

                    30%
                                                                                                       8%
                    20%
                                                  Top 5-1% MTR
                                                                                                       6%
                    10%                           Top 5-1% income share

                    0%                                                                                 4%
                          1962

                                 1966

                                        1970

                                               1974

                                                      1978

                                                             1982

                                                                    1986

                                                                           1990

                                                                                  1994

                                                                                         1998

                                                                                                2002
                         Fig 3. Hazard Rate [1-H(z)]/[z*h(z)] in the UK in 2004
              1.0
              0.9
              0.8
              0.7
Hazard Rate




              0.6
              0.5
              0.4
              0.3                                                   [1-H(z)]/(z h(z)) = 1/a
              0.2                                                   constant for Pareto
              0.1
              0.0
                            £50,000


                                      £100,000


                                                    £150,000


                                                               £200,000


                                                                          £250,000


                                                                                     £300,000


                                                                                                £350,000


                                                                                                           £400,000
                    £0




                                                 Annual Gross Earnings
                                    Fig 4. Optimal Simulated MTRs in the UK, e=0.5
                            100%
Optimal Marginal Tax Rate

                            90%
                            80%
                            70%
                            60%
                            50%
                            40%
                            30%                                              Utilitarian SWF
                            20%                                              Rawlsian SWF
                            10%
                             0%
                                                   £100,000

                                                              £150,000

                                                                         £200,000

                                                                                    £250,000

                                                                                               £300,000

                                                                                                          £350,000

                                                                                                                     £400,000
                                         £50,000
                                   £0




                                                         Annual Gross Earnings
III. ADDING PARTICIPATION EFFECTS

1. Empirical studies show that participation effects at the
   bottom are large (using expansions of in-work tax credits)

2. With participation effects, high tax rates at the bottom are
   no longer desirable and negative participation tax rates can
   be optimal (Diamond, 1980; Saez, 2002, Laroque, 2004)

3. With only participation effects:

              PTR/[1-PTR]=(1/eP) * [1-g(z)]

   eP is participation elasticity
   g(z) social marginal welfare weight at z
   g(z) decreasing and equal to 1 on average
III. SIMULATONS WITH PARTICIPATION EFFECTS

Key findings from Blundell-Shephard

+ Given empirical elasticities, in-work tax credits can be optimal
   under reasonable welfare weights

+ Current in-work credits go in the right direction and should be
   even increased for lone parents with school aged children.

Simple Policy Recommendation for the optimal tax system

+ Family credit with large earnings disregard (up to 5,000
   Pounds annual)
+ U-shape MTRs above earnings disregard: phasing out of
   credit combined with progressive tax rates on upper
   incomes
IV. OTHER TOPICS: OPTIMAL TAXES AND MIGRATION

Concern in the EU context that top skilled individuals move to
  low tax countries such as the UK or Ireland

Migration response is similar to an extensive response

Optimal top tax rate with migration elasticity (eM) + intensive
   elasticity (e) is:

   MTR=1/(1+a*e + eM)

Empirical work on eM is lacking but possible that eM is larger
  than e (previous top shares analysis might estimate e+eM)

What fraction of surge in top shares due to high-skill migrants?
How to obtain data on this issue?
IV. OTHER TOPICS: TREATMENT OF THE FAMILY

Debate about desirability of joint vs. individual taxation:

   + UK moved to individual base in 1990 for income tax but
   not for transfers (incentive issues for 2 earner families)

   + Progressive joint taxation is good for redistribution

   + Individual taxation good incentives (if tax is progressive
   and secondary earners more responsive)

Two important issues:
  + What is the fully optimal joint tax system?

   + What are the effects of within couple bargaining on the
   optimal tax system?
IV. OTHER TOPICS: TREATMENT OF THE FAMILY

Couple bargaining (within family redistribution):

   + Effect seems empirically important (Lundberg et al. 1997)

   + Remedy is first best government lump-sum transfers
   between couples (Kroft 2006)

Optimal Joint Taxation (across family redistribution):

   + Difficult multi-dimensional tax design problem

   + Kleven et al. 2006 shows (in simple context) that tax on
   spouse should decrease with earnings of primary earner
   + This is what the UK does!
IV. OTHER TOPICS: TIMING, FRAMING, UNDERSTANDING

•   Timing and Framing:

    Behavioral literature suggests that timing and framing of
    payments might be very important

    US EITC is paid one year late which often helps people at
    the wrong time and might reduce pro-work effects

    UK has tried to create an as-you-earn system but difficult to
    administer: compliance costs + people hate to repay

•   Future IT Advances will allow real time processing of family
    credits and make taxes/transfers more transparent

								
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