The Macroeconomics Effects of a Negative Income Tax

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1 The Macroeconomics Effects of a Negative Income Tax By MARTIN LÓPEZ-DANERI Draft: December 5, 2010 I study a particular revenue-neutral tax reform from the US Income Tax to a Negative Income Tax (NIT), in a life-cycle economy with individual heterogeneity and uninsurable idiosyncratic labor risk. I find that the optimal tax rate is 27:95% with a transfer of 10% of GDP per capita, roughly $4; 600. The exante average welfare gain amounts to a 6:33% annual increase of individual consumption in every state of the world. Low productivity agents reduce their workforce participation at the expense of high productive agents. I compare this reform with a Flat Tax and the NIT outperforms clearly the Flat Tax. JEL: E13, H21 and H24. Keywords: Negative Income Tax, Income Tax, Efficiency, Distribution The US Federal Income Tax is one of the most important sources of revenue for the Federal Government and a complex tax, with a considerable number of tax credits, deductions, overlapping provisions and increasing marginal rates. The cost of compliance is not trivial and the distortions generated are significant. It is not a surprise that there has been a continuous demand for reform and several proposals have been suggested with different degrees of success. Take, for instance, the significant reduction of marginal tax rates that took place in the eighties or the Flat Tax (R. Hall and A. Rabushka 1985), to name a few. This study is going to focus in a particular reform proposal named Negative Income Tax (NIT)(M. Friedman 1962), which despite of its popularity, it has not been analyzed in a general equilibrium setting 1. In this paper, I ask the following questions: What are the general equilibrium effects of replacing the Actual Income Tax with a NIT? Specifically, what are the macroeconomic effects Lopez-Daneri, Martin: University of Iowa, Economics Department, 108 John Pappajohn Business Building, Office: S361, Iowa City, IA , USA. martin-lopezdaneri@uiowa.edu. I would like to thank Gustavo Ventura for his continuous advice and supportive encouragement in the project. Special thanks to German Cubas, Srihari Govindan, B. Ravikumar, Guillaume Vandenbroucke, and seminar participants at Tow Economics Seminars, Iowa Alumni Workshop 2010, Missouri Economics Graduate Conference 2010 and LACEA 2010 for useful comments and suggestions that substantially improve the paper. The usual disclaimer applies 1 There was a failed attempt to introduce it as legislation during Richard Nixon s Presidency, but after all the modifications introduced in the Parliamentary debate, Milton Friedman who was a candid advocate, withdrew his support. 1

2 2 on income and earnings, labor supply, savings and welfare? Moreover, is this reform desirable? What makes the NIT an appealing tax scheme is the combination of a lump-sum transfer, in contrast of a fixed deduction, and a constant marginal tax rate. The presence of the transfer is the distinction of the NIT with the Flat Tax. Let us exemplify how the tax works. At the beginning of the fiscal year, all households receive a transfer from the Government, let us say $2; 000. During the period, all income made is taxed at a constant rate, let us say 20%. Then, households with yearly income of less than $10; 000 pay no taxes and receive a positive net transfer (negative tax). As income increases, the effect of the transfer dilutes. Not only have all households a minimum income assured but also the NIT is a simple tax with no trivial effects on insurance, efficiency and distribution. To tackle these questions, I study a life-cycle economy, where agents are heterogeneous and face idiosyncratic shocks and life uncertainty. The resulting heterogeneity arises from the agents shocks history, their level of asset accumulated and their age. To capture the evolution of labor productivity through the life cycle, I model it as a function of the shocks received and age. There is a Social Security System and agents receive benefits, once they are retired, in the form of lump-sum transfers. However, these are not the only transfers received: Accidental bequests are distributed evenly among all living agents 2. I calibrate this model to match the US economy, reproducing the level of concentration of labor earnings seen in the data. As the actual US Income Tax has an important degree of transfers, being the Earned Income Tax Credit (EITC) one clear example about it, I use a tax function that closely reproduces the effective average tax rates paid by households. Not doing so will invalid any comparison made. I focus on a Stationary equilibrium and find the level of transfers and marginal tax rate such as the reform is revenue neutral and the ex-ante welfare is maximized, i.e. before the agent is born and knows his type. My findings can be summarized as follows. First and foremost, the tax reform proposed is desirable with important welfare gains. A NIT with a marginal tax rate of 27:95% and a transfer of 10% of per capita GDP, roughly $4; 600, implies a welfare gain of a 6:33% increase in annual consumption in every state of the world. Low ability type agents in the lowest 20% of the distribution benefits the most with welfare gains that range from 12% to 64%. The level of transfers plays an important role in the results. A comparison with a proportional tax, i.e. a NIT with no transfers, has a welfare loss of 4:3%. A result that comes with no surprise 2 It is worth to notice that this benchmark economy has a level of transfers higher than what is actually seen in the data, especially for low income households, where accidental bequests and Social Security benefits are not as important in relative terms as they are in the model. This matter is not irrelevant as the transfer in the NIT will be relatively more important for low income than high income households.

3 THE MACROECONOMICS EFFECTS OF A NEGATIVE INCOME TAX 3 as the actual US Income Tax has an important level of distribution. Naturally, the sole elimination of transfers benefits only the highest productive agents, who are facing lower marginal tax rates. A similar comparison to a Flat Tax shows that a fixed deduction does not improve the picture. An optimal Flat Tax with a marginal tax rate of 18:47% and a fixed deduction of 33% of per capita GDP, roughly $15; 000 3, does not outperform the NIT as it entitles a welfare loss of 0:12% 4. Therefore, the replacement of lump-sum transfer by a fixed deduction is not welfare enhancing. Second, there is a negative relationship between the size of the transfers and per capita GDP, where in the optimal NIT decreases by 12:82%. The reason is simple: leisure is a normal good and the presence of the transfer enables agents to work when they are more productive. This fact implies a change in the composition of the labor force: high productive agents gain participation at the expense of low productivity types. A fact that is confirmed by the decrease in the labor supply measured in efficiency units ( 7:03%) which is less than the decrease in hours worked in the economy ( 17:59%). Consequently, the Gini coefficient for labor earnings deteriorates from 0:46 to 0:53. Third, the transfer reduces the need of precautionary savings and the saving rate drops %, implying a reduction in the capital stock and the capital output ratio of 22:63% and 11:26% respectively. Therefore, the wage rate decreases and the interest rate increases, resulting in an extra source of welfare gain for capital income earners (retirees and high productivity agents) and a welfare loss for wage earners (the youngsters and low ability type agents). An exercise where the assumption of an open economy is made shows that the welfare gains of keeping the prices fixed increases welfare by 3% with respect to the benchmark case. Nevertheless, there is a bigger decrease in the capital output ratio and per capita GDP ( 23:02% and 16:36% respectively). Fourth, the way accidental bequests are modeled plays an important role in the results. So far and as I said before, I have considered a generous scheme where all accidental bequests are returned as a lump-sum transfer to all agents. A scenario where all bequests are completely taxed by the Government shows that an optimal NIT implies a 40% increase in the welfare gains with respect to the benchmark case. As usual, the true state of the world lies somewhere in between the scheme considered and the extreme case of no accidental bequests. Last but not least, there is a negative relationship between the persistence of the shocks and the size of the transfers in the optimal NIT. I have considered two cases. In one of them, shocks 3 Hall and Rabushka (1985) propose a Flat Tax with a deduction of $22; 500 and marginal tax rate of 19%: 4 In order to put into perspective this welfare loss, it is necessary to note that I am not taking into account the transition dynamics and the comparison being made is between steady states. Also, the usual quantitative exercises that evaluate the desirability of a Flat Tax do not use tax functions that capture well the actual level of distribution present in the US Income Tax.

4 4 are more persistent than in the benchmark case and a shock takes twice the time to reduce its effects in half. In the other one, the opposite is true: shocks are less persistent and the effects of a shock are reduced in half in half of the time. In the first case, the welfare gains are 8:7%, which are higher than the baseline scenario and the transfer level is 11% of per capita GDP. In the less persistent case, the welfare gain is reduced to 2:6% and the transfer level is 9%. Clearly, the riskier the economy is the higher the gains from providing public insurance are. This quantitative approach of optimal taxation has been followed in several papers, with models similar to mine, where an artificial economy with heterogeneous agents and incomplete markets (e.g. M. Huggett (1993) and S.R Aiyagari (1994)) is simulated and the individual and aggregate effects of a tax reform is studied (e.g. G. Ventura (1999), D. Altig et al (2001), D. Domeij and J. Heathcote (2004), J. Diaz-Gimenez and J. Pijon-Mas(2005), S. Nishiyama and K. Smetters (2005), among others). For instance, G. Ventura (1999) studies the effects of a Flat Tax Reform of the US Income Tax and finds that a Flat Tax has a positive impact on capital accumulation and labor supply measured in efficiency units, increasing earnings, income and wealth concentration. D. Domeij and J. Heathcote (2004) study the distributional effects of reducing capital taxes and I. Correia (2010) shows the distributional and welfare effects of replacing the US Income tax with a Flat Tax on consumption plus lump-sum transfers. Her approach is different to mine as she studies an economy populated with infinitely lived agents, differentiated by the initial level of wealth and labor productivity, whereas in my model, agents are born with no assets and there are no fixed inborn differences in labor productivity. J.C. Conesa and D. Krueger (2006) focus on the optimal level of progressivity in the US income tax and find that a Flat Tax with a tax rate of 17:2% and a deduction of $9; 400 (Per capita GDP $42; 000) is optimal, with an ex-ante welfare gain of 1:7%. An important difference with my paper is that they restrict themselves to a particular set of tax functions, which does not allow for transfers, whereas I do allow for transfers and deductions. In the same lines, J.C. Conesa, D. Krueger and Kitao (2009) extend the work of J.C. Conesa and D. Krueger (2006) and allow for differences in the tax rates of capital income and labor earnings and show that capital should be taxed at a positive rate, in accordance to A. Erosa and M. Gervais (2002) results. In addition, my paper is related to the literature on the effects of redistributive taxation, in particular with two strands: the effects of earnings shocks and insurance (e.g. J. Eaton and S. Rosen (1980), M. Flodén and J. Lindé (2001) and D. Krueger and F. Perri (2009)) and the distortions to labor supply decisions (e.g. R. Rogerson (2008), E. Prescott (2002) and M. Feldstein (1973), among others). M. Flodén and J. Lindé (2001) study the provision of insurance through Government transfers in the US and Sweden and the optimal level of transfers, finding that a transfer

5 THE MACROECONOMICS EFFECTS OF A NEGATIVE INCOME TAX 5 of 15% of per capita GDP in the US and 1:6% of per capita GDP in Sweden is optimal with a welfare gain of 8:5% and 1:6% respectively. My work has one important difference with them: their aim is to find an optimal level of transfer without replacing any of the present taxes. On the contrary, I focus on a particular Revenue Neutral Tax reform that has a lump-sum transfer as an important component but it is not the only source of welfare gain: there will also be an efficiency gain given by the replacement of the increasing marginal tax rates in the Income Tax by a constant tax rate. This paper is organized as follows. Section I introduces the model and the definition of equilibrium. Section II presents the calibration strategy and the quantitative results. Section III shows a sensitivity analysis and Section IV concludes. I. Model. The modeling framework is a general equilibrium life-cycle economy, populated by J heterogeneous overlapping generations. Agents face idiosyncratic risk and life uncertainty. Time is discrete and there is no aggregate risk 5. There are no explicit insurance arrangements. A. Environment. At each date t, a continuum of ex-ante homogeneous agents is born. An agent of age j faces a conditional survival probability s jc1 to be alive in the next period but those who survive up to age J die for certain. There is an exogenous retirement age R, adding the first dimension of heterogeneity in the model: Agents can be classified as workers or retirees depending on their ages are higher or lower than R C 1. There is a fixed population growth rate n and the total measure of the population N t is normalized to be 1 in every period. Despite of the fact that the population size evolves through time, each age j generation represents a constant fraction j of the total population size, making the demographic structure stationary 6. All agents share a time separable utility function and value the expected discounted stream of leisure and consumption:! JP jq j 1 s j u c j;t ; l j;t jd1 id1 where c j;t and l j:t denotes consumption and leisure at age j and period t respectively. The 5 Krusell and Smith (1998) show that the inclusion of aggregate uncertainty, besides of introducing an extra layer of difficulty in the model, does not significantly change the results of a model with no aggregate uncertainty. 6 The weights j are obtained by the recursive formula jc1 D j :s jc1 =.1 C n/

6 6 momentary utility function is Cobb-Douglas: hc j;t 1 l j;t 1 i 1 u c j;t ; l j;t D 1 Consumption and leisure are not separable and the intratemporal elasticity of substitution is equal to 1. The parameter 2.0; 1/ shapes the time spent working and together with > 0 influence the degree of risk of aversion and the Frisch elasticity of labor supply 7 (J.V. Rios- Rull 1995) B. Agent s endowment and labor productivity. Agents are born with no assets and during their working life they are endowed with one unit of time. They receive a competitive wage rate w t and their labor productivity is a first order Markov Process Q zz 0 D P Z D z 0 =Z D z given by e.z 0 ; j/, which is a function of the shock z 0 2 Z, and their age j 2 J. ln e.z 0 ; j/ D j C z 0 and z 0 D z C "; where " N 0; 2 " Thus, agents differ in the efficiency units they supply to the market depending on their age and their history of shocks. Therefore, an agent s pre-tax earnings of age j and shock z are equal to w t l t e.z; j/, where l t is the amount of time that he decides to work. At age 1, the measure of agents with shock z is q.z/. Also, I assume that the transition probability Q is aperiodic and irreducible in order to ensure an invariant distribution. (H. Hopenhayn and E. Prescott 1992). The possibilities of insurance in this economy are limited. There no annuity markets and agents cannot trade contingent claims. Nevertheless, agents trade a one-period risk-free asset a j;t 2 A R C that will help them partially insure against these idiosyncratic shocks. Agents are not allowed to borrow. 7 The Frisch elasticity, which gives the elasticity of hours worked to changes in wages, keeping the marginal utility of consumption constant, is given by:.1 l/ [1.1 /].; ; l/ D l

7 THE MACROECONOMICS EFFECTS OF A NEGATIVE INCOME TAX 7 C. Firms and Technology. There is a representative firm that produces total output Y t function: with a Cobb-Douglas production Y t D K t.a t L t / 1 where K t and L t are the aggregate capital and labor (measured in efficiency units) at time t; and A t D A 0.1 C g/ t. The resource constraint is: C t C K tc1 K t.1 / C G t K t.a t L t / 1 Following conventional notation, is the depreciation rate, G t is public consumption and C t is total private consumption. D. Government and tax structure. At time t, the Government receives payments from the Social Security System and the Income Tax. The proceeds serves to finance Government consumption G t, pay Social Security Benefits SS t and transfers T R t. The Social Security System is fully funded by the Social Security taxes paid by the working agents, the budget is balanced and the bequests left are returned as a lumpsum transfer to all living agents. Agents do not derive any utility from Government consumption G 8 t. The actual US Income Tax system is the benchmark case and it is important to make a distinction between the statutory and the effective rates paid. An Agent pays taxes for his income, defined as the sum of their labor and capital income, according to an income scale given by 6 brackets. Each of them has a different marginal tax rate i that increases with the position of the bracket, making the tax progressive. However, the US Income Tax is quite complex and has a considerable number of tax credits, deductions and overlapping provisions, which implies that the statutory tax rates faced by an Agent are not necessarily the ones effectively paid. Moreover, the presence of the Earned Income Tax Credit (EITC) needs to be taken into account 9. Thus, I 8 I can think this assumption as whether all Government consumption is wasteful or that the consumption of Public Goods enters linearly in the agent s utility function. In any case, the message is the same. 9 The Earned Income Tax Credit is a refundable tax credit for low and middle income families, who satisfy certain requirements, and it is calculated based upon the number of children in the household, among other things. It was enacted in 1975 and has been expanded ever since. (R. Moffit 2003)

8 8 use an effective rate tax function which belongs to the following parametric form 10 : Average T ax Rate.Normalized I ncome/ D 1 C 2 log.normalized I ncome/ where I ncome is normalized by the Mean Household I ncome. Therefore, the total taxes paid by an Agent are: T Benchkamrk j;t.i ncome/ D Average T ax Rate.Normalized I ncome/ I ncome There is also a constant Corporate Income Tax k on capital income. As it was mentioned before, there is a Social Security System, where the benefits are constant for all beneficiaries, and Agents pay a marginal tax rate ss on their earnings to fund it 11. In the reform scenario, the Negative Income tax replaces the US Personal Income Tax, leaving the rest of the taxes and the Social Security System unchanged. Now, all agents receive a fixed lump-sum transfer T Rt N I T at the beginning of the period and pay a constant marginal tax rate for every unit of income earned. Then, the total tax liability for an agent of age j and shock z with income I j;t w t e.z; j/ l j;t Ca j;t r is: Tj;t N I T D I j;t T Rt N I T E. Agent s problem: recursive formulation. Let.A; A/,.Z; Z/ and.j; J / be measurable spaces, where A is the Borel on A; Z is the Borel algebra defined algebra defined on Z and J is the Power set of J. Let.X; X / D.A Z; A Z/ be a product space and.x; j/ 2 X J be the state vector. Let X; X ; j be the probability space, where j : X! [0; 1] is a probability measure. The measure of agents with state x D.a; z/ within the cohort of age j is j.x/ : I need to do standard transformations of the variables in order to express the model in terms of a dynamic programming formulation. Let a j.x/ a j;t A t ; l j.x/ l j;t ; c j.x/ c j;t A t be the 10 Several papers use the Gouveia and Strauss tax function (M. Gouveia and R. Strauss 1994) to approximate the average Tax rates paid instead of the function depicted above. Even though, it approximates the average tax rate well, it implies a lower marginal tax rate for higher incomes than the ones seen in the US Income Tax. Moreover, it behaves as a flat tax for incomes higher than twice the household mean income. On the other hand, the tax function that I am considering not only does approximate well the average tax rate but it also does a good job for the Marginal Tax rates. 11 This setting will not let me capture the actual degree of risk sharing present in the actual Social Security System. Even though, this assumption will underestimate the potential benefits of the reform, it will let me discard agents past contributions as a state variable.

9 THE MACROECONOMICS EFFECTS OF A NEGATIVE INCOME TAX 9 asset, labor supply and consumption decision rules; let w w t A t and r r t be the wage rate and interest rate; let G G t A t ; K K t A t and L L t be the aggregate Government consumption, capital and labor supply and let T R T R t A t and T j.x/ T j;t A t be the transfers and tax collection SS and SS j t be the social security benefits. 12 : Finally, let T : X J! X J be an.1cg/ j.rc1/ operator. Then, given prices fw; rg and a tax regime Tj k with k 2 fn I T; Benchmarkg, an agent of age j with state x needs to choose the amount of labor l j.x/ to supply to the market, how much to consume c j.x/ and the amount of assets a jc1.x/ to carry over the next period. Optimal decisions rules solve the following dynamic programming problem: 1) Working agents:.t v/.x; j/ D sup nu c j ; l j C.1 C g/.1 / E v a jc1 ; j C 1 o.c j ;l j ;a jc1/ subject to c j C a jc1.1 C g/ a j.1 C r/ C w.1 ss / e.i; j/ l j T k j.x/ C T R i f j R c j 0; a j 0; a jc1 0 and l j 2 [0; 1] 2) Retirees:.T v/.x; j/ D sup nu c j ; 0 C.1 C g/.1 / E v a jc1 ; j C 1 o.c j ;a jc1/ with c j C a jc1.1 C g/ a j.1 C r/ T k j.x/ C T R C SS j i f j > R c j 0; a j 0; a jc1 0 v.x; J C 1/ 0 12 Time subscripts have been dropped because I am interested in a stationary equilibrium.

10 10 F. Stationary Equilibrium. DEFINITION 1: A stationary equilibrium is a collection of value functions v.x; j/ ; decision rules c j.x/ ; l j.x/ and a jc1.x/ ; together with factor prices fw; rg ; a tax regime Tj k ; taxes paid T j.x/ and transfers T R; aggregate capital K and labor L; government consumption G and Social Security Benefits SS j ; with a collection of invariant distributions 1 ; : : : ; J such that: 1) Decision rules c j.x/ ; l j.x/ and a jc1.x/ together with a value function v.x; j/ solve the decision problem for an agent of age j and state x: 2) Factor prices are competitive: w D F 2.K; L/ r D F 1.K; L/ 3) Market clearing conditions are satisfied: a) P j R j X c j.x/ C a jc1.x/.1 C g/ d j.x/ C G D F.K; L/ C.1 / K b) P j R j X a jc1.x/ d j.x/ D.1 C n/ K c) P j R j X l j.x/ e.z; j/ d j.x/ D L 4) Law motion of distributions are consistent with individual decision rules: Z jc1.b/ D X P.x; j; B/ d j.x/ where P.x; j; B/ D 1 if a jc1.x/ 2 B; and P.x; j; B/ D 0 otherwise, 8B 2 X, j D 1; : : : ; J: 1.x/ is univocally determined by q.z/ as agents are born with no assets: 5) Government budget is balanced: G D X j j Z X T j.x/ d j.x/ 6) The Social Security System is fully funded: ss wl D JX jdrc1 j SS j

11 THE MACROECONOMICS EFFECTS OF A NEGATIVE INCOME TAX 11 7) Transfers are equal to accidental bequests:.1 C n/ T R D X j Z j 1 s jc1 a jc1.x/.1 C r/ d j.x/ X II. Results. A. Calibration. In this subsection, I discuss the calibration strategy and the assumptions made for the benchmark economy. I set the model period equal to 1 year. Table 1 summarizes the parameters values used in the calibration. Table 2 presents the results for the calibrated economy. DEMOGRAPHICS In my model, agents are born at age 21 (model period 1), work until age 65 (model period 45, i.e. R D 45) and die for certain at age 100 (model period 81, i.e. J D 81). Survival probabilities s jc1 are taken from the NVSS 13. Population growth n is set equal to 1:09% which is the average population growth for the US during PREFERENCES. I set equal to 4 and calibrate endogenously in order to achieve an average time spent working equal to a 1=3. The resulting value for is 0:383 which together with give an intertemporal elasticity of substitution approximately equal to a 1=2. The discount factor is calibrated endogenously to 1:005 in order to target a capital-output ratio equal to 2:89. This last figure is the average capital-output ratio for the period I calculate it following the Cooley and Prescott Methodology 15. TECHNOLOGY. I set equal to 0:35 that is the average of capital income over total income for the period (T. Cooley and E. Prescott 1995). The parameters for the labor augmenting technology are 13 National Vital Statistics Report, volume 58, number 10, March Economic Report of the President 2010, Table B Data for Residential and non-residential structures (equipment and software, structures) and consumer durables comes from Table 1.1. Current-Cost Net Stock of Fixed Assets and Consumer Durable Goods BEA April 2010 ( Data for the stock of Land comes from Flow Funds Accounts, Table B.100, Table B.102 and Table B.103. Inventories are taken from the Economic Report of the President 2010, Table B1.

12 12 calibrated as follows. The growth rate g is equal to 2:22% and is taken from the average growth rate of real per capita GDP during The parameter A 0 is a free parameter and I set it equal to 1. Also, I set the depreciation rate equal to 4% to assure an investment-output ratio equal to 21:38% 17, which was the average for the period. TAXES. I need to calibrate three taxes: the Social Security tax ss and the US Personal and Corporate Income Tax. For the first case, I calculate the average Social Security contribution as a fraction of total labor income for the period and set ss equal to 8:6%: 18. In the case of the US Personal Income Tax, the situation is more delicate. I need to adjust a parametric function to the effective average tax rate paid by an American Household. For that purpose, I use the N. Guner et al s (2008) estimates for married households. They use data from the US Internal Revenue Service for the year 2000 and calculate the average tax rate for every income bracket normalized by the mean household income for the period as: average tax rate D total amount of income tax paid number of taxable returns total ad justed gross income number of returns They fit the model: Average T ax Rate.Normalized I ncome/ D 1 C 2 log.normalized I ncome/ C where is the error term and obtain b 1 D 10:23% and b 2 D 7:33% with an R 2 D 99%: Figure 1 and 2 show the N.Guner et al (2008) and M. Gouveia and R. Strauss (1994) average and marginal tax rates estimates for the same data set. It is clear that there are no differences between the average tax rates for both tax functions. However, the Gouveia Strauss tax function displays a constant marginal tax rate for incomes higher than twice the mean household income. This situation does not correspond to the increasing marginal tax rates seen in the US Income Tax. On the other hand, Guner et al s. tax function reflects this fact quite well and that is the 16 Economics Report of the President 2010, Table B Investment comes from Economic report of the President 2010, Table B1. Consumption of durables is taken from Economic report of the President 2010 Table B I consider those contributions from Old Age, Survivors and DI programs. Social Security Bulletin, Annual Statistical Supplement, 2005, Tables 4:A:3.

13 THE MACROECONOMICS EFFECTS OF A NEGATIVE INCOME TAX 13 reason why I have chosen their tax function. What respects to the Corporate Income Tax, I set k equal to 7:48% in order to target the 1:74% average ratio of capital net of depreciations over total income for the 1987 and Prescott 1995) period(cooley IDIOSYNCRATIC SHOCKS. The efficiency profile e.z 0 ; j/ has an age-component j, which is taken from G. Hansen (1993), and an idiosyncratic shock-component z 0, which follows an AR.1/ process whose values are taken from J. Heathcote et al s(2010) estimation from the PSID data in the period They find a correlation coefficient of 0:973 and a variance for the innovations 2 " equal to 0:02. I use a Gaussian-Hermite quadrature procedure(g. Tauchen and R. Hussey 1991) to approximate this AR.1/ with a 21 states Markov process Q zz 0. I follow M. Flondé s (2008) approach that consists of taking a weighted average of the conditional and unconditional variance of the AR(1) as variance of the process and gives a good approximation for highly persistent processes. The initial distribution of shocks q.z/ follows a Gaussian Distribution with mean zero and a variance 2 z that is endogenously calibrated to match the 0:46 Gini coefficient for labor earnings in the US for the year Table 3 shows the 21 values of the shocks in log-scale with their initial and invariant distribution. B. Tax Reform s results. In order to understand the effects of a transfer in the tax scheme, I eliminate the implicit/explicit transfers in the actual US Income Tax through the introduction of a proportional tax, i.e. a NIT with 0% level of transfers, and then, I increase the transfer level in the NIT to 2:5% and 5% of per capita GDP in the benchmark economy. These quantitative exercises will let us evaluate the changes in the aggregate variables and understand how the transfer works.table 4 summarizes the results. In a world with a proportional tax, there is a drop in the marginal tax rate for higher incomes as it remains constant at a 12:28% level. This lower tax rate follows from the fact that there is no transfer to fund and no redistribution from high to low incomes. What is more, as GDP increases 10:13% from the benchmark case, the tax base is bigger and a lower tax rate manages 19 The interesting feature of this paper -and the difference with K. Storeletten et al.(2004)- is that they allow in their model for an endogenous supply of labor, which enables me to take directly their estimates for the AR(1) process. 20 US Census Bureau 2000.

14 14 to achieve a particular level of revenue. This means that medium and high productive agents are facing a lower tax bill while the opposite is true for low productive agents. Naturally, income and substitution effects come into play with opposite signs whether the agent has a low productivity or not. This is what it can be seen in the labor supply measured in efficiency units and hours worked. Both variables have increased but labor supply has increased more than hours (6:64% and 5:79% respectively). A lower marginal tax rate makes medium and high productive agents to supply more hours to the market (substitution effect), even though there is an income effect that works in the opposite direction. On the contrary, low productive agents deprive from their transfers face a negative income effect making them work more, while at the same time, a substitution effect, through high taxes, decrease the marginal rate of substitution between consumption and leisure. The effect is not symmetric and there is a change in the composition of the labor supply: high productive agents gain more participation at the expense of low productive agents. Therefore, average labor productivity has increased. To understand the increase in the supply of labor, it is necessary to take into account that in a model with endogenous labor supply decisions and incomplete markets, labor works as insurance for the working agents (J. Pijoan-Mas 2006). This fact together with the income and substitution effects above mentioned explains the significant increase in hours and labor supply. Naturally, the absence of transfers from the Income Tax has a positive impact on precautionary saving. The saving rate 21 increases 6:12% and this economy has a larger capital stock than the benchmark case. As a result, GDP has increased by the combination of more capital and labor. It is interesting to notice that the increase in capital (16:90%) and capital per unit of labor (6:64%) has increased the level of bequests (11:95%) and social security benefits (10:23%), and the wage rate (3:25%). Nevertheless, the increase is not enough to compensate the lack of transfers in the Income Tax and there is a welfare loss: the consumption equivalent variation (CEV) is 4:26%. Low and medium productive agents (type 1 thru 13) are worse off with welfare losses as high as 8%, while higher types (type 14 thru type 21) are better off with the most productive agents (type 21) experiencing the highest welfare gain of 15:13%. Let us move on to the scenario where the NIT has explicit transfers. The introduction of a transfer of 2.5%, roughly $1,150, reduces the welfare loss to a mere -0.55% and doubling the transfer to 5%, increases proportionally more the welfare gain to 2.6%. As the size of the transfer increases, the tax rate has to be increased to fund it and to make the tax reform revenue neutral. The marginal tax rate is 15.49% and 19.03% for the NIT with 2.5% and 5% level of transfers 21 I define the saving rate as the ratio of the difference of households assets holdings over GDP.

15 THE MACROECONOMICS EFFECTS OF A NEGATIVE INCOME TAX 15 respectively. The first thing to notice is that the higher the transfers, the less the need to save. In a setting with a 5% level of transfers, the saving rate has decreased -1.39%. The transfer is a source of insurance and the same picture repeats itself in hours, where from the original increase of 5.79% in the proportional tax setting, the increase reduces to 1.06% in the NIT with a 2.5% level of transfer (NIT 2.5%), to finally drop -4.27% in the NIT with a 5% level of transfers (NIT 5%). Labor supply that was 6.64% higher than the benchmark case starts to decrease with the increase of the transfer: 3.92% and 0.86% for the NIT 2.5% and NIT 5%. Interesting enough, in a NIT 5% labor supply remains practically the same as the benchmark case but there is a significant drop in hours worked. The change in the composition of the labor supply is more evident: average labor productivity has increased. As agents receive a transfer every period, they are in a better position to cope with a bad shock, working more when they are relatively more productive and consuming more leisure, which is a normal good, during bad times. Consequently, the NIT has a clear effect on insurance, through a reduction on precautionary savings and hours worked, and also on distribution and efficiency. The effect on distribution is reflected on the deterioration of the Gini coefficient on labor earnings from 0.46 to 0.47 in the proportional tax, 0.48 in the NIT 2.5% and 0.49 in the NIT 5% (see Table 5). The reason is simple: agents do not work during bad shocks and work more in good times, increasing the dispersion and concentration of labor earnings. Despite of the increase in inequality, welfare increases. The effect on efficiency comes from the fact that, for instance, in the case of NIT 5%, with less average hours worked and a decrease in the stock of capital, total output remains the same. The capital output ratio falls with the increase of the transfer. In a proportional tax setting, it increases 6.16%. In the NIT 2.5%, the increase is just 2.58% higher than the benchmark scenario and in the NIT 5% the capital output ratio drops 1.35%. A similar story happens to the capital per unit of labor: even though it is 3.9% higher in the NIT 2.5%, it falls -2.14% in the NIT 5%. Naturally, this situation has an effect on prices and transfers. The evolution of the wage rate from the proportional tax to a NIT 5% is characterized by a decrease from a 3.25% higher level than the benchmark to a -0.75% decrease. Obviously, an opposite phenomenon applies to the interest rate: from a decrease of -8.69% jumps to a 2.13% increase in the level. This story has a natural correspondence on distribution: young agents and low productive ones receive a significant proportion of their income through the retribution of their work, while retirees and high productive agents receive a larger share of capital income.

16 16 Retirees face an interesting trade off. On one hand, the drop in capital increases the interest rate and consequently, it has a direct benefit on them. On the other hand, social security benefits falls as the system is fully funded and the benefit is proportional to total labor earnings in the economy. What it can be seen is that the higher wages and labor supply, in the proportional tax setting, increase the social security benefits by 10.23%, and then this benefits starts to drop to remain practically in the same level in the NIT 5%. The fact that accidental bequests and social security benefits increase when there is a complete elimination of the Income Tax s transfers cushions the potential fall in welfare. Nevertheless, the opposite happens when transfers increase: their level will go down and they will ebb the welfare gains from higher transfers. This situation does not necessarily mean that retirees are worse off. Even though, social security benefits drop, transfers go up. Finally, a proportional tax, with the reduction of marginal tax rates for higher incomes, implies a welfare profile that is monotone increasing on productive types. The introduction of transfers change the picture: low productive agents benefits directly from the transfer while high productive types benefit from the lower marginal tax rates. The final outcome is a U-shaped figure for the welfare profile (see Figure 3). C. The Optimal NIT versus the Flat Tax. The NIT that maximizes ex-ante welfare, i.e. before the agent is born and knows his type, has a transfer level of 10% of the benchmark economy s per capita GDP, approximately $4,600, and a marginal tax rate of 27.95%. The welfare gain is equivalent to an impressive increase of 6.33% of individual consumption in every state of the world. The picture that emerges from this economy confirms many of the results seen in the previous exercise. Table 6 summarizes the results. The negative relationship between the size of the transfer and per capita GDP is repeated once again: GDP drops %, as a consequence of a % decrease in the capital stock and a -7.03% decrease in the labor supply measured in efficiency units. This decrease in capital confirms the drop in precautionary savings. The saving rate is reduced %, i.e. total savings falls more than the drop in GDP. The explicit transfer of the NIT enables agents to save less in order to cope with the uncertainty they face, implying a lower level of capital. The drop in labor supply is not explained by the decrease in hours worked. Actually, hours decreases %, a rate 2.5 times higher than the decrease in labor supply. A familiar picture from the previous exercise appears: agents substitute work by leisure when they are hit by a bad shock, working more when they are more productive. This means that the NIT provides

17 THE MACROECONOMICS EFFECTS OF A NEGATIVE INCOME TAX 17 agents with less incentives to use labor supply as means of insurance. Also, there is an income and substitution effects that come into play: the threshold that splits the active population into working and non-working agents has increased. As a result, inequality and the concentration of labor earnings increase. The Gini coefficient for labor earnings moves to 0.53 from 0.46, a significant 15% increase. The capital output ratio and the capital per unit of labor decrease % and % respectively. As a consequence, there is a change in prices: the wage rate decreases -6.23% and the interest rate increases 19.12%. Capital income earners are better off and the increase in the interest rate compensates them from the increase in the marginal tax rate. Social Security benefits and accidental bequests decrease % and % respectively. A natural consequence from the fall in savings, wage rates and labor supply. This fact does not necessarily mean that the total level of transfers in this economy, given by the sum of social security benefits, accidental bequests and the transfer from the NIT, has decreased. The Optimal NIT has lower marginal tax rates for the highest income than the US Income Tax. Nevertheless, the opposite situation is true for the low and medium incomes. The increase in the level of the marginal tax rate is a direct consequence of the size of the transfer, which in this case is not trivial. Thus, the welfare profile has changed from a clear U-shape of winners and losers to a figure with a single cutoff at the productive type 10: agents type 1 thru 9 experience welfare gains from 26% to 64% while the rest looses(see Figure 4). This result is understandable as shocks are extremely persistent, i.e. a shock, in this setting, reduces its level in half in 25 periods. Naturally, agents born with a low productivity shock need more time to recover themselves and want a transfer as high as possible in order to smooth consumption. On the contrary, agents with a good initial shock want the transfer to be minimal and low marginal tax rates. This tradeoff between low marginal tax rates and high transfers has a correspondence on the insurance and efficiency component of the NIT. The fact that the size of the transfer is important favors the insurance component over the efficiency aspect, i.e. the welfare gains comes from the fact that low ability type agents can insurance themselves against bad shocks. Now, I compare these results with a Flat Tax in order to put into perspective the potential welfare gains of the Optimal NIT and evaluate the desirability of the reform. I find that a deduction of 33% of the benchmark s per capita GDP ($46,000), i.e. $15,333, and a marginal tax rate of 18.47% maximize ex-ante welfare. It is clear that the NIT outperforms the Flat Tax, while the NIT implies a welfare gain of 6.33%, the Flat Tax implies a welfare loss of -0.12% This exercise does not take into account the welfare gains that may arise from the transition dynamics. Therefore,

18 18 This scenario is characterized by the replacement of the implicit/explicit transfers of the Income Tax with a fixed deduction. Therefore, the marginal tax rate will be lower than the Optimal NIT as there are no transfers to fund. There is one important difference from the previous case and is related in the way the welfare profile has changed. It is clear that high productive agents benefit but the picture is mixed for low productivity agents: the lowest ones are actually worse off. A result that it may look at odds from previous studies (e.g. G. Ventura (1999) and Diaz-Gimenez and J. Pijoan-Mas (2005)) but it is explained in the way the US Income Tax was modeled to capture the actual level of transfers present in the system (e.g. EITC, among others), which is not trivial for the lowest income. Naturally, these agents prefer a transfer rather than a deduction. As the productive types increase, the welfare profile starts to get a U-shape and a fraction of the low incomes are better off. This fact reinforces the idea that the election of the benchmark tax function deserves special attention. The per capita GDP increases 3.81% as a result of an increase on Capital (4.85%) and labor supply (3.26%). The latter has an increase higher than the increase in hours (1.96%), a natural consequence of the lower marginal tax rates that gives high productive agents more incentives to work and the increase in the lowest ability type s tax bill, due to the replacement of the transfer by a deduction. Agents in the low part of the distribution of productive types, between the lowest and the median, see a reduction on their tax bill while the medium types see the opposite phenomenon. This heterogeneous picture explains the mismatch between hours and labor supply and the fact that in some groups an income effect prevails over a substitution effect and vice versa. The saving rate remains practically at the same level with a modest increase of 0.89%. Nevertheless, total savings increases as a result of the elimination of the transfers and the need to increase precautionary savings. This loss of transfers is partially compensated by a 3.83% increase of social security benefits and the 5.91% increase of bequests. The wage rate increases 0.48% and the interest rate drops -1.33%. The increase in the wage rate partly offset the loss of the transfer for the low productivity types, whose main income comes from labor earnings. Summing up, a Flat Tax implies a higher GDP, capital accumulation and labor supply than the Optimal NIT but a considerable lower welfare. the welfare gains might have been positive if I had taken them into account. Nevertheless, the superiority of the NIT over the Flat Tax is such that taking them into account will not change the desirability of the reform.

19 THE MACROECONOMICS EFFECTS OF A NEGATIVE INCOME TAX 19 III. Sensitivity Analysis. In the previous section, I have established that the optimal NIT requires an important level of transfers due to the high persistent shocks and that there has been a change on prices, social security benefits and accidental bequests that dampens the potential welfare gains from the reform. Therefore, in this section, I analyze the role of prices by keeping them fixed, the elimination of accidental bequests and changes on the nature of the shocks present in the economy. 23 A. The role of prices: An Open Economy. In this exercise, I assume that the calibrated economy is open and therefore, the wage rate and the interest rate are kept fixed. I find that the optimal NIT in this scenario has a welfare gain of 6.5% and a transfer of 10% of the benchmark economy s per capita GDP. Even though the transfer level is the same as before, the marginal tax rate increases 2.8% to 28.74% (see Table 7). The reason of the increase lays on the shrinkage of the tax base: GDP decreases % against the % decrease from the previous exercise. This drop is completely attributable to a fall in the capital stock level. As the interest rate is constant, savings falls more than before, where the drop in savings was offset by the increase in the interest rate, exacerbating the fall in precautionary savings. Clearly, the saving rate falls %, doubling the % fall previously seen. On the other hand, labor supply increases, as it only drops -3.7% against the -7.03% drop. As the wage rate remains in the same level, leisure does not get cheaper as it did before, avoiding a higher decrease in labor supply. The same effect happens with hours worked (-12.14% versus %), where for one unit of decrease in labor, hours decreases 3.28 times. Naturally, leaving the wage rate in the same level gives more incentive to high productive type agents to supply more work, gaining more participation in the labor supply and changing its composition. Social Security benefits fall in a relation 1 to 3.5 (-3.6% versus %), compensating the fact that the interest rate is lower. Accidental bequests are reduced in half (-47.59% drop), experiencing a higher drop than in the original exercise (-29.24%). As can be seen, despite the transfer remains the same, there is a welfare improvement with agents working more hours, social security benefits rising and accidental bequests having a huge cut, while capital income earners and retirees are affected by the lower interest rate, and wage earners have their wage rate unaffected. This means that low productivity type agents, who benefit the most with the bequests, are better off if the wage rate does not change and this effect more 23 I will make all the comparisons against the Optimal NIT found in the previous section.

20 20 than compensate the fall in accidental bequests. On the other hand, retirees offset the interest rate effect with the high social security benefits. The fact that the interest rate is lower than it should be in a scenario with flexible prices, and that social security benefits remains at the same level, give agents less incentives to postpone consumption, explaining the increase in welfare. B. The role of accidental bequests. In the benchmark economy, the level of accidental bequests was calibrated as a lump-sum transfer to all living agents, a common assumption in this type of models. Nevertheless, the bequests are higher than what it is actually seen in the data for low incomes, lowering the potential gains from the reform. Therefore, in this exercise, I move to the opposite scenario and make the extreme assumption that all accidental bequests are completely taxed by the Government and the proceedings finance public consumption. Now, in order to the tax reform to be revenue neutral, it needs to raise enough revenue to compensate the replacement of the Income tax and the differences that may arise from the taxation of the bequests in the new scenario. Table 8 summarizes the results. The optimal NIT has a transfer level of 10% of the benchmark economy s per capita GDP and a marginal tax rate of 30.52%. The increase in the rate arises from the drop in the level of accidental bequests. As can be seen, the drop in precautionary savings implies a fall in the capital stock (-27.89% versus %) that leads to lower bequests and the need to raise the marginal tax rate to compensate the shrinkage of the tax base. In a world with no accidental bequests as lump-sum transfers, savings are higher from the very beginning and the introduction of the NIT s transfer makes the saving rate to fall more (-14.41% versus %). The welfare gains are an outstanding 8.8%, a 40% increment from the original experiment. The bequests are not as important for the high productive agents as they are for the low productive ones. Then, the introduction of a NIT with a 10% transfer implies welfare gains for the latter as high as 92%, while the changes in welfare for the former are not as spectacular. Labor supply drops -8.48% against the -7.03% originally seen, a 20% deterioration. This is explained by the higher marginal tax rate that gives disincentives to more productive types to supply more work. Hours deteriorates 10% (-19.32% versus %) and the message is the same as before: high productive types crowd-out low productive ones and the average labor productivity by hour worked increases. The higher fall in labor supply and capital implies a higher drop in GDP (-15.80% versus %). There is a change in prices with a lower wage rate (-8.04% versus -6.23%) and a higher