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Abstract

  1. Top of page
  2. Abstract
  3. 1. The Economy
  4. 2. Intergenerational Dynamics
  5. 3. Inheritance (Bequest) Taxation
  6. 4. Conclusions
  7. References
  8. Supporting Information

Ideas about what is ‘fair’ influence preferences for redistribution. We study the dynamic evolution of different economies in which redistributive policies, perception of fairness, inequality and growth are jointly determined. We show how including beliefs about fairness can keep two otherwise identical countries on different development paths for a very long time. We show how different initial conditions regarding how ‘fair’ is the same level of inequality can lead to two permanently different steady states. We also explore how bequest taxation can be an efficient way of redistributing wealth to correct ‘unfair’ past accumulation of inequality.

The poor want to tax the rich but that is not all what determines redistributive policies. Views about what is ‘fair’ and what is an acceptable level of inequality matters, above and beyond the individuals’ position in the income ladder.1 The same level of inequality may be more or less acceptable depending upon different beliefs about how wealth has been accumulated, namely by virtue of effort and ability or, on the contrary, by virtue of luck, connections or corruption. In one word, it matters for individual preferences whether different levels of income and wealth are ‘deserved’ or not, as confirmed by extensive empirical evidence.2 These views about inequality and justice (which we label ‘ideology’) determine tax rates and the evolution of the distribution of income and wealth. The latter generates changes in the proportion of wealth inequality due to effort or to other factors including luck and government policies. As a result of these developments, individuals’ preferences for redistribution evolve accordingly.

In this article we provide a politico economic model that can trace over time the evolution of policies (income taxes, wealth taxes and transfer schemes), the evolution of inequality, and of the preferences for redistribution, as a function of the changes in what individuals perceive as fair and unfair wealth differences. Generations of voters are linked by bequests; thus redistributive policies in the past, and past beliefs about what was ‘fair’ inequality matter for today's initial conditions and therefore for today's voters’ preferences. We focus upon several issues. The first one is how different initial conditions regarding fairness lead to two different steady states. We consider two economies with the same initial level of inequality. In one, all the inequality is ‘unfair’, whereas in the other, inequality is all ‘fair’. We show that even though all the observable characteristics of the two countries are identical (including initial inequality), the two countries may converge to two different steady states. We can think of the initial period as the first one in which tax policy is decided democratically and the initial conditions those determined by different pre-democratisation histories. For instance, a history of feudalism and rigid class divisions in Europe versus a more merit-based and more recent American capitalism. This result formalises the role of the perception of poverty and social justice as an explanation of differences in welfare policies on the two sides of the Atlantic as discussed informally in Alesina and Glaeser (2004). Second, we explore how a temporary shock to preferences, for instance a change in what is viewed as ‘fair’ inequality, may lead to long lasting dynamic consequences. Third, we study how different forms of taxation, income taxation versus bequest taxation, interact with the perceptions about fairness. Under certain conditions, a high level of bequest taxation is superior to income taxation to reduce the perceived level of ‘unfairness’ in inequality. This result is closely related to the issue of equalising opportunities at birth.

This article is related to the work of Alesina and Angeletos (2005a). However there are many differences. First of all, in the present article we use a probabilistic voting model rather than median voter model as they use. This allows us to be more flexible and to analyse various types of redistributive schemes, including multi-dimensional policies. Second, and related to the previous point, we can study in depth bequest taxation in addition to income taxation. This is crucial as the issue of equalising opportunity at birth can be central in a discussion about fairness. Third, given our rich dynamic specification, we can address issues of ‘shocks’ to preferences and to other parameters of the model, contrary to the static model by Alesina and Angeletos (2005a).3 This allows us to make statements about the endogenous evolution of ideology and tax policy. In addition, our framework is sufficiently flexible that it could incorporate Piketty's (1995) intra-dynasties evolution of heterogeneous beliefs about the incentive costs of redistribution. Another possible extension would be to incorporate Bénabou and Tirole's (2006) important point, namely allowing beliefs to be shaped not only by the actual data but also by agents’ psychological needs and objectives.

The present article is organised as follows. Section 1 describes the model. Section 2 illustrates the dynamic evolution of the model and reports the most representative simulation results. Section 3 extends to wealth taxation as distinguished from income taxation. The last Section concludes. The Matlab codes used in the present article are available from the authors upon request.

1. The Economy

  1. Top of page
  2. Abstract
  3. 1. The Economy
  4. 2. Intergenerational Dynamics
  5. 3. Inheritance (Bequest) Taxation
  6. 4. Conclusions
  7. References
  8. Supporting Information

We consider non-overlapping generations of individuals, indexed by t. The size of the population is constant, there is one active individual per-family, and the total mass of families is normalised to one. Each individual, indexed by i  ∈  [0,1], lives for one period and has a certain level of endurance to effort, βi > 0, luck, ηi ∈ R, and inner abilities, Ai > 0; average luck is zero, that is inline image. These family-specific variables are assumed to be fully persistent over time but our results are robust if we allow for non-persistent luck.4 Each individual i cares about consumption, cit, and how much wealth to bequeath to the next generation, kit– which we label ‘capital’. Effort, eit, on the job enters negatively in the utility function. All choice variables are constrained to be non-negative. The ‘private’ utility function is:

  • image(1)

0 < α < 1. The end-of-life gross wealth is:

  • image(2)

For simplicity, capital yields zero rate of return. Each generation votes on the proportional tax rate, τt, which is applied to end-of-life gross wealth zit; tax revenues are redistributed lump sum to all individuals, and the government budget is always balanced. For now we impose that income and initial wealth taxes are the same; in Section 3, we allow for different tax rates on income and wealth. End-of-life post-tax and transfer wealth is:

  • image(3)

where inline image is the per capita transfer. Individual income is yit = (Aieit + ηi)(1 − τt) − τtkit−1 + Gt, and the aggregate income of generation t is

  • image

which is identical to per capita income due to the population normalisation.

The warm glow intergenerational altruism implies that fraction α of end-of-life wealth is bequeathed, as seen by maximising uit subject to cit + kit = wit. Therefore, plugging the optimal consumption and bequest into the private utility function, we obtain:

  • image(4)

Individuals vote on the tax rate at the beginning of life, before deciding on effort. Maximising uit, using (4), (2) and (3), gives

  • image

which shows the distortion on the supply of effort induced by expected taxation; effort increases with the individual work ability and decreases in the disutility of effort.5

The definition of a period needs discussion. In the model the period is one generation and it is also the length of time for which the redistributive policy cannot be changed. The choice of a ‘tax rate’ should not be interpreted as the day-to-day or year-to-year changes in fiscal policy but the broad redistributive stand of a certain period in a certain country. For instance, more redistribution in the US with the Great Society in the 1960s, or with the New Deal in the 1930s, less redistribution starting with the 1980s in the US and England. In Europe an increase in redistribution at the end of the 1960s, possibly a slowing down today etc. In the numerical simulations, we can generalise the model on this point and allow a distinction between the time span of the life of a generation and that of the choice of a tax rate.6

1.1. Inequality and Fairness

In addition to the standard utility function described above, individuals care also about some measure of inequality. In our benchmark case, we assume that individuals tolerate inequality arising from innate ability and effort but are averse to inequality arising from everything else, luck and government policies. More specifically, let us define ‘fair’ utility and wealth as follows:

  • image

As each agent chooses kit = αwit, where α represents the generosity towards the next generation, we define fair consumption, fair bequest and fair disposable wealth as:

  • image(5)

U it , is then defined as:

  • image(6)

where

  • image(7)

and γ > 0 is the parameter which measures the importance of fairness. This representation of utility implies that individuals dislike deviations from a distribution of wealth/utility in which everybody gets only the benefits from effort and innate ability. Note that the difference between total wealth and fair wealth is due to luck and government intervention with taxes and transfers. The higher the tax rate, the lower the equilibrium choice of effort; therefore the larger is the percentage of individual income due to luck rather than effort and the larger the proportion of differences across individuals due to luck rather than effort.

1.2. The Polity

We use a probabilistic voting model.7 There are two parties –L, for ‘left’, and R, for ‘right’– each of which simultaneously and credibly commits to a tax rate τP ∈ [0, 1], P = L, R, at the beginning of each period. The individuals vote for a party at the beginning of their life, then they choose effort. The party that obtained the majority of the votes is elected to office, and it implements the announced tax rate and redistributes accordingly. Finally, individuals choose their consumption and bequest. Individuals have heterogeneous degrees of party identification: the complete utility function is then:

  • image

P denotes the party that wins the election, and can be L or R. Indicator function χL(P) is 1, if P = L and 0 if P = R. The random variable σit represents individual i’s pro-party L ideological bias, whereas ɛt is an aggregate random variable capturing party L’s popularity for time t. While we assumed (for simplicity) that individuals’ pecuniary utility and luck shocks are fully persistent across generations, political popularity may change from generation to generation both at the aggregate and at the family level. ɛt is uniformly distributed on support inline image, and individual specific variables σit are uniformly distributed on support inline image. All random variables are independent. Therefore, in the support of the corresponding distributions, the density function of aggregate popularity of party L is ψ > 0, and family-specific density functions are ϕi > 0, with the correlated (aggregate) component of the party identification assumed less variable than the individual components – that is ψ > ϕi, ∀i  ∈  [0, 1]. The two parties commit to their tax rates before they know the realisation of the random variables ɛt and σit. They only care about winning the election, and hence choose their policies inline image and inline image by trying to maximise the probability of being elected, pP, P = L, R.

The ‘popularity shocks’ should not be viewed as the day ebbs and flows of electoral politics. Given our definition of a period as one generation, these shocks should be seen as long-term switches of one generation to the left (say the 1960s) or to the right (say the 1980s in the US).8

1.3. Equilibrium

After simple substitutions, and momentarily neglecting the party L bias components, we obtain the indirect utility function of each individual in each generation. That function ultimately depends on exogenous parameters, on expected taxation, and on all the actual and fair wealth distribution of the previous generation:

  • image(8)

where inline image. The proof of Lemma 1 is in online Appendix A.

Lemma 1.  In pairwise majority voting, there exists a unique equilibrium in which the two parties will select the same policy variable, inline image, given by

  • image(9)

The same equilibrium policy variable would also be chosen by a biased social planner who maximises the following weighted aggregate welfare function:

  • image(10)

with each individual's indirect utility function (where effort, consumption and bequest are all optimal) being weighted inversely to vulnerability, 1/ϕi, to party-related attributes. In the special case in which individuals have the same densities ϕi = ϕ, Lemma 1 implies that inline image. Note that, from (8), the equilibrium tax rate inline image depends on generation t − 1’s bequest distribution kt−1, generation t − 1’s fair bequest distribution inline image and on the parameter vectors δ and η; that is inline image.

Under the benchmark symmetry assumption, ϕi = ϕ, and normalising by ϕ, we can simplify the relevant welfare function to:

  • image

The equilibrium tax rate inline image determines the level of capital and fair capital for each family of the current generation. Therefore, the link between different generations is summarised by the dynamics of kit and inline image:9

  • image(11)
  • image(12)

1.4. Discussion

Note that in (12), ‘fair’ bequests are obtained by removing the effects of the ‘luck’ variable, ηi, and of the taxes paid to and transfers received by the government from the parental end-of-life wealth. However, the indirect effect of tax rates on individual efforts is included in this definition of fairness. It could be debated whether or not ‘(1 − τt)’ should enter the ‘fair wealth’: after all, it is an individually rational response to the distortion induced by taxation and indeed eit = (1 − τt)Aiβi. If redistribution did not exist in the model, the individual would have exerted a first best effort level inline image.10 We have also run simulations under such a different view of fairness, based on ‘potential’ rather than actual efforts, without much change in the results about the dynamics of kit. By (12), it simplifies the dynamics of inline image, which would tend to αδi/1 − α. However, the results of our computations do not change qualitatively.11

2. Intergenerational Dynamics

  1. Top of page
  2. Abstract
  3. 1. The Economy
  4. 2. Intergenerational Dynamics
  5. 3. Inheritance (Bequest) Taxation
  6. 4. Conclusions
  7. References
  8. Supporting Information

Starting from an initial vector of actual and fair wealth levels, inline image, we use (8), problem (9) and (11) and (12), to iterate the model for an arbitrary number of generations and calculate the sequence of equilibrium values of the endogenous variables of our dynamic economy for all parameter vectors, initial wealth distributions and initial fair wealth distributions. By simulating the model for a sufficiently high number of generations, we can approximate the stable steady state value of the endogenous variables associated with each initial condition.

Generation t’s pair of distributions inline image describe the interaction of real and ‘ideal’ variables at time t. More precisely, the comparison between how society currently is – the actual distribution (kit)i ∈ [0,1]– and how society thinks it ‘should be’– the fair distribution inline image– sets the goals of the political action; together with the method of political competition – i.e. pairwise majority voting – this describes the political ideology prevailing for generation t in that economy. The resulting political equilibrium generates the evolution of inline image and therefore the political ideology (i.e. policy goals) prevailing in the next generation. Thus, we trace the evolution of ideology, fairness and redistribution, as well as the aggregate GDP per capita.

2.1. US versus Europe: Fair and Unfair Initial Conditions

Define as time zero the first period in which tax policies are decided democratically with full participation.12 Therefore, the initial distribution of ‘fair’ and ‘unfair’ wealth inline image is the result of previous history from t =  − ∞ to 0. Before democratisation, tax policy was chosen in political systems in which only a (wealthy) minority decided tax policy. In Europe, a history of feudalism and wealth related to nobility is clearly different from the history of the US, where modern capitalism developed without a long previous history of privilege and rigid class separations. Thus, for a given total level of inequality at time zero (full democratisation), the degree of ‘unfair’ inequality can be safely assumed to have been higher in Europe.13

The first experiment looks only at the effect of different initial conditions, namely different conditions at the time of democratisation. After democratisation the two countries become identical. The ‘United States’ would be represented by our Country A, whereas ‘Europe’ would be Country B. The two countries have the exact same level of inequality at time zero, but in the US it is all ‘fair’, whereas in Europe it is all ‘unfair’. In other words, the ‘ideal’ level of inequality in the US is the one actually observed, in Europe it is totally different, namely Europe would like to have perfect equality as all the inherited one is unfair. Obviously this is an extreme example which generalises to different ratios of fair versus unfair wealth in the two places. In the online Appendix B, we describe how a different social welfare function before democratisation and/or a different pattern of ‘luck’versus effort may have led to different distributions of ‘fair’ and ‘unfair’ wealth at the time of democratisation, which we label time zero. Here we examine the post-democratisation dynamics.

To isolate fully the effect of initial conditions, we have assumed that after the democratisation the two countries are totally identical. They have the same wealth distribution, the same technology, the same preferences and the same process determining luck. As can be seen from Figure 1, the effect of these initial differences in ‘fairness’ lead to two different steady states. Country A converges to a steady state characterised by low unfairness, low redistribution and high GDP, whereas Country B to a steady state characterised by high unfairness, high redistribution and low GDP.

image

Figure 1. Unfair and Fair Initial Conditions

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The intuition is simple. By striving to redistribute wealth to correct unfairness in the initial conditions generated by the past role of luck in individual success, Country B chooses higher tax rates, which discourages individual effort, thereby self-perpetuating luck as a source of income differences. Thus, Country B reintroduces luck in an attempt to eliminate past accumulated ‘luck’. As a consequence of the implied higher tax rates, its GDP never catches up with that of Country A. We have two steady states only for some parameter values (but for a vast range of them). For other parameter values, the two countries converge more or less slowly to the same steady state distribution of actual and fair wealth.

Higher values of the parameter γ, which represents the importance of fairness in society, and of the intergenerational generosity α, increase the possibility of having multiple steady states. In fact, if fairness is considered important, differences in the initial level of unfairness have stronger influence on tax policies: a country which starts with an unfair distribution of wealth implements higher tax rates. Similarly, the persistence of wealth and ideology depends highly on the intergenerational generosity parameter α. The higher parameter α, the higher the influence of parental wealth and ideology on children. Therefore, different initial conditions are more likely to have long-term influence, including leading the economy to different steady states.

2.2. A Temporary Shock; the ‘Hippie’ Generation

In this subsection, we study the effects of a one period unexpected ideological shock; we label it the ‘hippie’ generation of the 1960s with its leftist turn. We can model this ideological shock in various ways but one which seems appealing is as follows.14 Imagine that the hippie generation becomes not only averse to ‘unfair inequality’, as in our benchmark model but also becomes averse to inequality per se, as measured by the variance in end-of-life post-tax wealth. In other words, the ‘hippies’ turn against inequality even when generated by differences in hard work and ability. Thus, they have preferences for redistribution in which:

  • image

The effects of this shock are shown in Figure 2.

image

Figure 2. Temporary Shock

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To evaluate the effect of this temporary shock, we consider two countries in the same initial steady state (defined by the model parameters). Country A illustrates the benchmark without the ideological shock, Country B has the shock. The ‘hippie’ generation of Country B raises taxes, with a consequent immediate reduction in total inequality, measured by the Gini coefficient. This policy also reduces per capita GDP and wealth. What is interesting is that, although the egalitarian ideological shock lasts only one generation, the high level of redistribution reduces fairness due to the large government redistributive intervention which has not distinguished between luck and effort. When ideological preferences against unfairness revert to normal, to correct the consequences of the previous wave of redistribution, taxes and transfers are heavily downsized, overshooting even the steady state.15 Examples of oscillations like these may capture the Thatcher and Reagan reaction to the 1960s and 1970s, and then an adjustment by Blair and Clinton.

2.3. Extensions

In the working paper version of this article we describe several additional simulation experiments and examples. For instance, we have also investigated several alternative definitions of fairness. First we consider the case in which tax and transfers are considered part of fair wealth. Second, we have looked at cases in which the effect of Ai is part of luck. One may argue that being born intelligent is part of a sort of genetically induced ‘luck’. Alternatively, one may argue that intelligence is fostered by growing up in a rich family with more child care and investment in education. Finally, we have considered the case in which individuals dislike inequality per se, namely any deviation of wealth and utility from equality for all at the average is costly. The latter would be an extreme definition of fairness, in which any difference in wealth even if arising from harder work and more effort is unfair.

3. Inheritance (Bequest) Taxation

  1. Top of page
  2. Abstract
  3. 1. The Economy
  4. 2. Intergenerational Dynamics
  5. 3. Inheritance (Bequest) Taxation
  6. 4. Conclusions
  7. References
  8. Supporting Information

Our model, which focuses on ‘social justice’, is especially useful to discuss inheritance taxation. Taxing wealth, or more precisely inheritance/bequests, can be an especially useful and a ‘quick’ way of re-establishing ‘fairness’ without having to tax income for many generations. A bequest tax which redistributes at the beginning of the individuals’ life is also closely related to the issue of equal opportunities at birth. Our probabilistic voting structure allows multi-dimensional voting and so we can consider different wealth taxes and income taxes, which in the previous Sections were constrained to be the same. To keep the analysis as simple as possible, we model taxation in two polar cases, stacking the deck in its favour first, (labelled ‘inheritance taxation’) and against it in the second (labelled ‘bequest taxation’).

3.1. Non-Distortionary Inheritance Taxation

3.1.1. The economy

Each generation votes on the wealth tax rate, τwt, which is proportionally applied to beginning-of-life gross wealth kit−1 and on the income tax rate τyt; all tax revenues are to be redistributed lump sum to all individuals. The government budget is always balanced. Using the previous definitions, the end-of-life wealth of each individual is

  • image(13)

where inline image

Notice that, consistently with the ‘warm glow’ altruism16 by parents, the future taxation of inherited capital, voted for by generation t is not internalised by generation t − 1.

Individual income is yit = (Aieit + ηi)(1 − τyt) − τwtkit−1 + Gt, and the aggregate income of generation t is

  • image(14)

which is identical to per capita income due to the population normalisation. Warm glow intergenerational altruism implies that fraction α of end-of-life wealth is bequeathed, as seen by maximising uit subject to cit + kit = wit. Therefore, plugging the optimal consumption and bequest into the private utility function, we obtain:

  • image(15)

Individuals vote on taxation at the beginning of their life, before deciding on effort. Maximising uit, using (13) and (15), gives

  • image(16)

which shows that individual effort gets discouraged only by expected income taxation, and is increasing in the individual work ability and decreasing in the disutility of effort. This suggests that our inheritance tax rate could be the best fiscal instrument to reduce unfairness because it does not discourage individual effort. In fact, in light of (16) and (14), aggregate income becomes:

  • image(17)

As inheritance taxation is non-distortionary,17 to maximise GDP one should use only the inheritance tax and set the income tax to zero. This would apply to a standard model but not in our set up, as our voters care both about consumption (thus GDP) and fairness. The next subsection will clarify this point. The law of motion of actual and fair wealth of each family i can now be written as:

  • image(18)

and

  • image(19)

They are simply the equivalent of (11) and (12), after decomposing τt into τyt and τwt. As before, we use a probabilistic voting model, no changes in the structure of the polity. The equilibrium tax rates18inline image are used to determine the level of capital kit and fair capital inline image, whose distribution will be the state variable of period t + 1.

3.1.2. Equilibrium tax rates

We can characterise the equilibrium inheritance tax rate as follows:

Proposition 1.  The equilibrium value of the wealth tax rate inline image, at all dates t is:

  • image(20)

Proof.  See online Appendix A.

According to Proposition 1, τwt is high if luck plays a large part in explaining beginning-of-life wealth (i.e. cov(ηs, kst−1) is high) and actual inheritances are not positively related with fair inheritances (i.e. inline image is low). Will voters always prefer a zero income tax rate to maximise aggregate income? As we shall see, this is not the case, unless people do not care about fairness: as long as γ > 0, the distortionary income taxation will be used to correct unfairness in period t. Indeed we have:

Corollary 1.  The steady state equilibrium income tax rate inline image is always positive, if γ > 0.

Proof.  See online Appendix A.

Numerical simulations show the following:

  • (i )
     The transition to the steady state is generically faster than in the case of τyt = τwt = τt .
  • (ii)
     The steady state inline image is unique.
  • (iii)
     The wealth tax rate is often large and income tax small.
  • (iv)
    The use of both income and wealth taxes always delivers a superior macroeconomic performance, in terms of aggregate income and long-run wealth, than the use of income tax only.

We can find an explicit solution analytically for an important special case. Most notably:

Corollary 2.  If all the inequality derives from luck, i.e. if inline image and inline image, then the steady state levels of inline image and inline image are:

  • image

Proof.  See online Appendix A.

3.1.3. What if inheritance is viewed as luck?

So far we have assumed that the agents consider bequest as a fair component of wealth, for the part that depends on the ability and effort of their parents. In the opposite scenario, people would think that being born in a rich family is just luck. Hence, assuming that the individuals consider any difference in the inherited capital endowment as undeserved, and hence unfair, it is relatively straightforward to prove19 that if the variance of ‘luck’, inline image, is not less than 25% of the variance of the combined ability inline image, the steady state inheritance tax rate becomes 100%. Moreover, if ability and luck are not persistent but instead are independently and identically distributed over the generations, then20inline image, for all t.

3.2. Distortionary Bequest Taxation

We now consider a wealth tax levied at the end-of-life, but now we allow it to be different from the income tax. The sum of both taxes would be a tax on total end-of-life wealth. As bequests are taxed, at rate τbt, before being transmitted to the next generation, the parents' savings get taxed while they are still alive, with the proceeds being redistributed within their generation. This suggests the need to reconsider the distortionary character of bequest taxation, with the potential to discourage individual effort and therefore lead to lower equilibrium values of the bequest tax rate than in the previous subsections’ inheritance tax rate.

In this subsection we therefore assume that, when evaluating end-of-life utility according to (1), the parents take into account net bequests, that is:

  • image

Within the stylised demographics of our model, this structure is reminiscent of the Unified Gift and Estate Tax system used until recently in the US, in which taxation is levied on the estate transferred, regardless of the transfer happening after death (by a will) or before (as a gift). A similar estate tax system is currently in existence in the UK. Intergenerational altruism implies that fraction α of the end-of-life wealth is bequeathed, as seen by maximising uit subject to cit + bit = wit. Therefore, substituting the optimal consumption and bequest into (1), we obtain:

  • image(21)

and hence:

  • image

As before, fiscal policy platforms are voted by each generation before exerting their effort choices. Income tax rate, τyt, is proportionally applied to end-of-life incomes. All tax revenues are to be redistributed lump sum to all individuals. Hence,

  • image(22)

The government budget is always balanced and, after rearranging, can be written as:

  • image

As taxation is known at the beginning of life, before the effort choice is taken, maximising uit, using (21), (1) and (22), gives optimal effort choice

  • image

which shows that individual effort will be discouraged by expected taxation, and is increasing in the individual work ability and decreasing in the disutility of effort.

Hence equilibrium lump sum transfers are:

  • image

Consequently, the reduced form private utility is:

  • image(23)

The generation t individual i utility, Uit, after fairness considerations are included and before including the political party bias, is:

  • image(24)

where

  • image(25)

The laws of motion of actual and fair wealth of each family i now become:

  • image(26)

and

  • image(27)

As in the case of the previous subsection, with perfectly symmetric political bias the resulting probabilistic voting equilibrium will maximise the utilitarian welfare functional, that is

  • image(28)

In the following subsection we illustrate some numerical simulations on inheritance and bequest taxation.

3.3. Numerical Simulations

We have run several simulations of the different scenarios in the presence of multi-dimensional policy, and tracked the evolution of ideology, fiscal policy, GDP and inequality in the presence of taxes on inheritance/bequests. The inheritance tax along the lines of Section 3.1 has strong beneficial effects on the economy, whereas the bequest taxation of Section 3.2 does not add to per capita income anything substantial, especially when simulated using data calibrated to match some empirical moments.

In particular, with data calibrated to the UK, the increase in steady state per capita GDP from having the two tax instruments compared to the only presence of an income tax, is a scanty 1%. The economic intuition from this result is easily given: as (23) shows, the bequest tax rate distorts effort no less than does the income tax rate but it does not selectively correct the effects of luck, as partially achieved by the income tax rate.

Instead the inheritance taxation of Section 3.1 can be very beneficial. In what follows, we allow a switch to the non-distortionary inheritance tax regime sketched in Section 3.1. That is first we assume that the country initially adopts a distortionary bequest tax regime stylised in Section 3.2, then we make the country switch to a non-distortionary inheritance tax regime voted by the inheritance recipients. In both cases, voters also vote for an income tax rate. We assume the economy to be initially in a steady state and, considering the average individual, we find values of parameters21α, inline image and γ that allow the best match of the following moments of the British economy: the net national per capita income, final consumption expenditure as a percentage of GDP and taxes on income, as well as bequest and gift taxes, as a percentage of GDP (2008 data).

Figure 3 depicts, in a highly stylised way, the current approximated situation22 in solid line (Country A) and the new fiscal regime (Country B), in dashed lines.

image

Figure 3. Policy Shock

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We assume that the fiscal reform takes place in period 5, just to facilitate the illustration of the initial steady state. As the simulated dashed lines show, convergence to the new steady state is achieved in just two periods. The income tax rate converges to a very small but positive level (0.02%) in one period, whereas the initial wealth tax rate, after an initial overshooting, tends in two periods to its new steady state level of about 24.69%.

As is clear from Figure 3, our simulation confirms the strong potential gains from introducing a tax targeted to inheritance-related wealth, confirming what we had expected based on our previous analytical results: the new fiscal policy would allow income taxation to be reduced drastically and stimulate a huge increase in GDP. Per capita GDP increases from £23,293 to £26,148, with 12.26% growth. The transition to the new steady state seems quite rapid. Interestingly, due to this change in the tax composition, the total tax collection increases along with a permanent increase in per capita GDP. Notice that per capita GDP, negatively depending on the income tax rate as per (17), converges monotonically to its new steady state, insensitive to the inheritance tax's non-monotonic pattern.

4. Conclusions

  1. Top of page
  2. Abstract
  3. 1. The Economy
  4. 2. Intergenerational Dynamics
  5. 3. Inheritance (Bequest) Taxation
  6. 4. Conclusions
  7. References
  8. Supporting Information

We have shown how the evolution of the political ideology regarding the fairness of the constellation of income and wealth in society can generate economic and political persistence in inequality, redistribution and growth. We have shown how the perception about what is ‘fair’ or not may generate very different policy choices even in countries which would otherwise be identical. We have also shown how temporary shock to preferences/ideology may have long lasting effects. Finally, we have explored in detail the issue of inheritance taxation. We have shown under which conditions inheritance taxes can be used to reduce more quickly than otherwise the accumulated stock of unfair inequality embodied in bequests. This result is closely connected with the discussion of equalisation of opportunities at birth.

Footnotes
  • 1

     See for instance the recent survey of preferences for redistribution by Alesina and Giuliano (2010) and the references cited therein. Alesina et al. (2004) discuss different levels of inequality tolerance in various countries. Alesina and Glaeser (2004) focus on a comparison between Continental Europe and US. Persson and Tabellini (2000) provide an excellent overview of politico economic models of redistributive policies.

  • 2

     See Alesina and Giuliano (2010) for a survey of the literature on this point.

  • 3

     For additional results along the same lines see Alesina and Angeletos (2005b). For a comment see Di Tella and Dubra (2010).

  • 4

     See the working paper version of this article, Alesina et al. (2009).

  • 5

     As in Heckman (2008), we could distinguish between cognitive abilities (here summarised by Ai) and non-cognitive abilities (1/βi).

  • 6

     See the working paper version of the present article for an extensive discussion of this point.

  • 7

     Note that this voting model, due to Lindbeck and Weibull (1987, 1993) does not require single peakness of preferences.

  • 8

     See Song (2012) for an interesting model of political economy with persistent political ideology shocks.

  • 9

     Note that the distribution of δi should be high enough relative to the support of the distribution of ηi in order for end-of-life wealth never to be negative. See Lemma A1 in online Appendix A for a sufficiency condition.

  • 10

    Di Tella and Dubra (2010) show that in the static versions of the Alesina and Angeletos (2005a, b) model this assumption, namely that fair income does not include taxes and transfer, is crucial to obtain the two equilibria results. In our dynamic extension of the Alesina and Angeletos (2005a) model, the point raised by Di Tella and Dubra (2010) does not apply.

  • 11

     Another objection could be raised against purging additive luck ηi rather than both luck and ability Ai. Formally, luck enters additively while ability as the marginal product of effort: both could be viewed as ‘gifts of nature’. Replacing Ai with inline image and using inline image as the valued added component of the end-of-life wealth, however, would not change the qualitative results. In fact, individual ability, Ai, would still enter multiplicatively indirectly via optimal effort choice. Hence, we can say that all the main qualitative results from the simulations are robust to the introduction of multiplicative luck, provided that also additive luck is present. Notice that, while in the previous case replacing Ai with its expected value in the direct abilities reduced the variance of δi (due to the elimination of the quadratic exponent on abilities), eliminating the variance of Ai completely could even increase the variance of δi.

  • 12

     Historically democratisation has been a long and gradual process but for simplicity we abstract from this here.

  • 13

     We do not consider here issues of slavery and race relations in the US as a determinant of inequality and preferences for redistribution. See Alesina and Glaeser (2004) for an extensive discussion.

  • 14

     An alternative way would be an increase in γ. This can be easily studied as well.

  • 15

     This overshooting occurred in all the simulations we have tried, exploring a wide range of parameter values.

  • 16

     See Andreoni (1989) for introducing the Assumption that ‘people derive some utility from the act of giving’ (p. 1457). That is, ‘parents derive utility by giving to their children, independently of the extent to which their children actually benefit from the bequest’ (Aghion and Bolton, 1997, p. 154). This Assumption about preferences is also shared by Galor and Zeira (1993) and Alesina and Angeletos (2005a).

  • 17

     Generation t cares about gross bequest and the inheritance tax is a lump sum tax freely decided by the next generation.

  • 18

     See Lemma A2 in online Appendix A for a more technical discussion.

  • 19

     See Proposition A1 in online Appendix A.

  • 20

     See Corollary A1 in online Appendix A.

  • 21

     Namely, α = 0.3135, inline image, and γ =  3.553.

  • 22

     In our model, the approximated income tax/GDP is 10.92% and the approximated bequest tax/GDP is 0.006%.

  • 23

     Simple graphing shows that any parabola y = ax2 + bx + c sloping down at x = 1 and positive at x = 0, will be positive for all 0 ≤ x < 1.

  • 24

     The intersection from above is a minimiser of the social welfare functional, and hence it will not be an equilibrium.

References

  1. Top of page
  2. Abstract
  3. 1. The Economy
  4. 2. Intergenerational Dynamics
  5. 3. Inheritance (Bequest) Taxation
  6. 4. Conclusions
  7. References
  8. Supporting Information
  • Aghion, P. and Bolton, P. (1997). ‘A theory of trickle-down growth and development’, Review of Economic Studies, vol. 64(2), pp. 15172.
  • Alesina, A. and Angeletos, G. M. (2005a). ‘Fairness and redistribution’, American Economic Review, vol. 95(4), pp. 96080.
  • Alesina A. and Angeletos, G. M. (2005b). ‘Corruption, inequality and fairness’, Journal of Monetary Economics, vol. 52(7), pp. 122744.
  • Alesina, A. and Giuliano, P. (2010). ‘Preferences for redistribution’, in ( J. Benhabib and A. Bisin, eds.), Handbook of Social Economics, pp. 93131, Amsterdam: North Holland.
  • Alesina, A. and Glaeser, E. L. (2004). Fighting Poverty in the US and Europe: A World of Differences, New York: Oxford University Press.
  • Alesina A., Di Tella, R. and McCulloch, R. (2004). ‘Inequality and happiness: are Europeans and Americans different?’, Journal of Public Economics, vol. 88(9–10), pp. 200942.
  • Alesina A., Cozzi, G. and Mantovan, N. (2009). ‘The evolution of ideology, fairness and redistribution’, NBER Working Paper No. 15587.
  • Andreoni, J. (1989). ‘Giving with impure altruism: applications to charity and Ricardian equivalence’, Journal of Political Economy, vol. 97(6), pp. 144758.
  • Bénabou, R. and Tirole, J. (2006). ‘Beliefs in a just world and redistributive politics’, Quarterly Journal of Economics, vol. 121(2), pp. 699746.
  • Di Tella, R. and Dubra, J. (2010). ‘A note on fairness and redistribution’, Working Paper, No. 11–059, Harvard Business School.
  • Galor, O. and Zeira, J. (1993). ‘Income distribution and macroeconomics’, Review of Economic Studies, vol. 60(1), pp. 3552.
  • Heckman, J. (2008). ‘Schools, skills, and synapses’, Economic Inquiry, vol. 46(3), pp. 289324.
  • Lindbeck, A. and Weibull, J.W. (1987). ‘Balanced-budget redistribution as the outcome of political competition’, Public Choice, vol. 52(3), pp. 27397.
  • Lindbeck, A. and Weibull, J. W. (1993). ‘A model of political equilibrium in a representative democracy’, Journal of Public Economics, vol. 51(2), pp. 195209.
  • Persson, T. and Tabellini, G. (2000). Political Economics: Explaining Economic Policy, Cambridge, MA: MIT Press.
  • Piketty, T. (1995). ‘Social mobility and redistributive politics’, The Quarterly Journal of Economics, vol. 110(3), pp. 55184.
  • Song, Z. (2012). ‘Persistent ideology, and the determination of public policies over time’, International Economic Review, vol. 53(1), pp. 175202.

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. The Economy
  4. 2. Intergenerational Dynamics
  5. 3. Inheritance (Bequest) Taxation
  6. 4. Conclusions
  7. References
  8. Supporting Information

Appendix A. Proofs.

Appendix B. US versus Europe.

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ECOJ_2541_sm_AppendixA-B.pdf114KSupporting info item

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