TAXATION OF INHERITANCE: EVIDENCE FROM NORWAY

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TAXATION OF INHERITANCE: EVIDENCE FROM NORWAY

Jørgen Mørkved Opjordsmoen

Samfunnsøkonomisk analyse

Department of Economics University of Oslo

November, 2019

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ACKNOWLEDGEMENTS:

I would like to express my heartiest gratitude and sincere thanks to Paolo Giovanni Piacquadio, associate professor, Department of Economics, University of Oslo for not only providing me crucial guidance and feedback as a supervisor throughout this study, but also for introducing me to Rolf Aaberge and his project on inequality at Statistics Norway. These were both invaluable to my thesis. I would also like to sincerely thank Rolf Aaberge, researcher at Statistics Norway, and everyone at Statistics Norway for the fantastic opportunity to write my thesis as a part of the project on inequality and be allowed access to their data as well as financial support. I was incredibly fortunate to get this opportunity. Finally I’d like to thank my parents for their support and encouragement throughout my years of study and through the process of this thesis.

Jørgen Mørkved Opjordsmoen

Abstract

There is debate among economists and the public about the role of inheritances and their taxation. Recent literature has found large inheritances to increase inequality in the long run. The arguments for and against its taxation are therefore about efficiency and equity. I describe how the taxation in Norway was reduced in the late 20th century and beginning of the 21th, before being removed in 2014. I use a simple life cycle hypothesis model to show why households leave inheritances whether they have a bequest motive or not. I then present various motives for bequeathing and show how bequests resulting from such motives change the efficiency of a tax on inheritance compared to bequests left as a result of uncertainty in lifetime. Assuming the motives exist, I set up a simple theoretical model to make predictions of how a tax on inheritances might affect households’ behavior.

I then test my predictions using econometric regression on tax return data sets from Statistics Norway. I find that there is a significant effect of the tax on the households’ behavior. Increasing the tax rate by one percent is predicted to reduce the inheritances by more than one percent. This result holds both for parents that are simply bequeathing because it’s the end of their life and they have no choice of whether to do it now or later, and for those that live on in later years. My findings suggest that taxation of inheritance comes with a significant efficiency cost.

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1 Introduction

The role of inheritance and its optimal taxation has been a debated topic among economists and in the public audience for a long time. The opposing arguments are about equity and efficiency. Large inheritances have long been considered to increase wealth inequality (Wedgwood, 1928). With large inheritances, each generation of a rich family may earn a rent on their inheritance. This in turn lets each generation become richer with little risk of becoming poor (Piketty, 2011). Recent literature such as: Boserup et al.

(2016), Elinder et al. (Forthcoming), Karagiannaki (2017), Wolff (2002) and Nekoei et al. (2018), has found the opposite effect, but this seems to only hold in the short term.

In the short term, the effect on inequality is found to be negative because of high intergenerational wealth mobility. In the long-run the effects of the inheritances on wealth inequality are determined by the behavioral responses they induce and how they differ across the wealth distribution. The majority of heirs consume their wealth, while the wealthiest heirs leave most of their inheritances intact.

In his Principles of Political Economy (1848), Mill argued that bequests go against the ideal of free competition, since they create an inequality between individuals. However, Mill also argued that in the case of a testimony of the deceased, one should respect the deceased’s will to give. In the case of deaths where there is no will left behind, this aspect is removed. In that case, there is therefore support for a confiscatory tax of the inheritance. In this case the whole bequest would be levied by the government as tax revenue. This is why there has been a conventional view in public finance that such bequests should be subject to a confiscatory tax (Kaplow, 2010).

There are three objections that have been raised against this. Blumkin and Sadka (2004) argue that a non-confiscatory tax on accidental bequests has the desirable con- sequence of making the demogrant of an optimal linear income tax system effectively non-uniform. It will act as an additional instrument and increase the efficiency of the tax system. Second, Cremer et al. (2012) observe that bequests, when publicly observ- able, have informational content if they are correlated with relevant characteristics of tax- able agents. This content must be incorporated in the design of optimal tax struc- tures. Third, Fleurbaey et al. (2018) argue that the 100% taxation view of accidental

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bequests doesn’t take into account that the timing of death generates inequalities not only among the descendants of the deceased because of the their inequalities in bequests, but also among the deceased themselves because of the inequalities in consumption and longevity.

In this paper I contribute to this debate by studying taxation of inheritance in Norway and identifying the effects of such a tax. Building on the literature, I assume that taxation of inheritance promotes wealth equality. Both by reducing the inheritances and by levying taxes that can be redistributed. I also assume that there is an efficiency effect associated with the tax. I assume that households’ behavior is affected by the tax. But how large is this effect? How much of what households leave as inheritances is a conscious decision? It seems possible that a substantial part of inheritances are actually meant as savings intended for later consumption, rather than to be left as an inheritance. This paper will test the assumption that households’ behaviors are affected by taxation of inheritance and quantify the magnitude of this change, so as to best be able to give a policy recommendation about inheritance taxation.

Studying Norwegian data allows me to gain insights about the preferences of Nor- wegian households. These insights will however not necessarily be those of humans in general. Norwegian households have a unique culture, wealth and income that might differ from other countries. These factors may affect how a tax on inheritance affects the households. In countries where there is a lot of poverty and low levels of opportunity, one might expect that households have a large interest in making sure they leave as much wealth as possible for the welfare of their children. On the other hand, households in rich countries might believe that their children will have good opportunities in life whether they get a large inheritance or not. The household would then be less concerned about leaving an inheritance. In such a situation one would expect that households in the rich country would have a more elastic desire to leave bequests, while the poor households would have more inelastic preferences. The households in the rich country might substitute away from leaving bequests since part of every bequest they now leave is worth less than before, and they would therefore be better served using more for consumption instead. For the poor households, I’m assuming that they face less of an alternative cost when it comes to leaving an inheritance. They’re consuming far less and saving most of their income. The poor households would in this case not substitute away from inheritance to the same degree as the rich households. One could even imagine that bequesting would be an inferior good to the poor households. In this case they would

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increase the share of their income they use for bequests. This could be because there is a specific minimum amount they want their heirs to get. From this thought-experiment I’d assume that Norwegians would have a relatively large response to the tax compared to the rest of the world. Norway is relatively rich (UN, 2018) with good security nets. If the government added additional costs to bequests I’d therefore expect for Norwegians to decide to consume relatively more of their wealth instead of saving it for bequests. The results from this paper would therefore be most relevant to countries similar to Norway, but if similar results could be found in other countries like Norway this would imply that humans in societies like Norway’s have similar preferences.

Economic analysis of inheritance is a very difficult subject. The first and biggest problem is that data on bequests and inheritances is extremely scarce. Even with data from Statistics Norway I did not have the variable for bequests given, but worked with bequests and gifts recieved. In countries with lesser data gathering institutions getting data on these variables will be extremely difficult. An aspect about inhertitances that complicates the study of them is the fact that they aren’t “flows” like most other economic variables. Most economic variables change from year to year letting us observe them in relation to other variables and through this control for changes in the inheritance that actually stem from changes in those other variables. Inheritances are generally only different from zero in one instance, which means there is only one observation per person and no other years to compare it to. This means that to study changes in the inheritance one must compare individuals with other individuals. But unless one has extremely detailed variables about each person it’ll be hard to find why the inheritance differs. In this paper I solve this problem by creating groups in each period and comparing the groups between the periods.

In section 2 of this paper I give an overview of the history of inheritance taxation in Norway. Section 3 provides an overview about economic theory about inheritance taxation. Based on the theory, I present a model in section 4 to predict how the households might be affected by the tax. In section 5 I present my data and method of estimation.

Based on the model in section 4 and the data from section 5, using Stata I perform regressions in section 6 to research behavioral effects of inheritance taxation. I present the results of my regression in section 7. Finally, in section 8 I will conclude what my findings are and quickly discuss inheritance and its taxation’s relevance to inequality in Norway.

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2 Taxation of inheritance in Norway

Taxation of inheritance was first introduced more than two centuries ago in 1792, while Norway was still part of Denmark. Although it changed multiple times throughout the next century, it stayed relatively low, never being higher than 4% until after the first world war. At this point there was a marked increase. In 1925/26 the highest tax rate on children and other inheritors like stepchildren was increased from a maximum of 4%

to a maximum of 30% for bequests larger than 485,000 NOK. The tax rates on other tax groups faced similar increases. In the interwar period and for a time after the second world war the tax rate remained relatively constant, going from a progression from 1%

to 30% to a progression from 2% to 35%, while the tax bases were slightly changed. Tax exempt bequests were continually decreased until 1965, while the tax base of the top tax rate was sometimes increased and sometimes decreased.

Furthermore, from 1947 to 1967, there was an additional tax on bequests made to wealthy heirs. This tax was calculated based on the heir’s current wealth, increasing with increasing wealth. The thought was that the tax should primarily hit those that had the largest capacity to pay it. The tax did not consider the wage of the heir. The wealth used to calculate the tax was determined by the wealth at the start of the year, but this calculation had many special rules. This additional progressive tax on wealthy heirs was eventually removed in 1967 since it was work intensive to administrate, while only bringing in a small additional amount of revenue.

In 1965, there was a large increase in the bequests exempt from the tax, going from 2,000 NOK to 10,000 NOK. Two years later the tax base of the top tax rate was increased by decreasing the boundary for the top tax rate from 400,000 NOK to 200,000 NOK.

Since then both boundaries on the bequests exempt from the tax, and the bequests paying the maximum tax rate have only increased, while the tax rates have mostly decreased.

In the period from 1985 to 2008 the tax rates stayed constant while the boundaries were slightly increased. These increases could be looked at as simply adjusting for inflation. Which would mean that the tax stayed relatively the constant in real value in this period. From 2008 to 2009 there was a reform in the tax, both increasing the thresholds from 250,000 to 470,000 and 555,000 to 800,000, and decreasing the marginal tax rates from 8% to 6% and 20% to 10%. These tax rates and thresholds remained until Erna Solberg’s government chose to remove it from 2013 to 2014.

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Period Tax base Marginal tax rate 1965-1966 0-10,000 NOK 0 %

10,000-350,000 NOK 6-35%

350,000 NOK 35 %

1967-1974 0-10,000 NOK 0 % 10,000-200,000 NOK 6-35%

200,000 NOK 35 %

1975-1977 0-25,000 NOK 0 % 25,000-200,000 NOK 6-35%

200,000 NOK 35 %

1978-1981 0-50,000 NOK 0 % 50,000-200,000 NOK 8-35%

200,000 NOK 35 %

1982 0-75,000 NOK 0 %

75,000-200,000 NOK 8-30%

200,000 NOK 30 %

1983 0-100,000 NOK 0 %

100,000-200,000 NOK 8-25%

200,000 NOK 25 %

1985-1998 0-100,000 NOK 0 % 100,000-400,000 NOK 8 %

400,000 NOK 20 %

1999-2002 0-200,000 NOK 0 % 200,000-500,000 NOK 8 %

500,000 NOK 20 %

2003-2008 0-250,000 NOK 0 % 250,000-555,000 NOK 8 %

555,000 NOK 20 %

2009-2013 0-470,000 NOK 0 % 470,000-800,000 NOK 6 %

800,000 NOK 10 %

2014 0 NOK 0 %

Table 1: Inheritance tax bases and marginal tax rates.

Source: Norges offentlige utredninger 2000: 8 (2000) and wikipedia (2019).

«Arveavgiften rammer ofte de med lave og vanlige lønnsinntekter, og det oppleves som svært urettferdig å måtte betale en høy avgift for å arve et barndomshjem eller familiens fritidsbolig. Å fjerne arveavgiften vil lette generasjonsskifter i familiebedrifter og være et viktig forenklingstiltak.»¹ was the reason for the removal stated by the Norwegian

1Translation:”The tax on inheritance often affects those with low to average wages, and it feels especially unfair to have to pay a large tax to inherit a childhood home or the family cabin. Removing

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finance minster Siv Jensen (2013). In other words the government’s stated reason as to the removal of the tax was because they considered the costs it caused the lower and middle class to be higher than the benefit of the revenue gained from this tax, and that it felt unfair to pay a tax to inherit a childhood home or the family cabin. The removal would also make generation shifts of family companies easier and be an important simplification process. I will not test these statements in this paper, but I will investigate possible effects the removal might’ve had and if a government should consider bringing the tax back.

3 Taxation of inheritance: theory

The explanation in this section is inspired by Norges offentlige utredninger 2000: 8 (2000).

There are primarily two reasons the government might have for taxing the inhabitants of its state: to create room for public consumption and to redistribute wealth. In order to maximize the welfare of the people in a nation, these two goals should be considered in an economic light. In other words the goals should be reached through the most efficient use of the nation’s resources. The government must determine what levels of public goods and redistribution are preferred, and then reach these goals with as low of an efficiency cost as possible. While it can be discussed what levels of public goods are ideal, the decided levels should always be obtained using the most cost-efficient method available.

By confiscating private purchasing power to make room for public consumption and investments, the state and municipalities affect the distribution of wealth between the public and private sector through taxes. However, taxes don’t only affect the distribution of resources, they might also affect how individuals behave in the market by changing the prices the individual faces. For example a tax on income leads to the wage paid by the employer to be higher than the real wage the employee receives after paying the tax.

This may cause distortions in the employer or employee’s behavior. Such distortions are generally considered to reduce economic efficiency.

The rest of this section will be dedicated to explaining various reasons and motives for why households leave bequests, so I can further explain why taxation of bequests may

the tax on inheritance will lighten the load in generational shifts in companies run by families and be an important simplification measure.

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cause distortions in some situations but not in others.

3.1 The life cycle hypothesis

When considering an individual’s choices in regard to saving and consumption it is generally assumed that individuals desire a relatively stable amount of consumption in their lives. This implies that high consumption in one period and low in the next is not preferred to same amount of total consumption being spread over the two periods.

Therefore, they borrow and save so this can be achieved. The consumption is affected by preferences, income opportunities and expectations of the future. High expected income in the future leads to higher consumption in the present.

For a given expected lifetime income, distribution of consumption over the individual’s lifetime is central. The life cycle hypothesis gives an intuitive explanation of how individuals wish to distribute their consumption throughout their lifetime. In this hypothesis the choice to save is the result of weighing consumption in present day against consumption in the future. In the simple version of this theory, uncertainty is disre- garded, both in terms of life expectancy and in terms of lifetime wealth. The individual only faces the problem of how to distribute their lifetime wealth, throughout their life in a way that will maximize their welfare. It must also be assumed that the individual can’t consume more than he/she earns throughout his/her life.

A likely time profile given these assumptions would be one where the individuals accumulate wealth by saving in their working years and consume this accumulated wealth as retirees. The purpose of saving is consumption in old age, and the amount of savings necessary is determined by how much the individual consumes and how long the individual will be a retiree. This simple model is illustrated in figure 1. It is assumed that the individual desires constant consumption, and that the individual’s wage is increasing with age until retirement and zero after. We see that the individual goes into debt while young to have a higher consumption than their current income. The wealth then increases in the following years until the individual retires, at which point the wealth is quickly consumed before death.

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Figure 1: Lifetime wealth, consumption and income profile of a hypothetical individual in the lifetime hypothesis.

Figure inspired by: Norges offentlig utredninger 2000: 8 (2000)

As mentioned, this model makes various assumptions that are unrealistic when comparing to reality. One of these is the lack of uncertainty in the time of death in the model.

An individual might die before they’ve consumed all their wealth. The remaining wealth would then be left as an inheritance for the heirs of the individual. If one were to expand the model to include this type of uncertainty, the individual must now keep a reserve in case it requires further funds for consumption than was initially expected. This saving is security motivated.

3.2 The life cycle hypothesis with uncertain lifetime

When considering the expected lifetime of an individual, one must recognize that this increases with age. A man that expects to become 81 years old when he is 67, might expect to become 87 when he is 81 if he actually lives to be 81. If an individual each year distributes their wealth over the expected remaining life time, this would lead to

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a gradually decaying consumption in old age. This change from the previous model is illustrated in figure 2. When an individual becomes one year older their life expectancy does not diminish by one full year, and the remaining wealth must then be redistributed so it might last longer than expected. When an individual dies their remaining wealth is left as inheritance for their heir.

Figure 2: Lifetime wealth, consumption and income profile of a hypothetical individual in the lifetime hypothesis with uncertain time of death.

Figure inspired by: Norges offentlig utredninger 2000: 8 (2000)

In the previous illustrations there is no pension paid by the government to retirees.

In Norway there is obligatory pension security where each individual must pay a certain amount through their working years. The reasoning for this might be that the government doesn’t consider the public to have the patience to properly save for the future. Another possible problem is people deciding not to save because they believe society will make sure they still have sufficient funds to live. This would be a free rider problem.

There are also two other aspects that affect individuals desire to keep their consumption between years constant. Savings might give a positive real return after taxes. This would mean that by not consuming the same amount every year, but instead having some savings in earlier periods accruing interest, the individual might be able to consume more in total. This would lead to people wishing to save more. On the other hand, people

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generally prefer consumption in the current period over consumption in the future. This would affect the individual the opposite way, making consumption in the current period more attractive. The degree of impatience between everyone varies, and one reasoning for obligatory savings for retirement is the government not considering the public to be sufficiently patient, to save sufficiently on their own.

3.3 Bequest motives

According to a Norges offentlig utredninger 2000: 8 (2000), empirical studies show that people often save more than the life cycle hypothesis would suggest. There are two possible explanations for this. First, individuals may simply not be very good at estimating how much they’ll need for old age. This “mistake” should be fairly easy to rectify by simply consuming more than originally planned in old age though. On the other hand, the individual might have a motive to leave an inheritance to their heir. The idea of such planned inheritance has a long tradition in the literature.

“A man can have no stronger stimulus to energy and enterprise than the hope of rising in life, and leaving his family to start from a higher round of the social ladder than that on which he began.» is a possible rationalization of why a household might make a conscious decision to leave a bequest, given by economist Alfred Marshall in his book

«Principles of Economics» (1891).

Masson and Pestieau (1997) propose a division of inheritance and various inheritance motives into three main categories:

1. Accidental bequests: These are the types of bequests that were described previously. Bequests that aren’t the result of a wish to leave wealth for later generations, but are the result of other types of saving, like saving for old age when time of death is uncertain.

2. Planned inheritance: bequests that stem from a bequest motive. These motives can be split into four categories.

• Possibly the most important motive is that the households are altruistic towards their children. Their children’s preferences have an impact on their own and they

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would like to transfer some of their lifetime wealth to their children for them to use (see Barro, 1974, and Becker, 1974).

• Joy of giving is another possible motive. In this case the household is happy simply to leave some wealth behind for someone else. Who the recipient is or how much they receive is unimportant for this motive. Therefore it differs from the previous type in that the amount left is what the person leaving the bequest derives value from, rather the amount recieved by the inheritor (see Andreoni, 1989, and Blinder, 1974).

• Bequests can also be strategic, where the household wants to affect their children’s behavior by leaving a bequest. This can for example be an implicit payment for attention and care during old age (see Bernheim et al., 1986).

• There may be other motives such as social norms as well. It might be the norm to leave as much of an inheritance as the household itself inherited.

3. Capital transfers: some inheritances are simply capital transfers, inheritance stemming for wealth accumulation of the household. Some households accumulate wealth above all consumption needs, and are instead motivated by power or dynasty building etc.

In this paper, I focus on whether inheritances are intentional or not, and potential efficiency costs.

As previously described inheritances can either be the result of uncertainty about life expectancy, income and commitments, or they can be planned transfers of wealth from an individual to their heir. The difference between these two is important in an economic efficiency sense.

3.4 Comparing households with different preferences

Inheritances caused by saving because of uncertainty are unlikely to be affected by taxation, while inheritances caused by a desire to leave a bequest are likely to be distorted.

To understand why, consider two households 1 and 2 with a certain amount of lifetime wealth that can either be used for consumption or saved for consumption in old age or

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inheritances. In figure 3 the households’ lifetime budget constraint, with and without a tax on inheritances, and their indifference curves are shown. Household 1 has no preference for leaving a bequest but it needs a certain amount of savings s to live of off as a retiree. This causes its indifference curve to be flat. Household 2 on the other hand has a preference both for consumption and for leaving bequests. Household 2’s indifference curve is therefore curved as shown in figure 3.

Figure 3: Indifference curves of two households with different preferences for leaving bequests but the same budget constraint, and their budget constraints before and after the introduction of a tax on inheritance. Point C on the Consumption axis shows how much a household can consume of it spends all its income on consumption. Point S along the savings axis show how much a hosuehold can save if it doesn’t consume at all. In this model what is saved is left as a bequest, and the bequest is what the household derives utility from. The line from C toS is the budget constraint of the households when there is no tax. PointS−tshows the maximum the households can bequest after a tax on inheritances is introduced. The straight lineU₁is household 1’s indiferrence curve. It is flat and horizontal to show that the household is inidifferent about having savings. Ideally this household would spend its whole budget on consumption, but it is assumed that it needs to have some savings in case it lvies for a longer time than expected. Point c shows how much household1 consumes and points shows how much it saves. These remain unchanged after the tax is introduced. Pointbshows how much is bequeathed after the tax is introduced. The curve U2shows household 2’s indifference curve. Individual 2 values both leaving bequests and consumption and thus has a more conventional curved indifference curve.

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Now consider a scenario where the government imposed a tax t on every unit bequeathed. Effectively this causes the price of leaving a bequest to increase. It is no longer a one to one ratio since part of the inheritance will go to the government rather than to the household’s heir. Household 1 will be completely unaffected by this change.

For household 1 the budget constraint does not change. The household is still only concerned with having a certain amount of savings s. The distance from s to b represents the tax the bequest is subject to. This comes at no utility cost to the household leaving the bequest as this household is indifferent to what happens to its savings.

For household 2 the situation is not so simple. Since household 2 derives utility from leaving its wealth as inheritance, the lower line from C toS−tbecomes its budget constraint. Its indifference curve has to shift to a lower point where it tangents the budget line with the new tax. How the indifference curve moves is dependent on how strong the income and substitution effects are. The substitution effect affects the household’s solution by making it more expensive to bequest, thus making it relatively cheaper to consume. This then makes the household wish to consume relatively more compared to saving for bequests. There is also an effect on the household’s relative wealth. The individual’s real wealth has decreased, so its ability to enjoy both goods has decreased.

This effect affects both goods negatively. Unless bequests is an inferior good for the individual, bequests are likely to decrease, while the change in consumption depends on how strong the substitution effect is.

In figure 4, the substitution effect is so strong that the consumption actually increases while the bequest and savings decrease. The line between b₁ and b₁−t shows how much tax revenue the government would have levied if the household did not change its lifetime wealth allocation. The line between b₂and b₂−t shows what the government levies in tax revenue after the household reallocates. In this case, the tax distorts the households allocation. A tax that causes distortions in behavior is generally considered to decrease the efficiency in a market. This means that there is an efficiency cost associated with taxing the inheritance if the household has a preference for bequesting, and is able to change their allocation between saving and consumption before their death.

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Figure 4: Budget constraints of a household that walues consumption and bequests before and after the introduction of a tax on bequests, as well as indifference curves for both situations. Point C on the Consumption axis shows how much the household can consume of it spends all its income on consumption. Point B along the Bequests axis show how much the household can bequest if it doesn’t consume at all. The line from C to B is the budget constraint of the household when there is no tax.

Point B−t shows the maximum the household can bequest after a tax on inheritances is introduced.

The curveU₂shows the highest indifference curve the household can reach before the tax is introduced.

The household chooses its amount of consumption and bequests where the indifference curve tangents the budget constraint. Points b1and c1show its respective bequest and consumption before the tax is introduced. The curve U₃shows the household’s highest indifference curve it can reach after the tax is introduced. The household chooses its amount of consumption and bequests where the indifference curve tangents the budget constraint. Pointsb2−tandc2show its respective bequest and consumption after the tax is introduced.

An important question to the government when making the decision between taxing inheritances or not is then what the general preference curves of the public actually look like.

To investigate this I define a simlple theoretical model in order to do an econometric analysis of Norwegian inheritance choices.

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4 A simple model of a household’s lifetime consump- tion and savings allocation

This model is inspired by the one presented by Fleurbaey et al. (2018).

4.1 Basic overlapping generations model with housing, savings and illiquid assets

A household lives for two periods, t ∈ {1,2}. When young, t = 1, the household works and consumes. It supplies labor inelastically and earns a labor income w₁ > 0.

The household receives an inheritanceB ≥0. The household can either rent or purchase the house it lives in. Letq₁ be the rental price andp₁ be the purchase price of the house;

denote by H₁ ∈ {0,1} the decision to buy the house. There are two additional types of financial assets the household can invest in. First, a liquid asset s₁, giving the rate r₁ >0. This asset can be negative, meaning the agent borrows. Second, investments in illiquid assets z1 ≥ 0, providing a rate of return R1 > r1. The budget constraint of the household when young writes as:

c₁+s₁+z₁+p₁H₁+q₁(1−H₁)≤w₁+B (1) With probability π, the household survives to the second period. When old, t = 2, the household gets a pension w₂ > 0. The choice of consumption and investment is similar to the previous period and delimited by the following budget constraint:

c₂+s₂+z₂+p₂H₂+q₂(1−H₂)≤w₂+ (1 +r₁)s₁+ (1 +R₁)z₁+p₂H₁

| {z }

accumulated wealth

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The additional decision of the old household concerns the inheritance to leave to the next generation. If the household dies early, all the accumulated wealth is bequeathed; let

b₂ = (1 +r₁)s₁+ (1 +R₁)z₁+p₂H₁ (3) be this early bequest. Otherwise, the bequest is b₃:

b₃ = (1 +r₂)s₂+ (1 +R₂)z₂+p₃H₂ (4)

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4.2 Preferences:

The household has preferences to consume, bequest and have liquid funds. Holding liquid assets is assumed to grant utility because of the convenience it provides the household, as in Barnett, Fisher and Serletis (1992). The household maximizes their utility by allocating resources between these three applications. Let u, v and m be increasing and concave functions decribing the agent’s utility from consumption, bequests and holding liquid assets respectively. Assuming a discount factor of β∈(0,1), the expected lifetime utility is:

U(c, b, s) = u(c₁) +m(s₁) +β(1−π)v(b₂) +βπ[u(c₂) +m(s₂) +v(b₃)] (5)

4.3 Restrictions on borrowing:

I assume that investment in illiquid assets cannot be financed with debt, i.e., s < 0 implies z = 0. Without this assumption the agent might want to borrow in the liquid asset to invest in the illiquid asset. Because of the higher return of the illiquid asset, the household would then be able to earn a rent. I choose to prohibit the household from doing this since it is not something we see households do in reality (see Deaton, 1989).

I also assume that the household can not leave a negative bequest, debt, to their inheritor. Debt is not inherited in Norway, so the lenders of s will not be reimbursed by the household’s inheritor’s if the household dies before they are able to repay their debt.

Assuming that the lenders want to maximize their return, they will never lend more than they think the household can repay. Since the debt can’t be inherited, the lender will only lend if the accumulated wealth of the household in the next period isn’t negative.

The household then faces restricions for borrowing:

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06(1 +r₁)s₁ + (1 +R₁)z₁+p₂H₁

| {z }

accumulated wealth

06(1 +r₂)s₂ + (1 +R₂)z₂+p₃H₂ It can then be shown that the household’s limit on borrowing is:

−s₁ = (1 +R₁)z₁ +p₂H₁ (1 +r₁)

−s₂ = (1 +R₂)z₂ +p₃H₂ (1 +r2)

However, if the household borrows, then they can’t invest in the illiquid asset:

−s₁ = p2H1

(1 +r₁)

−s2 = p₃H₂ (1 +r₂)

The household is only allowed to borrow if they buy a house. This result stems from the combination of the lender requiring that the household accumulates wealth sufficiently to repay the loan in the next period, and the household’s only investment option being a house in the case they borrow.

4.4 Optimality

The household maximizes their total utility 5 subject to constraints 1, 2, 3 and 4. In the optimum 1, 2,3 and4 are binding since the household wants as much consumption and bequests as they can afford. The household’s Lagrangian becomes:

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L =m(s₁)+ u(c₁) +β(1−π)v(b₂) +βπ[m(s₂) +u(c₂) +v(b₃)]

+λ₁[c₁+s₁+z₁+p₁H₁+q₁(1−H₁)−w₁−b₁]

+λ₂[c₂+s₂+z₂+p₂H₂+q₂(1−H₂)−w₂−(1 +r₁)s₁−(1 +R₁)z₁−p₂H₁] +λ₃[b₂−(1 +r₁)s₁−(1 +R₁)z₁−p₂H₁]

+λ₄[b₃−(1 +r₂)s₂−(1 +R₂)z₂−p₃H₂]

After some calculations (see Appendix A) we’re left with these six conditions:

u⁰(c^∗₁) = m⁰(s^∗₁) +β(1 +r₁)[πu⁰(c^∗₂) + (1−π)v⁰(b^∗₂)] (6)

u⁰(c^∗₂) = m⁰(s^∗₂) +v⁰(b^∗₃)(1 +r₂) (7)

βp₂[πu⁰(c^∗₂) + (1−π)v⁰(b^∗₂)]−u⁰(c^∗₁)[p₁−q₁]S0 (8)

v⁰(b^∗₃)p₃−u⁰(c^∗₂)[p₂−q₂]S0 (9)

u⁰(c^∗₁) =β(1 +R₁) [πu⁰(c^∗₂) + (1−π)v⁰(b^∗₂)] (10)

u⁰(c^∗₂) = v⁰(b^∗₃) (1 +R2) (11) Since there are multiple expressions foru⁰(c^∗₁) andu⁰(c^∗₂)we can combine these to get more conditions (see Appendix B). This gives us:

m⁰(s^∗₁) = R₁−r₁ (12) and

m⁰(s^∗₂) = R₂−r₂ (13) There are eight conditions and four pairs describing the same decision but in different periods. The first pair, (6) and (7), describe whether the household would like to consume or invest in the liquid asset in the first and second periods. In (6) we see that the household weighs the immediate benefit of getting to consume right now, versus the benefit of having a liquid asset and being able to consume or bequest more in the next

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period. In the optimal allocation, the household’s marginal utility from increasing the right or the left hand side is the same. The decision is largely the same in the second period (7), but the household won’t be able to consume in the next period in this case.

Therefore, the household weighs consumption in the second period against the benefit of having more liquid assets and being able to bequest more after passing on.

The next pair of expressions, (8) and (9), are different from the rest in that they’re not necessarily equations. Unlike consumption, investment in liquid assets and investment in illiquid assets, investment in a house is not a continous number that can slightly increased or decreased to make the expressions equations. The investment is one or zero, so the optimal allocation is the highest of these options. If (8) and (9) are positive expressions, it means that increasing the housing by one is a net benefit, and buying a house is the optimal allocation. If they’re negative however, the household would rather rent, and would sell if they already own a house. And in the unlikely scenario where they’re exactly equal, the household would be indifferent. In both periods the agent weighs the cost of the buying a house in the current period against the benefit of the house in the next period. In both periods the actual price of buying the house depends on both the price of the actual house and of renting. If the price of renting is almost the same as of the house, there is barely any relative cost of buying a house. While if there is a large difference then buying a house becomes relatively more expensive. Like in the decision of whether to save or not, buying a house in the first period can be used for consumption in the next period or bequesting in the case of prematurely dying. And a house bought or not sold in the second period can only be used to bequest.

The third pair, (10) and (11), are similar to (6) and (7), describing the relation between how much the household would like to invest in the illiquid asset consume in the current period.

The last pair of equations, (12) and (13), describe how much the agent would like to invest in the liquid asset in the two periods. We see that as long as the marginal utility of the liquid asset is larger than the difference between the return of the two assets, the household would prefer to invest in the liquid asset. However, as soon as they are equal the household would prefer to invest in the illiquid asset because of the higher return.

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4.5 Introducing a tax on inheritance

Assume now that the government introduces a tax τ on all bequests. A part of the wealth left to be inherited is now turned into tax revenue for the government. This doesn’t change the household’s budget, but it does change the expression for bequests.

The leftover wealth is now split between the bequest and the tax. Introducing the tax, expression (3) and (4) become:

b₂(1 +τ) = (1 +r₁)s₁+ (1 +R₁)z₁ +p₂H₁ (14) in the case of early death. And:

b₃(1 +τ) = (1 +r₂)s₂+ (1 +R₂)z₂ +p₃H₂ (15) if the household lives to old age.

This impacts the household’s allocation in equilibrium:

L =m(s₁)+ u(c₁) +β(1−π)v(b₂) +βπ[m(s₂) +u(c₂) +v(b₃)]

+λ₁[c₁+s₁+z₁+p₁H₁+q₁(1−H₁)−w₁−b₁(1−τ)]

+λ₂[c₂+s₂+z₂+p₂H₂+q₂(1−H₂)−w₂−(1 +r₁)s₁−(1 +R₁)z₁−p₂H₁] +λ₃[b₂(1 +τ)−(1 +r₁)s₁−(1 +R₁)z₁−p₂H₁]

+λ₄[b₃(1 +τ)−(1 +r₂)s₂−(1 +R₂)z₂−p₃H₂]

Performing the same calculations as in the previous section (see Appendix C), we get the following first order constraints:

u⁰(c^∗₁) =m⁰(s^∗₁) +β(1 +r₁)[πu⁰(c^∗₂) + (1−π)v⁰(b^∗₂)

(1 +τ) ] (16)

u⁰(c^∗₂) =m⁰(s^∗₂) + v⁰(b^∗₃)

(1 +τ)(1 +r₂) (17)

βp₂[πu⁰(c^∗₂) + (1−π)v⁰(b^∗₂)

(1 +τ) ]−u⁰(c^∗₁)[p₁−q₁]S0 (18)

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v⁰(b^∗₃)

(1 +τ)p₃−u⁰(c^∗₂)[p₂−q₂]S0 (19) u⁰(c^∗₁) =β(1 +R1) [πu⁰(c^∗₂) + (1−π)v⁰(b^∗₂)

(1 +τ) ] (20)

u⁰(c^∗₂) = v⁰(b^∗₃)

(1 +τ)(1 +R₂) (21)

Again we combine the expressions (16) and (20), and (17) and (21) (see Appendix D).

⇒m⁰(s^∗₁) =R₁−r₁ (22)

⇒m⁰(s^∗₂) =R2−r2 (23) Equations (22) and (23) are unchanged from (7) and (11) from the case where there was no tax. All the other equations however have been impacted by the tax. Like (6) did before, (16) shows how the household weighs the immediate benefit of getting to consume right now, versus the benefit of having a liquid asset and being able to consume or bequest more in the next period. The part of the equation describing the household’s benefit of allocation one more unit towards saving in case of a premature death, is now divided by the tax. This means that for the same allocation of resources the right hand side of the equation has become smaller. To uphold the equality the household must either increase c^∗₁ or decrease s^∗₁, c^∗₂ and b^∗₂. The tax causes the household to substitute towards more consumption and less saving in the first period, and away from consumption or potential bequest in period 2. In (17) we see the same result but between the second and third period. The household must substitute towards consumption in the second period, and away from saving and bequesting in the third, to uphold the euality.

The expressions (18) and (19) describe the household’s decision to buy a house or not in period 1 and 2, in the case where there is a tax on bequests. Compared to (8), and (9) the left hand sides of the expressions in (18) and (19) are smaller after the addition of the tax. Since the household will only buy a house if the left hand sides are larger than 0, the introduction of the tax has skewed the household towards not wanting to buy a house.

Like (10) and (11) were similar to (6) and (7) in the case with no tax, equations (20)

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and (21) are similar to (16) and (17). Just like the household substitutes away from saving towards consumption, it also substitutes away from investing in the illiquid asset.

The model clearly predicts that introducing, or increasing an already existing tax on inheritance, would lead to a decrease in savings and investments and an increase in consumption. The size of these decreases and increases is dependent on the form of the household’s utility functions for consumption and bequesting. In the rest of my paper I investigate if I can find evidence for this hypothesis in the data and provide a magnitude to this effect.

5 Data and estimation method

This paper uses datasets for the yearly tax returns of the Norwegian population from the years 1993 to 2016. These sets contain economic variables of individual Norwegians, such as their incomes, economic assets and gifts they received. The individuals are linked between the sets with anonymized personal social security numbers.

Additionally, a data set containing dates of birth and death as well as intergenerational and marital connections between the individuals, is used. Each individual in this set has the same anonymized personal social security number as they did in the yearly tax return data sets.

5.1 Construction of analysis population

The cross-sectional datasets are combined to create a panel data set, showing the history of each individual from 1993 to 2016. Since the anonymized personal social security numbers in the two sets refer to the same people, I can combine the two sets to add the additional information about the anonymized personal social security number from the other set. By doing this I gain a dataset showing both panel data of the history of the individual’s economic history, and also its various personal info, like date of birth and death and its intergenerational linkages. Because I have the linkages I can also find each individual’s parents’ variables. I rewrite the variable name of the personal social security numbers in the panel data set to be the variable name of the personal social security numbers of the fathers and mothers in my combined panel data set. I can then

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combine the two sets again, matching the personal social security numbers of the fathers and mothers. This then results in a panel data set containing each individual’s economic variables from year to year, as well as their parents’ variables for the same year. I focus on the individuals that receive a bequest in at least one of the years.

5.2 The inheritance variable

There is no variable describing what each individual bequests, only what each individual receives in bequests. This means that I don’t know whether it was the mother or the father that bequeathed it. My solution to this problem is to combine the father and mother’s variables into one household variable. Thus, any received inheritance of an induvial is their mother and father’s household’s bequest. While this was the best way I could find to obtain this variable, there is at least one open issue. The individual may have received a bequest from someone besides their parents. For example from their grandparents or an uncle or aunt. This creates error and inaccuracy in the variable.

However, as long as these type of bequests are more infrequent and less significant than those between parents and child, the results remain valid. Finally, the variable for bequests does not count those below 10,000 NOK for years before 2008, and 100,000 NOK for 2008 and the years after. So small bequests won’t cause much error.

5.3 Inheritance distributions

Using this variable, I constructed a series of plots to preemptively investigate how much the households’ saving allocation is affected by the taxation of inheritances. These plots can be found in Appendix B. In these figures I have plotted the distribution of inheritances for various years. A theoretical representation of the distribution of bequests in a year might look something like figure 6, the distribution being skewed to the right with a long tail to the right. We might expect a distribution like this, since this is how a wealth distribution would look like, and the size of an inheritance is likely correlated with the household’s wealth.

As described earlier there have been various thresholds where the marginal tax increases when the bequest passes the threshold. If the households in the distribution are

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affected by such a tax, this smooth distribution would be distorted. Assuming that the household has the ability to control how much is bequeathed, and that it is bequesting because of an altruistic motive towards their heir, we might expect to see kinks in the distribution around the tax thresholds. Multiple households’ allocations will form a kink around the areas before the higher marginal tax rate comes into effect. Such a kink might look like the one in figure 7.

Figure 8 shows denity plots for inheritances in 5 periods. each plot is accumulated over multiple years in the same period. The periods are determined by the marginal tax rates on inheritances. The thresholds for each period is also included in order to compare the peaks of the distribution to the thresholds. Figure 8 is quite messy, so it is easier to gain insights when looking at the periods more closely by themselves.

In figure 9 the periods before and after the tax change from 1998 to 1999 are compared.

There are kinks around the thesholds, but the kinks seem to be at the same places in both periods. The density increases at every interval of 100,000 NOK. This implies that the kinks in this case are more due to 100,000, 200,000, 300,000, etc. being “tidy” numbers, rather than adjusting for the tax. Especially since there doesn’t seem to be much of a difference before and after the tax change. On the other hand, the change was quite small, only increasing each threshold by 100,000 NOK, which could be argued as simply adjusting for inflation.

In figure 10 we see the same plot as in figure 9, but now each year is represented individually. What’s interesting here is that the years before and after the reform are close to the other plots for their respective period. This implies that there is an effect from the tax. If there was no effect we wouldn’t expect the plots to be any closer to the ones of their respective tax period than the plots fromt the other period.

In figure 11 the periods before and after the tax change from 2002 to 2003 are compared. We see some of the same tendencies as before, kinks around intervals of 100,000

NOK, but the plot in the second period now also forms a kink around 250,000NOK about the same size as the one around 200,000 NOK, while this kink in the previous period is far smaller. This is an implication the density changed as a result of the tax change.

In figure 12 we see that the individual plots follow the other plots from their periods even closer than before.

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In figure 13 we get some interesting results. The distributions in both periods peak around their lower thresholds rather than at a 100,000NOK interval. The distribution in second period especially looks a lot like the kind of theoretical distribution in figure 7.

Recall that the tax reform from was larger in magnitude than the previous ones. The tax reform from 2008 to 2009 both increased the thresholds for the tax rates, and decreased the tax rates themselves.

Figure 14 shows about what we’d expect, but the distributions before the reform seem more spread than for the other periods.

In figure 15 and 16 there are again kinks around the lower threshold. This peak does not disappear after the tax is removed, however. If the distribution behaved as the theoretical one we’d get a distribution as in figure 6. The kinks do however simply move to 500,000NOK and 1,000,000NOKwhich I hypothesized might be because they’re “tidy”

numbers.

In nearly all of the figures there is little no kinks around the higher threshold. While this doesn’t support the theory it doesn’t necessarily invalidate it either. Since the tax is marginal, only applied to further increased inheritance once the inheritance reaches the thresholds rather than being applied to the whole inheritance, the kinks don’t necessarily have to be around the thresholds. The important thing is that the kinks shift significantly from period to period and they look similar to the ones in their own periods.

6 Regression

The goal of this paper is to observe the change in bequests stemming from a change in taxation of bequests. A regression model regressing individuals’ change in tax on their change in bequests might seem like a good start.

b_it =α_it+β_it¹∆τ_it+β_it²X_it+ε_it

In this model b_it is household i’s bequest at time t, α_it is the household’s regression constant,τ_itis the household’s tax level,X_itis a vector of the household’s other variables, β_it¹ and β_it² are the coefficients of the variables, and ε_it is the error term.

This basic regression is unfortunately highly unlikely to give any meaningful insight

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into the change in behavior of the households. Reverse causality is a huge problem with this model. Since the level of tax you pay is determined by the level of bequest, changes in the level of tax will be far more affected by the bequest than the bequests will be affected by the tax. The level of the tax is endogenous since it it determined by the other variables of the model rather than exogenous variables from outside the model.

A solution to this could be to restrict both what the period for the regression and what levels of bequests are being regressed on. The idea here would be to compare bequests before and after one tax reform and restricting the levels of bequests being regressed on to all be subject to the same change in level of taxation with none of the change coming from different levels of bequests. For example looking at the reform from 2008 to 2009;

the thresholds went from 250,000 and 555,000 to 470,000 and 800,000, and the levels were also changed from 8% and 20% to 6% and 10%. A bequest over 800,000 would have a 20% marginal tax rate before 2009 but 10% after. A bequest between 250,000 and 470,000 would have an 8% marginal tax rate before 2009 but a 0% after. These changes in the marginal tax level from 20% to 10%, or 8% to 0% are not endogenous. They come from the government changing the tax rates rather than changes in the levels of bequests.

We can then use the periods where these tax levels were used. The initial tax levels were in the years 2003 to 2008. The tax levels after the reform were in the years 2009 to 2013.

Figure 5 shows the marginal tax rates before and after the tax reform. The previously described regression would look at an interval of bequests where the tax rate was changed.

For example from 555,000 to 800,000. Everyone in this interval faced the same shock from 20% to 6% marginal tax. This way I’d remove the issue of the tax rate being endogeneous.

However, there is still a big issue. The problem is that I wouldn’t look at the same people before and after the tax reform. The path of each households’ bequest history is very different from their other economic variables. Most economic variables generally have some dependence on its magnitude in previous years. If a household earns a lot of money in one year they’ll likely earn a lot of money the next year as well. If a household has a lot of wealth they’ll most likely have a lot of wealth the next year as well. Of course, there might be big changes, especially for young and old households, but there is a “flow” from year to year, where if one controls for all other variables one might be able to observe the change one variable has on another for an individual. Bequests are

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Figure 5: Marginal tax rates before and after the tax reform of 2009

different since we generally observe one or a few bequests per individual, and zero in all other years. This makes it impossible to say how anything affected their bequest from one year to the next, since we have no other years to compare it to. This explains why this revised basic regression would also be flawed. If the household made a bequest each year, like it has a wage each year, or a wealth each year, I could compare each individual before and after the exogenous change in the tax rate. Since the households do not have such a “flow” from year to year it becomes impossible to compare them to previous or later years to learn anything about the effect of the tax.

The idea of the previous regression is to look at the changes in bequests in an interval that was subject to a tax change from the first to the second period. However, I wouldn’t be able to observe any changes in the bequests since those that might have left a bequest in the interval in the first period might give a higher or lower bequest than the interval in the second period as a result as of the tax change. And vice versa there might be those that would have given lower or higher bequests in the previous period that in the second period leave a bequests in the interval.In this case I wouldn’t be able to observe the effects of the tax change.

To solve this problem I decided to aggregate people into types. By aggregating people

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into types, the bequest variable becomes similar to the other economic variables. For each type it will change from year to year, letting us observe the magnitude of it. One could split the households into types in countless ways. I simply chose to aggregate the households based on their bequests for each year. This means that based on their bequests I split them into bins. I assigned them to bins based on what percentile their bequest was. All households in each bin then had their variables aggregated into one average. This gives each bin one representative number for the variable for the households the bin contains. Ideally I would prefer to have as many bins as possible. The more bins I have, the more I can see changes between the various percentiles. The problem with creating more bins however, is that there will be less people in each bin. If I have 100,000 households and split them into 100,000 bins, then each bin is just one household rather than an aggregate of many. Since I want to aggregate the households into types it is then necessary that each bin is made up of multiple households. This is necessary since the aggregate bin I compare between years should be fluctuating because I’m looking at the bin from another year, not because in another year this bin is a different person.

This way we can compare a percentile in one year with a percentile in the next year.

For example we can compare the 50% percentile in 2008 with the 50% percentile in 2009.

The percentiles are a substitution for individuals that lets us see the change in bequests from year to year.

After manipulating the data to get these bins, I decided on the following regression model:

∆logb_kt=α_kt+β_kt¹∆τ_kt+β_kt²X_kt+ε_kt

Where ∆b_kt is the change in percentile k’s bequest from year t−1 to year t, α_kt is percentile k’s regression constant,∆τ_ktis percentilek’s change in marginal tax rate from year t−1to year t, X_kt is a vector of the percentile’s other economic variables, β_kt¹ and β_kt² are the coefficients of the variables, and ε_kt is the error term.

The idea of this regression is to compare each bin from one year to the next and see how a change in the tax rate changes the bequests. The other economic variables in this regression help reduce changes in the bequest stemming from other variables. For example the households in a bin might be richer in the next year compared with the last. This could likely lead to the households in the bin to bequest more. This change in bequests would now stem from something else than the change in tax rate and is

TAXATION OF INHERITANCE: EVIDENCE FROM NORWAY