Non-linear taxation of distributions with two tax bases static income shifting vs. dynamic tax planning. Seppo Kari a and Jussi Laitila b

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1 Non-linear taxation of distributions with two tax bases static income shifting vs. dynamic tax planning Very preliminary, do not quote Seppo Kari a and Jussi Laitila b a Government Institute for Economic Research (VATT), PO Box 1279, Helsinki, Finland b University of Helsinki, Department of Biosciences, PO Box 65, 5205 University of Helsinki, Finland Abstract We study the effects of non-linear taxation of entrepreneur s income in a life cycle model of a firm. There are two tax bases, one for dividends and one for labor income, both taxed at progressive schemes. One scheme is equipped with carry forward of unused allowances. Previous analyses have shown that a nonlinear tax on dividends generates incentives to start distribution early over the life cycle (early distribution incentive, EDI). We show that without carry forward EDI applies to both income types. With carry forward EDI disappears. Dividends are deferred to the steady state. However, the lack of carry forward in labor taxation results to early payments of labor income. As a result pay-out policies for dividends and labor income reflect very different optimization rules. As a result momentary substitution between the income types disappears. Our analysis contributes to understanding behavior under Nordic dual income tax, in particular the effects of the reform of Swedish split rule in 2006 analyzed e.g. by Alstadsaeter and Jacob (2013). We explain observed behavior stressing the importance of tax incentives and life-cycle optimization. 1. Introduction While dual income taxation (DIT) involves important efficiency benefits, policy makers face difficult problems when designing its details, the rules for small business taxation in particular. Sørensen (1994) wrote of the Achilles heel of DIT two decades ago. The most discussed question is probably income shifting between different tax bases, but there are other aspects as well. As the Nordic experience has shown, the necessary measures to prevent tax planning may increase complexity and have harmful implications on efficiency. The purpose of this paper is to assess the efficiency implications of certain standard structures of DIT using a life-cycle model of the firm. One key method to prevent income shifting under DIT is to limit the amount of income subject to the low tax rate on capital income to normal return on invested funds and tax the rest as earned income (income splitting). One problem with implementation of this method is how to define the normal return (base and rate) to achieve neutrality. Another issue is how to avoid incentive problems caused by tax thresholds with sharp jumps in tax rates. Indeed, the tax differentials were 1

2 initially high in the Nordic countries, even 40 percentage points in certain cases. They have declined but may still exceed 20 percentage points. These issues have been subject to considerable attention among researchers in recent years. Lindhe et al. (2002, 2004), Alstadsaeter and Wangen (2010), Alstadsaeter and Thoresen (2010) and Kari and Karikallio (2006) study the effects of Nordic splitting systems. They detect income shifting and distortions to investment incentives in several places. Kari and Laitila (2012) address the implications of the second potential problem of DIT, the effects of tax thresholds with sharp jumps in tax rates. They argue that a non-linear tax schedule on entrepreneur s income produces an incentive to even out distributions overtime. Early distributions may reduce investments of a financially constrained firm and lead to slower growth. They show that equipping the non-linear scheme with carry forward of unutilized exemptions, implemented for example by Norway and Sweden in their dual income tax systems, and proposed by Mirrlees Review (2011), may cure the disease. 1 The model by Kari and Laitila (2012) addresses the effects of tax thresholds and carry forward using a very stylized model. They include one type of income from the firm and no outside income sources. The set up may reveal the generic incentive effects created by a non-linear rate structure, but is not the most fruitful framework to provide predictions for empirical analysis of more complex tax systems. In this paper we extend the analysis to a dual income tax system with two tax bases and two differing non-linear tax schedules. Using this set up we are able to address a richer variety of incentive effects produced by the Nordic tax systems. One example of more complex non-linear tax systems nests in Sweden s taxation of entrepreneurial income. Sweden introduced in 2006 a reform that lowered the tax rate on dividends from personally owned companies. The reduced effective rate was 20% compared to the standard rate of 30% on all capital income. The allowance was targeted at active owners of closely held companies. Dividends subject to this reduced taxation were constrained alternatively by a normal return on new equity (general rule) or, as a new element, by a lump sum amount of SEK (2012) (simplification rule). The part of dividends that exceeded either of the ceilings was taxed as labor income, subject to municipality tax of on average 31.5% and two levels of state taxes of 20% and 5% at different thresholds. 2 As already before the 2006 reform, any unutilized allowances were subject to carry forward with interest. Hence if the firm chooses in one year to distribute an amount below the ceiling, the 1 For the carry forward method, see Sørensen (2005), Alstadsaeter and Fjaerli (2009) and Lindhe and Södersten (2012). 2 Labor income is additionally subject to social security contributions and dividends are burdened by corporate tax, with the result that the combined marginal tax rate is much higher for labor income than dividends for a large share of small business owners. Alstadsaeter and Jacob 2013 calculate that at the top the tax rate differential is as high as 26 %-points. 2

3 unutilized amount of the maximum allowance can be transferred to subsequent years. Moreover, the transferred amount is marked up with interest to maintain the value of the relief. 3 The Nordic countries have responded very differently to the problems caused by tax thresholds. Sweden and Norway give the opportunity to carry forward unutilized allowances, while Finland does not. As in Sweden, Finland s dual income tax system includes income splitting with two separate tax thresholds. One threshold limits tax exempt dividends to normal return on equity (gross assets minus debt), and the other sets up a lump sum ceiling for the tax exempt normal return. Neither threshold is equipped with carry forward. Alstadsaeter and Jacob (AJ henceforth) analyze the effects of the Swedish dividend tax cut in a series of papers. AJ (2013) stresses two findings that they see puzzling. First, it observes no or only some income shifting from the labor income base to preferentially taxed dividends after reform. Hence, wages and dividends were not substitutes from the point of view of the owners, usually assumed and observed in income shifting literature (Gordon and Slemrod, 2000, Fjaerli and Lund, 2001, Lindhe et al. 2002, and Harju and Matikka, 2013a). Second, even if firms introduced or increased dividend payments, the firms did not take full benefit of the dividend tax allowance. Only a share of firms reacted and the data shows no bunching the ceiling of the allowance. The purpose of this paper is to analyze the incentive effects of tax thresholds in a framework that includes two differently taxed bases. A special aim is to contribute to understanding entrepreneurs responses to the dividend tax rules in Finland and Sweden. We implement the analysis by extending the dynamic investment model by Kari and Laitila (2012) to include two income types, both taxed at non-linear rates, one equipped with carry forward and one not. The model is a growth model of an equity financed firm, where the firm grows slowly due to costly external financing. The extra financing costs could well derive from information asymmetries or flotation costs of equity issues, but here they are a result of non-neutral taxation. A tax system that includes dividend taxation, but no taxation on retained earnings, encourages the firm to finance from retained profits. Profits accrue only gradually and this sluggishness leads to a slow adjustment of the firm s capital stock to its steady state size. The results indicate that without carry forward the firm remunerates the owner both with dividends and wages throughout the firm s life cycle. This occurs despite the fact that the owner has other sources from which to finance consumption. The early distribution incentive slows down the firm s growth and postpones the moment at which the firm reaches its steady-state production. After introduction of carry forward of unused dividend allowances, a growing firm pays out wages but does not distribute dividends. Moreover, in the steady state the firm is indifferent to the timing of dividends, but necessarily pays out wages subject to higher tax than dividends. 3 Observe that this element is also included in Mirrlees Review s (2011) proposal for the UK s tax rules for capital income from risky investments. 3

4 The no-dividends result can be understood using the insights given in Kari and Laitila (2012). Because of carry forward of unused allowances, no tax benefits are lost if dividend distributions are postponed. Moreover, by postponing dividends the firm can free funds to finance profitable investments. Therefore, the firm prefers investment to dividends during the growth phase. But since wage taxation does not include any carry forward, the firm is encouraged to take full benefit of the low tax rate in the first bracket of the labor tax schedule. Therefore the firm rewards the owner with wage up to the ceiling of the first tax bracket. Postponing the wage payments would lead to lost tax savings and to a higher life-cycle tax rate on distributions. Our results provide a new perspective to understand the results of AJ (2013) stressing the importance of tax incentives and inter-temporal optimization. Their second finding says that the dividend allowance is not used by firms efficiently. This is easily explained by our results. In the presence of carry forward, a growing firm has no incentive to distribute dividends while paying wages. There is neither any exclusive incentive for dividend pay outs during maturity. Hence wage is the primary form of remuneration. As to their first finding, our analysis suggests that firms do not substitute dividends for wages because carry forward cuts the connection between these income types. Under carry forward, dynamic considerations point to no dividends during growth, while the lack of carry forward in wage taxation results to efficient use of the amount of labor income taxable at low rate. Hence the optimizing firm applies very different life-cycle rules to these income types and therefore momentary substitution between the income types vanishes. Our analysis also contributes to understanding the incentives produced by Finnish tax rules. Without carry forward a growing firm distributes up to the thresholds, and income with the lowest tax rate is paid out first. Some empirical analyses indeed report results in line with these results. Kari et al. (2006, 2009) report of bunching at the thresholds and Harju and Matikka (2013a) provide evidence of sharp income-shifting responses to changes in the tax-rate differential. The model still has some obvious caveats. The infinite horizon assumption excludes the analysis of how the relative taxation of realized capital gains may affect the firm s remuneration and investment choices. Yet, the realization of shares is one alternative way to withdraw funds from business activity. This may be a limitation also because the Nordic rules concerning carry forward of unutilized allowances give an offset against capital gains. Developing the model in this respect would improve its potential to contributive insights. Further we do not consider the liquidity constraints of households, yet important factor affecting individual behavior. The remainder of this paper is organized as follows. In section 2 we set up a dynamic model of the firm and specify the schedular income tax system. Section 3 provides the results for the model without carry forward. The results for the model with carry forward are given in section 4 and conclusions in section 5. 4

5 2. The growth model of the firm Household and Firm The model considers investment, financing and pay-out decisions of a closely-held corporation (CHC) in the presence of a dual income system. The firm is owned by a single household which maximizes utility derived from consumption. It sells equity capital Q and labor L for the firm in exchange for dividends D and wages W. Labor supply is exogenous to avoid unnecessary complexity. The household has access to the financial markets, where it is able to borrow and lend at the common market rate of interest ρ > 0. The firm produces output with non-depreciating capital K and labor (exogenous, suppressed in what follows). The firm finances its operations through profits π(k) and new equity Q. Debt is ruled out to simplify. All prizes are normalized to one. The firm spends its resources on remunerations to its owner Y and investments I. The firm s budget constraint is The firm s stock of capital develops π(k) + Q = Y + I. (1) K = I. (2) The profit function π(. ) is twice differentiable and strictly concave and satisfies the usual Inada conditions. The start-up stock of capital K(0) = K 0 0 is determined endogenously. New equity is required to be non-negative Q 0 to rule out tax exempt distributions through repayment of equity. Tax system To avoid complexity, only personal taxes on dividend and labor income are considered. Both income types are taxed progressively. Dividends are tax exempt up to a lump-sum ceiling E 1 and the excess amount is taxed jointly with wages as labor income at a progressive rate. 4 Labor income is taxed at rate τ 1 up to a lump-sum ceiling denoted E 2 and at rate τ 2 > τ 1 on the excess amount. Hence, both dividends and wages are taxed at non-linear schedules. The schedules are not separate; rather there is a link between the two income forms: excess dividends (dividends that exceed their threshold) are taxed jointly with wage income. Alternatively we could assume a tax system where tax schedules are fully separate. The effect on results would be small, however, and to be able to contribute to applied debate, we take the rough structure of Swedish and Finnish tax 5 systems of closely held companies as the starting point. To model progressive tax on labor income, denote income subject to the lower tax rate W 1 and income subject to the higher tax rate W 2 and set up the following constraints: 4 To simplify we assume that preferentially taxed dividends are tax exempt rather than taxed at a low rate. 5 Observe that to simplify we concentrate here on a lump sum threshold and overlook the other type of ceiling which is calculated as the normal return on equity. 5

6 0 W 1 E 2 and W 2 0. (3) The same approach is followed to model dividend taxation: dividends are tax exempt up to E 1 and taxable as labor income on the excess amount. Recall that now the tax system includes a mechanism of carry forward of unused allowances. If dividend exemption is not utilized fully in one year, the unused part can be saved for later years. This means that the effective ceiling for tax exempt dividends is not necessarily E 1, but depends on previous pay-out decisions. To model this dynamic constraint, let R denote the amount of accumulated unused tax exemptions and i the rate of interest applied to compound the stock. The stock R develops over time as follows R = E 1 D + ir. (4) In line with Kari and Laitila (2012) and Lindhe et al. (2002) we model carry forward by including (4) and the following constraints into the model: R 0, R(0) = 0, D 0. (carry forward) (5) Dividends and the reserve R are non-negative and the start-up value of the reserve is assumed to be zero. If there is no carry forward, the following condition replaces conditions (4) and (5): The expression of owner s net income from the firm is 0 D E 1. (no carry forward) (6) Y n = D + (1 τ 1 )W 1 + (1 τ 2 )W 2. (7) Optimal policy The owner has access to capital markets, where it can borrow and lend at the market rate of interest. This aspect splits the problem into two distinct decisions concerning consumption and investment. While the firm s goal is to maximize the value of its shares, the household aims at optimizing the time paths of consumption and saving while taking the value of the firm as given (Fisher separation; e.g. Sinn, 1987). The initial market value of the firm s shares V at time t = 0 is V 0 = [Y n (t) Q(t)]e ρt 0 The firm s problem is to find the start-up capital stock K 0 and the time paths of dividends D, labor income W 1 and W 2, and new equity issues Q, so that the net value of the firm s shares Z after initial investment is maximized: dt. max {K0,D,W 1,W 2,Q } Z = V 0 K 0. (8) s.t. conditions (1)-(5). 6

7 Hence, the investment decision of the original consumer-producer model reduces to Problem (8) which is essentially Sinn s (1991a) life-cycle model augmented with an additional income type and progressive tax schedules. Why this model framework? The firm grows slowly towards the steady state financing from retained earnings. This aspect is important since, the special incentive effects caused by progressive taxation materialize just in those circumstances (Kari and Laitila, 2012). In the present framework the incentive to finance investments internally is produced by a tax penalty on dividends. Due to this extra cost the firm prefers retained earnings to external funds and adapts its investment program to the slowly accruing financing flow Firm s policy - no carry forward In this chapter we illustrate the firm s investment, financing and pay-out policies in the case of two income types absent any carry forward of unused allowances. The model serves as a benchmark in the analysis of the effects of carry forward in the next chapter. Moreover, it provides an analysis which may be useful to understand behavior under Finland s dividend taxation, which does not include carry forward. Initial considerations There are three decisions the forward looking firm must make: (i) the choice of the long-run stock of capital, (ii) the choice of the source of financing investments, and, (iii) the amount and the form of the remuneration for the owners. All these choices are interdependent and all are dynamic. As noted above, taxation of dividends creates and extra cost for external equity leading the firm to prefer internal equity to external funds. As a result the firm finances just a small share of its longrun capital stock from external equity. Since profits are limited, the firm can be seen to be financially constrained. The firm adapts its investment program to the slowly accruing financing flow. This affects the speed of investment, and, further, the time in which the firm reaches its steady state size. The tax rate on dividends and the size of profits affect the relative shares of the steady state capital stock, which are financed 1) from external equity at the start-up stage, and 2) retained profits during the internal growth phase. The firm also decides how to reward the entrepreneur. Both dividends and labor income are taxed progressively but at different rates. The model assumes that up to a ceiling (E 1 ) dividends are subject to an allowance which effectively abolishes the tax burden. Hence the cheapest form of remuneration is dividends upto E 1. The excess amount is then taxed as labor income. The firm s decision concerns the type of income and the amount paid out. A good guess might be that the 6 An obvious alternative way to model internally financed growth were to assume non-tax costs for external financing as among others Fazzari et al. (1988) do. This approach would provide very similar considerations as the current one, but would increase complexity. 7

8 firm takes benefit first of the cheapest income form, the tax rate on which is the lowest, and then the second cheapest income form. Observe that the decision concerning the size of the pay-out may affect financing and investment. Kari and Laitila (2012) show, that progressive taxation induces firms to start dividends early over the life cycle. This slows down growth of a firm which finances from retained earnings. As noted above, consumption needs do not affect these choices. In the presence of efficient capital markets the firm is devoted to optimizing its investment, financing and pay-out policies without any attention to consumption choices. Household chooses the time pattern of consumption while taking the value of the firm as given and covering the potential deficits (surpluses) by borrowing (investing). Optimal policy The firm s optimal policy over its life cycle is given in Proposition 1. The result focuses on a highincome case, where the firm s profit is high enough so that, when the entire profits is paid out, the owner s income is taxed at rate τ 2 in the margin. Let condition π (K ) = ρ define the steady state capital stock of a linear dividend tax system and of no taxation. K depicts the steady-state stock of capital in a case where it is not distorted by taxes. Propostion 1. Assum that no carry forward is available and π(k ) > E 1 + E 2. Then problem (8) has an optimal solution with the following properties: (i) The firm starts with a capital stock strictly lower than the long-run optimal stock of capital: K 0 = γ 0 < K. (ii) After start-up there is a growth phase 0 < t < t 1, where D = E 1, W 1 = W 2 = Q = 0 and K = π(k) E 1. (iii) There is a second growth phase with slower growth t 1 < t < t 2, where D = E 1, W 1 = E 2, W 2 = Q = 0 and K = π(k) E 1 E 2. (iv) In the steady state phase t t 2 we have D = E 1, W 1 = E 2, W 2 0, Q = 0 and K = 0 and K = K. The formal derivation is given in Appendix (Section 1). The firm begins with a small start-up stock of capital K 0 = γ 0 invested by the owner as an initial equity injection. After start-up the firm grows financing investments from retained earnings. There are two distinct growth phases. In the first, the firm distributes the maximum amount of tax exempt dividends D = E 1 and invests the rest of profits. In the second growth phase the firm pays out dividends D = E 1 and labor income W 1 = E 2 and invests the rest. At maturity the firm distributes all of the profits, the marginal remuneration form being W 2 taxed at rate τ 2. The steady state capital stock K = K is not distorted by taxes. 7 7 This result reflects the new view of dividend taxation. 8

9 It may be instructive to compare the solution to behavior in linear taxation and to a simpler nonlinear tax system with only one income form. In both linear tax and the present case, the firm accumulates a part of its steady state capital stock during an internal growth phase. This reflects the discouraging effect of a tax on remunerations to external equity. The main distinctive feature between linear and progressive tax systems is that in linear taxation the firm does not remunerate the owner during the growth phase. The incentive to reward the owner early over the firm s life cycle reduces funds available to investment and therefore slows down the firm s growth. Kari and Laitila (2012) show, that this incentive produced by the non-linear tax schedule, may lead to production losses in the economy. Compared to behavior under a single non-linear dividend tax, analyzed by Kari and Laitila (2012), the main qualitative difference is that, while we here have two distinct growth regimes, the single tax case includes only one growth regime. In both cases the owners are rewarded during growth. As expected, the firm starts remunerations from the most lightly taxed income form and continues with the next cheapest. Yet, pay-out policy is still driven by life-cycle optimization: the firm evens out distributions over its life cycle to take the most of low tax rates on dividends and wage income. There is still a trade-off between returns on additional investments and benefits from a full use of tax allowances. In the first growth phase, the tax saving from taking benefit of dividend tax exemption is so high that the firm prefers dividends to investment. But the tax saving from wage income in the first tax bracket is low compared to benefits from investment. Therefore the firm sets W 1 = 0 and rather invests the funds. Wage payments start only in the second growth phase where the marginal return on investment is sufficiently low, so that paying out wage income is profitable. The model predicts that in a cross-section of firms with different ages, we should observe a group of firms which have set their dividend and labor income to the level of the tax thresholds. Therefore we should see bunching at those thresholds in data. Our model suggests that this can be explained by inter-temporal optimization in the presence of progressive tax rates. Kari and Karikallio (2007) and Harju and Matikka (2013b) provide evidence of such behavior in Finland. To sum up, with two income forms taxed at non-linear rates: The early distribution incentive applies to both income forms. This reflects dynamic responses to tax thresholds. While life cycle motives dominate, the firm yet follows a rule in pay out whereby lightly taxed income is paid out first and highly taxed last. The model predicts that in a cross section of firms one should find bunching at tax thresholds 9

10 4. Firm s policy when carry forward is available Consider next the general model which includes carry forward of unused exemptions. If the firm pays out an amount lower than the static ceiling E 1 the difference is transferred to later years and the amount transferred is compounded with interest. The amount transferred to later years changes over time as follows R = E 2 D + ir The ceiling for dividends becomes essentially a dynamic constraint instead of a static constraint of the basic model. This means that the firm may optimize the timing of dividend distributions quite freely without taking into account of the benefits received from the annual use of the tax free amounts. Kari and Laitila (2012) analyze carry forward in the case of a single non-linear dividend tax and show that on certain conditions concerning the interest i used to compound the stock of unused allowances, carry forward abolishes the early distribution incentive. They interpret that the result is a consequence of the transition from a static annual constraint to a dynamic life-cycle constraint. In this chapter our aim is to study how carry forward affects investment and pay-out behavior in a more complex environment where the tax system includes two separate progressively taxed income types, dividend and wage. Only the first income form is equipped with carry forward. The questions addressed are: What is the effect on the size of compensation? How does the choice between income types change? How is the dynamic pattern of investment affected? The firm s optimal policy throughout the firm s life cycle follows the pattern of the following Proposition 3. Again, it focuses on a special case where the firm s profit is sufficiently high to be taxed at the marginal tax rate τ 2 (when the whole profit is distributed). Proposition 3. Assume i = ρ and xx > yy [condition in the making]. The firm s policy is: (i) The firm starts with a capital stock strictly lower than the long-run optimal stock of capital: K 0 = γ cf 0 < K. (ii) After start-up 0 < t < t cf 1 there is a growth phase, where K grows from γ cf 0 to γ cf 1. During this phase D = W 1 = W 2 = Q = 0 and K = π(k). (iii) There is a second growth phase t cf 1 < t < t cf 2, where K grows from γ cf 1 to K*. During this phase D = 0, W 1 = E 2, W 2 = Q = 0 and K = π(k) E 2. (iv) In the steady state t t cf 2 we have, W 1 = E 2, Q = 0, K = 0 and K = K. The variables D and W 2 satisfy the conditions D = π(k) E 2 W 2, D 0, W 2 0. Proof is given in Appendix 2. 10

11 With two progressively taxed income types from which one is subject to carry forward with interest, the steady state capital stock is still K and it exceeds the start-up capital stock, K 0 = γ 0 cf < K. This implies that the optimal solution necessarily includes a phase where the firm grows financing investments from internal financing. This outcome is a direct implication of a tax system that imposes a tax penalty on remunerations to the owner compared to retained earnings. As in the previous chapter the firm s growth path is split into two distinct policies. After start-up the firm uses all accruing profits on investments. No dividends or labor income is paid. In the second growth phase the firm rewards the owner with labor income W 1 = E 2. In the steady state the firm pays out its entire profits in labor income and dividends. Timing of dividends is however indeterminate and the (momentary) amount paid may vary between: 0 D π(k) E 2. The effect of carry forward is seen when we compare to the case without carry forward. The main qualitative difference concerns dividend distributions. While without carry forward the firm distributes dividends throughout its lifecycle, with carry forward it does not distribute dividends during the growth phase, and is indifferent with respect to distributions in the steady state. Other policy choices are qualitatively the same. Hence, in the presence of carry forward, dividends are never distributed during internal growth. The intuition of this result is that due to carry forward the firm loses nothing if it distributes tax exempt dividends at a later stage. The present value of the tax saving is independent of timing of distributions, which follows from compounding the transferred amount with the firm s discount rate ρ. Moreover, abstaining from distributions allows the firm to use more funds on investments, which yield a high return in the growth phase, π > ρ. During growth, therefore, the firm faces a clear incentive to postpone dividend payments to the steady state phase and invest the funds instead. Progressively taxed labor income is still distributed during the growth phase. Carry forward is not extended to labor taxation and therefore the firm pays the owner W 1 = E 2 during the growth path. The early distribution incentive shows up in labor taxation. In the steady state phase the firm faces no incentive to postpone dividends any more. Profitable investment opportunities have been run down and now the firm s problem turns from investment and financing to the question: what are the optimal amounts of dividends and labor income? Proposition 3 implies that, while the firm necessarily pays out W 1 = E 2, the policy with respect to D is indeterminate. Due to carry forward with interest at rate i = ρ, the firm is indifferent with respect to the amount distributed as dividends, assumed however that the accumulated exemptions are fully used in the long run. W 2 is the residual income type. If the firm pays out less than E 1 as dividends, then the difference is paid out in the form of W 2. But later the firm must balance these deviations from the long run policy. The indifference with respect to timing of dividends can be shown by considering the value of the firm in the steady state. Solve first the budget equation (1) for W 2 and then the equation of 11

12 motion for unused allowances (4) for D and substitute both into the expression of net income Y n in (7). Use this and the expression of firm s value becomes: 0 V = τ 2 E 1 + (τ 2 τ 1 )E 2 + (1 τ 2 )π(k ) + τ 2 ρr(t) τ 2 R(t) e ρt dt When we solve the integral, we observe that the firm s value is constant in the steady state. This implies that it is independent of the time path of dividends. Hence, a value maximizing firm may chooses dividend payments freely within the limits given in Proposition 3. This indifference means that taxation is neutral with respect to timing of dividends. Some quantitative aspects of the optimal solution such as the size of the initial capital stock, the length of the growth path and the moment the firm switches from the first to the second growth phase can be shown to be sensitive to tax parameters. The evaluation of these quantities is best illustrated using numerical simulations, which is beyond the scope of the present version of this paper. The results have some interesting implications. In the Introduction of this paper we raised the question, how Swedish closely held companies should have responded to the dividend tax cut, implemented as from The rule introduced a lowered effective tax rate for dividends up to a lump sum ceiling. Alstadsaeter and Jacob (2013) wonder in their empirical paper why they do not observe any larger substitution between wages and dividends after this cut. According to our analysis a growing firm does not pay out dividends but may well pay labor income. Similarly, a mature firm necessarily rewards its owner with labor income but still may retain from paying out dividends. Without carry forward, dividends and labor income are substitutes and tax rates determine the order in which the firm uses them as compensation to the owners. But with carry forward this direct link between the income types breaks. Optimization over the firm s life cycle starts to dominate. Allowing carry forward for one income form but not for the other, leads to a setting where the life cycle rules are very different. While payments of labor income are driven by the motive to even out payments over the life cycle to take full advantage of the low tax rate on the first tax bracket, the deferral of dividend payments is motivated by the aim to channel profits to investment to speed growth. Our model does not facilitate taking into account the links to capital gains income taxation. In the present model there are no capital gains due to the infinite horizon. However, this extension would be important since: 1) in Norway s and Sweden s (?) tax systems the unused dividend allowances carried forward can be deducted against taxable capital gains from the sale of the firm s shares. Thus, it is a relevant element of the tax system. 2) It would also raise the issue of income shifting between the labor income and capital gains tax bases. This is an old and potentially important theme in tax policy debates. However, we can produce the following interpretation based of our results. Assume that capital gains are taxed at the same tax rate as dividends (in our model =0), and that the unused allowances can be deducted from the capital gains tax base. Now our steady state result that 12

13 dividends can be deferred to later years can be interpreted to suggest that distributions can be deferred to the sale event. No dividends are ever paid; instead the owner receives the remuneration in the form of wages and capital gains. Observe however that there is no clear tax incentive to defer the distributions to the time of the sale if the stock of transferred allowances is compounded with ρ. The tax system is neutral in this respect. 13

14 5. Conclusions Studies the effects of tax thresholds and methods to relieve the behavioral effects of these thresholds; framework: dynamic investment model with two income forms, progressive tax rates, carry forward; corresponds to taxation of entrepreneurs income in Nordic dual tax systems extends the analysis of Kari and Laitila (2012) provides implications o for empirical work o for policy Results o if both dividends and labor income taxed progressively, then EDI applies to both o if tax rates differ the pecking order is: income with lowest tax rate paid out first and income with highest tax rate last o carry forward abolishes EDI for the income type in question; still EDI applies to the other income type o CF: different life-cycle rules => no substitution Caveats o consumption pattern and pay out pattern disconnected (in order to simplify) o model cannot address other motives for carry forward o simplification of the tax system; no capital gains o effects on timing of dividends could be analyzed using a simpler model 14

15 Appendix 1. Model without carry forward Model of the firm max {K0,D,W 1,W 2,Q} (Y n Q)e ρt dt 0 K = I K(0) π ( K ) + Q = I + Y Y n = Y T = D + (1 τ 1 )W 1 + (1 τ 2 )W 2 0 D E 1, 0 W 1 E 2, W 2 0, Q 0 where Y n = net income from the firm D = tax exempt dividend W 1 = labor income, first bracket W 2 =labor income, second bracket Q = new equity financing K = capital stock I = investment T = owner level taxes The Hamiltonian of the model is H = D + (1 τ 1 )W 1 + (1 τ 2 )W 2 Q + q 1 [π(k) + Q D W 1 W 2 ] + μ 1 D+ μ 2 (E 1 D) + μ 3 W 1 + μ 4 (E 1 W 1 ) + μ 5 W 2 + μ 6 Q Where q 1 is the co-state variable i.e. the shadow price of capital K, and μ i, i [1,6] are the shadow prices of lower and upper constraints of D, W 1, W 2 and Q respectively. F.O.C. H D = 1 q 1 + μ 1 μ 2 = 0 H W 1 = 1 τ 1 q 1 + μ 3 μ 4 = 0 H W 2 = 1 τ 2 q 1 + μ 5 = 0 H Q = 1 + q 1 + μ 6 = 0 q 1 = ρq 1 π q 1 q 1 (0) = 1 (A1) (A2) (A3) (A4) (A5) (A6) 15

16 Analysis Preference order of remuneration Consider first the order in which the firm uses the compensation forms to remunerate the owner. If W 1 > 0, then, by condition (A2), q 1 = 1 τ 1 μ 4 1 τ 1. Substitute this onto condition (A1) and get μ 2 = τ 1 + μ 3 > 0. This implies D = E 1 > 0. Using the same argument we can show that, if W 2 > 0, then necessarily W 1 = E 1 and D = E 1. Hence, the firm only distributes W 2 after its has fully exploited the possibility to pay out tax exempt dividends D. Hence, if the firm distributes W 1 or W 2 it necessarily distributes D. We conclude that the preferred order of compensation is D W 1 W 2 The simple intuition of this result is that in the framework of the tax system of the basic model the firm starts distributions from the cheapest income form and after full use is taken of it the firm goes forward to the next cheapest income form. To derive the optimal dynamic policies of the firm, we first consider different steady states of the model, i.e. states where all variables take constant values. Potential steady state policies: S1: W 2 0 μ 5 = 0 q 1 = 1 τ 2 (constant) Conditions (A1), (A2) and (A4) imply D = E 1, W 1 = E 2 and Q = 0. Condition (A5) determines the firm s optimal steady state capital stock π = ρ. This implies K = 0 Jointly these properties give condition π(k ) = D 1 + W 1 + W 2 > E 1 + E 2 S2: W 2 = 0, 0 W 1 E 2 μ 3 = μ 4 = 0 q 1 = 1 τ 1 (constant) Condition (A1) implies D = E 1. Condition (A5) gives π = ρ which means K = 0. Now π(k ) = E 1 + W 1 > E 1 S3: D 0 & W 1 = W 2 = 0 μ 1 = 0 q 1 = 1 (constant again) Condition (A5) gives π = ρ which means K = 0 and further π(k ) = D 1 < E 1 Potential growth policies: If D = 0 the shadow price of capital exceeds 1. In this case the firm issues new shares and hence grows financing both from retained profits and new share issues. This policy is however not optimal since our initial condition requires q 1 1 after start-up stage. This shows that the firm necessarily pays out remunerations during the growth stage. 16

17 G1: W 2 = 0, W 1 > 0 μ 3 = 0, μ 5 > 0 q 1 = 1 τ 1 μ 4 < 1 Condition (A1) implies μ 2 = τ 1 + μ 4 > 0 D = E 1 and consdition (A4) μ 6 > 0 Q = 0. Further, μ 4 > 0 W 1 = E 2. Otherwise q 1 = 1 τ 1 K = 0 (steady state). The budget constraint implies K = I = π(k) E 1 E 2. Hence, K > 0 if π(k) > E 1 + E 2. G2: W 1 = W 2 = 0, but D > 0 μ 1 = 0, μ 3 > 0 q 1 = 1 μ 2 1 Condition implies (A4) μ 6 0 Q = 0. In condition (A1) μ 2 > 0 D = E 1. Otherwise q 1 = 1 K = 0 (steady state). Budget constraint implies I = π(k) E 1. Hence K > 0 if π(k) > E 1. G3: W 1 = W 2 = D = 0 μ 1 0 q 1 = 1 + μ 1 1 Condition (A4) implies ) μ 6 0 Q 0. Budget constraint requires K = I = π(k) + Q > 0. Outline of the optimal solution If π(k ) E 1 + E 2, the solution is: K 0 G2 G1 S1 Hence, 2 growth regimes with different remuneration policies. 17

18 2. Model with carry forward Augment the model of section 1 with the following conditions: R = E 1 D + ir, with R(0) = 0, R 0. The non-negativity constraint for R replaces the upper ceiling of tax exempt dividends D E 1. The Hamiltonian of the model is H = D + (1 τ 1 )W 1 + (1 τ 2 )W 2 Q + q 1 [π(k) + Q D W 1 W 2 ] + q 2 [E 1 D + ir] μ 1 D + μ 2 R + μ 3 W 1 + μ 4 (E 1 W 1 ) + μ 5 W 2 + μ 6 Q The first order conditions are H D = 1 q 1 q 2 + μ 1 = 0 H W 1 = 1 τ 1 q 1 + μ 3 μ 4 = 0 H W 2 = 1 τ 2 q 1 + μ 5 = 0 H Q = 1 + q 1 + μ 6 = 0 q 1 = ρq 1 π q 1 q 1 (0) = 1 q 2 = ρq 2 iq 2 μ 2 (A1 ) (A2 ) (A3 ) (A4 ) (A5 ) (A6 ) (A7) Analysis In what follows, assume i = ρ. Potential steady state regimes S1a cf : W 2 > 0 & R > 0 μ 5 = 0 q 1 = 1 τ 2 ; μ 2 = 0 q 2 = 0 Conditions (A2 ) and (A4 ) imply W 1 = E 2 and Q = 0. Condition (A1 ) implies μ 1 = τ 2 q 2 0 Hence, we cannot rule out q 2 > τ 2 μ 1 > 0 D = 0. D indeterminate D = 0 or D > 0. From (A5 ) it follows π = ρ, K = K, K = 0 π(k ) = W 2 + E 2 + D 0 D < (K ) E 2. Since π(k ) and E 2 are constants, the firm is indifferent with respect to how much it pays out in the form of W 2 and D. S1b cf : W 2 0 & R = 0 μ 2 > 0 Insert in (A7 ) q 2 <0. If i = ρ. Impossible as steady state policy. 18

19 Potential growth regimes Using condition (A4 ) it is obvious that the firm does not use new equity after start-up where q 1 (0) = 1 by condition (A6 ). Therefore the firm may only grow using internally financing as the source of investment. Observe that regimes where W 2 > 0 are steady state regimes since μ 5 = 0 q 1 = 1 τ 2 q 1 = 0 π = ρ. The same applies to cases 0 W 1 E 2 and 0 D E 1. G1a cf : W 2 = 0 & W 1 = E 2 μ 5, μ 4 > 0, μ 3 = 0, R > 0 μ 2 = 0 These imply 1 τ 2 q 1 1 τ 1 & q 2 = 0. During growth π > ρ; by (A5 ) we now get q 1 < 0; further, by (A1 ) q 1 = μ 1 < 0; since μ 1 is nonnegative and decreasing it must in fact be strictly positive μ 1 >0 which implies D = 0 When K grows and reaches K=K*, q 1 convergates smoothly to its steady state value q 1 = 1 τ 2. G1b cf : As regime G1a cf but R = 0 q 2 > 0 q 2 < 0 R = 0 requires D = ir + E 1 > 0 μ 1 = 0 q 1 = q 2 > 0; which is, by (A5 ) not possible when K grows G2a cf : π E 1 ; W 2 = W 1 = 0 1 τ 1 q 1 1; R 0 μ 2 = 0 q 2 = 0 (vakio) q 1 = μ 1 < 0; since μ 1 is nonnegative we may now conclude that it must be strictly positive μ 1 >0 in the regime, which implies D = 0 Since D = W 2 = W 1 = 0, K = π(k) > 0 Outline of the solution Assume π(k )is high (condition in making). The solution is: K 0 G2a cf G1a cf S1a cf Hence two growth regimes; both show no dividend payments. And indifference with respect to the size of dividends in the steady state. In the latter growth regime the firm remunerates the owner with labor income. 19

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