- Email: [email protected]
Top income measurement and undistributed profits
Accepted Manuscript Top income measurement and undistributed profits Pablo Guti´errez C., Ram´on E. L´opez, Eugenio Figueroa B. PII: DOI: Reference:
S0165-1765(15)00286-4 http://dx.doi.org/10.1016/j.econlet.2015.07.013 ECOLET 6827
To appear in:
Economics Letters
Received date: 5 November 2014 Revised date: 12 July 2015 Accepted date: 13 July 2015 Please cite this article as: Guti´errez C., P., L´opez, R.E., Figueroa B., E., Top income measurement and undistributed profits. Economics Letters (2015), http://dx.doi.org/10.1016/j.econlet.2015.07.013 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
*Highlights (for review)
Highlights
Simply adding retained profits to other personal incomes is in general incorrect
Proposes a method to transform retained profits into business-accrued capital gains
Shows sufficient conditions for business-accrued capital gains to distribute Pareto
*Title Page
Top income measurement and undistributed profits
Pablo Gutiérrez C. 1 Ramón E. López
Eugenio Figueroa B.
Department of Economics, University of Chile
Abstract We develop a method that allows transforming retained business profits in a particular year into business-accrued capital gains of the same year. These capital gains thus estimated can be simply added to other sources of personal income of top earners to obtain a consistent measure of their total income.
Keywords: Top income distribution; Undistributed distribution; Business-accrued Capital gains
profits;
Pareto
JEL classification: D31; H24
1
Correspondence to: Universidad de Chile, Diagonal Paraguay 257, Santiago, Chile. Tel.:+56229783422. Fax.: +56229783455. E-mail addresses: [email protected], [email protected]
*Manuscript Click here to view linked References
Top income measurement and undistributed profits1
1.
Introduction
Recent literature has greatly focused on the measurement of top incomes and their participation on the national income (Atkinson et al., 2011; Alvaredo et al., 2013; Alvaredo and Londoño, 2013; Burdin et al., 2014, among others).2 Most previous studies have considered only labor and other personal incomes excluding capital gains3. More recently, a few studies have explicitly considered realized capital gains as part of the total income of the rich, showing that their inclusion greatly increases the share of the top income earners in national income.4 However, the use of realized capital gains as part of the income of individuals in a particular period has been criticized because they may reflect capital appreciations that have taken place over years before the period in which the incomes are actually being measured (Armour et al, 2012; Smeeding and Thompson, 2010). Conversely, a large portion of the business-accrued capital gains obtained by individual investors in a particular period are often not realized in the same year and, therefore, are omitted when the conventional approach of accounting for only realized capital gains is used. This paper develops a new approach that deals with the above two problems. The key premise of the approach is that retained profits in a particular period 1
The authors thank an anonymous reviewer, this Journal Editor, Professor Samwick, and Alfonso Montes for useful comments and criticisms. 2 In this respect, Alvaredo (2011) has provided important insights by relating top incomes to the measurement of the Gini coefficient. 3 This is due to the fact that most tax systems cover capital gains imperfectly. Also, in several countries capital gains are not taxed at all, and thus are not reported. 4 For a complete discussion, see Atkinson et al., 2011.
1
are a fundamental source of capital appreciation during the same period.5 We develop a method that allows transforming retained business profits in a particular year into business-accrued capital gains of the same year. These capital gains thus estimated can then be simply added to the firm shareholders’ other sources of personal income to obtain a consistent measure of their total income. We also show that the approach of directly adding retained profits to labor income and other capital incomes as recently used, for example, by López et al, 2013 and Fairfield and Jorratt, 2015 among others, is in general inconsistent. This is due to the fact that retaining one dollar in the firm does not necessarily translate into one additional dollar of business-accrued capital gain to shareholders, due to the structure of observed tax systems. We show the special conditions under which this approach would be correct. Moreover, we discuss how the probability distribution of business-accrued capital gains is related to the distribution of retained profits. Finally, to address the potential practical importance of the proposed methodological innovation, we develop an empirical application using data from Chile.
5
The distinction between fundamental and non-fundamental capital gains is important. While the former are based on the profitability of the enterprises, the latter are mostly originated in financial market imperfections often causing asset price bubbles or asset price collapses that are unrelated to the performance of the enterprises.
2
2.
From undistributed profits to business-accrued capital gains
We use the measure of income developed by Haig (1921) and Simons (1938) where personal income of individual at time t is equal to her/his consumption Ct plus the net change of wealth ∆NWt (to simplify notation we drop subscript ): t Ct ∆NWt
(1)
One may alternatively define as the sum of the personal income yt, which includes labor income, distributed dividends and other personal incomes, plus business accrued capital gains, , and plus other capital gains (such as real state capital gains and others). t yt Gt
(2)
In an economy subject to a variety of taxes the value of a dollar of retained profits by a firm cannot be directly attributed to the income of the stockholder from such firm. That is, the potential capital gain caused by retaining one dollar in the firm does not necessarily directly translate into one additional dollar of accrued capital gain. Define, the opportunity cost of a retained dollar in terms of foregone dividend as, ≡
(3)
Where is the tax rate on firms` profits, my is the personal tax rate on dividends, z is the tax rate on capital gains, and 0 # $ # 1 is the fraction of the 3
tax paid by the firm that is allowed as a tax credit to the stockholder (that is, $ measures the degree of tax integration). This formula is a slight generalization of the well-known formula developed by King (1974); unlike King`s formulation, which assumes either no or complete tax integration (i.e., $ 0 or $ 1, our specification allows for the existence of partial or total integration as measured by the parameter $. Also, it is assumed that the tax rate on dividends is nondecreasing in y. The following proposition shows the relationship between retained or undistributed profits &' and business-accrued capital gains, Proposition 1. In equilibrium, business-accrued capital gains are related to retained profits as follows, Gt θτ, my, z; sπ, t,
(4)
Proof: Equilibrium in the capital market implies (King, 1974): 1 - . /0 1 1 - 20 1 - 0
(5)
where 0 is the value of the firm in time and 1 is the net after-tax dividend paid by the firm. We generalize (5) to allow for different degrees of tax integration (s),
1 - ./0 1 0 1 - 0 1 - 2
(6)
Using the definition of in equation (3), (6) can be written as: /0
34
0 1 - 0
4
(7)
Using that
34
1 - & - &' and noting that in equilibrium /0 1 -
&, we have, ≡ 0 1 - 0
(8)
&'
(9)
Then, we obtain that:
Thus, using equations (2) and (9) we have, It yt θτ, my, z; sπ, t
(10)
The following corollary follows, Corollary 1.1. Only in the special case where 1 it is legitimate to add -on retained profits to the other incomes of shareholders to estimate their true total income. Proof: Follows directly from Proposition 1. Thus, the approach of directly adding up retained profits to other income sources to estimate incomes of shareholders would be appropriate only if θ 1. However, under most tax regimes θ 6 1. If θ 7 1 the opportunity cost of one dollar of foregone dividend is greater than one dollar, implying that firms would have incentives to distribute all their profits and hence that π, 0. In practice, however, firms often may retain parts of their profits even if θ 7 1. The case where θ 8 1 is more interesting because it is often encountered in most tax systems. In this case firms have incentives to distribute the minimum possible dividends required by law and, hence, retained profits are likely to be 5
large. As a result, stockholders share the benefits of the firm mostly through fundamental capital gains rather than dividends to the extent possible. In this case, directly adding the retained profits to the rest of the shareholders incomes will over estimate their true incomes. In summary, according to Proposition1, we can transform retained profits into business-accrued capital gains by multiplying retained profits corresponding to an individual taxpayer by the factor associated to his/her income using equation (9). 3. Probability distribution of business-accrued capital gains and retained profits. The fact that depends on y -a random variable- may imply that capital gains distribute differently from retained profits. This means that even under the assumption that profits follow a Pareto distribution there is no guarantee that θτ, my, z; sπ, distributes according to the same distribution. However, since we are dealing with top incomes one might assume that my m9:; , equal to the highest marginal personal income tax rate, in which case is independent of the random variable y . In this case, as the following lemma shows it, capital gains may follow the same distribution as retained profits. Lemma 1. Assume that .= .>? with .>? @ .A for all , that 2 is constant and independent of the shareholder`s income, and that π, is ruled by a Pareto distribution. Then , .>? , 2; $&/ distributes Pareto. Proof: Since is constant then , .>? , 2; $&/ distributes Pareto because &' distributes Pareto which is a scale-free distribution.
6
4. An empirical illustration We first estimate the value of θ using Equation (3) and the tax parameters prevailing in Chile during the period considered (2005-10).6 Table 1 shows the values of θ which fluctuated between 0.72 and 0.75 during the period. Table 1 provides estimates for the share of the top 1% comparing the López et.al. (2013) estimates with those obtained using our methodology. As can be seen, measuring capital gains correctly makes a large difference for the estimates of the share of the top 1%. This is due to the fact that capital gains are significantly lower than retained profits and that capital gains constitute an important component of the richest segments in society. Thus, over the period considered using the methodology proposed here reduces the share of the top 1% in national income by about 2 percentage points or by about 7-9%. Table 1. Share of top incomes estimated using retained profits versus using business-accrued capital gains
Year
2005
2006
2007
2008
2009
2010
Share of the top 1% using retained profits. 31.8
31.8
32.3
35.0
35.0
31.1
Share of the top 1% using businessaccrued capital gains. 29.5 0.72 Source: López et.al. (2013) and our estimates.
29.4 0.72
30.1 0.72
32.5 0.72
32.7 0.72
29.0 0.75
5. Conclusion This paper shows that using retained firms’ profits as a direct measure of business-accrued capital gains is in general wrong. The reason is that there is a wedge between the value of a dollar retained in the firm and the value of it to 6
The parameters used to compute are: . 0.4, 2 0, and = 0.17 in the years 2005-09 and 0.2 in 2010. Since Chile had full tax integration we use s=1.
7
the shareholder once the dollar is distributed as a dividend. This is so because once distributed the dollar is affected by other personal and capital gain taxes relevant to the shareholder. Also, we have shown that this wedge between the value of a dollar retained and a dollar distributed is affected by the degree of integration of the tax system. Using the example of Chile we have illustrated the practical importance of measuring capital gains correctly.
References Armour, P., Burkhauser, R. V., & Larrimore, J. (2013). Deconstructing Income and Income Inequality Measures: A Crosswalk from Market Income to Comprehensive Income. American Economic Review, 103(3), 173-177. Alvaredo, F. (2011). A note on the relationship between top income shares and the Gini coefficient. Economics Letters, Volume 110, Issue 3, Pages 274-277. Alvaredo, F., & Londoño, J. (2013). High incomes and personal taxation in a developing economy: Colombia 1993-2010 (No. 12). CEQ Working Paper. Alvaredo, F., Atkinson, A. B., Piketty, T., & Saez, E. (2013). The Top 1 Percent in International and Historical Perspective. Journal of Economic Perspectives, 3-20. Atkinson, A.B., Piketty, T. & Saez, E. (2011). Top Incomes in the Long Run of History, Journal of Economic Literature, 49(1): 3-71. Burdín, G., Esponda, F., & Vigorito, A. (2014). Inequality and top incomes in Uruguay: a comparison between household surveys and income tax micro-data. CEQ Working Paper No. 21. Fairfield, T., & Jorratt De Luis, M. (2015). Top income shares, business profits, and effective tax rates in contemporary Chile. Review of Income and Wealth. Haig, R. M. (1921). The concept of income-economic and legal aspects. The Federal Income Tax, 1(7). King, M. A. (1974). Taxation and the cost of capital. Review of Economic Studies, 2135. López, R., Figueroa, E., & Gutiérrez, P. (2013). La ‘parte del león’: Nuevas estimaciones de la participación de los súper ricos en el ingreso de Chile. Serie Documentos de Trabajo, 379.
8
Piketty, Thomas and Emmanuel Saez. (2003) "Income Inequality In The United States, 1913-1998.", Quarterly Journal of Economics, vol. 118 (1,Feb): 1-39. Simons, H. C. (1938). Personal income taxation: The definition of income as a problem of fiscal policy (pp. 28-30). Chicago: University of Chicago Press. Smeeding, T. M., & Thompson, J. P. (2011). Recent Trends in Income Inequality. Research in Labor Economics, 32, 1-50.
9
S0165-1765(15)00286-4 http://dx.doi.org/10.1016/j.econlet.2015.07.013 ECOLET 6827
To appear in:
Economics Letters
Received date: 5 November 2014 Revised date: 12 July 2015 Accepted date: 13 July 2015 Please cite this article as: Guti´errez C., P., L´opez, R.E., Figueroa B., E., Top income measurement and undistributed profits. Economics Letters (2015), http://dx.doi.org/10.1016/j.econlet.2015.07.013 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
*Highlights (for review)
Highlights
Simply adding retained profits to other personal incomes is in general incorrect
Proposes a method to transform retained profits into business-accrued capital gains
Shows sufficient conditions for business-accrued capital gains to distribute Pareto
*Title Page
Top income measurement and undistributed profits
Pablo Gutiérrez C. 1 Ramón E. López
Eugenio Figueroa B.
Department of Economics, University of Chile
Abstract We develop a method that allows transforming retained business profits in a particular year into business-accrued capital gains of the same year. These capital gains thus estimated can be simply added to other sources of personal income of top earners to obtain a consistent measure of their total income.
Keywords: Top income distribution; Undistributed distribution; Business-accrued Capital gains
profits;
Pareto
JEL classification: D31; H24
1
Correspondence to: Universidad de Chile, Diagonal Paraguay 257, Santiago, Chile. Tel.:+56229783422. Fax.: +56229783455. E-mail addresses: [email protected], [email protected]
*Manuscript Click here to view linked References
Top income measurement and undistributed profits1
1.
Introduction
Recent literature has greatly focused on the measurement of top incomes and their participation on the national income (Atkinson et al., 2011; Alvaredo et al., 2013; Alvaredo and Londoño, 2013; Burdin et al., 2014, among others).2 Most previous studies have considered only labor and other personal incomes excluding capital gains3. More recently, a few studies have explicitly considered realized capital gains as part of the total income of the rich, showing that their inclusion greatly increases the share of the top income earners in national income.4 However, the use of realized capital gains as part of the income of individuals in a particular period has been criticized because they may reflect capital appreciations that have taken place over years before the period in which the incomes are actually being measured (Armour et al, 2012; Smeeding and Thompson, 2010). Conversely, a large portion of the business-accrued capital gains obtained by individual investors in a particular period are often not realized in the same year and, therefore, are omitted when the conventional approach of accounting for only realized capital gains is used. This paper develops a new approach that deals with the above two problems. The key premise of the approach is that retained profits in a particular period 1
The authors thank an anonymous reviewer, this Journal Editor, Professor Samwick, and Alfonso Montes for useful comments and criticisms. 2 In this respect, Alvaredo (2011) has provided important insights by relating top incomes to the measurement of the Gini coefficient. 3 This is due to the fact that most tax systems cover capital gains imperfectly. Also, in several countries capital gains are not taxed at all, and thus are not reported. 4 For a complete discussion, see Atkinson et al., 2011.
1
are a fundamental source of capital appreciation during the same period.5 We develop a method that allows transforming retained business profits in a particular year into business-accrued capital gains of the same year. These capital gains thus estimated can then be simply added to the firm shareholders’ other sources of personal income to obtain a consistent measure of their total income. We also show that the approach of directly adding retained profits to labor income and other capital incomes as recently used, for example, by López et al, 2013 and Fairfield and Jorratt, 2015 among others, is in general inconsistent. This is due to the fact that retaining one dollar in the firm does not necessarily translate into one additional dollar of business-accrued capital gain to shareholders, due to the structure of observed tax systems. We show the special conditions under which this approach would be correct. Moreover, we discuss how the probability distribution of business-accrued capital gains is related to the distribution of retained profits. Finally, to address the potential practical importance of the proposed methodological innovation, we develop an empirical application using data from Chile.
5
The distinction between fundamental and non-fundamental capital gains is important. While the former are based on the profitability of the enterprises, the latter are mostly originated in financial market imperfections often causing asset price bubbles or asset price collapses that are unrelated to the performance of the enterprises.
2
2.
From undistributed profits to business-accrued capital gains
We use the measure of income developed by Haig (1921) and Simons (1938) where personal income of individual at time t is equal to her/his consumption Ct plus the net change of wealth ∆NWt (to simplify notation we drop subscript ): t Ct ∆NWt
(1)
One may alternatively define as the sum of the personal income yt, which includes labor income, distributed dividends and other personal incomes, plus business accrued capital gains, , and plus other capital gains (such as real state capital gains and others). t yt Gt
(2)
In an economy subject to a variety of taxes the value of a dollar of retained profits by a firm cannot be directly attributed to the income of the stockholder from such firm. That is, the potential capital gain caused by retaining one dollar in the firm does not necessarily directly translate into one additional dollar of accrued capital gain. Define, the opportunity cost of a retained dollar in terms of foregone dividend as, ≡
(3)
Where is the tax rate on firms` profits, my is the personal tax rate on dividends, z is the tax rate on capital gains, and 0 # $ # 1 is the fraction of the 3
tax paid by the firm that is allowed as a tax credit to the stockholder (that is, $ measures the degree of tax integration). This formula is a slight generalization of the well-known formula developed by King (1974); unlike King`s formulation, which assumes either no or complete tax integration (i.e., $ 0 or $ 1, our specification allows for the existence of partial or total integration as measured by the parameter $. Also, it is assumed that the tax rate on dividends is nondecreasing in y. The following proposition shows the relationship between retained or undistributed profits &' and business-accrued capital gains, Proposition 1. In equilibrium, business-accrued capital gains are related to retained profits as follows, Gt θτ, my, z; sπ, t,
(4)
Proof: Equilibrium in the capital market implies (King, 1974): 1 - . /0 1 1 - 20 1 - 0
(5)
where 0 is the value of the firm in time and 1 is the net after-tax dividend paid by the firm. We generalize (5) to allow for different degrees of tax integration (s),
1 - ./0 1 0 1 - 0 1 - 2
(6)
Using the definition of in equation (3), (6) can be written as: /0
34
0 1 - 0
4
(7)
Using that
34
1 - & - &' and noting that in equilibrium /0 1 -
&, we have, ≡ 0 1 - 0
(8)
&'
(9)
Then, we obtain that:
Thus, using equations (2) and (9) we have, It yt θτ, my, z; sπ, t
(10)
The following corollary follows, Corollary 1.1. Only in the special case where 1 it is legitimate to add -on retained profits to the other incomes of shareholders to estimate their true total income. Proof: Follows directly from Proposition 1. Thus, the approach of directly adding up retained profits to other income sources to estimate incomes of shareholders would be appropriate only if θ 1. However, under most tax regimes θ 6 1. If θ 7 1 the opportunity cost of one dollar of foregone dividend is greater than one dollar, implying that firms would have incentives to distribute all their profits and hence that π, 0. In practice, however, firms often may retain parts of their profits even if θ 7 1. The case where θ 8 1 is more interesting because it is often encountered in most tax systems. In this case firms have incentives to distribute the minimum possible dividends required by law and, hence, retained profits are likely to be 5
large. As a result, stockholders share the benefits of the firm mostly through fundamental capital gains rather than dividends to the extent possible. In this case, directly adding the retained profits to the rest of the shareholders incomes will over estimate their true incomes. In summary, according to Proposition1, we can transform retained profits into business-accrued capital gains by multiplying retained profits corresponding to an individual taxpayer by the factor associated to his/her income using equation (9). 3. Probability distribution of business-accrued capital gains and retained profits. The fact that depends on y -a random variable- may imply that capital gains distribute differently from retained profits. This means that even under the assumption that profits follow a Pareto distribution there is no guarantee that θτ, my, z; sπ, distributes according to the same distribution. However, since we are dealing with top incomes one might assume that my m9:; , equal to the highest marginal personal income tax rate, in which case is independent of the random variable y . In this case, as the following lemma shows it, capital gains may follow the same distribution as retained profits. Lemma 1. Assume that .= .>? with .>? @ .A for all , that 2 is constant and independent of the shareholder`s income, and that π, is ruled by a Pareto distribution. Then , .>? , 2; $&/ distributes Pareto. Proof: Since is constant then , .>? , 2; $&/ distributes Pareto because &' distributes Pareto which is a scale-free distribution.
6
4. An empirical illustration We first estimate the value of θ using Equation (3) and the tax parameters prevailing in Chile during the period considered (2005-10).6 Table 1 shows the values of θ which fluctuated between 0.72 and 0.75 during the period. Table 1 provides estimates for the share of the top 1% comparing the López et.al. (2013) estimates with those obtained using our methodology. As can be seen, measuring capital gains correctly makes a large difference for the estimates of the share of the top 1%. This is due to the fact that capital gains are significantly lower than retained profits and that capital gains constitute an important component of the richest segments in society. Thus, over the period considered using the methodology proposed here reduces the share of the top 1% in national income by about 2 percentage points or by about 7-9%. Table 1. Share of top incomes estimated using retained profits versus using business-accrued capital gains
Year
2005
2006
2007
2008
2009
2010
Share of the top 1% using retained profits. 31.8
31.8
32.3
35.0
35.0
31.1
Share of the top 1% using businessaccrued capital gains. 29.5 0.72 Source: López et.al. (2013) and our estimates.
29.4 0.72
30.1 0.72
32.5 0.72
32.7 0.72
29.0 0.75
5. Conclusion This paper shows that using retained firms’ profits as a direct measure of business-accrued capital gains is in general wrong. The reason is that there is a wedge between the value of a dollar retained in the firm and the value of it to 6
The parameters used to compute are: . 0.4, 2 0, and = 0.17 in the years 2005-09 and 0.2 in 2010. Since Chile had full tax integration we use s=1.
7
the shareholder once the dollar is distributed as a dividend. This is so because once distributed the dollar is affected by other personal and capital gain taxes relevant to the shareholder. Also, we have shown that this wedge between the value of a dollar retained and a dollar distributed is affected by the degree of integration of the tax system. Using the example of Chile we have illustrated the practical importance of measuring capital gains correctly.
References Armour, P., Burkhauser, R. V., & Larrimore, J. (2013). Deconstructing Income and Income Inequality Measures: A Crosswalk from Market Income to Comprehensive Income. American Economic Review, 103(3), 173-177. Alvaredo, F. (2011). A note on the relationship between top income shares and the Gini coefficient. Economics Letters, Volume 110, Issue 3, Pages 274-277. Alvaredo, F., & Londoño, J. (2013). High incomes and personal taxation in a developing economy: Colombia 1993-2010 (No. 12). CEQ Working Paper. Alvaredo, F., Atkinson, A. B., Piketty, T., & Saez, E. (2013). The Top 1 Percent in International and Historical Perspective. Journal of Economic Perspectives, 3-20. Atkinson, A.B., Piketty, T. & Saez, E. (2011). Top Incomes in the Long Run of History, Journal of Economic Literature, 49(1): 3-71. Burdín, G., Esponda, F., & Vigorito, A. (2014). Inequality and top incomes in Uruguay: a comparison between household surveys and income tax micro-data. CEQ Working Paper No. 21. Fairfield, T., & Jorratt De Luis, M. (2015). Top income shares, business profits, and effective tax rates in contemporary Chile. Review of Income and Wealth. Haig, R. M. (1921). The concept of income-economic and legal aspects. The Federal Income Tax, 1(7). King, M. A. (1974). Taxation and the cost of capital. Review of Economic Studies, 2135. López, R., Figueroa, E., & Gutiérrez, P. (2013). La ‘parte del león’: Nuevas estimaciones de la participación de los súper ricos en el ingreso de Chile. Serie Documentos de Trabajo, 379.
8
Piketty, Thomas and Emmanuel Saez. (2003) "Income Inequality In The United States, 1913-1998.", Quarterly Journal of Economics, vol. 118 (1,Feb): 1-39. Simons, H. C. (1938). Personal income taxation: The definition of income as a problem of fiscal policy (pp. 28-30). Chicago: University of Chicago Press. Smeeding, T. M., & Thompson, J. P. (2011). Recent Trends in Income Inequality. Research in Labor Economics, 32, 1-50.
9