A dynamic general equilibrium model to evaluate income tax reforms in Colombia* Oliver Pardo National Planning Department, Directorate of Economic Studies [email protected]

First draft: August 2006 This version: July 2007

Abstract

This paper presents a dynamic general equilibrium model designed to evaluate the effect of income tax reforms on efficiency, welfare and economic performance. Agents are classified by their years of schooling and their years of working experience, which in turn determine their labor productivity. Their decisions over asset accumulation, consumption and labor supply are affected by the taxes. The parameters of the model are estimated and calibrated to reflect some characteristics of the Colombian economy and its income tax structure. In order to provide a numerical example of the model, the original 2006 tax reform proposed by the government is simulated. Quantitative responses of some aggregates and welfare indicators are obtained, both in the steady state and during the transition.

Keywords: Tax Reform, Dynamic Computable General Equilibrium Models. JEL classification: D58, H24, H25.

*

A former version of this paper, titled “Efectos macroeconómicos y distributivos de la reforma sobre el impuesto a la renta en Colombia: una aproximación mediante un modelo de equilibrio general dinámico”, was presented in the ECLAC XIX Regional Seminar on Fiscal Policy. The author appreciates the comments of both the participants of this seminar and the participants of the weekly meetings of the Directorate of Economic Studies of the National Planning Department. The model’s algorithms were programmed using MATLAB® and can be found in http://oliverpardo.googlepages.com/. Opinions, errors and omissions are exclusive responsibility of the author and do not represent the official position of the National Planning Department.

1

Resumen

Este trabajo presenta un modelo de equilibrio general dinámico diseñado para evaluar el impacto de las reformas al impuesto de renta sobre la eficiencia, el bienestar y el desempeño económico. Los agentes se clasifican según su logro educativo y su experiencia laboral, los cuales determinan su productividad laboral. Sus decisiones con respecto a la acumulación de activos, el consumo y la oferta laboral se ven afectadas por los impuestos. Los parámetros del modelo son estimados y calibrados para reflejar algunas características de la economía Colombiana y su estructura tributaria. Con el fin de ejemplificar numéricamente el modelo, se simula la propuesta original de la reforma tributaria estructural presentada por el gobierno en el 2006. Se reportan las respuestas cuantitativas para algunos agregados y algunos indicadores de bienestar, tanto en el estado estacionario como durante la transición.

1. Introduction

From time to time in Colombia, structural tax reforms are encouraged by academics, policy makers, entrepreneurs and others. This obeys to the great complexity and inefficiencies of the tax structure. High statutory tax rates, various exemptions and narrow tax bases characterize the tax structure in Colombia1. In this sense, the usually suggested policy is the removal of exemptions, the widening of the tax base and the reduction of tax rates.

Structural tax reforms have a widespread effect on efficiency, welfare and economic performance. Thus, a quantitative estimate of the macroeconomic responses is a crucial step in order to evaluate structural tax reforms proposals. For Colombia, several papers have attempted to elucidate the quantitative effects of tax reforms, including Rutherford and Light (2002), Rutherford, Light and Hernandez (2002), Rutherford, Light and Barrera (2003), Escobar et al. (2003), Karl (2004) and Ramirez et al. (2006). These papers are based on Computable General Equilibrium (CGE) models which are static or recursive. These kinds of models are not strictly dynamic, in the sense that agents do not try to make an optimal intertemporal choice. Nevertheless, a crucial effect of taxes is precisely the distortion on the

1

See, for example, Cardenas and Mercer-Blackman (2006).

2

intertemporal allocation of resources. Therefore, a quantitative evaluation not based on dynamic optimization misses some of the benefits (or costs) of tax reforms.

Other models, like Fergusson (2003) or Suescún (2007), evaluate the effect of tax reforms in Colombia in the context of dynamic general equilibrium models. But they do so with infinitely living agents, and hence cannot model the effect of tax reforms across different generations. The tax structure proposed in these models is very simple (this is partially explained by the questions addressed by the models), and thus cannot model some particular policy measures.

This paper is focused on the dynamic effects of income tax reforms. It presents a dynamic general equilibrium model that intends to capture some of the main characteristics of the income tax structure in Colombia. Agents try to choose an optimal allocation of consumption, leisure and savings along their lifecycle. Nevertheless, income taxes alter the relative prices of labor, capital and consumption, distorting the efficient allocation of resources. Different generations overlap each other, so the effect of tax reforms on welfare across generations can be modeled. The parameters of the model are estimated and calibrated to reflect some characteristics of the Colombian economy and its income tax structure. In order to provide a quantitative example of the dynamics of the model, the 2006 original structural tax reform proposed by the government is simulated2.

The model follows the literature on tax reforms pioneered by Auerbach and Kotlikoff (1987). Similar models designed to evaluate tax reforms are Altig et al. (1997), Ventura (1999), Heer and Trade (2003) and Díaz-Giménez and Pijoan-Mas (2005). The computational algorithms used to solve the steady state of the model and the transitional dynamics were inspired by these works and the one of Heer and Maussner (2005).

The rest of the paper is organized as follows. Section 2 describes the model, states the assumed tax structure and defines the equilibrium conditions. Section 3 presents the parameters estimate and calibration. Section 4 describes the main points of the original 2006 tax reform proposal related to the income tax, and the way they are incorporated into the

2

See Carrasquilla (2006) and DIAN (2006) for details.

3

model. Section 5 reports the effects on some macroeconomic variables and welfare indicators, both in the steady state and during the transition to it. Section 6 concludes and suggests some possible extensions of the model.

2. Model

This is an overlapping generations model with heterogeneous agents and perfect foresight. In order to study the effects on welfare distribution, we assume that heterogeneity comes from different educational attainments. This educational attainment affects labor productivity, which in turn affects earnings, asset accumulation and thus capital earnings along the lifecycle. There is no intergenerational altruism, so initial financial assets are zero. Thus different income profiles are caused by different endowments of “human capital”, but not by different endowments of physical capital.

Labor productivity for each agent depends only on her working experience and her years of schooling. Agent’s years of schooling are exogenous, while her working experience is a function of her age and her years of schooling. There is no technological progress, so labor productivity is not affected by the agent’s birth date.

Government collects taxes on labor income, capital income and consumption. We assume that the capital income tax is analogous to the corporate income tax, and that the labor income tax is analogous to personal income tax. Government has an exogenous trajectory for its expenditures. For every period, we assume that tax revenues equal public expenditures. Consumption tax adjusts endogenously to satisfy this equality, leaving labor and capital income taxes as policy instruments.

We are assuming that this is a closed economy and that there is no public debt. The only assets available to consumers are property rights over the firms stock of capital. The impossibility of foreign asset accumulation will be discussed in section 5.

2.1 Demographics, preferences, technology and tax structure

Demographics: 4

We assume all agents live for T periods and that there is a compulsory age of retirement T TR. Inside each generation, agents are differentiated only by their years of schooling. Agent i has T - TR - Ti years of schooling, where Ti is her number of periods in the job market. We leave aside the behavior of consumers while they are studying, and just assume they “get into the economy” when they are Ti + TR periods of life left. Years of schooling vary from 0 to 21, so there are 22 types of agents for each generation. Agents are indexed by their educational attainments, so i = T - TR - Ti. Each agent has an exogenous relative weight of µi ∈ [0,1] inside her generation. We assume that there is no population growth, so we can normalize the size of all the population “alive” (those working or retired) to one. Thus, the number of agents with T - TR - Ti years of schooling is µi /(Ti + T R ) in every period.

Preferences: Agents maximize the present value of their utility discounted by a discount factor β . Instant utility in period t for an agent with i years of schooling and age z is a function of her consumption cti, z and her leisure lti, z :

U = i t

Ti +T R

∑β z =1

z −1

u (cti+ z , z , lti+ z , z )

(1)

We assume instant utility is given by:

⎡( ci ) ρ ( l i )1− ρ ⎤ t+z,z ⎢ t+z,z ⎥⎦ u (cti+ z , z , lti+ z , z ) = ⎣ 1−σ

1−σ

−1 (2)

where ρ ∈ (0,1) is a participation parameter and σ ∈ (0, ∞) is the inverse of the intertemporal elasticity of substitution.

Budget constraints:

5

For each period, agents receive labor and capital earnings that they allocate to consumption, savings and tax payments. Let wt be the wage per efficient unit in period t. Let hzi be the labor productivity per unit of time for agent i whose age is z. We assume that in each period agents are endowed with a unit of time that can be allocated to work and leisure. Thus, their labor earnings are (1 − lti, z ) wt hzi . Let kti, z be her stock of assets in t and rt the interest rate. If taxti, z denotes their tax payments (which are a function of the tax structure, the relative prices and their own decisions), their budget constraint in t is: (1 − lti, z ) wt hzi + rt kti, z ≥ cti, z + (kti+1, z +1 − kti, z ) + taxti, z

(3)

For z = 1, … , Ti, leisure must satisfy lti, z ∈ [0,1] . For z = Ti + 1, … , Ti + TR, compulsory retirement implies lti, z = 1 .

Taxes:

The following tax structure aims to reflect some characteristics of the Colombian tax regime. Capital income tax is associated with the corporate income tax, while labor income tax revenue is associated with the personal income tax. As long as capital gains are deductible form the personal income tax, as happens in Colombia, this assumption is valid. Nevertheless, these assumptions must be seen with caution. In the Colombian economy -as in many others developing economies-, there are a lot of economic activities in which it is very difficult to elucidate if income derives from labor or capital sources. Thus, some firm owners declare their profits to the tax authority as if they were personal income. Moreover, a lot of low scale firms do not report their revenues at all. Therefore, informal economies, tax evasion and tax elusion tend to reduce the effect of any tax reform. These phenomena are treated and discussed in section 3, where we calibrate the parameters. Government imposes a tax rate per unit of consumption equal to τ tc in period t. There is a single marginal tax rate on capital earnings equal to τ tk . However, a fraction ψ ∈ [0,1] of the asset accumulation is tax deductible. This parameter allows the introduction of a full deductibility on investment, which reduces the distortions on the intertemporal allocation of

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resources, as we are going to see below. If taxwti, z denotes the tax payments on labor income, total taxes payments are equal to:

taxti, z = τ tc cti, z + τ tk ⎡⎣ rt kti, z −ψ (kti+1, z +1 − kti, z ) ⎤⎦ + taxwti, z

(4)

Marginal tax rate on labor income depends on the amount of labor income itself. There is a series of income brackets and a percentage of labor income exempted from taxes. For taxed labor income in income bracket [ I m −1 , I m ] there is a marginal tax rate τ mh ,t . Let ϕ denote the percentage of labor income exempted from the labor income tax. Thus, for someone whose labor income implies (1 − ϕ )(1 − lti, z ) wt hzi ∈ [ I m−1 , I m ] , her labor income tax payments are:

taxwti, z = τ mh ,t ⎡⎣(1 − ϕ )(1 − lti, z ) wt hzi − I m−1 ⎤⎦ + τ mh −1,t [ I m −1 − I m− 2 ] + ... + τ 1,ht [ I1 − 0]

(5)

Labor productivity:

In the model, agents start their lifecycle when they join the labor market. Therefore, at the end of each period there is an additional year of working experience. In turn, labor productivity is increasing in the working experience and the years of education. We assume the following productivity functional form, following the mincerian equations literature:

ln hzi = α 0 + α1 (T − Ti − T R ) + α 2 (T − Ti − T R ) 2 + α 3 ( z − 1) + α 4 ( z − 1) 2

(6)

The coefficients associated with the latter equation are estimated in section 3.

Technology:

We assume that perfectly competitive firms hire labor (Lt) and capital (Kt) to produce a good that can be consumed or accumulated as physical capital for the next period. Let δ be the capital depreciation rate and assume the following Cobb-Douglas net-of-depreciation production function:

7

F ( K t , Lt ) = K tα L1t−α − δ K t

(7)

Government:

Government has an exogenous trajectory for its expenditures, which do not affect utility or production. For every period t tax revenues equal government expenditures (Gt):

µi

R 21 Ti +T

Gt = ∑ i =0

∑ T +T z =1

R

taxti, z

(8)

i

Consumption tax rate ( τ tc ) adjusts it self endogenously to guarantee this latter equation.

2.2 Consumers problem

Each consumer sets a trajectory for consumption, labor and assets that maximize her discounted sum of instantaneous utilities, subject to the budget constraints and the feasibility of her time allocation. The problem for consumer i born in period t is: 1−σ

max

Ti +T R T +T R

{cti+ z −1, z ,lt + z −1, z , kt +1+ z −1, z }zi=1

∑ z =1

⎡( ci ) ρ ( l i )1− ρ ⎤ t+ z,z ⎢ t+z,z ⎥⎦ β z −1 ⎣ 1−σ

−1

s. t.

(1 − lti+ z −1, z ) wt + z −1hzi + rt + z −1kti+ z −1, z ≥ cti+ z −1, z + (kti+1+ z −1, z +1 − kti+ z −1, z ) + taxti+ z −1, z

for z = 1, …, Ti+TR 0 ≤ lti+ z −1, z ≤ 1

for z = 1, …, Ti

lti+ z −1, z = 1

for z = Ti+1, …, Ti+TR

kti,1 = 0

(9) where taxti+ z −1, z is defined by equations (4) and (5).

8

If for some period the solution implies 0 < lti, z < 1 and (1 − ϕ )(1 − lti, z ) wt hzi ∈ ( I m −1 , I m ) , the marginal rate of substitution between leisure and consumption must equal the ratio between its relative prices:

ρ / cti, z (1 + τ tc ) = (1 − ρ ) / lti, z ⎡⎣1 − (1 − ϕ )τ mh ,t ⎤⎦ wt hzi

(10)

Furthermore, for every t the marginal utility of consumption in t must equal the marginal utility of consumption in t+1 discounted by β and multiplied by the net return on capital:

⎛ cti, z ρ (1−σ ) −1lti, z (1− ρ )(1−σ ) ⎞ ⎛ 1 −ψτ tk+1 + (1 − τ tk+1 )rt +1 ⎞ ⎛ cti+1, z +1ρ (1−σ ) −1lti+1, z +1(1− ρ )(1−σ ) ⎞ ⎜⎜ ⎟⎟ = β ⎜ ⎟⎟ ⎟ ⎜⎜ (1 + τ tc ) 1 −ψτ tk (1 + τ tc+1 ) ⎝ ⎠⎝ ⎝ ⎠ ⎠

(11)

Note that if ψ = 0, the net return on capital is 1 + (1 − τ tk+1 )rt +1 . But if ψ = 1 and τ tk = τ tk+1 , the net return is 1 + rt +1 . Thus, if all investment is deductible (ψ = 1) and both τ tc and τ tk are constant, equation (11) reduce to one that characterizes an efficient allocation, eliminating the distortion of capital taxation in the intertemporal allocation of resources.

2.3 Equilibrium

For a set of policy instruments, a trajectory for the government expenditures and an initial distribution of assets k0,i z over z = 1, …, Ti+TR and i = 0, …, 21, an equilibrium is defined as a trajectory for wt , rt , cti, z , lti, z , kti+1, z and τ tc such that:

1) For every agent i and every period t, the trajectories for cti, z , lti, z and kti+1, z are a solution to consumers problem stated in (9).

2) Factors are remunerated by their marginal productivity:

rt = α ( K t / Lt )α −1 − δ

(12) 9

wt = (1 − α )( K t / Lt )α

(13)

3) Supply equals demand in the factor markets:

µti, z

R 21 Ti +T

Kt = ∑

∑ T +T

i =0

z =1

i =0

µti, z

∑ T +T z =1

kti, z

(14)

(1 − lti, z )hzi

(15)

i

R 21 Ti +T

Lt = ∑

R

R

i

4) Supply equals demand in the goods market:

α 1−α

K t Lt

µti, z

R 21 Ti +T

− δ Kt = ∑ i =0

∑ T +T z =1

µti, z

R 21 Ti +T

R

c + Gt + ∑ i t,z

i =0

i

∑ T +T z =1

R

(kti+1, z +1 − kti, z )

(16)

i

5) In every period government expenditures equals its revenues, thus equation (8) is satisfied.

3. Parameters

This section presents the values assigned to the parameters of the model, in order to simulate an example of a tax reform in section 4. Some of the parameters were estimated or obtained from other sources, while others were calibrated to reflect some stylized facts of the Colombian economy.

Demographics:

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Figure 1 Relative frequency of the educational attainments on working population 0.25

0.2

Freq.

0.15

0.1

0.05

0 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

years of schooling

Source: Author’s estimations based on Encuesta Continua de Hogares (ECH) 2005.

It is assumed that agents spend 10 years retired, so TR = 10. If agents live for 70 years (whatever their educational achievement is) and they can start to study with 6 years, the number of years Ti varies from 54 for i = 0 to 39 for i = 21. The relative weight µi of agent i is set equal to the percentage of the working population whose years of schooling are equal to i, as presented in figure 1.

Preferences: There are two scenarios for the inverse of the intertemporal elasticity of substitution σ . In the first, it is equal to 1.5, while in the second it is equal to 4.0. The discount factor β is adjusted until in the steady state of the model the capital output ratio is equal to 2.143. For σ = 1.5 , the

β value is 0.933, and for σ = 4.0 , it is 0.952. The participation parameter ρ for consumption in the composite good is calibrated until agents spend (on average) a third of their time in working activities. For both σ values, a ρ value equal to 0.39 matches this criterion.

3

This is the average capital output ratio from 1994 to 2001, calculated by the author based on Directorate of Economic Studies of the National Planning Department (DEE-DNP) data.

11

Taxes: Until 2006, 30% of the investments were deductible from the corporate income tax, so ψ is set equal to 0.3 in the benchmark. Statutory corporate tax rate on tax income is 35%, but tax evasion, which affects the marginal tax rate, is pervasive in Colombia. To obtain an approximation to the effective marginal tax rate τ k , the statutory tax rate is multiplied by the percentage of income declared to the tax authority. According to DIAN (2006), 35% of the taxable income is not reported, so τ k is assumed to be equal to 22.8% (= 35% * (1 - 35%)).

The treatment of tax evasion in the model is a very rough approximation. Tax evasion is highly sensitive to the specific economic activity and particularly on the firms scale. In Colombia, corporate tax revenues accrue mainly from the biggest enterprises. As a fact, this partially explain the high statutory tax rate -the smaller the tax base, the greater the tax rate necessary to obtain some given tax revenues-. Therefore, marginal tax rates vary according to firms scale. Furthermore, tax evasion is an endogenous decision, affected by the tax rate itself4.

Other exemptions and surtaxes also affect the marginal corporate tax rate. Author’s estimations based on Avila and Leon (2006) find an effective marginal rate very close to the statutory one. However, the omission of these other exemptions leaves out the distortions produced by them. Certain economic activities -like cattle breeding- have a privileged tax treatment. Modelling the removal of these kinds of distortions would require a multisectorial model. The income brackets for personal income are legally defined in terms of minimum wages5. The marginal tax rates associated with each income bracket are the following: From 0 to 4.7 minimum wages, the marginal tax rate is 0%. From 4.7 to 8 minimum wages, it is 20%. From 8 to 19 minimum wages, it is 29%. For 19 minimum wages or more, it is 35%. In Colombia, almost 90% of the workers earn less that 2 minimum wages. Thus, the vast majority of people are exempt from the labor income tax (except for a tax withholding not modeled here). The 4

For a survey of the theory on tax evasion, see Andreoni, Erard and Feinstein (1998). For studies on tax evasion in Colombia, see Steiner and Soto (1999) and Valencia (2004). 5 In 2005, an annual minimum wage was around US$ 1.970 (without purchasing power parity adjustments)

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model can be used to evaluate the welfare and distribution effects of an increase in taxable income, albeit this is not done here.

The percentage of exempt labor income is 25%. Nevertheless, as in the case of the corporate tax, tax evasion is pervasive. Non-declared labor income is equivalent to an increase on the exempt labor income. Assuming that the percentage of non-declared labor income is 35%, the value for 1 − ϕ would be 0.49 (= (1 - 0.25)*(1 - 0.35)). Again, this treatment of tax evasion is a rough approximation.

Labor productivity:

The coefficients associated with equation (6) are estimated regressing the logarithm of individual wages against the years of schooling, the years of working experience and the squares of these two variables. The results, based on the 2005 national households’ survey (ECH) data, are reported in table 1.

Table 1 Coefficients for the log of wage per hour constant

α0

education

α1

education^2

α2

experience

α3

experience^2

α4

Number of Obs. R^2:

-1.3360 (-165.88)** 0.0052 (3.86)* 0.0064 (92.04)** 0.0336 (80.83)** -0.0004 (-53.97)** 207,222 0.3547

* significance of 5% or better; ** significance of 1% or better

The wages referenced in table 1 are in Colombian pesos. We want that the nominal wages inside the model are expressed in minimum wages. Therefore, the scale parameter α 0 is adjusted until the average labor income equals 1.34 minimum wages. This corresponds to the

13

Colombian average labor income measured in minimum wages, according to the author’s estimate based on the 2005 ECH data.

Technology: The participation of capital in national income ( α ) is 0.34. This corresponds to the participation of capital rents on net-of-taxes national income in 20016. Annual depreciation rate for capital is set equal to 4.9%7.

Government:

Government expenditure (Gt) is calibrated to be 14.9% of the GDP. This corresponds to the Colombian central government tax revenues as a percentage of the GDP in 20058. The consumption tax rate ( τ tc ) which equals tax revenues to government expenditures is 12.7% if

σ = 1.5 and 12.5% if σ = 4.0 . Table 2 summarizes the parameter values of the model.

Table 2 Parameter values for the benchmark

σ = 1.5

σ = 1.5

σ = 4.0

Demographics

Ti TR

10

µi

τk ψ τc ( I1 , I 2 , I 3 , I 4 ) (τ 1h ,τ 2h ,τ 3h ,τ 4h ) ϕ

β ρ

from 39 to 54

Preferences 0.933

0.952

0.390

0.390

See figure 1 Taxes

α0 α1 α2 α3 α4

0.2284 0.3 0.1271

0.1254

(4.7, 8.0, 19.0, +Inf) (0.00, 0.20, 0.29, 0.35)

Labor productivity 0.3221

0.3542 0.0052 0.0064 0.0336 -0.0004

0.51

α δ

Government

G

σ = 4.0

0.3045

0.3033

6

Author’s estimate based on DANE national accounts. Source: DEE-DNP. 8 Source: CONFIS (2006) 7

14

Technology 0.344 0.049

4. Simulation

In order to exemplify quantitatively the effect of tax reforms, the following policy shock is simulated. It is based on the original structural tax reform that the Colombian government presented to the congress at the beginning of the second half of 2006. The principal proposals related to personal and corporate income tax were9:

1. Reduce gradually the statutory tax rate, one percentage point per year, until it reaches the level of 32%.

2. Remove the exemptions on corporate income tax.

3. Let 100% of the investment be deductible from the corporate tax income.

4. Remove the percentage of exempt labor income, but increase the lowest labor income bracket from 4.7 to 7 minimum wages.

5. Replace the three marginal tax rates on personal income (20%, 29% and 35%) by two new marginal tax rates: 15% from 7 to 25 minimum wages and 32% for 25 minimum wages and from there on.

The estimated effect of the first two policies on the capital marginal tax rate is based on Avila and Leon (2006). The marginal tax rate τ k jumps from 22.8% to 24.1% as a consequence of the removal of tax exemptions. Then it drops to 23.4% the next period and then to 22.8%. Thus, the decrease on the statutory tax rate offset the removal of tax exemptions, leaving the marginal tax rate almost unchanged some periods later. But this conceals the benefits from the removal of distortions associated with the allocation of resources to different kinds of economic activities, as warned above. The remaining policies are easy to introduce. Full deductibility of investment implies that ψ jumps from 0.3 to 1. The removal of the exempt labor income implies that ϕ jumps from 0.51 9

Source: DIAN (2006)

15

to 0.35 (only the non-declared labor income does not tribute). Labor income brackets and its associated marginal tax rates adjust accordingly. The overall policy shock simulated in the model is presented in table 3. Table 3 Simulated policy shock marginal tax rate on corporate income deductibility of corporate investment exempted labor income income brackets marginal tax rates on labor income

τ ψ ϕ ( I1 ,..., I M ) (τ 1h ,...,τ Mh ) k

from

to

22.84%

24.1%, 23.4% and then to 22.8%

0.30

1.00

0.51

0.35

(4.7, 8.0, 19.0, +Inf)

(7.0, 25.0, +Inf)

(0.00, 0.20, 0.29, 0.35)

(0.00, 0.15, 0.32)

5. Results

Welfare effects of policy shocks depend not only on the personal productivity profile, but also on the birth year relative to the date of the policy shock. Of course, someone older, who is consuming her accumulated stock of capital, would have a lesser benefit from a capital income tax reduction that someone younger, who is starting to save. To elucidate the effect of tax reforms across different generations, transitional dynamics are necessary to be modeled. This has the advantage of quantifying the behavior of the macroeconomic variables between steady states, and thus, shed light on the possible short run trade offs faced by policy makers.

5.1 Steady state

The effects of the discussed policy shock on the steady state values of some macroeconomic variables are presented in table 4. The effects vary according to the assumed elasticity of substitution ( σ ). For both scenarios the increase on long run GDP is close to 8%. This is due to an increase on investment of 2 percentage points of the GDP, which increases the long run stock of capital around 1.24 times. Labor supply is almost unaffected. This is no surprise, given the low coverage of labor income tax on working population. Therefore, the effect on aggregates comes mainly from the full deducibility of investment, given that the marginal tax rate on capital income is almost unaffected.

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Table 4 The effect of the proposed tax reform on steady state aggregates

σ = 1.5

GDP

Labor supply (L)

stock of capital (K)

Aggregate consumption

Invesment output ratio

wage per efficient unit (w)

interest rate (r)

benchmark

2.036

1.365

4.361

1.517

10.5%

0.98

0.11

simulated

2.195

1.374

5.359

1.628

12.0%

1.05

0.09

∆%

7.8%

0.7%

22.9%

7.3%

14.0%

7.1%

-17.7%

σ = 4.0

GDP

Labor supply (L)

stock of capital (K)

Aggregate consumption

Invesment output ratio

wage per efficient unit (w)

interest rate (r)

benchmark

2.0429

1.3703

4.375

1.525

10.5%

0.98

0.11

simulated

2.2095

1.3795

5.425

1.640

12.0%

1.05

0.09

8.2%

0.7%

24.0%

7.6%

14.7%

7.4%

-18.4%

∆%

Equivalent variation measured in minimum wages is used as a welfare indicator. Table 5 reports the equivalent variation for each of the 22 types of agents. The reported numbers must be read as minimum wages transferred at the beginning of the lifecycle. These are welfare measures for all generations born once the economy gets into its new steady state, and so they are an approximation to the tax reform’s “long run impact” on welfare.

17

Table 5 The effect of the simulated tax reform on the steady state welfare (equivalent variation measured in minimum wages) years of education 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

relative weight 10.3% 3.3% 5.1% 5.8% 4.6% 14.8% 4.7% 5.0% 4.6% 5.0% 3.3% 20.1% 1.4% 2.1% 2.4% 1.1% 5.0% 0.6% 0.5% 0.2% 0.1% 0.1%

σ

= 1.5 1.2 1.2 1.2 1.2 1.3 1.4 1.5 1.6 1.8 2.0 2.3 2.6 3.1 3.6 4.3 5.2 6.3 7.8 9.8 12.3 15.4 19.4

σ

= 4.0 1.2 1.3 1.3 1.3 1.4 1.5 1.6 1.8 1.9 2.2 2.5 2.8 3.3 3.9 4.6 5.5 6.8 8.4 10.5 13.1 16.3 20.5

Agents of all educational achievements, and therefore of any income profile, get a positive benefit from the simulated tax reform. Nevertheless, the net benefit increases with personal productivity. Equivalent variation ranges from 1.2 annual minimum wages for those with no education to almost 20 for those who have 21 years of schooling. The larger labor productivity, the larger the asset accumulation possibilities along the lifecycle, and thus, the larger the benefits from the full deductibility of investment.

5.2 Transition path

Figure 4 present the transition path for some macroeconomic variables, assuming that the economy starts in the benchmark steady state and that the tax reform is suddenly implemented in t = 64. Table 6 present the growth rate for some of these variables during the transition. In the moment of the policy shock, agents react increasing their savings. These additional savings are obtained by a significant decrease on consumption and an increase on 18

labor supply. Capital adjusts rapidly, and then consumption tends to the higher new steady state level. Meanwhile, labor supply decreases towards its new steady state level, slightly higher than in the benchmark setup.

Figure 2 Transition path of some aggregate variables

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Table 6 GDP, consumption, labor suply and capital growth rates along the transition path GDP t 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

Consumption

Capital

σ = 1.5

σ = 4.0

σ = 1.5

σ = 4.0

σ = 1.5

1.8% 0.8% 0.5% 0.6% 0.6% 0.5% 0.4% 0.4% 0.3% 0.3% 0.2% 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0%

1.0% 0.6% 0.5% 0.6% 0.5% 0.5% 0.4% 0.4% 0.4% 0.3% 0.3% 0.3% 0.2% 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1%

-8.6% 2.9% 2.5% 1.5% 1.3% 1.1% 1.0% 0.9% 0.8% 0.7% 0.7% 0.5% 0.4% 0.3% 0.3% 0.2% 0.2% 0.2% 0.1% 0.1% 0.1%

-5.8% 1.5% 1.4% 1.0% 0.9% 0.8% 0.8% 0.7% 0.7% 0.6% 0.6% 0.5% 0.4% 0.4% 0.3% 0.3% 0.2% 0.2% 0.2% 0.2% 0.2%

0.0% 3.9% 3.0% 2.3% 1.9% 1.6% 1.4% 1.2% 1.0% 0.9% 0.7% 0.6% 0.5% 0.4% 0.3% 0.2% 0.2% 0.2% 0.1% 0.1% 0.1%

Labor

σ = 4.0 0.0% 2.5% 2.1% 1.8% 1.6% 1.5% 1.3% 1.2% 1.1% 0.9% 0.8% 0.7% 0.6% 0.6% 0.5% 0.4% 0.4% 0.4% 0.3% 0.3% 0.2%

σ = 1.5

σ = 4.0

2.8% -0.8% -0.8% -0.2% -0.2% -0.1% -0.1% -0.1% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

1.5% -0.3% -0.3% -0.1% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

The increases on factors supply translate into in an immediate increase in GDP. In the period when the tax reform is implemented, GDP increases by 1.8% and 1.0%, for σ = 1.5 and

σ = 4.0 respectively. Consumption decreases during the same period by 8.6% and 5.8%. Then consumption starts to increase until it is 7.3% and 7.6% higher than the benchmark consumption level. After twenty years, the shock is almost vanished and all endogenous variables are close to their new steady state values.

The sudden jump of savings, labor supply and GDP and the sudden slump of consumption at the beginning of the shock are due to the rapid adjustment of the stock of capital to its new steady state level. This suggests that a more realistic transition path will be obtained if investment adjustment costs are introduced into the model. Besides, the drastic decrease in consumption when the tax reform is implemented seems implausible in the context of an open economy. A substitution from foreign assets to domestic ones would evade the need of a sharp decrease on consumption. As a matter of fact, consumption would increase immediately instead of decreasing, as foreign assets allow getting into debt against a higher future income. This certainly would imply an increase on the trade balance deficit and/or an appreciation of the domestic currency. Again, these effects would be smoother if investment adjustment costs are introduced. 20

Figure 3 Consumption tax revenue as GDP percentage

The behavior of consumption formerly presented is enhanced by the behavior of the consumption tax rate ( τ c ). As investment increases, so are the deductions from it. Thus the government needs higher consumption tax revenues to evade a budget deficit until the economy reaches the new steady state. Figure 3 presents the dynamics for consumption tax revenue as a GDP percentage. The initial tax revenue needed to evade the budget deficit is around 0.8 to 1.3 percentage points of the GDP. This can be seen as a rough approximation to the budget deficit entailed by a tax reform like the simulated one here. Of course, and accurate estimation would require the introduction of public debt into the model, in order to obtain the possibility of budget deficits.

As mentioned above, welfare effects depend on the birth date relative to the date when the shock is introduced. Figure 4 presents the equivalent variation in annual minimum wages as a function of the birth date. The equivalent variations reported are those of the agents with a higher relative weight on the population: the ones with 0, 5, 11 or 16 years of education. Remember that the date of the shock is t = 64. Those born before the shock but still alive when the tax reform is implemented are nevertheless affected by it. 21

From figure 4 it can be seen that the younger the generation, the greater the benefit of the tax reform. Moreover, those with longer years of education but too old when the reform is implemented are actually worse off as a consequence of the reform. They are those who reduce their savings more rapidly but still had to pay a higher consumption tax.

Figure 4 Equivalent variation along the transition path

6. Conclusions

The dynamic general equilibrium model presented here tries to replicate some characteristics of the income tax structure in Colombia. Its purpose is to elucidate the quantitative responses of some macroeconomic variables and welfare indicators to structural tax reforms. Changes on marginal tax rates, removals of exemptions, investment deductibility and income brackets adjustments can be evaluated with this tool.

The largest effect of the simulated tax reform comes from the full deducibility of investment. The estimated effect of this policy on the GDP is an accumulated increase of 8%. Welfare increases across all income profiles, but the largest gains are concentrated on those who earn the highest income. In the short run, the necessity of increasing savings to finance investment induces a temporary decrease on leisure and consumption. This suggests that, in 22

the context of an open economy, the tax reform would imply and increase on the indebtedness with the foreign sector and/or a depreciation of the domestic currency.

Some extensions of the model would improve its accuracy to replicate the responses of the economic variables, particularly in the short run. The introduction of foreign assets would shed light on the effect of the tax reforms on the external balances of the economy. Investment adjustment cost would smooth the transition responses of the variables, generating more realistic trajectories.

References Altig, D., A. Auerbach, L. Kotlikoff, K. Smetters and J. Walliser (1997) “Simulating U.S. tax reform”, NBER working paper, No. 6248. Andreoni, J., B. Erard and J. Feinstein (1998) “Tax Compliance”, Journal of Economic Literature, 36. Auerbach, A. and L. Kotlikoff (1987) Dynamic fiscal policy. Cambridge University Press. Avila, J. and I. Leon (2006) “Una nota acerca de la tarifa efectiva del impuesto sobre la renta en Colombia para el año gravable 2004”. Cuadernos de trabajo de la Dirección de Estudios Económicos de la DIAN. Cárdenas, M. and V. Mercer-Blackman (2006) “Análisis del sistema tributario Colombiano y su impacto sobre la competitividad”. Cuadernos de Fedesarrollo, No. 19. Carrasquilla, A. (2006), “Reforma tributaria: El acercamiento a la tributación optima del capital”. Carta Financiera, No. 135, ANIF. CONFIS (2006), “Revisión Plan Financiero 2006”, Documento Asesores, No. 04/2006. Diaz-Giménez, J and J. Pijoan-Mas (2005) “Flat tax reforms in the U.S: A boon for the income poor”, mimeo. DIAN (2006), “Proyecto de Reforma Tributaria 2006: Documento de apoyo para la exposición de motivos”, mimeo. Escobar, A., G. Hernández, G. Piraquive and J.M. Ramírez (2003) “Elementos para el análisis de la incidencia tributaria”. Archivos de Economía, No. 224, National Planning Department of Colombia. Fergusson, L. “Tributación, crecimiento y bienestar: el caso Colombiano (1970-1990)” Documento CEDE, No. 2003-02, Universidad de los Andes. Karl, C. (2004) “How can tax policies and macroeconomic shocks affect the poor? A quantitative assessment using a computable general equilibrium framework for Colombia”. Ensayos sobre Política Económica, No. 46-II, Banco de la República, Colombia. Heer, B and A. Maussner (2005). Dynamic general equilibrium modelling. Springer, Berlin. Heer, B. and M. Trede (2003), “Efficiency and distribution effects of a revenue-neutral income tax reform”, Journal of Macroeconomics, 25. Steiner, R. and Soto, C. (1999). Cinco ensayos sobre la tributación en Colombia. Tercer Mundo, Bogotá.

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Suescún, R. (2007) “The role of fiscal policy in human development and growth”, The World Bank, mimeo. Ramirez, M., O. Acosta, C. Karl and O. Gracia (2006). “Fiscal adjustment, income distribution and poverty in Colombia: Value added tax reform and public transfers”. MPIA Network Session Paper, Addis Ababa, Ethiopia. Rutherford, T. and M. Light (2002). “A general equilibrium model for tax policy analysis in Colombia: The MEGATAX model”. Archivos de Economía, No. 188, National Planning Department of Colombia. Rutherford, T., M. Light and F. Barrera (2003). “Equidad y eficiencia de costos de incrementar los ingresos impositivos en Colombia”. Informe para la misión del ingreso público, Fedesarrollo. Rutherford, T., M. Light and G. Hernandez (2002). “A dynamic general equilibrium model for tax policy analysis in Colombia”. Archivos de Economía No. 189, National Planning Department of Colombia. Valencia, O. (2004) “Economic growth and optimal income tax evasion”. Conference papers and proceedings ECOMOD 2004. Ventura, G. (1999), “Flat tax reform: A quantitative exploration”, Journal of Dynamics and Control, 23.

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