On the Implications of Taxation for Investment, Savings and Growth: Evidence from Brazil, Chile and Mexico
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Espino, Emilio; González-Rozada, Martín Working Paper On the Implications of Taxation for Investment, Savings and Growth: Evidence from Brazil, Chile and Mexico IDB Working Paper Series, No. IDB-WP-560 Provided in Cooperation with: Inter-American Development Bank (IDB), Washington, DC Suggested Citation: Espino, Emilio; González-Rozada, Martín (2015) : On the Implications of Taxation for Investment, Savings and Growth: Evidence from Brazil, Chile and Mexico, IDB Working Paper Series, No. IDB-WP-560, Inter-American Development Bank (IDB), Washington, DC, https://hdl.handle.net/11319/6915 This Version is available at: https://hdl.handle.net/10419/115505 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by-nc-nd/3.0/igo/legalcode
On the Implications o f Taxation for Investment, Savings and Growth: Evidence from Brazil, Chile and Mexico Emilio Espino Martín González-Rozada Department o f Research and Chie f Economist IDB-WP-560 IDB WORKING PAPER SERIES No. Inter-American Development Bank April 2015
On the Implications o f Taxation f or Investment, Savings and Growth: Evidence from Brazil, Chile and Mexico Emilio Espino Martín González-Rozada Universidad Torcuato Di Tella 2015 Inter-American Development Bank
Cataloging-in-Publication data provided by the Inter-American Development Bank Felipe Herrera Library Espino, Emilio. On the implications of taxation for investment, savings and growth: evidence from Brazil, Chile and Mexico / Emilio Espino, Martín González-Rozada. p. cm. — (IDB Working Paper Series ; 560) Includes bibliographic references. 1. Taxation—Brazil. 2. Taxation—Chile. 3. Taxation—Mexico. 4. Spendings tax—Brazil. 5. Spendings tax—Chile. 6. Spendings tax—Mexico. I. González Rozada, Martín. II. Inter-American Development Bank. Department of Research and Chief Economist. III. Title. IV. Series. IDB-WP-560 http://www.iadb.org Any dispute related to the use of the works of the IDB that cannot be settled amicably shall be submitted to arbitration pursuant to the UNCITRAL rules. The use of the IDB’s name for any purpose other than for attribution, and the use of IDB’s logo shall be subject to a separate written license agreement between the IDB and the user and is not authorized as part of this CC-IGO license. Following a peer review process, and with previous written consent by the Inter-American Development 2015 Copyright © Inter-American Development Bank. This work is licensed under a Creative Commons IGO 3.0 Attribution-NonCommercial-NoDerivatives (CC-IGO BY-NC-ND 3.0 IGO) license ( http://creativecommons.org/licenses/by-nc-nd/3.0/igo/legalcode) and may be reproduced with attribution to the IDB and for any non-commercial purpose. No derivative work is allowed. Bank (IDB), a revised version of this work may also be reproduced in any academic journal, including those indexed by the American Economic Association’s EconLit, provided that the IDB is credited and that the author(s) receive no income from the publication. Therefore, the restriction to receive income from such publication shall only extend to the publication’s author(s). With regard to such restriction, in case of any inconsistency between the Creative Commons IGO 3.0 Attribution-NonCommercial-NoDerivatives license and these statements, the latter shall prevail. Note that link provided above includes additional terms and conditions of the license. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the Inter-American Development Bank, its Board of Directors, or the countries they represent.
Abstract1 This paper explores the qualitative and quantitative implications of taxation for growth and savings in three Latin American countries: Brazil, Chile and Mexico, studying a small open economy in the context of an endogenous growth model where the domestic interest rate depends on the level of domestic debt. The model’s parameters are calibrated to the Brazilian, Chilean and Mexican economies. The …ndings suggest that, in order to implement the optimal tax regime, Brazil must tax capital at a considerably lower rate than at present. Consumption should be heavily taxed in Brazil and Mexico and optimal labor taxes should be lower than actual taxes in Brazil and Chile. However, while sub-optimal taxes seem to imply lower long-run growth in these three countries, low saving rates do not seem to be a direct consequence of sub-optimal taxation. JEL Classi…cation: E61, E62, H21 Keywords: Optimal …scal policy, endogenous economic growth, savings. 1The authors gratefully acknowledge the …nancial support of the Inter-American Development Bank (IDB). The authors are thankful to Agustina Hatrick, Giselle Montamat and Ernesto Pienika, who provided excellent research assistance.
1 Introduction Despite successful stabilization programs and reforms during the last decades, Latin America saving rates have remained relatively stagnant, especially in comparison with the East Asian "miracle" economies. As Figure 1 illustrates, national saving in Latin America has averaged, during the past decade, less than 20 percent of GDP, in comparison with over 30 percent in six rapidly growing East Asian economies. Each economy of Latin America and the Caribbean (LAC) had a saving rate substantially below that recorded in the Asian "miracle" economies, and in several LAC economies saving rates were only about one-third of the Asian "miracle" average. This is far too striking. Does this indicate some sort of misallocation? If so, what are their main determinants of these di¤erences? Figure 1. National Savings as a Percentage of GDP in East Asia and LAC Countries Source: Authors’calculations using the World Bank WDI database. These questions lead to key policy issues, as one of the dominant views in the literature highlights that Latin America’s low rate of saving condemns the region to an ine¢ cient allocation of resources that delivers low investment and consequently low sustainable growth rates (see Gavin, Hausmann and Talvi, 1997). 2
As saving rates are just endogenous variables reacting optimally to incentives, policies should concentrate on removing impediments to growth rather than trying to establish programs aimed directly at promoting saving that are likely to be of dubious e¤ectiveness and may involve economic ine¢ ciencies. As a matter of fact, policy should aim to establish an environment conducive to high and sustainable growth, trusting saving to follow in response to the incentives that such an environment provides. While policies aimed at increasing saving may exhibit a substantial overlap with those aimed at removing impediments to growth, the shift of emphasis in the policy objective from saving to growth is non-trivial. Figure 2 below shows that taxes in Latin America are substantially higher than taxes in East Asia and the Paci…c. Average tax revenues in Latin America have been almost 13 percent of GDP between 1991 and 2007, while in East Asia and the Paci…c this …gure amounts to only 9 percent. Consequently, we study the role played by …scal policies, more precisely taxes, on economic growth and their implications for domestic savings (see Attanasio and Wake…eld, 2010). More precisely, this paper aims to answer the following questions: What are the implications of sub-optimal taxation for sustainable growth? How much of the relatively low levels of saving rates is a consequence of these sub-optimal policies? The answers to these questions are not straightforward, as many e¢ ciency-raising, growth-promoting policies are likely to have an adverse e¤ect on savings that, although temporary, may last for many years (see Gavin, Hausmann and Talvi, 1997). In order to answer these questions, we study the e¤ect of optimal taxation on growth and savings under full commitment to …nance an exogenous path of public expenditures in a small open economy in the context of an endogenous growth model. The model economy for analyzing these issues includes some non-standard assumptions to capture particular features of Latin American developing countries. The informal sector in these countries produces between 25 to 76 percent of gross domestic product or GDP (Schneider and Enste, 2000). Therefore, the design of public policies must especially consider this peculiar feature: a large share of labor market relationships cannot be monitored by governments. So, in the model economy there are two sectors, tradable and non-tradable, that can hire labor in the formal or in the informal labor market. There is a neoclassical technology to produce commodities and non-tradable goods that displays constant returns to scale. Additionally, the domestic interest rate has an extra component determined by the level of domestic debt. We quantify the behavior of this economy along the competitive equilibrium balanced growth path to understand how changes in taxes a¤ect variables in the long run. Then, using the characterization of the competitive equilibrium, we study the design of optimal tax policy. That is, we solve a dynamic optimal taxation problem to provide a quantitative analysis in a calibrated economy in which we …rst we characterize and compute the optimal allocations, 3
Figure 2. Tax Revenue as a Percentage of GDP in East Asia and LAC Countries, 1991-2010 Source: Authors’calculations using the World Bank WDI database. 4
that are decentralized as competitive equilibrium, and the corresponding optimal taxes, and then we compute the competitive equilibrium allocations stemming from actual (potentially suboptimal) tax systems and compare these economies. In this way it is possible to quantify the negative impact on welfare and sustainable levels of growth, as well as consequent implications for domestic savings. As shown by Espino and González-Rozada (2013) in a similar setting, the negative impact might not be trivial, and therefore its quanti…cation might be of interest on several fronts.2 The quantitative results obtained outline not only the optimal design of …scal policies but also the challenges governments face in implementing them. The …ndings point out the costs in terms of growth, savings and welfare of deviating from these optimal policies in three Latin American countries: Brazil, Chile and Mexico. In order to do so, we compare this optimal design with non-optimal tax schemes, including the status quo and a counterfactual tax scheme, given by the tax structure of one of the East Asia “miracle”countries: Thailand. The rest of the paper is organized as follows. Section 2 presents a review of the related literature. Section 3 provides a detailed description of the model, a small open economy with endogenous growth, and two sectors, tradable and non-tradable, that can hire not only formal but also informal labor. Commodities and non-tradable goods are produced with a constant returns to scale neoclassical technology, and the domestic interest rate depends on the level of domestic debt. Section 4 formalizes the competitive equilibrium, characterizes the corresponding balanced growth path and provides detailed computed examples to study the impact of taxes on alternative equilibrium variables. The evidence found in this section suggests that the introduction of an informal sector into the economy has a negative impact on the long-run growth rate but does not a¤ect private savings in the three countries analyzed. Increasing labor taxes induces a reduction in the long-run growth rate, and an increase in the capital tax rate produces a fall in private savings along the balanced growth path. Additionally, and as expected, increasing labor taxes reduces the time devoted to work in the formal sector and increases the time allocated to work in the informal sector of the economy. However, the reduction in working time in the formal sector of the three countries is larger than the increase in working time in the informal sector, resulting in a decline in total time allocated to work. Increasing consumption taxes has similar e¤ects, as does increasing labor taxes. That is, an increment in the consumption tax rate slows down the economy but does not a¤ect private savings along the balanced growth path. Finally, increasing government expenditures induces an increase in both the growth rate and private savings in the three 2The solutions that we obtain are time-inconsistent, a common characteristic of models of this type. This is not unreasonable, since this is a normative analysis. These models do not seek to develop testable implications but rather to provide quantitative guidelines for optimal decision-making by governments, which is the main purpose of this study. 5
capital and consumption as well as issuing debt. We assume that Gt=gY N tfor all t, where g2(0;1) is the ratio of government spending to non-tradable output. There is no international labor mobility and physical capital is domestic. Production of new capital is domestic, but investment is imported from abroad at the (exogenous) price Pt. Let Ktdenote the domestic stock of capital at date t. The linear technology to produce new capital is standard and renders the law of motion for capital given by Kt+1 =It+ (1 K)Kt where K2(0;1) denotes the depreciation rate Itdenotes investment at date t. The government can levy a tax of k t2[0; K]on the the net return on capital, (rtK)Kt, where rtdenotes the domestic rental price of capital before taxes.8Think of k tas a tax on corporate pro…ts that is levied on …rms operating in the country. The government can also tax consumption at the rate c tand the formal sector at the rate w t. As stressed above, the informal sector does not pay taxes. There is a one-period bond to trade internationally at the price qt= 1=Rt, where Rt denotes the gross interest rate, which will be determined endogenously. The government and households have access to the credit market. Let Bp tand Bg tdenote private and government debt holdings, respectively and Bt=Bp t+Bg t. The government’s budget constraint is (1 + Rt)Bg t+PN tGt=c tPN tCt+w twF tLF t+k trtKtk tKKt+Bg t+1 where Bg t+11 t=0 is further restricted by a no-Ponzi condition speci…ed later. We denote =c t; w t; k t; Gt; Bg t+11 t=0 as a …scal policy. The domestic interest rate depends positively on the domestic debt-tradable output ratio as follows Rt=RBt YT t where R0>0: Domestic agents take this rate as given; i.e., they do not internalize the impact of alternative debt choices. The market clearing conditions for the market of non-tradable goods, domestic capital and domestic formal and informal labor are Ct+Gt=YN t 8Following the convention in the literature we assume that return on capital after depreciation is taxed. 12
Kt=KT t+KN t utHt=LT;F t+LN;F t vtHt=LT;I t+LN;I t for all t. 4 Competitive Equilibrium Analysis In this section, we formalize the corresponding competitive equilibrium concept (Subsection 4.1), and then we quantify the behavior of the economy along the balanced growth path (BGP, Subsection 4.2). The goal of this section is twofold. First, we …nd it useful to understand how changes in taxes a¤ect the variables in the long run. Second, we use the characterization of the competitive equilibrium to study the design of the optimal tax policy discussed in Section 5. 4.1 Fiscal Policy and Competitive Equilibrium Given a …scal policy =c t; w t; k t; R t; L t; Gt1 t=0 and prices rt; wF t; wI t; Pt; PN t1 t=0, the representative household solves max fCt;xt;ut;vt;et;Ht+1;Kt+1;Bp t+1g 1 X t=0 tCt(xt)1 1, subject to (1 + c t)PN tCt+PtIt+ (1 + Rt)Bp t(1) = ((1 w t)wF tutHt+wI tvtHt) + (1 k t)rt+k tKKt+Bp t+1 Ht+1 =AHetHt+ (1 H)Ht(2) Kt+1 =It+ (1 K)Kt(3) lim T!1 T Y j=0 Bp T (1 + Rj)0(4) where (K0; H0; Bp 0= 0) are given and xt= (1 dutvtet). Notice that consumption as well as labor and capital taxes are paid by households. In equilibrium, it is indistinct if factor taxes are paid either by …rms or workers. 13
Firms in the tradable and non-tradable sectors take prices as given and, respectively, solve the static problems max (LT;F t;LT;I t;KT t)0nFT(KT t; LT;F t; LT;I t)wF tLT;F twI tLT;I trtKT to and max (LN;F t;LN;I t;KN t)0nPN tFN(KN t; LN;F t; LN;I t)wF tLN;F twI tLN;I trtKN to Given a …scal policy and a price system Rt; wF t; wI t; rt; PN t; Pt1 t=0, denote fCt(); xt(); ut(); vt(); et()Kt+1(); Ht+1(); Bp t+1(); LT;F t(); LT;I t(); KT t(); LN;F t(); LN;I t(); KT t; KN t()g1 t=0 as the corresponding solutions to the representative household’s problem and the …rms’ problem in the tradable and non-tradable sector. We say that a …scal policy is feasible if (1 + Rt)Bg t() + PNGt=c tCt() + w twF tut()Ht() + Bg t+1() +k trtKt()k tKKt(); for all t; that is, a …scal policy is feasible if it satis…es the government budget constraint evaluated at the allocation that is a solution. We restrict ourselves to feasible …scal policies without any further reference. De…nition 1. Given a …scal policy =c t; w t; k t; Gt; Bg t+11 t=0 and investment prices fPtg1 t=0, a competitive equilibrium (CE) is an allocation fCt; xt; ut; vt; Kt+1; Ht+1; Bp t+1; LT;F t; LT;I t; KT t; LN;F t; LN;I t; KT t; KN tg1 t=0 and a price system Rt; wF t; wI t; rt; PNt1 t=0 ;such that the following conditions are satis…ed: CE.1. Given and Pt; Rt; wF t; wI t; rt1 t=0, the allocation fCt(); xt(); ut(); vt(); et()Kt+1(); Ht+1(); Bp t+1()g1 t=0 solves the representative household’s problem. CE.2. Given and Pt; Rt; wF t; wI t; rt1 t=0, fLT;F t(); LT;I t(); KT t(); LN;F t(); LN;I t(); KT t; KN t()g1 t=0 solves the …rms’static problems in the tradable and non-tradable sector, respectively. CE.3. Fiscal policy =c t; w t; k t; Gt; Bg t+11 t=0 is feasible. 14
CE.4. There is consistency of the domestic interest rate; that is, for all t Rt=RBt=Y T. Notice that, as we couple the government’s and the domestic agent’s budget constraints, we obtain the last equilibrium condition (Bp t+Bg t) (1 + Rt) + PtIt=FT(KT t; LT t) + Bp t+1 +Bg t+1 4.2 Balanced Growth Competitive Equilibrium: Quantitative Implications We are particularly interested in studying the balanced growth path in this setting that displays some novel features. First, the growth rate is endogenously determined by the fact that the interest rate depends on a measure of relative indebtedness. This friction will be critical for closing the model for the developing economies we study. Second, the degree of informality in the economy is determined endogenously and it depends, among other things, on the design of the …scal policy. In what follows, we analyze the quantitative implications of alternative tax structures for three Latin American countries, Brazil, Chile and Mexico. We are particularly interested in studying the BGP. 4.2.1 Only Formal Sector The …rst exercise consists of removing the informal sector of the economy (= 1) to see how Kand wa¤ect the BGP. Figure 3 shows how capital and labor taxes a¤ect the economy’s growth rate in this scenario. As Figure 3 illustrates, in the three countries, increasing the labor tax rates reduces the growth rate along the BGP. Without capital and labor taxes the growth rate is around 3.7 percent in Chile, 4.3 percent in Mexico and 5.4 percent in Brazil. Increasing the labor tax rate by 20 percent reduces growth around half a percentage point in the three countries. This is expected, since distortionary tax rates should slow down the economy. The e¤ect of increasing the capital tax rate on growth goes in the same direction as increasing labor taxes, but the magnitude is much lower, almost imperceptible in the …gure. When looking at private savings the picture is the opposite. Figure 4 shows the impact of capital and labor taxes on what we called private savings as a percentage of total income. Private savings are de…ned as total income, tradable and non-tradable, minus non-tradable consumption as a fraction of total income. That is, in this 15
Figure 3. Growth Rate along the BGP, Formal Sector Only (in percent) Source: Authors’estimations. de…nition private savings include investment and bond savings. As is clear from the …gure, while increasing capital taxes reduces private savings in the three countries, an increase in the labor tax rate does not seems to a¤ect savings along the BGP. Increasing the capital tax rate to around 20 percent reduces private savings from around 35 to 33 percent in Chile, from 29 to 26 percent in Mexico and from 48 to 45 percent in Brazil. Consumption taxes play a similar role as labor taxes. Increasing the consumption tax rate induces a reduction in growth along the BGP and does not a¤ect private savings in the three countries, as can be seen in Figures 5 and 6. Figures 7 and 8 show the impact of changes in capital and labor taxes on the disaggregated components of private savings (investment and bond savings). As can be seen in Figure 7, increasing the capital tax rate induces a fall in investment measured as a percentage of total income in the three countries. This e¤ect is larger for Chile and Brazil, where an increase of capital tax rate from zero to 0.18 reduces investment by around 16 percent along the BGP. Labor taxes do not seem to a¤ect investment in any of the three countries. Figure 8 shows that, when there is no informal sector, there is no bond savings in the three countries, and a rise in the capital tax rate induces an increase in debt along the BGP. Again, Chile and Brazil are the countries where the impact on debt of increasing 16
Figure 4. Private Savings along the BGP, Formal Sector Only (in % of Total Income) Source: Authors’estimations. 17
Figure 5. Growth Rate along the BGP, Formal Sector Only (in percent) Source: Authors’estimations. capital taxes is larger. In both countries, increasing the capital tax rate from zero to 0.18 induces an increment in debt along the BGP of approximately 20 percent. The impact of increasing consumption taxes on investment and bond savings is similar to the impact of increasing labor taxes and so they are not shown here. Figure 9 shows the impact of an increase in government expenditure (de…ned as a percentage of the non-tradable output) over growth along the BGP. As can be seen in the …gure, as government increases its expenditures there is an increase in growth in the three countries analyzed here. The growth rate when there is no capital tax and the government expenditure is zero is around 2.6 percent in Chile, 3.7 percent in Mexico and 3 percent in Brazil. Increasing government expenditures by 20 percent induces an increase in growth of around 19 percent in Chile, 11 percent in Mexico and 17 percent in Brazil. Increasing government expenditures also induces an increase in private savings along the BGP in the three countries as illustrated in Figure 10. Figure 11 shows the e¤ect of increasing capital and labor taxes on the time devoted to work in the formal sector of the economy. As labor taxes increase, the time devoted to work decreases, while an increase in the capital tax rate does not seem to a¤ect the time devoted to work, in the three countries. 18
Figure 6. Private Savings along the BGP, Formal Sector Only (in % of Total Income) Source: Authors’estimations. 19
Figure 7. Investment along the BGP, Formal Sector Only (in % of Total Income) Source: Authors’estimations. Overall, the intuition behind these results is that increasing labor taxes leads to a decrease in the time devoted to human capital accumulation. The reduction in the time devoted to human capital accumulation induces a reduction in the growth rate along the BGP. A similar e¤ect can be obtained when increasing consumption taxes. The same mechanism operates with the capital tax rate, although much more smoothly. Increasing capital taxes induces a mild reduction in the time devoted to accumulate human capital, and this latter reduction implies a slight fall (almost imperceptible in the …gures) in the long-run growth rate. In the case of labor and consumption taxes, increases in both tax rates reduce the time devoted to work in the formal sector of the economy, implying a non-trivial increase in the time devoted to non-market activities, i.e., leisure. It is important to interpret leisure in a broad sense, as modeled, and thus it must include non-market production goods. In other words, an agent who devotes less time accumulating human capital is not necessarily at home doing nothing; rather, he or she could be engaged in non-market activities (i.e., producing goods). Increasing capital taxes also has a positive e¤ect on time devoted to leisure. Since increasing labor taxes increase the time allocated to non-market activities, reducing the time devoted to accumulating human capital and the total time allocated to work there is an intra-temporal substitution between work and leisure and private consumption does not 20
Figure 8. Bond Savings along the BGP, Formal Sector Only (in % of Total Income) Source: Authors’estimations. 21
Figure 17. Growth Rate along the BGP (in percent) Source: Authors’estimations. Figure 18. Private Savings along the BGP (in % of Total Income) Source: Authors’estimations. 28
Figure 19. Brazil: Time Devoted to Work, Formal and Informal Sectors (in percent) Source: Authors’estimations. However, the …gure also suggests that the total time devoted to work decreases with this tax rate, implying that the disincentive to work in the formal sector is, on average, greater than the incentive to work in the informal sector. Increasing the capital tax rate does not have an impact on the time devoted to work in both sectors. As before, the e¤ect of the consumption tax rate is very similar to the labor tax rate, that is, increasing the consumption tax rate reduces the time devoted to working in the formal sector and increases the time devoted to work in the informal sector of the economy. The introduction of informality reduces the total time devoted to work compared with the economy without an informal sector. 29
Figure 20. Chile: Time Devoted to Work, Formal and Informal Sectors (in percent) Source: Authors’estimations. Overall, the evidence found in this section suggests that the introduction of an informal sector into the economy and increasing labor and consumption taxes have a negative impact on the long-run growth rate. This last e¤ect is expected, since distortionary taxes should slow down the economy. Increasing capital taxes reduces private savings in the three countries analyzed here. Additionally, and again as expected, an increase in labor taxes reduces the time devoted to work in the formal sector and increases the time devoted to work in the informal sector. However, the reduction in the formal sector is greater than the increase in the informal sector, resulting in a decline in total time allocated to work. An increase in capital taxes seems not a¤ect the time devoted to work both in the formal and informal sectors. A rise in consumption tax rates reduces the time devoted to work in both sectors, formal and informal. Therefore, increasing labor or consumption taxes increases the time devoted to leisure and diminishes the time devoted to human capital accumulation, and this mechanism induces a fall in the growth rate along the BGP. In the next section, we study the behavior of this type of economy along the BGP when the government sets optimal tax rates. 30
Figure 21. Mexico: Time Devoted to Work, Formal and Informal Sectors (in percent) Source: Authors’estimations. 5 Optimal Fiscal Policies This section describes the Ramsey approach to optimal taxation in regard to the problem faced by a benevolent government that chooses optimal taxes and transfers given that only distortionary tax instruments are available. The government sets taxes that it has available so that, within the set of competitive equilibria, the utility of the representative agent is maximized. In other words, the government choose the optimal tax scheme that ensures …nancing an exogenous path of public expenditures and, at the same time, maximizes the representative agent’s utility. More precisely, the formal de…nition is the following. De…nition 2. Given a …scal policy =c t; w t; k t; Gt; Bg t+11 t=0, let fC(); x(); u(); v(); K(); H(); Bp(); LT;F (); LT;I(); KT(); LN;F (); LN;I(); KT(); KN()g be the corresponding competitive equilibrium allocation. The optimal …scal policy is de- …ned as the solution to max 1 X t=0 tCt() (xt())1 1, Solving this problem directly might be a nontrivial task. There are two common approaches to solving Ramsey problems. The …rst is the primal approach, which characterizes 31
a set of allocations that can be implemented as a competitive equilibrium with taxes. By implementation we mean the following: for a set of taxes, …nd a set of (consumption and labor) allocations and equilibrium prices such that these allocations are a competitive equilibrium given taxes. Conversely, a set of (consumption and labor) allocations is implementable if it is possible to …nd taxes and equilibrium prices such that these allocations are a competitive equilibrium given these prices and taxes. Implementation often makes it possible to simplify a Ramsey problem by reformulating a problem of …nding optimal taxes as the problem of …nding implementable allocations. This reformulation of the problem is referred to as a primal approach to Ramsey taxation, and its application in this setting is discussed in detail in the Technical Appendix. 5.1 Optimal Fiscal Policies: Quantitative Implications In this section we compute the optimal tax structure and compare its implications on growth and labor market participation with the CE allocation stemming from the actual tax systems. In addition, we perform a counterfactual exercise in which we quantify the implications of imposing the tax in one of the fast-growing Asian economies (Thailand in our examples). Tables 1, 2 and 3 report the results for Brazil, Chile and Mexico, respectively. The …rst row in each table shows the result of the competitive equilibrium when the economy has a formal and informal sector. The second row in each table reports the optimal tax structure computed from the Ramsey problem, and the last row reports a counterfactual exercise imposing on the economy the actual tax structure of Thailand and computing the competitive equilibrium. As mentioned, Appendix A details the calibration. Consider …rst the case of the Brazilian economy. Table 1 shows that optimality dictates that labor and capital should be taxed substantially less than observed while consumption should be heavily taxed instead. The impact on growth is large, an increase of more than 30 percent, while there is a non-trivial reallocation of labor from the informal sector to the formal sector. On the other hand, optimal taxation reduces the savings rate around 4 percent with respect to the competitive equilibrium. If the actual tax system were replaced with the tax structure of a fast-growing East Asian economy the growth rate along the BGP would increase by almost 20 percent, while the savings rate should also increase by 3 percent. Table 2 shows the results for Chile. Actual taxes imply a growth rate along the BGP of 3 percent and private savings of around 33 percent of total income. The second row of the table shows the optimal taxes. As can be seen, the government should tax consumption less and tax capital and labor substantially less to obtain an increase of 30 percent in the 32
Table 1. Brazil: quantitative implications cwk u v Savings Competitive equilibrium 17.00 30.00 15.00 4.00 26.98 10.62 45.79 Ramsey allocation 22.27 16.00 4.09 5.28 34.07 7.71 43.95 Comp. equil. (Thailand) 16.60 0.62 0.71 4.77 31.02 9.06 47.13 Source: Authors elaboration. growth rate and 6 percent in private savings along the BGP. Optimal taxes also suggest a reallocation of labor from the informal to the formal sector of the economy. Tax structure in Thailand is similar to the optimal case, where capital, consumption and labor taxes are lower than actual taxes in Chile. This situation produces higher growth and private savings along the BGP than the competitive equilibrium. Table 2. Chile: quantitative implications cwk u v Savings Competitive equilibrium 19.00 7.00 18.50 3.00 27.63 7.37 32.97 Ramsey allocation 17.36 1.78 0.24 3.90 31.43 6.50 34.98 Comp. equil. (Thailand) 16.60 0.62 0.71 3.24 28.16 7.41 35.05 Source: Authors elaboration. Finally, Table 3 shows the results for Mexico. In this case optimality suggests taxing consumption more heavily and taxing capital substantially less to obtain a slightly higher growth rate. The table also shows that optimal tax structure does not a¤ect competitive equilibrium private savings. In contrast with the other two countries, in Mexico labor in the informal sector is larger than in the formal one. Optimal taxes imply a little reallocation of labor from the informal to the formal sector. Thailand taxes labor substantially less than the actual and optimal situations and taxes consumption more than the actual situation but less than the optimal case. This counterfactual situation produces values for the growth rate, private savings and allocation of labor in the formal and informal sector very similar to the competitive equilibrium situation. Table 3. Mexico: quantitative implications cwk u v Savings Competitive equilibrium 13.90 7.90 8.50 4.00 15.18 24.02 28.08 Ramsey allocation 21.93 7.10 0.28 4.16 16.20 23.40 28.10 Comp. equil. (Thailand) 16.60 0.62 0.71 3.96 15.29 23.74 28.24 Source: Authors elaboration. 33
Overall, the evidence found in this section suggests that sub-optimal taxes imply lower long-run growth in the three countries analyzed here. However, it seems that the low levels of saving rates are not a direct consequence of sub-optimal taxation, as optimal taxes imply a case, Brazil, where private savings are lower than the actual situation; a case, Chile, where optimality induces larger private savings and a case, Mexico, where the optimal tax structure does not a¤ect private savings. In the three countries, optimal taxes reallocate labor from the informal to the formal sector. 6 Policy Recommendations The …ndings in the last sections provide some policy implications for Brazil, Chile and Mexico. First, we measured how much the actual tax structure should be modi…ed to reach the optimal tax scheme and second, we estimated the impact of these changes along the BGP on the long-run growth rate, private savings and the allocation of time between the formal and informal labor market. In the case of Brazil, implementing the optimal tax regime would imply a signi…cant change in the actual tax rates. Labor taxes should be reduced almost 47 percent and consumption taxes increased more than 70 percent, while the capital tax rate should decrease more than 30 percent. This last …nding is important because, unlike conclusions in previous studies, capital should be taxed in the long run and, as a matter of fact, at a relatively high rate. The optimal tax system translates into a signi…cant reallocation of time between formal and informal work. Time devoted to work in the informal sector declines around 26 percent while time devoted to work in the formal sector increases by around the same magnitude when implementing the optimal tax structure. Notice that in the case of Brazil, optimality will imply a higher growth rate but lower private savings along the BGP. Comparing optimal tax rates to those observed in the Chilean economy suggest, similar to the Brazilian case, that the tax rate changes needed to decentralize the Ramsey allocations are signi…cant. In this case, capital should be taxed minimally as the optimal tax rate on capital is almost zero ,and there labor should be taxed substantially less as the optimal tax rate on labor is only 1.78 percent compared to the actual 7.00 percent. Implementing the optimal tax regime will induce an increase in both the growth rate and private savings along the BGP. Optimal taxation will additionally reallocate labor from the informal to the formal sector as in the case of Brazil. However, these changes are not as large as in Brazil. Optimality in Mexico suggests that, in comparison to those actual taxes observed, consumption should be more heavily taxed and capital should be taxed substantially less. 34
Implementing the optimal tax regime would imply a 4 percent higher long-run growth rate but no signi…cant changes in private savings along the BGP. Reallocation of labor between the formal and informal sector is of small magnitude. Some of these results are in line with the …scal reform proposed by Antón, Hernández and Levy (2012) in order to mitigate the harmful e¤ects of informality on the labor market. These authors’reforms would shift taxation to cover social insurance from labor to consumption, eliminating labor taxes and setting a uniform value added tax rate of 16 percent. The quantitative exercise presented here suggests shifting taxation towards consumption while lowering capital taxes. 7 Conclusions This paper has made progress in characterizing competitive equilibrium and optimal …scal policies in the context of a small open economy with the following characteristics: the interest rate is endogenously determined and some workers can be hired in the informal market. We have addressed two questions in this setting. The …rst is Ramsey’s (1927) normative question: What choice of tax rates will maximize consumer utility, consistent with given government consumption and with market determination of quantities and prices? The second is positive and quantitative: How much di¤erence does it make? Our quantitative exercises show that, from a baseline economy, the inclusion of an informal sector reduces the growth rate over the BGP but does not a¤ect private savings in the three countries analyzed here. Increasing labor and consumption taxes also reduces the long-run growth rate. Increasing capital taxes reduces private savings in Brazil, Chile and Mexico. Additionally, and as expected, an increase in labor taxes reduces the time devoted to work in the formal sector and increases the time devoted to work in the informal sector. However, the reduction in the formal sector is greater than the increase in the informal sector, resulting in a decline in total time allocated to work. Optimal taxes (stemming from the Ramsey allocation) suggest that the tax rate changes needed to implement this optimal tax structure are signi…cant. Sub-optimal taxes imply lower long-run growth in the three countries. However, it seems that the low levels of saving rates actually observed are not a direct consequence of sub-optimal taxation as optimal taxes imply a case, Brazil, where private savings are lower than the actual situation; a case, Chile, where optimality induces larger private savings and a case, Mexico, where the optimal tax structure does not a¤ect private savings. Finally, in the three countries, optimal taxes reallocate labor from the informal to the formal sector. 35
8 Appendix A: Calibration Before presenting the parameters values, we describe the ones used. The relative productivity of tradable to non-tradable sector was obtained from Soto and Valdés (1998) for Chile, and from Urrutia and Meza (2010) for Mexico. ATwas chosen so that AN AT=1 PN YT=Y YN=Y LN;F =L LT;F =L 1T 1N for Brazil (PN=pN pTwas obtained from Carrera and Restout (2008), as an average of the real exchange rate from 1970-2000). The value of ANwas just a normalization for all countries. We chose AHto match an annual growth rate of 3 percent for Chile, 4 percent for Mexico and 4 percent for Brazil when we included an informal sector. Tand Nwere obtained from Urrutia and Meza (2010) for Mexico. For Brazil and Chile, they were calculated with data from national accounts. To estimate d; we considered the following relationship: d=wF wI(1 w);where the ratio of formal to informal wages were obtained from Frankema (2010) for Brazil and Mexico, and from Sánchez and Álvarez (2010) for Chile. The value of satis…es: h(1 T)YT Y+ (1 N)YN Yi=wFLF Y, where wFLFrepresents formal labor’s share of income. For g; we used the average of the government spending to non-tradable GDP ratio, from 1960 to 2000 for Chile, 1961 to 2012 for Mexico, and 1960 to 2012 for Brazil. As for K;we calculated it using the gross and net capital stock series presented by Pérez Toledo (2003) in the case of Chile, and considered estimates by Loría and de Jesús (2006) for Mexico, and Morandi and Reis (2004) for Brazil. The value of Pwas normalized to one. The variables and bbelong to the particular speci…cation that was used of the function R(:), taking the form: RBp+Bg YT=R+hefb+Bp+Bg YTg1i where Ris the international interest rate. For b; we used the average of the Net International Investment Position to tradable GDP ratio, from 1997 to 2008 in the case of Chile, 1998 to 2008 in the case of Mexico, and 2005 to 2012 for Brazil. For R, we used the average one year treasury bill rate, as a measure of the international interest rate that the economies faced on an annual basis. We chose to validate the statement (1 + R)=1;which is standard in literature on small open economies. We took the value of from Arrau (1990) and chose the value of to be 1. We follow Lucas (1990) to make = 0:5. Therefore, the values of and calibrated jointly determine the corresponding Frish elasticities of labor supply in the range of 1.31 for Mexico to 1.56 for Chile, which are in line with the roughly 1.3 value estimated by Keane (2009) in the classic life-cycle model augmented to include human capital accumulation. Taxes on consumption, capital and labor were obtained from Antón (2005) for Mexico; from Gandullia, Iacobone and Thomas (2012) for Brazil; and from OECD data for Chile. 36
The following table summarizes the calibration done for Chile, Mexico and Brazil: Table 4. Calibrated Parameters Chile Mexico Brazil AT0.3 0.516 0.36 AN1 1 1 AH0.158 0.16 0.18 T0.6 0.48 0.6 N0.5 0.35 0.45 0.85 0.512 0.83 K0.02 0.012 0.04 H0 0 0 g0.17 0.157 0.295 0.96 0.96 0.96 1.6 1.6 1.6 1 1 1 R0.04 0.04 0.04 1 1 1 b0.33 -0.0116 0.025 P1 1 1 c0.19 0.139 0.17 w0.07 0.079 0.3 k0.185 0.085 0.15 d1.17 1.26 1.044 0.5 0.5 0.5 Source: Authors elaboration. 37
max (Ct;xt;ut;vt;Ht+1;Bt+1;LT;F t;LT;I t;KT t;LN;F t;LN;I t;KN t) 1 X t=0 tV(Ct; xt;) W0; subject to AH(1 dutvtxt) + (1 H)Ux(Ct; xt)(53) = Ux(Ct+1; xt+1)(1 H) + AH(1 xt+1) Ht+1 =AH(1 dutvtxt)Ht+ (1 H)Ht(54) Ct= (1 g)ANKN tNLN t(1N))(55) where LN t=LN;F t1 + (1 )LN;I t1 1 : Bt(1 + Rt) + PtIt=ATKT tTLT t(1T)+Bp t+1 +Bg t+1;(56) where LT t=LT;F t1 + (1 )LT;I t1 1 : KT t+1 +KN t+1 =I+ (1 K)(KT t+KN t);(57) utHt=LT;F t+LN;F t(58) vtHt=LT;I t+LN;I t(59) Notice that (56) and (57) reduces to Bt(1 + Rt)+PtKT t+1 +KN t+1 (1 K)(KT t+KN t)=ATKT tTLT t(1T)+Bp t+1 +Bg t+1; (60) We denote the corresponding (date t) Lagrange multipliers by tn tfor n= 1; :::; 6. The necessary …rst order conditions that characterize a Ramsey allocation are given by Ct:t3 t=tVC(Ct; xt;) +tUxC(Ct; xt)1 tAHet+ (1 H)1 t1AH(1 xt) + (1 H) (61) 44
xt:tVx(Ct; xt;) = t2 tAHHt +tUxx(Ct; xt)1 t1AH(1 xt) + (1 H)1 tAHet+ (1 H) +tUx(Ct; xt)AH1 t1 t1(62) ut:t5 tHt=t2 tAHHtd+tUx(Ct; xt)dAH1 t; vt:t6 tHt=t2 tAHHt+tUx(Ct; xt)AH1 t; KT t+1 :t4 tPt=t+1 4 t+1 ATTKT t+1T1LT t+1(1T)+Pt+1 (1 K); KN t+1 :t4 tPt=t+1 3 t+1(1 g)ANNKN t+1N1LN t+1(1N) +t+1 4 t+1 Pt+1 (1 K);(63) Ht+1 :t2 t=t+1 2 t+1 AH(1 dut+1 vt+1 xt+1) + (1 H) +t+1 5 t+1ut+1 +6 t+1vt+1;(64) Bt+1 :t4 t=t+1 4 t+1 1 + RBt+1 YT t+1 LT;F t:t5 t=t4 tAT(1 T)KT tTLT t(T)@LT t @LT;F t LT;F t:t6 t=t4 tAT(1 T)KT tTLT t(T)@LT t @LT;I t LN;F t:t5 t=t3 t(1 g)AN(1 N)KN tNLN t(N)@LN t @LN;F t LN;I t:t6 t=t3 t(1 g)AN(1 N)KN tNLN t(N)@LN t @LN;I t AHet+ (1 H)Ux(Ct; xt) = Ux(Ct+1; xt+1)AH(1 xt+1) + (1 H)(65) Ht+1 =AH(1 dutvtxt)Ht+ (1 H)Ht(66) Ct= (1 g)ANKN tNLN t(1N))(67) Bt(1 + Rt) + PtIt=ATKT tTLT t(1T)+Bp t+1 +Bg t+1; KT t+1 +KN t+1 =It+ (1 K)(KT t+KN t);(68) utHt=LT;F t+LN;F t(69) 45
vtHt=LT;I t+LN;I t(70) where for j=T; N et= (1 dutvtxt) Lj t=Lj;F t1 + (1 )Lj;I t1 1 : @Lj t @Lj;F t =0 @+ (1 ) Lj;I t Lj;F t!1 1 A 1 1 @Lj t @Lj;I t = (1 )0 @(1 ) + Lj;F t Lj;I t!1 1 A 1 1 9.5 Balanced Growth Analysis: Ramsey Allocation Notice that VC(C; x;) = (1 + (1 ))UC(C; x) = (1 + (1 ))Cx(1); Ux(Ct; xt) = UC(Ct; xt) C x1; UxC(Ct; xt) = UC(Ct; xt)(1 )x1; Uxx(Ct; xt) = UC(Ct; xt)((1 )1) x2C: Along the balanced growth path (BGP), the following (normalized) variables are constant, namely, ~1=1 tand ~n=n t UC(Ct;xt)for n= 2; :::; 6. The following conditions characterize the BGP of a Ramsey allocation ~3= (1 + (1 ))(1 )x1~1AH(1 xe); (1 + (1 )) c x1=AH~2+c~1((1 )1) x2(1 xe); ~5= ~2AHd+ ~1d AHc x1; (71) ~6= ~2AH+ ~1AHc x1; (72) P= ATTkTT1lT(1T)+P(1 K);(73) 46
P= ~3 ~4(1 g)ANNkNN1lN(1N)+P(1 K);(74) ~2= ~2+~5u+ ~6v;(75) 1 = 1 + R b AT(kT)T(lT)(1T)!! (76) ~5= ~4AT(1 T)kTTlT(T) + (1 )lT;I lT;F 1 !1 1 (77) ~6= ~4AT(1 T)kTTlT(T)(1 ) (1 ) + lT;F lT;I 1 !1 1 (78) ~5= ~3(1 g)AN(1 N)kNNlN(N) + (1 )lN;I lN;F 1 !1 1 (79) ~6= ~3(1 g)AN(1 N)kNNlN(N)(1 ) (1 ) + lN;F lN;I 1 !1 1 (80) 1 = AH(1 x) + (1 H)(81) =AH(1 du vx) + (1 H)(82) c= (1 g)ANkNNlN(1N)(83) b 1 + R b AT(kT)T(lT)(1T)!!+P(kT+kN)(+K1) = ATkTTlT(1T) (84) u=lT;F +lN;F (85) v=lT;I +lN;I (86) where for j=T; N lj=lj;F 1 + (1 )lj;I1 1: The optimal taxes can be obtained from the balanced growth conditions of the competitive equilibrium. 47
~=c AHx r=ATT(kT)T1(lT;F )(1T)(lT;I)(1T)(1) wF=AT(1 T)(kT)T(lT;F )(1T)1(lT;I)(1T)(1) wI=AT(1 ) (1 T)(kT)T(lT;F )(1T)(lT;I)(1T)(1)1 ~ =~ dAH (1 w)wF YN=AN(kN)N(lN;F )(1N)(lN;I )(1N)(1) PN=wFlN;F +wIlN;I +rkN YN w= 1 dwI wF k=rp(RK) rK c=1 ~ PN1 48
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