Collective savings pension policy in an economy with heterogeneity and informality

Albagli, Elías; Arias Gutiérrez, Agustín H.; Kirchner, Markus Article Collective savings pension policy in an economy with heterogeneity and informality Estudios de Economía Provided in Cooperation with: Department of Economics, University of Chile Suggested Citation: Albagli, Elías; Arias Gutiérrez, Agustín H.; Kirchner, Markus (2024) : Collective savings pension policy in an economy with heterogeneity and informality, Estudios de Economía, ISSN 0718-5286, Universidad de Chile, Departamento de Economía, Santiago de Chile, Vol. 51, Iss. 2, pp. 325-381 This Version is available at: https://hdl.handle.net/10419/314462 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. 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Págs 325-381 Collective Savings Pension Policy in an Economy with Heterogeneity and Informality* Sistema de pensiones de ahorro colectivo en una economía con heterogeneidad e informalidad ELÍAS ALBAGLI** AGUSTÍN H. ARIAS*** MARKUS KIRCHNER**** Abstract We compare the macroeconomic effects of a fully funded individual defined contribution (IDC) pension scheme, an unfunded pay-as-you-go (PAYG) system, and a collective defined contribution (CDC) regime. Under the latter, contributions of workers from a given cohort are invested in capital markets and repaid to that cohort upon retirement; its collective nature arises from an intragenerational progressive redistributive rule. Our results from an overlapping generations model calibrated for Chile show that the CDC scheme has similar macroeconomic effects as an IDC plan, including a moderate positive effect on the formal labor market, aggregate savings, and output. The PAYG system has negative effects on all these dimensions. Critical for the success of the CDC scheme is conditioning benefits on contributions, to incentivize formal labor status. We conclude that a CDC policy stands as a sustainable alternative for countries with significant labor informality and income inequality. Key words: Overlapping generations models; Pension system; Informal labor market; Heterogeneous agents. JEL Classification: E26, E27, H55, J46. * ** *** **** The views and conclusions expressed in this paper are exclusively those of the authors and do not necessarily reflect the position of the Central Bank of Chile or its Board members. The authors would like to thank Juan Guerra, Matías Tapia, Alberto Naudon and Ignacio Rojas for their comments and support, as well as Alejandra Cox and seminar participants at the conference “50 years of Estudios de Economía” at the University of Chile, the 28th Colloquium on Pensions and Retirement Research and the Central Bank of Chile for useful comments and suggestions. Monetary Policy Division, Central Bank of Chile, [email protected]. Economic Studies Area, Central Bank of Chile, [email protected]. Macroeconomic Analysis Area, Central Bank of Chile, [email protected]. Received: August, 2023 Accepted: August, 2024 326 Estudios de Economía, Vol.51 - Nº 2 Resumen Se comparan los efectos macroeconómicos de sistemas de pensiones de capitalización individual, reparto y de capitalización colectiva. Bajo este último, las contribuciones de los trabajadores de una cohorte determinada son invertidas en los mercados de capitales y utilizados para pagar las pensiones de esa misma cohorte una vez que esta se retira. Su naturaleza colectiva surge de una regla de redistribución intrageneracional progresiva. Nuestros resultados basados en un modelo de generaciones solapadas calibrado para Chile muestran que este sistema tiene efectos macroeconómicos similares al régimen de capitalización individual, incluyendo un efecto positivo moderado sobre el mercado laboral formal, el ahorro agregado y la actividad. El sistema de reparto tiene efectos negativos en todas estas dimensiones. Central para el desempeño exitoso del sistema de capitalización colectiva es el condicionar pensiones en las contribuciones de los trabajadores, de manera de incentivar el trabajo formal. Concluimos que la implementación de un sistema de capitalización colectiva es una política sostenible para países con significativa informalidad laboral y desigualdad de ingreso. Palabras clave: Modelos de generaciones solapadas; Sistema de pensiones; Mercado laboral informal; Agentes heterogéneos. Clasificación JEL: E26, E27, H55, J46. 1. INTRODUCTION In many countries, demographic changes, economic transformations and social demands for better living conditions put increasing pressure on existing pension regimes. Although these challenges are faced by both developed and developing countries, the latter often need to cope with them in an environment of high-income inequality, significant degrees of labor informality and fiscal sustainability concerns in the midst of ageing populations and changing international interest rates. Given this context, this paper examines the effects of alternative pension system reforms in an economy with large labor heterogeneity in terms of income and employment status. We set up a general equilibrium overlapping generations model (OLG) featuring heterogeneous agents and a dual labor market calibrated to the Chilean economy, which serves as our case study, and we use this model to quantitatively evaluate the long-term macroeconomic effects of alternative pension reforms, comparing individual capitalization with collective pension schemes with a redistributive component. 327 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner Collective defined contribution (CDC) schemes are one sort of collective pension policy. Under such a scheme, contributions of workers from a given cohort are pooled into one common fund and invested in capital markets, and the proceeds are repaid to the same cohort upon retirement. This type of scheme has been proposed as an alternative to individual defined contribution (IDC) programs, where contributions are deposited into individual accounts, in order to improve risk sharing. CDC schemes are often considered a “third way” between IDC schemes, where all risks are taken on individually, and defined benefit (DB) schemes such as many pay-as-you-go (PAYG) systems that propose a secure retirement income but are more difficult to maintain, especially in the face of slowing population growth. A similarity of CDC schemes with IDC schemes is that they are fully funded, contrary to unfunded PAYG systems. However, unlike IDC schemes, CDC schemes imply some intragenerational redistribution. The properties of collective pension schemes have been analyzed from different perspectives in the literature, including risksharing or stability of participation if participation is voluntary (see Gordon and Varian, 1988; Shiller, 1999; Ball and Mankiw, 2007; Gollier, 2008; Cui et al., 2011; Chen et al., 2016, 2017; Kurtbegu, 2018). However, to our knowledge no existing study has attempted to quantify the macroeconomic effects of such schemes, which are critical to evaluate their overall costs and benefits in comparison to alternative pension policies. In addition, no study has analyzed these issues, nor the design of intragenerational redistributive rules for pension benefits, for economies with large informal labor markets and income heterogeneity, such as in many developing countries. Hence, in this paper we study the long-term macroeconomic effects of implementing alternative pension system reforms in an economy with a significant informal sector and income heterogeneity. To understand these effects, and to quantitatively evaluate them, we construct an OLG model with specific features relevant for developing and emerging economies. We calibrate the model for Chile, a country whose individual retirement pension accounts system has been a model for many countries.1 We consider four different pension schemes, all financed through an identical increase of pension contributions taking the form of a payroll tax, that solely differ from each other in the way they treat the additional funds and allocate them among retirees. In particular, we consider two versions of a CDC scheme that differ in whether they make pension benefits depend upon the degree of labor effort during working life, 1 Chile has switched to a private retirement accounts system in the early 1980s. Many other Latin American countries have followed the Chilean model. These include (with years of adoption in parentheses): Peru (1993), Colombia (1994), Argentina (1994), Uruguay (1996), Bolivia (1997), Mexico (1997), El Salvador (1998), Costa Rica (2001), the Dominican Republic (2003), Nicaragua (2004), and Ecuador (2004) (see Krasnokutskaya et al., 2018). 328 Estudios de Economía, Vol.51 - Nº 2 i.e., a conditional (C-CDC) scheme and an unconditional (U-CDC) scheme, and compare their macroeconomic performance to an IDC scheme and a PAYG alternative.2 The collective nature of the CDC schemes arises from a progressive redistributive rule that allocates proportionally more benefits to lower-income workers. These are also the workers with more participation in informality. Conditioning the receipt of benefits on employment status within a redistributive design is the key aspect that incentivizes a strong formalization of labor supply at low-income levels, which are those who make for the largest share of informal work, surpassing the effects found under the IDC plan. Our results show that the C-CDC scheme has similar macroeconomic effects as an IDC plan, including a moderate positive effect on the formal labor market, which together with the rise of compulsory savings and the capital stock, generates and expansion of output. Moreover, the C-CDC scheme produces a stronger reduction of informality than the IDC plan. While the C-CDC scheme also induces opposite incentives at higher wages, the lower formal sector participation at the low end of the skill distribution delivers an overall increase of labor formality in the economy. The macroeconomic performance of the CCDC policy is significantly better than that of the PAYG system, which has a strong negative effect on all dimensions. The conditionality of pension benefits upon labor effort under the C-CDC plan is critical for these positive results, as a comparison with the UCDC scheme shows. Furthermore, the C-CDC plan shares with the IDC alternative the ability to cope with deterioration of the old-age dependency ratio, contrary to the PAYG system. Structural models, as the one we develop here, are well suited for the analysis of pension policies, as well as for other public policies, for several reasons. First, they allow for consistent exercises, in the sense that if a given policy has, for instance, an impact on the labor supply of households but this effect depends, in turn, on how the policy affects their saving decision, a structural model will be able to capture the interaction between the decisions on both margins, something that cannot be addressed in models where these decisions are taken separately. Among other benefits, this consistency allows understanding the general equilibrium effects of a given policy. For example, changes in agents’ propensities to save implied by alternative pension reforms have different effects on capital accumulation in equilibrium, and through this channel, on wages and labor market outcomes. Without a structural model, it would be impossible to determine how these second-round effects operate, or whether they are relevant. In addition, a structural model permits a quantitative evaluation of the effects of alternative policies, as long as its parameters are appropriately calibrated (estimated) to capture the main characteristics of agents and of the relevant markets at play. 2 All of these options — IDC, CDC and PAYG schemes — have been under discussion as part of the proposals to reform the Chilean pension system over the last years. 329 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner Since a finite life-time horizon for households is critical to capture the labor, saving and consumption decisions of agents over both a working and a retirement period, we depart from a standard OLG model with three generations. Into that framework we incorporate an informal sector, which can be thought of as home production, and where workers are exempt of paying pension contributions and taxes. The introduction of this dimension responds to the significance that informality has in many developing and emerging economies; in Chile, for example, the informal economy accounts for about a third of total employment. Faced with higher pension contributions, agents will have incentives to switch to informality to avoid paying a perceived tax — an incentive particularly relevant for low-productivity households.3 We also allow for different skill groups and discount factors, as well as different productivities across sectors, permitting us to better match the income distribution, the observed saving rates, and labor market participation in the economy. These sources of heterogeneity in the model are crucial for understanding the distributional implications of the different pension reforms that we consider, as well as for capturing the differential effects that a given policy can have on distinct agents. Finally, the model features certain small open economy characteristics that allow us, for example, to capture the weighted dependency of pension founds’ returns on both the domestic and the international interest rate; following the observation that about 40% of the total founds’ resources are invested abroad.4 Pension policies work mainly through mandatory contributions and, therefore, their effects depend on the ability of agents to revert forced savings 3 Attanasio et al. (2011), when analyzing the 2008 pension reform in Chile, found that even though pensions increased, the probability of paying into the pension system of workers older than 40 years decreased by 4.1%. Camacho et al. (2014) found that the component corresponding to a 10% tax increase in Colombia in 1993 to finance a health plan led to an increase of 4% in informality. 4 Our model features a single investment instrument, precluding agents from choosing among different investment portfolios for their pension funds. In Chile, under the current IDC pension system, agents can opt between 5 alternatives, which differ from each other in their domestic/foreign, fixed/variable-income composition. The implementation of an additional contribution may affect this composition and, thus, the funds’ returns. For simplicity and tractability, we abstract from this dimension. However, it is worth noticing that a CDC scheme is not suited for an individual choosing the portfolio composition. It could be assumed that the investment strategy that such a scheme would follow would be similar to the default strategy of the current system, i.e., when agents do not actively choose a portfolio, their funds are invested following an age-dependent default strategy. Evidence suggests that allowing agents to move their funds between portfolio types — under an IDC scheme — is detrimental for the funds’ performance; see Contreras et al. (2022). As such, our results may be biased in favor of the IDC scheme. Our main goal is to study the structural differences between the different pension schemes considered. The investment strategies they would follow lie beyond the scope of this paper. 330 Estudios de Economía, Vol.51 - Nº 2 by reducing voluntary ones. In this regard, empirical evidence suggests that agents do face both financial and informational frictions that limit their access to credit or the degree in which they associate current contributions with future pension payments and, consequently, their ability or willingness to reduce private savings. To this end, we include a simple mechanism that proxies for informational frictions that lead to an incomplete internalization of future pension benefits. Akin to the role of borrowing constraints, this mechanism prevents mandatory savings from being completely offset by higher indebtedness throughout working life. Indeed, the literature suggests that, though significant, substitution of mandatory savings is not perfect. This mechanism is crucial for our results, as it makes agents react to pension contributions as if they were, partially, taxes. Attanasio and Rohwedder (2003), exploiting the temporal and cross-sectional variation of three pension reforms, find that this substitution is somewhere between 0.65 and 0.75 for men older than 45, weaker for younger men, and non-existent for basic pensions, which suggest liquidity constraints or lack of information. Attanasio and Brugiviani (2003) find similar results for Italy. Botazzi et al. (2006) further find that substitution is higher for more informed individuals. For Chile, Morandé (1998) finds results in the same line, with a degree of substitution of about 0.5. Regarding the degree to which agents comprehend pension systems and their own need to save, the literature shows a large dispersion among individuals, and that many workers ignore how their pension plans actually work. Lusardi (1999) shows how household savings in the United States are typically insufficient when retirement arrives. Gustman and Steinmeier (2005), also for the U.S., find that, on average, workers’ expectations on their future pensions are not strongly aligned with reality. Other empirical evidence shows how individuals use costly credit sources even though they have access to less expensive credits, or how they simultaneously hold liquid assets with low returns and credit card debts. The explanations for this kind of behavior range from lack of financial education to inconsistent intertemporal preferences; see, for example, Laibson (1997), Angeletos et al. (2001) and Campbell et al. (2011). These reasons are consistent, in turn, with the so-called retirement consumption puzzle (or retirement savings puzzle), which describes the significant drop in consumption after retirement (Attanasio and Weber, 2010). Other explanations include a problem to process information, which is not the result of lack of information and cannot be overcome by public education; see New (1999). A salient point of this paper is the study of the interaction of the different pension schemes with the informal sector. As mentioned above, the introduction of a new pension system creates incentives for agents to move into informality where they can avoid the payment of those contributions. However, we find that under both the IDC and the CCDC plans informality actually de- 331 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner creases, and that this effect is stronger for the second scheme. This differs from the conclusions presented in Joubert (2015), who finds that rising the pension contribution paid by workers from 10 to 15% in Chile would increase informality by about 10%. The reason for the different results is the framework, in particular, the presence of two features. First, in our model agents internalize — though imperfectly — that the newly introduced pension contributions will translate into future pensions. This has a lower effect on the total net return of formal labor than a plain tax that is used by a government to, say, pay expenses, affecting labor supply decisions less. Second, our general equilibrium model — Joubert (2015) uses a partial equilibrium one — allows for second-round effects that operate expanding the economy and creating incentives to move into formality, whenever the introduction of a pension plan increases total savings. These two differences explain why the ultimate result we find is a reduction of informality under the IDC and the C-CDC plans. The strand of literature that addresses the effects that social security reforms tend to concentrate on particular aspects, such as job mobility, retirement timing, savings, capital market development, and economic growth; see Thomas and Spataro (2016) for a review of econometric works that consider the effects of pension funds, and Kohl and O’Brien (1998) for a survey on the empirical literature on the effects of PAYG systems, mostly on savings. In this group of studies, Holzmann (1997), using a Solow residual specification of TFP, finds that the 1981 pension reform in Chile had a positive effect on economic growth through the improvement of financial markets. In the same line, Schmidt-Hebbel (1998) concludes that the same reform boosted private investment, the average productivity of capital and TFP. Encina (2013), using the pension reform of 2008 in Chile as a treatment and panel data, finds that the improvement of the pension conditions to the poorest individuals in Chile induced a higher withdrawal from the labor market and less periods contributing to the pension system by these individuals. This is to be expected, as the mechanism determining those agents’ pensions depends negatively on their pension level (stemming from their actual contributions). We feature such a mechanism in our U-CDC scheme, and a similar force is at play, though other complementary specifications and initial conditions deliver different results in some dimensions. Davis and Hu (2008), in turn, using a panel of 38 OECD and emerging economies find that the pension-assetsto-GDP ratio has a significant positive effect on growth. Our study contributes to this literature through an analysis of the general equilibrium effects of alternative pension schemes in a model with a dual labor market and income heterogeneity. Parallel and independent work by Frassi et al. (2019) is closely related to our paper. They study the effects on the labor market and on capital accumulation of three different pension plans: a PAYG system, and two fully funded 332 Estudios de Economía, Vol.51 - Nº 2 ones, including an intragenerational redistributive component. However, we differ from their work in several dimensions: first, we set up a richer calibrated model, providing an empirically realistic quantification of the effects of introducing different pension plans. Second, we show the importance that incorporating informational and/or financial frictions has on the conclusions reached; for example, contrary to their findings, an IDC scheme is no longer neutral on capital, consumption, GDP and the labor market when agents do not fully internalize future pensions. Finally, and most importantly, we consider the effects that pension plans have on informality, a margin that supports a C-CDC-type scheme. Overall, our results are especially relevant for developing and emerging economies similar to Chile, which present significant labor informality and income inequality. These results show that properly designed CDC schemes may be an economically sustainable and politically viable pension policy in such a context.5 The rest of the paper is organized as follows. In the next section we present the details of the model, including the main equations that describe the problems faced by the different agents and their optimal decision rules.6 In section 3, we discuss the calibration of the model. In section 4, we present the results of the quantitative analysis of the different reform scenarios, together with some robustness analysis. In section 5, we present an exercise to analyze how the different schemes perform when the population growth rate decreases. Finally, section 6 concludes. 2. THE MODEL The model is based on the neoclassical growth models with overlapping generations following the works of Samuelson (1958) and Diamond (1965). To capture aspects relevant to developing or emerging economies and in particular the Chilean case, we add several features to an otherwise standard OLG model with three generations. These extensions include, first, endogenous labor supply with heterogeneous productivities, as in Brunner (1996) and Somma5 A limitation of our model is that it largely abstracts from fiscal policy, since the only fiscal instrument is a tax rate on formal labor income to create a wedge between net and gross income. A richer tax structure, including other instruments such as taxes on firms or consumption, its interaction with informality and its role in the financing of pension systems — partially or totally, directly or through debt — could be a relevant extension. While this is an important topic that deserves attention, it lies outside the scope of this paper. Additionally, for simplicity, we abstract in the model from the current solidarity pillar in Chile. 6 A detailed description of the model and the steady state computation is provided in the appendix. 339 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner while the individual pension paid out to each individual when retired can be written as (11) PRSRS it F tit PF m tit PF y it it ,, , , , ,,       2121 1 2242            PPP t F t BS it W ii 23 22 01 3 1  max, , where 1 ii < is an indicator function taking the value 1 when ii< and 0 otherwise, and where Pt BS +2 denotes a basic solidarity pension — expressed in per capita terms — defined as (12) PP PN N t BS t F i i it W it i i it              22 1 1 2 1 1 1 3 1 ,, , The latter is relevant only for the third scheme (  31  ). Notice Pt BS +2 is defined so as to exhaust Pt F +2 among all retirees in t+2 .12 For the second scheme (µ2 = 1), we define (13)  it it t pts PTS , ,    2 2 2 as the fraction of the funds of the component financed by the firms’ contributions, Pt F +2, that each retiree of skill group i receives. Here PTSp ts N ti n it it l   212 ,, are the total aggregated points assigned under this scheme and where the individual points, ptsit s,+, are assigned according to the following rule (actuarially fair), which agents know and internalize in their decisions: (14) ptsRptsRpts Rl W it st it m tit y tit mit m ,,, , ,        211 20 1 1  WW Rl W W t mtit yit y t y                              1 10 11   , ,          The parameters  00  and  1  R control the redistribution intensity of the rule, and WNWN t y ti n it y it l     11 / ,, and WNWN t m ti n it m it l     111 1/ ,, 12 Following the logic behind the solidarity pillar in place in Chile until recently, under the third scheme (  31 ), we assume that those agents for whose self-financed pension, Pit W ,+2, is lower than a certain upper bound Pit MAS ,+2 — from Pensión Máxima con Aporte Solidario in Spanish — are entitled to a pension according to the formula PPPPP it F t MAS it W t BS t MAS ,, max, /      2222 2 0, where Pt BS +2 is the highest pension that any agent could receive under this pillar, i.e., when Pit W , 20. As a simplifying assumption, we implement this scheme assuming a constant ratio, PP t BS t MAS   22 13// . 340 Estudios de Economía, Vol.51 - Nº 2 denote the average salaries of both age groups.13 For the fourth scheme (  4 1 ) we define two auxiliary variables,  it,2 and xt+2, where the first variable denotes the fraction of Pt F +2 corresponding to each worker and where the second variable denotes a replacement rate. The latter emerges as the solution to the following system of equations: (15)  it t F tit m it mt P RW l xi , ,,     22 211 2  i i 05.� (16) i n it it lN   121  ,, Equation (15) ensures that P t F +2 is distributed such that all retirees get the same replacement rate with respect to their formal middle-aged labor income, while the second equation further guarantees that all funds are used. The solution to this system of equations is given by (17)  it tit m it m t m RW l WL , ,,    2 211 1 (18) xP WL t t F t m    2 2 1 where WL RN t m tW it i nl it m     1211, ,.14 Total and individual pensions paid out each period are the sum of both pension components and are, respectively, given by: (19) PP P tt W t F  (20) PPP it it W it F ,,,  Public savings (in the form of the pension found) are defined as (21)SS RS SSRS S t P t PW m tt PW y t PW y t PF m tt PF y      ,, ,, , 11231  tt PF y,  13 One can show that in the special case where g=0 , implying WAWA it y tit m t ,, // 1, the second scheme (  2 1 ) with parameters  0 0 and  11 is equivalent to the first scheme of individual defined contribution (  11  ) since, under these special conditions, one has that  it t F tit PF m tit PF y PRSRS ,, , , ,      22 21 1. Relaxing the conditions on e and g , i.e., when e<1 and/or g>0 , both schemes are only approximately equivalent when α 0 and α 1 are set to 0 and 1 respectively. 14 Depending on the definition of the replacement rate, Rt+2 could be removed from the above equations and from the definition of WL t m +1 . The presence of the term R t+2 is to express income in terms of its value in the period in which pensions are paid. 341 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner and the budget constraint of the aggregate pension found in period t is given by (22) PS RS SS SS tt P tt P t PW m t PW y t PF m t PF y    1 ,, ,,    levied taxes 2.4 Workers of Skill Group I We address now the problems faced by the households in this economy. Each worker’s life-time utility is a function of their consumption when young, Cit y ,, middle-aged, Cit m ,+1, and old,Cit o ,+2, of the labor they supply in the formal sector when young and middle-aged, l it y , and lit m ,+1, and of the labor they dedicate to home production, also when young and middle-aged, h it y , and hit m ,+1. For in l  1, ,, it takes the following form: (23) U CCC it it y i it m i it o i , ,,,              1 1 1 22 1 11 1   ,, ,, , , ,, t yit y it y it y iit mit m it m lh hlh              1 11    hit m ,  1 where A  0 is the inverse of the elasticity of intertemporal substitution,  1 determines the wage elasticity of labor supply, which equals 11 /    ,  i  01, is the subjective discount factor of skill group i, and  0 stands as a specific cost for working at home.15 The variable Θ it j ,, with jym=, , is an endogenous preference shifter based on Galí et al. (2012) that is taken as given by the workers and satisfies it y it it y t AC A , ,             1 it m it it m t AC A , ,           1 11   with    01, and  i  0. The purpose of this preference shifter is to allow for an incomplete wealth effect on labor supply. When  0 , we obtain it j i,  , and, thus, the standard constant relative risk aversion (CRRA) utility function implying a non-zero wealth effect; instead, when  1 , there is no wealth effect.16 15 This specific cost can be justified, for instance, by the lack of health insurance, or by job insecurity. 16 In any case, the disutility of work is assumed to grow with the factor At 1  so that the model has a balanced growth path when  1 . 342 Estudios de Economía, Vol.51 - Nº 2 Home production is implemented through a decreasing returns to scale production function, with labor as the only input; with Ab ha ti t i            1 as the return for both the young and middle-aged workers, and with bb b nn ll    11 0. This specification allows for labor productivity differences between the formal sector and the informal sector, while productivity growth is equal across sectors. Letting S it y , and S it m , denote voluntary savings when young and middleaged, respectively, a given generation’s budget constraints for periods t , t+1 , and t+2 satisfy: (24) CWlAbhah S it yW it y it y ti t iit y it y ,, ,, ,            1 1    (25) CWlAbhah it mW it m it m ti t ii,, ,,              1111 1 1 1    tt m tit y it m RS S    11 1 ,, (26) CR SP it o tit m it ,, ,   22 12 where τ is an income tax used for the calibration of the informal labor supply.17 Following Joubert (2015), we will set ξ so that a 5 percentage points income tax increase yields a 10% increase in informal work. The budget constraints can be combined into the perceived intertemporal budget constraint (IBC) that agents use to make their decisions: (27) Here, the parameter  i   01, determines the fraction of the present value of the future pension, P RR it tt ,+ ++ 2 12 , that agents internalize in their consumption, 17 Note that the third equation incorporates the simplifying assumption that individuals have finite horizons and, therefore, choose to end up with zero assets when they die (i.e., they make no bequests). 343 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner saving and labor decisions. This is a simple, reduced-form strategy to capture two different types of frictions, financial and informational. For instance, ϕ i can account for borrowing constraints, meaning that only a fraction of future pensions can be used as collateral. Alternatively, ϕ i reflects the ignorance of agents about how the pension system works, capturing, for example, the perception that agents may have of pension contributions as taxes, without any beneficial counterpart. It could also capture, for instance, the confidence agents have on the future promised payments to actually materialize, which is not necessarily a negligible factor, at least in emerging economies. The practical purpose of this specification is to prevent a perfect substitution between mandatory savings — in the form of pension contributions — and voluntary savings, which is achieved for those agents with  i  1.18 Workers, then, face the problem of maximizing their life-time utility (23) subject to (27), (20), (9), (11), (13) ,(14), (17) and the definitions for Sit kj , ,, for kPWPF=, and jym=, , treating Θ it y ,, it m ,1, W it y ,, Wit m ,+ 1 , P t BS +2 , Wt y, Wt m +1 , PTSt+2, WLt m +1, Pt F +2, Rt+1, and Rt+2 as given.19 Next, we present the firstorder conditions associated with this problem. First, the equations for labor supply in the formal sector, l it y , and l it m , are given by (28) it y it y it y it y t y lh CW ,, ,, ,       1 l  (29) it m it m it m it m t m lh CW ,, ,, ,          11 1 1 11  l  where net salaries are defined as (30) WW W W P t y it y i W i Fit y t y t l l ,, , ,         11 12 1 2 1 1     FF t W PTS                            2 3 1 3  (31) WW W W t m it m i W i Fit m t l l ,, , ,           11 12 1 1 1 11 1      mm t F t Wt F t m P PTS P WL                     1 2 2 34 2 1 1 3 The above equations show how, at the optimum, agents work up to the point where the disutility of working — both in the formal and informal sector — equals the marginal utility of consuming the perceived net returns on that 18 See the introduction for a discussion of related literature. 19 We assume here, for simplicity, that agents do not internalize the effects of their labor efforts on P t F +2 . A similar assumption is made in Sommacal (2006). 344 Estudios de Economía, Vol.51 - Nº 2 work, which depends on the pension scheme in place. Second, the equations associated with labor supply in the informal sector, h it y , and h it m ,, are given by (32) h CAb haW it y it y it y ti t iit y , , , ,  § © ¨ ¨ · ¹ ¸ ¸ § © ¨ ¨ ¨ ¨ ¨ · ¹ ¸   T [ K N 4 1  ¸¸ ¸ ¸ ¸ ª ¬ « « « « « « º ¼ » » » » » » § © ¨ ¨ · ¹ ¸ ¸!   1 1 1 0 I [ K if Ahba W t t ii t y ,l  otherwise  ® ° ° ° °° ¯ ° ° ° ° (33) h CAbhaW it m it m it m ti t iit m , , , ,         § © ¨ ¨ · ¹ ¸ ¸ 1 1 1 1 1 1 T [ K N 4  §§ © ¨ ¨ ¨ ¨ ¨ · ¹ ¸ ¸ ¸ ¸ ¸ ª ¬ « « « « « « º ¼ » » » » » » § © ¨ ¨ · ¹ ¸    1 1 1 1 1 I [ K if Ah t t¸¸ ! ba W ii t m l ,1 0  otherwise  ® ° ° ° ° ¯ ° ° ° ° Accordingly, at the optimum, agents spend time working in the informal sector only if the income they obtain from working in that sector is larger than what they perceive they could earn if they were to work in the formal sector. Finally, we can derive the following consumption equations for C it y , and C it m ,: (34) C Wl Wl RAb h it y W it y it yit m it m t ti t , ,, ,,               111 1                        1 1 1 12 12 1 1 ah RRR iit y ititt , ///  /  + Abhah R P RR R ti t iit m t i it tt i                1 1 1 1 2 12 1 1     , , / tt itt RR         1 12 12 1     /// (35) C RS Wl Abh it m tit yW it m it m ti t , ,,,            1 1111 1 1             ah P R R iit m i it t it , , // 1 2 2 1 2 1 1    The consumption when old, Cit o ,+2, is determined by equation (26). Therefore, young and middle-aged workers consume a fraction of the present value of their perceived total life-time income (which decreases as ϕ i decreases, implying a larger friction), and save the rest. When old, the workers simply 345 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner consume all their savings plus, if applicable, the pension received from the government. 2.5 Aggregation We now close the model by specifying a number of definitions and aggregate conditions, that are required to hold in equilibrium. Total formal labor supply of each skill type and cohort needs to equal the corresponding labor demand, which requires (36) lN L it y it it y ,, , = (37) lN L it m it it m ,, , 1 for in l  1, ,.20 Aggregate voluntary private saving is defined as (38) SSS tt y t m  where SS N t y i n it y it l  1 ,, and SS N t m i n it m it l  11 ,, , while mandatory public saving, St P, is defined in (21). Given that only a fraction 1  of total savings, SSS t T tt P  , is invested into capital, while the remaining fraction γ is invested abroad, capital each period satisfies (39) KS tt T t   11  * Notice that we allow, in addition, for foreigners to own some exogenous fraction of the domestic capital stock,  tt t AN ** , where  *0.21 This last assumption, together with the assumption stating that part of domestic savings are invested abroad, amount — as already mentioned — to a simple and stylized strategy to model financial openness in a small open economy as the Chilean one.22 Finally, aggregate consumption in period t is defined as (40) CC CC tt y t m t o  where CC N t y i n it y it l  1 ,, , CC N t m i n it m it l  11 ,, and CC N t o i n it o it l  12 ,, 20 Note that Nit, young individuals of type i are born each period t , while, also in period t , there are Nit,−1 middle-aged individuals, and Nit,−2 old individuals, both of type i . 21 We assume γ t * grows with AN tt , in order to have a balanced growth path. 22 It is possible to show that this way of modelling financial openness, implies that the interest rate differential is decreasing in the level of domestic savings. 346 Estudios de Economía, Vol.51 - Nº 2 are the corresponding aggregate consumption levels for each cohort. And, aggregate taxes amount to TWLWL ti n it y it y it m it m l     1,, ,, 3. CALIBRATION The model is calibrated to match a series of statistics of the Chilean economy. Table 2 summarizes the base calibration. The duration of a period, given by parameter T , is set to be 20 years. Therefore, the model implies that agents are retired for 20 years following a working life of 40 . We assume there are 5 different skill groups in the economy, i.e., nl = 5, that are representative of the income quantiles.23 The subjective discount factors of the different skill groups, β i for in l  1, ,, in turn, are calibrated to replicate the average saving rates for each income quantile, which are computed from the Family Budget Survey (Encuesta de Presupuestos Familiares — EPF) from 2012, using the methodology proposed by Madeira (2015, 2018).24 The matched saving rates are 9% , −01.% , 42.% , 82.% and 17% for the first to fifth quantile, respectively, computed as the average savings during active life. These rates imply an aggregated saving rate, weighted by income, of 77.% .25 The social security contribution rate paid by the workers, τ W, is set at 10% , in line with the defined contribution of the current pension system in Chile. The social security contribution rate paid by the firms on behalf of workers, τ F, is set to 0% in the initial steady state of the model and it is increased to 5% when the alternative pension reforms are implemented in the different exercises. The parameter that determines the disutility of work, χ i, is calibrated so as to set relative total work — formal and informal — across ability groups to 048. , 063. , 074. , 086. , and 1 , i.e. implied by the 36% , 47% , 56% , 65% , and 75% participation rates of each quantile (the model has no unemployment).26 The annual population growth rate, n , is set to 05.% , and the technological growth rate corresponding to the growth rate of output per capita, wages and other per capita variables in the model, g , is set to 2% , in line with the 23 Quantile number 1, represents the lowest income group, and, therefore, the less skilled group. 24 Source: National Statistics Institute (Instituto Nacional de Estadísticas — INE). 25 This number is close to the aggregate saving rate for Chile that was estimated to be between 8.3% and 9.8% since 2010 by the OECD (https://data.oecd.org/hha/household-savings.htm). 26 Source: the data is provided by the Ministerio de Desarrollo Social y Familia, Subsecretaría de Evaluación Social, based on information from the Encuesta Casen and the Encuesta Casen en Pandemia 2020. In a robustness exercise total labor participation is set equal accross skill groups; results hold. 347 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner average growth trend estimated for Chile until 2050 in the base projection scenario of Albagli et al. (2015).27 Following the same study, the labor share in production, 1  , is set to 52% , which corresponds to the 2008-2013 average of the ratio between salaries paid by the corporate sector and the aggregate value of that sector, net of taxes, according to National Accounts data for Chile.28 The capital depreciation rate, δ , is set at 4% per year. 27 This last estimation is based on data and estimations from the Central Bank of Chile, National Socioeconomic Characterization Survey (Encuesta de Caracterización Socioeconómica Nacional — CASEN), the INE and the OECD. Its methodology is based on the production function. 28 Source: Central Bank of Chile. TABLE 2 BASELINE CALIBRATION, * QUANTILES quantiles  QQQQQ 12345 ,,,, Parameter Description Value/Target Source T Duration of a period 20 years -  i T   11 /Annual discount rates Saving rates Madeira (2018) τ W Employee contribution rate 10% Existing rate in Chile τ F Employer contribution rate 05→% Exercise τ Income tax 30% - χ i Labor disutility li      048063 074086 1.,.,.,., CASEN and CASEN en Pandemia 2020 n Annual population growth rate 0.5% Albagli et al. (2015) g Annual technological growth rate 2% Albagli et al. (2015) θ Intertemp. elasticity of subs., inv 1 Literature φ Labor supply elasticity, inverse 3 Orsi et al (2014) α Capital share 0.48% Albagli et al. (2015) 11 1    / T Annual depreciation 4% Litearture κ Work at home specific cost. 1.3 informal return between gross-net formal return ξ Informal sector prod. fct. 0.53 10% informality increase  :%30 35 η Informal sector prod. fct hin first ss t            1 1. .Normalization 348 Estudios de Economía, Vol.51 - Nº 2 The parameter that determines the specific utility cost of working at home, κ , is set to 13. , so as to make the return in informality lower than the gross wage and larger than the net wage. The parameter ξ , in turn, is set so that a 5 percentage points income tax increase, yields a 10% increase in informal work following Joubert (2015), and η is set so that ht            1 equals 1 in the first steady state. Joubert (2015) finds that informality increases 10% when a 5 percentage points increase in the pension contribution is introduced in a model for Chile, not as a consequence of an increase of the income tax. However, the model of Joubert (2015) is a partial equilibrium one where the pension contribution behaves more closer to an income tax as the one introduced here, than to a pension contribution. The parameter υ , which determines the size of the wealth effect on labor supply is set to 1 . This specification favors the ϕ iFriction 0505050505., ., ., ., .*   Literature υ Preference shifter 1 Greenwood et al. (1998) ρ Labor elasticity of subs. b/ skills 0.33 Ciccone and Peri (2005) a5 Productivity, F. sector, skill gr. 5 1 Calibration targets a4 Productivity, F. sector, skill gr. 4 0.48 Labor income quantiles a 3 Productivity, F. sector, skill gr. 3 0.21 (CASEN 2015) a2 Productivity, F. sector, skill gr. 2 0.19 a1 Productivity, F. sector, skill gr. 1 0.05 429714 5211505.,., ., ., .*     ab 55 Product. Inf. sector, skill gr. 5 0.21 Calibration targets aggregate ab 44 Product. Inf. sector, skill gr. 4 0.09 participation in informal sector ab 33 Product. Inf. sector, skill gr. 3 0.06 and quantile distribution ab 22 Product. Inf. sector, skill gr. 2 0.04 (NESI 2012) ab 11 Product. Inf. sector, skill gr. 1 0.02 57 18 18 17 14,,,, *    355 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner — mainly due to the general equilibrium effect of higher aggregate savings and capital — and strongly decreases for the lower skilled ones, which now perceive a lower net income for working in the formal sector and therefore, decide to relatively intensify their informal labor. Let us now try to understand why the increase in activity as a consequence of implementing the IDC scheme is larger than when implementing the CCDC one under the baseline calibration, whereas this reverses under the heterogeneous one. In the C-CDC case, the most skilled agents reduce their voluntary savings less than under the IDC one because their perceived additional pension, given the newly imposed contribution, ends up being lower under this scheme than under the IDC one. In other words, they cannot allow themselves to reduce their private savings as much, since, as a consequence of the redistributive features of the C-CDC system, for each unit contributed they get paid a lower future pension than under the IDC one. The lower skilled groups, on the other hand, receive higher pensions per unit contributed under the C-CDC scheme than under the IDC one, so they tend to undo a higher fraction of the new mandatory savings under the former scheme than under the latter in an attempt to smooth consumption. 356 Estudios de Economía, Vol.51 - Nº 2 TABLE 4 LONG-TERM MACROECONOMIC EFFECTS, CONDITIONAL COLLECTIVE DEFINED CONTRIBUTION SCHEME. *: EXPRESSED IN PERCENTAGE POINT CHANGES. CONSUMPTION ENCOMPASSES TWO ROWS, THE UPPER ONE SHOWS THE PERCENTAGE CHANGE WHILE ACTIVE, WHEREAS THE LOWER ONE WHEN RETIRED. Expressed in percentage changes Baseline calibration Friction sensibility Openness robustness Aggregate Skill groups ϕ γ 5 4 3 2 1 1 0 Heteroge. 0 ++ Wages -2.2 -1.1 -2.5 -3.4 -4.3 -6.6 -4.5 0.1 -1.8 -1.1 Formal work 0.8 -0.9 1.3 2.6 4.1 8.0 0.5 0.1 0.9 1.5 Informal work -2.7 8.3 -1.9 -6.7 -12.3 -2.6 -3.9 -0.1 -2.2 -4.8 Formal net income 2.4 1.3 2.3 2.9 3.6 6.1 3.6 0.1 1.9 3.5 0.8 0.5 0.7 0.9 1.0 2.0 0.7 0.1 0.6 1.9 Voluntary savings/GGP* -2.5 -0.8 -0.6 -0.5 -0.5 -0.2 -4.4 -0.8 -2.2 -2.7 Public savings/GDP* 4.3 4.7 3.9 4.3 4.4 Total savings/GDP* 1.8 0.3 3.1 2.0 1.7 Annual interest rate* -0.1 -0.0 -0.2 -0.1 -0.2 Capital 6.6 1.0 10.9 7.5 9.8 Consumption 6.3 1.2 2.2 2.9 3.6 3.6 2.9 7.9 6.9 7.4 4.5 16.7 26.7 41.3 34.3 Formal GDP 3.5 0.7 5.2 4.1 5.4 357 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner Now, when moving from the baseline to the heterogeneous calibration, the lowest skilled agents under the C-CDC scheme respond by increasing their savings relatively more than the same skilled agents under the IDC scheme. The reason is that when the degree of internalization decreases, under the CCDC scheme, agents also stop internalizing the redistributive benefits of the scheme. Therefore, savings under the heterogeneous calibration increase relatively more for the C-CDC scheme than for the IDC one, pushing the activity change under the C-CDC system above the change under the IDC one. Other general equilibrium effects are also at play, such as the change in public savings which depends on the changes in wages and in formal employment. 4.3 Unconditional Collective Defined Contribution Table 5 presents the results obtained from implementing the U-CDC reform. Under this scheme the two most skilled groups of agents are not entitled to an additional pension, even though firms do pay a payroll contribution on their behalf.35 The remaining skill groups, in turn, receive an additional pension, financed through the firms’ contributions, that is decreasing in the first component of their pension, i.e., the one financed through the employees’ contributions. The model predicts a much lower output growth between the initial and final steady states, of only 1%. This is partially explained by the lower capital stock growth, about 4.6% in the long run, and, mainly, by the significantly larger reduction in formal labor, -2.3%. This lower aggregate performance ultimately increases informality in the economy, showing how a redistributive mechanism in a collective defined contribution scheme can be a poor design. In fact, informality under this scheme increases considerably, 4.1% in aggregate terms. This pension plan does, notwithstanding, improve the consumption of the three less qualified skill groups in the economy. Notice that for those skill groups that benefit from this scheme, 1 to 3, there is an implicit tax because for each additional unit they receive from their self-financed pension, the fraction of their pension that is financed through firms’ contributions decreases by 1/3 units (similarly to the solidarity pillar currently in place in Chile). This is also responsible for the dynamics that end in a larger informality and in a reduction of formal work. 35 This assumption follows the redistribution currently used in the pension scheme in place in Chile, where only two thirds of the retirees, the least skilled ones, are entitled to redistributive benefits. 358 Estudios de Economía, Vol.51 - Nº 2 TABLE 5 LONG-TERM MACROECONOMIC EFFECTS, UNCONDITIONAL COLLECTIVE DEFINED CONTRIBUTION SCHEME. *: EXPRESSED IN PERCENTAGE POINT CHANGES. CONSUMPTION ENCOMPASSES TWO ROWS, THE UPPER ONE SHOWS THE PERCENTAGE CHANGE WHILE ACTIVE, WHEREAS THE LOWER ONE WHEN RETIRED. Expressed in percentage changes Baseline calibration Friction sensibility Openness robustness Aggregate Skill groups ϕ γ 5 4 3 2 1 1 0 Heteroge. 0 ++ Wages -1.6 -2.0 -2.1 -0.3 -0.3 -0.4 -3.3 0.1 -0.8 -1.1 Formal work -2.3 -1.6 -1.6 -4.1 -4.1 -4.0 -4.6 0.1 -1.3 -1.5 Informal work 4.1 2.5 1.5 10.5 10.3 0.4 8.3 -0.1 2.3 3.4 Formal net income -2.4 -2.0 -2.1 -2.9 -2.9 -3.0 -4.7 0.1 -1.4 -1.8 Voluntary savings/GGP* -2.6 -0.3 -0.1 -0.7 -0.8 -0.8 -4.5 -0.8 -1.8 -2.8 Public savings/GDP* 4.1 4.3 4.0 4.1 4.2 Total savings/GDP* 1.5 -0.2 3.1 2.2 1.4 Annual interest rate* -0.1 -0.1 -0.2 -0.2 -0.2 Capital 4.6 -1.6 10.9 7.5 6.8 Consumption 3.5 -3.4 -3.3 4.0 8.0 17.9 -1.5 7.9 5.7 4.1 -6.9 -7.0 34.4 69.7 172.1 Formal GDP 1.0 -3.2 5.2 2.9 2.5 359 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner 4.4 Pay-As-You-Go Finally, Table 6, shows the effects predicted by the model if a PAYG system would be implemented. This scenario is significantly worse than the previous pension reforms in all dimensions considered. In particular, it is the only system that produces a negative impact on capital, consumption, and output; all of them significant. The decrease in savings, caused by the initial transfer to the old generation leads to a contraction of total savings and, consequently, of the capital stock. This lower capital stock level, in turn, reduces the demand for labor of the firms beyond the direct effect on the labor supply implied by the tax on wages. This reduces formal labor around 4.1%, while increasing informality for all skill groups. As a consequence, GDP in the long run decreases about 4.8%. It is worthwhile mentioning that the rule that determines the distribution of funds is proportional to the contributions made by each agent. This reduces the distortions in the labor market, by strongly linking contributions and future benefits. Other alternative pay-as-you-go schemes should have additional negative effects to the ones predicted here. Clearly, all modelling and calibration exercises are subject to a substantial degree of uncertainty. In particular, it is difficult to calibrate the financial/ informational frictions that make agents internalize only partially the future benefits under the different schemes. Notwithstanding, as it can be observed, the ranking of the different alternatives, in terms of their aggregate effects is relatively robust: the individual defined contribution and the conditional collective defined contribution schemes, have the most positive (or least negative) effects in terms of capital, GDP, and labor, while the unconditional collective defined contribution scheme and, in particular, the pay-as-you-go system, have the (less positive) most negative effects on those variables. In addition, only the first two schemes are able to reduce informality.36 36 The collective defined contribution scheme behaves exactly the same as the other first two schemes when the informational and/or financial friction is set to 0 across skill groups, as expected. 360 Estudios de Economía, Vol.51 - Nº 2 TABLE 6 LONG-TERM MACROECONOMIC EFFECTS, UNCONDITIONAL COLLECTIVE DEFINED CONTRIBUTION SCHEME. *: EXPRESSED IN PERCENTAGE POINT CHANGES. CONSUMPTION ENCOMPASSES TWO ROWS, THE UPPER ONE SHOWS THE PERCENTAGE CHANGE WHILE ACTIVE, WHEREAS THE LOWER ONE WHEN RETIRED. Expressed in percentage changes Baseline calibration Friction sensibility Openness robustness Aggregate Skill groups ϕ γ 5 4 3 2 1 1 0 Heteroge. 0 ++ Wages -5.4 -5.4 -5.5 -5.5 -5.5 -5.5 -6.2 -4.2 -5.4 -6.3 Formal work -4.1 -4.1 -4.1 -4.1 -4.1 -4.1 3.3 -4.9 -4.1 4.7 Informal work 6.0 11.8 8.3 8.0 7.9 -0.2 4.6 7.1 6.2 8.3 Formal net income -5.4 -5.4 -5.5 -5.5 -5.5 -5.5 -6.2 -4.2 -5.3 -6.3 -2.0 -2.0 -2.1 -2.1 -2.1 -2.1 -0.5 -4.2 -2.3 -3.2 Voluntary savings/GGP* -0.6 -0.3 -0.1 -0.1 -0.1 -0.0 -0.8 -0.3 -0.6 -0.4 Public savings/GDP* -0.7 -0.9 -0.5 -0.7 -0.8 Total savings/GDP* -1.3 -1.7 -0.7 -1.3 -1.2 Annual interest rate* 0.0 0.1 -0.0 0.0 0.1 Capital -5.5 -6.3 -3.8 -5.4 -7.8 Consumption -4.0 -5.7 -5.7 -5.7 -5.7 -5.7 -4.7 -2.9 -3.9 5.0 -1.9 -1.2 -0.6 0.2 -1.7 Formal GDP -4.8 -4.8 -4.4 -4.7 -6.2 361 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner 5. DEMOGRAPHIC TRANSITION One particularly relevant aspect of pension schemes is their ability to handle population dynamics, such as a decrease in the fertility rate or an increase of life expectancy. In this section we use our model to analyze the first of those situations, simulated by a drop in the population growth rate, and how the different pension schemes can accommodate such a change. We consider a simple steady state transition exercise in which the economy departs form the steady state associated to each pension scheme analyzed, and simulate a drop of n from the calibrated annual 05.% to 025.% . In other words, we consider what happens under each of the four alternative pension reforms after they have been fully implemented and the population growth rate drops by half. The upper-left graph shows the basic population dynamics triggered by the drop in the growth rate n . Remember that each period in the model corresponds to 20 years. In particular, besides the propagation of the shock through the active and total populations, one can observe how as the population growth falls, the amount of passive agents in the economy relative to active workers increases. When the economy stabilizes at its new steady state the ratio of passive individuals relative to the active ones is about 3 percent points higher. Moreover, as population growth slows down, capital becomes relatively more abundant in the economy inducing a decrease in the interest rate. By the same mechanism the relatively more scarcity of workers induce an increase in wages. This increase in wages, in turn, generates a movement of workers from the informal to the formal sector (see upper-left graph in Figure 1). The higher wages together with the increase in formal labor make pension contributions increase. Under the case of the first three schemes, IDC, C-CDC and U-CDC, the drop in n ultimately translates into higher pensions. However, under the PAYG pension alternative, average pensions increase less, as now relatively less workers finance the passive individuals in the economy. It is interesting to note that for all four cases, during the transition, pensions unequivocally decrease, though more strongly under the PAYG scheme. The reason is the decrease in the interest rate and the fact that during the first two periods, the funds used to pay out pensions have been totally or partially in period 2 constituted under the original steady state (when salaries and formal work were lower). The lower-right graph shows the dynamics of the second component of total pensions, for three pension systems, for the conditional collective defined contribution, for the individual defined contribution, and for the PAYG schemes. We can see how in the case of the PAYG alternative the drop of the second component, the one financed by firms’ contributions, is the one pushing total pensions downwards under that scheme. The first component — not shown — behaves in the same way under all four schemes, as is to be expect- 362 Estudios de Economía, Vol.51 - Nº 2 ed. Hence a pension system that is fully articulated as a PAYG system would endure more severe problems, in terms of pensions, in the face of a population growth deceleration. FIGURE 1 DEMOGRAPHIC TRANSITION As shown in Figure 2, the slow down in population growth yields larger GDP, consumption and capital stock, for all pension schemes. However, it is worthwhile noticing that the performance of the economy with a PAYG system is clearly dominated by the other three schemes here considered, in particular, by the C-CDC and IDC alternatives. FIGURE 2 DEMOGRAPHIC TRANSITION 363 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner 6. CONCLUDING REMARKS In this paper we present a quantitative analysis of the long-term macroeconomic effects of implementing alternative pension system reforms in an economy with a significant informal sector. For this, we construct a three-period OLG model with five skill groups, informational and/or financial frictions and labor informality that we calibrate to the Chilean economy. We consider four different pension schemes — all financed through an identical increase of pension contributions taking the form of a payroll tax — that only differ from each other in the way they treat the additional funds and allocate them among retirees. In particular, we consider two versions of a CDC scheme that differ in whether they make pension benefits depend upon the degree of labor effort during working life or not, and compare their macroeconomic performance to an IDC scheme and a PAYG alternative. Conditioning the receipt of benefits on employment status within a redistributive design is the key aspect that incentivizes a strong formalization of labor supply at low income levels, which are those who make the largest share of informal work, surpassing the effects found under the IDC plan. In particular, the informational and/or financial frictions play the main role in the dynamics of our model as they restrict the degree in which agents internalize how pension contributions translate into future pension payments. The quantitative results suggest that the C-CDC scheme has similar macroeconomic impacts as an IDC plan under the baseline calibration, including a moderate positive effect on the formal labor market, which together with an increase in capital due to the rise of compulsory savings, generates an expansion of output and consumption. With respect to the effect these schemes have on the informal sector, the C-CDC creates stronger incentives to move away from informality among lower-income workers, and since these are precisely the ones more present in informality, we observe a stronger reduction of aggregate informality under this pension plan. This, despite the opposite effect produced among higher-income workers. The U-CDC alternative, in turn, has a negative effect on the labor market, since by making future benefits independent of contributions, low-income agents no longer have an incentive to move into formality. The additional capital is, therefore, no longer complemented by more work, and total output only increases marginally. This reduces employment and formality. The PAYG system constitutes the most adverse scheme of all the ones considered. The important reduction of the capital stock, of around 5.5%, reduces the demand for labor beyond the negative effect of the imposed contribution on firms. Formal employment falls around 4.1% and informality increases about 6%, while GDP and consumption fall 4.8 and 4% respectively. 364 Estudios de Economía, Vol.51 - Nº 2 Finally, we find that like the IDC plan, the C-CDC scheme’s solvency is robust to population ageing, the main shortcoming of unfunded pay-as-you-go (PAYG) systems. Hence, our results suggest that a C-CDC scheme may be an economically sustainable and politically viable alternative for countries with significant labor informality and income inequality. REFERENCES Albagli, E., G. Contreras, C. de la Huerta, E. Luttini, A. Naudon, and F. Pinto (2015). “Crecimiento Tendencial de Mediano Plazo en Chile”, Technical report, Central Bank of Chile. Angeletos G. M., D. Laibson, A. Repetto, J. Tobacman, and S. Weinberg (2001). “The Hyperbolic Consumption Model: Calibration, Simulation and Empirical Evaluation”, Journal of Economic Perspectives, Vol. 15(3); 47–68. Attanasio O., and A. Brugiavini (2003). “Social Security and Households’ Saving”, The Quarterly Journal of Economics, Vol. 118(3); 1075–1119. Attanasio O., C. Meghir, and A. Otero (2011). “Pension, Work, and Informality: The Impact of the 2008 Pension Reform”, mimeo. Attanasio O. and S. Rohwedder (2003). “Pension Wealth and Household Saving: Evidence from Pension Reforms in the United Kingdom”, American Economic Review, Vol. 93(5); 1499–1521. Attanasio O. and G. Weber (2010). “Consumption and Saving: Models of Intertemporal Allocation and Their Implications for Public Policy”, Journal of Economic Literature, Vol. 48(3); 693–751. Ball L., and N. G. Mankiw (2007). “Intergenerational Risk Sharing in the Spirit of Arrow, Debreu, and Rawls, with Applications to Social Security Design”, Journal of Political Economy, Vol. 115(4); 523–547. Botazzi R., T. Japelli, and M. Padula (2006). “Retirement Expectations, Pension Reforms, and their Impact on Private Wealth Accumulation”, Journal of Public Economics, Vol. 90(12); 2187–2212. Brunner J. (1996). “Transition from a Pay-as-you-go to a Fully Funded Pension System: the Case of Differing Individuals and Intragenerational Fairness”, Journal of Public Economics, Vol. 60(1); 131–146. Busato F., and B. Chiarini (2004). “Market and Underground Activities in a Two-Sector Dynamic Equilibrium Model”, Economic Theory, Vol. 23(4); 831–861. Busato F., B. Chiarini, and G. Rey (2012). “Equilibrium Implications of Fiscal Policy with Tax Evasion: a Long Run Perspective”, International Review of Law and Economics, Vo. 32(2); 197–214. 371 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner (60) wawl l it y it t iit , ,            1 (61) wgaw l l it m it t iit , ,            1 1   (62) ll l n it it yit m t ,, ,  1 for in l  1, ..., _ . And, also, (63) ww t y i n it y i l  1,  (64) ww t m i n it m i l  1,  (65) wl rl t m tw it m i ii nl it m   11, ,  (66) yk gnl t t t t             11 1   (67) lal ti n iiit l         1 1  , / (68) wy l tF t t    1 1   (69) twlwl gn ti n it y it yit m it m t l         111 ,, ,, (70) ry k gn t kt t t      11 (71) rr r tt k      11   * (72) ss s gn tt yt m t      11 (73) ss t y i n it y i l  1,  (74) ss t m i n it m i l  1,  (75) ssrs gnssr t Pt PW m tt PW y t t PW yt PF m          ,, , , 1 123 11  tt t PF y t t PF y s gn s               1 11 , , 372 Estudios de Economía, Vol.51 - Nº 2 (76) pp p tt W t F  (77) prsrs gns t F tt PF m tt PF y tt PF              123112 411 ,, ,mm ttt PF y gnns        111 2 1 , (78) prsrs t W tt PW m tt PW y     11 2 ,, (79) sw l t PW y i nW iit y it y l , ,,  1  (80) sw l t PW m i nW iit m it m l , ,,  1  (81) sw l t PF y i nF iit y it y l , ,,  1  (82) sw l t PF m i nF iit m it m l , ,,  1  (83) ks s tt t P      11  * STEADY STATE Let variables without time subscript denote steady state values. We solve for the steady state by means of numerical methods, using as starting values for the numerical solver the analytical steady state solution for the special case where  WF 0 (note that imposing  F 0 is equivalent to  1 234 0  ,  i y i m  for all i ,  ij  for all i and j,  1 and   0. From (46) to (48) crsrwl gb hah rs c i o i m i m i m iii m i y i m                    1 1                     rwlgbhah rwlebh i m i m iii m i y i y i 1 11                      ah cc ii y i y i m and we also have from (49) through (53) and (75) through (82) that (84) ss ppp i PW y i PW m i W i F i ,, = = = = =0 for in l  1, ,, and that 373 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner (85) ss ssspppp PPWy PW mPFy PF mWFBS = = = = = = = = = ,,,, 0 From (41) through (43) and the previous results, crsrwl gb hah rs c i o i m i m i m iii m i y i == 43 42 1 1                mm         = 41 11 1                rwlgbhah rw lrbh i m i m iii m i y i y i                ah rc c ii y i y i m ⇔ crcrc rwlgbhah rw lr i o i m i y i m i m iii m i y i y              2 1 1   bb hah ii i y                    1 We also have that, (86) crc i m ii y   and crc i o ii m   therefore, cr cr c i o ii m ii y    2 Combining both results, we obtain that (87) c wl gb hah rw lrbh i y i m i m iii m i y i y i                  1 11        ah r ii y ii  21 From (60), and (61), and since  1 , wa w i y i = wgaw i m i   1 Thus, (88) ww g i yi m 1    374 Estudios de Economía, Vol.51 - Nº 2 From (58) and (59), and as long as  i y i m ,  1 , (89) ha bhw i y i i i y                                   max    1 1 1 ,, 0                   (90) hga bhw i m i i i m   § © ¨ ¨ · ¹ ¸ ¸ § © ¨ ¨ · ¹ ¸ ¸ ª ¬ « « « « « « º ¼ » » » » »  max1 1 [ K FN »»  ® ° ° ° ¯ ° ° ° ½ ¾ ° ° ° ¿ ° ° °  1 1 0 I , if b i< 0 we have that, hh i y i m = =0 else, ha bhw i y i i i y                                      1 1 1                                 1 11 1 1 1 gga bhw i i i m               1 1        1 1 1 1 ghi m  which holds also for bi ≥ 0. We further choose bi such that (91) hlw bh i yi y i            1 375 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner and (92) hlw bh i mi m i            1 In addition, assuming that such a bi is constant over i, we have that, (93) cgl rl r aw i yi m i y ii i      1 1 2 2  and (94) cgl rl aw i m i i m i y ii i      1 12 2 From (56) and (57), law w bh i yi i y i                 1 1 1 1 (95)     i m i m i i lgaw w bh              1 1 11 1 lw bh aw i y i i i y                    1 11 1 1     and (96) lw bh gaw i m i i i m                      1 1 1 1 1 1     Then, if  1 , we have (97) ll g i y i m       1 1 1 1  376 Estudios de Economía, Vol.51 - Nº 2 Therefore, young and middle-aged formal work satisfy the same proportion as young and middle-aged informal work. Then, from (62), (97) and (96), (98) ll l nlg l n iii yii m ii mii m           1 1 11 1 1                              ii m i lgn g n 1 1 1 111 1 1 1 1 1                      1 11 1 1 w bh aw i i i m     To normalize li to 1 - in this steady state - one needs to set 11 11 1 1 1 1                                   g nw bh i i                    1 aw ii m      i mi i g nw bh                               11 11 1 1 1 1                1 aw i From (67), and since li = 1, (99) la la i n ii ii n ii ll    11  Then, using (97) in (93), we can write c gr g r awl i y ii ii m             11 1 1 2 1 1 2   ll g i y i m       1 1 1 1  377 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner (100) c gr g r awl i y ii ii m             11 1 1 2 1 1 2   From (41), we have that (101) swlb hah c awlga i y i y i y iii y i y ii m                     1 1 1 1 1iii m ii i wl g gr g r awl 1 1 11 1 1 2 1 1 1 1 2                      ii m ii g gr g r                          1 1 11 1 1 1 1 1 1 2             2awl ii m From (42), we have that swlgbhah rs c gawl i m i m i m iii m i y i m ii m               1 1 1   11 1 1 11 1 1 1 1 1 1 2                    galw rg gr g ii m ii                      r aw lc ii m i m 2 (102) 378 Estudios de Economía, Vol.51 - Nº 2 Starting from (83), ks   1  = 72 11 11           ss gn y m = 73 74 1 111                   i n ii yi m lss gn = 101 102 1     i n iii lg gr g r                     1 1 1 1 1 2 1 1 11 1 1 1 1                                 gn gr g i ii 111 111 1 1 1 2                            2awl ii m =   ij w    12 1 1 11 1 1 1 11 1 1 1 1 2                       g gr g r gn ii                                     1111 1 1 1 2 gree g i ii                      i n iii m lal 1  = 98 1 1 1 1 12 1 1 1 1 1 1 11 1                         w gn g gr g                          1 1 2 1 1 1 1 11 11 1    ii r gn gr g                                      11 1 2 1   i ii i n i lal ii      379 Collective Savings Pension Policy in an Economy... / E. Albagli, A. H. Arias, M. Kirchner = 99 1 1 1 1 12 1 1 1 1 1 1 11 1                          gn g gr g                           1 1 2 1 1 1 1 11 11 1    ii r gn gr g                                    11 1 2   i ii wl = 66 68 1 1 1 121 1 1 1                       gn 1 1 11 1 1 1 11 1 1 1 1 2                       g gr g r gn ii                                      11 111 1 1 1 2 gr g i ii                               1 11    gn k ll Then, the capital labor ratio is then a non linear function of r , and the model parameters, k lgn gn                            112 11 1 1 1 1 1 1 1          (120) 1 1 11 1 1 1 11 1 1 1 1 2                       g gr g r gn ii                                      11 111 1 1 1 2 gr g i ii                                 and thus, using (99), we can obtain the steady state value for k ,   380 Estudios de Economía, Vol.51 - Nº 2 (104) kk ll= From (66) and (68), then, (105) wk gnl               111   Next, we derive the bi that ensures that (91) and (92) are satisfied and show that this bi is common for all i . For this, we depart from equations (91) and (92) and use (58), (59), (95), (96) as well as (86), (97) and (100), blw hh ww bh aw i i y i y i i i y                                 1 1 1 1 11 1 1 1 1                                        a bhw h i i i y          1  bh w bh bhw bh i i i i                                       1 1 1 1 11 1 1                                     w (106) bhwbhww ii                                         11 1 for all i . The same result is found if departing from (107) blw hh i i m i m            1