Elsevier

Review of Economic Dynamics

Volume 36, April 2020, Pages 134-157
Review of Economic Dynamics

Why hasn't Social Security changed since 1977?

https://doi.org/10.1016/j.red.2019.09.001Get rights and content

Abstract

Despite increasing earnings inequality and aging population, there has been no major reform of Social Security since 1977. To account for this puzzling observation, I construct a heterogeneous agent model with incomplete financial markets. There is a government who chooses the replacement rate schedule by maximizing the weighted welfare of all generations alive. I specify the Pareto weights as a function of household's age and identify them both in 1977 and 2018. I find that there was a slight bias towards younger workers in 1977. However, the bias has shifted towards older households in 2018. This shift is a result of counteracting forces induced by: 1) population aging and 2) increased labor productivity risk and increased college premium. The effect of population aging turns out to be stronger quantitatively.

Introduction

In 1977 the U.S. Congress introduced the Social Security Amendments, whose main purpose was to stabilize future replacement rates, defined as the ratio of an individual's pension benefit to this individual's average lifetime earnings. Upon signing the Amendments, President Carter announced that “the provisions of this Law are tremendous achievements and represent the most important Social Security legislation since the program was established.”

Since the adoption of the Amendments, the U.S. economy has changed significantly. In particular, earnings inequality has increased sharply and the U.S. population has continued to age. Nevertheless, there has been no major reform of Social Security (henceforth – SS) since 1977. In this paper, I explore one potential reason for why the SS system did not adjust to these important developments in the U.S. economy.

I use a general equilibrium overlapping generations model with incomplete markets and labor-augmenting technological progress in the style of Huggett (1996). Pension benefits are determined by a replacement rate schedule with one key policy variable that controls the level of the replacement rate schedule. The government sets this policy variable in order to maximize the weighted welfare of all generations alive.1 Furthermore, the government chooses the replacement rate schedule once-and-for-all. Given the replacement rate schedule, the SS tax rate adjusts in each period to satisfy the government budget. Apart from running the pension system, the government distributes lump-sum transfers across all agents and pays for other expenses (wasted in the context of my model), both of which are financed by exogenous linear income taxes.

I assume that Pareto weights in the government maximization problem depend on agent's age according to a power function with one unknown parameter, which I refer to as the age bias. The age bias reflects the preferences of the government over inter-generational income redistribution, the provision of public insurance against labor productivity risk, etc. In the absence of the age bias, the government's problem boils down to a utilitarian social welfare function. As I show, this specification of the Pareto weight function allows me to clearly identify the bias parameter using the level of the replacement rate schedule in the data.

I calibrate the benchmark model to the U.S. data in 1977, assuming that the U.S. economy is in a steady state. Then I adjust some key model parameters which capture the major changes in the U.S. economy between 1977 and 2018 and resolve the model assuming that the economy is in a steady state in 2018. The first change in the model parameters refers to population aging. I account for this by reducing the birth rate and increasing age-dependent survival rates, which control agent's longevity. The second change refers to a drastic rise in cross-sectional earnings inequality. Consistent with the data, I capture this through a deterministic and a stochastic component. In particular, I adjust the deterministic skill premium and the share of college graduates and increase the dispersion of the idiosyncratic labor productivity risk.

Assuming that it was optimal for the government to sustain the SS Amendments of 1977 as an optimal policy, I compute the age bias parameter both in 1977 and 2018. I find that there is a slight bias towards young workers in 1977. On the contrary, the age bias has shifted towards older households in 2018. As I show, these results are largely in line with the observed changes in voter turnout rates in the data. The shift in Pareto weights in the model turns out to be a result of two major counteracting forces. On the one hand, population aging is solely responsible for the rise in SS tax rate between 1977 and 2018. Everything else equal, the government should have reduced the replacement rates to reduce the upward pressure on the SS tax. Given that it optimally decided not to so, the Pareto weights must have shifted towards older agents. On the other hand, increased labor productivity risk raised the demand for publicly provided insurance as well as ex-post income redistribution. Similarly, the increase in the college premium further pushed the demand for ex-post income redistribution. Everything else equal, the government should have raised the replacement rates to protect those with low realizations of earnings. Given that this didn't happen on the equilibrium path, the Pareto weights must have shifted towards younger households. Quantitatively, the effect of population aging turns out to be stronger leading to an overall rise in Pareto weights between 1977 and 2018.

The paper builds upon three strands of the literature. The first strand takes SS as given and studies macroeconomic implications of transiting from the publicly provided to a fully funded pension system. Conesa and Krueger (1999), Fuster et al. (2007), and Nishiyama and Smetters (2014) find that quantitatively SS plays an important role as a partial insurance device against idiosyncratic risk. In my paper, I confirm the importance of SS as a partial insurance device. However, in my model SS arises endogenously.

Second, the paper relates to the macroeconomic literature which endogenizes government policies. Corbae et al. (2009) assume a utilitarian social planner in order to account for the observed level of the income tax rate in the U.S. Not surprisingly, the equilibrium tax rate in their model exceeds the one in the data. As opposed to this study, I use a weighted social welfare function. Song et al. (2012) uses a social planner's approach with Pareto weights on retired households to account for the level of public good provision and public debt in the U.S. Relative to this literature, my paper focuses on SS and calibrates the Pareto weights inside the model.

Bachmann and Bai (2013) and Chang et al. (2018) are two noteworthy exceptions. Bachmann and Bai (2013) recover Pareto weights which make the equilibrium contemporaneous correlation between output and government purchases in their model consistent with the U.S. data. Note that their model misses any form of income redistribution, which is the key aspect of my paper. Chang et al. (2018) develop a quantitative heterogeneous agents model with progressive income taxes. They uncover Pareto weights in the social welfare function for a large set of countries that justify the observed redistribution policy. As opposed to this paper, I focus on SS and analyse changes in Pareto weights over time.

Third, this paper also builds upon the growing literature on the inverse optimum (or revealed preference) approach. Bourguignon and Spadaro (2012), Lockwood and Weinzierl (2016), and Saez and Stantcheva (2016) combine analytical results from optimal tax theory in the Mirrleesian framework with assumptions on economic parameters to infer the marginal social welfare weights prevailing in the data. Bai and Lagunoff (2013) assume a weighted majority voting process in which an individual’s vote share depends on this individual's wealth holdings according to a power function and show how to recover the parameter of this function from the observed policy. Similar to my work, Lockwood and Weinzierl (2016) not only recover but also use the positive, empirical estimates of the weights in order to provide normative assessments of the income tax policies in the U.S. All of these studies, however, are based on stylized static model economies, which is not the case in my paper.

Section snippets

Statutory replacement rate schedule

In the U.S., a pension benefit is determined using a pension benefit formula. The key variable in this formula are the average indexed monthly earnings (AIME). These are the average monthly earnings over an individual's 35 highest years of their working career adjusted for the growth in economy-wide taxable earnings. The pension benefit formula maps the AIME into a pension benefit as follows. There are three AIME brackets with a constant marginal replacement rate within each bracket. The AIME

Model

The model is based on Huggett (1996), which is a general equilibrium overlapping generations model with production, capital accumulation, incomplete financial markets and idiosyncratic labor productivity risk. There is no aggregate productivity risk.

Even though I will assume that the U.S. economy is in a steady state both in 1977 and 2018, the transitional dynamics will be essential when it comes to estimating the Pareto weights. For this reason and in order to avoid confusion, I maintain the

Calibration of the benchmark model

I assume that the U.S. economy in 1977 is in a steady state, which is why I drop time index t in this section to simplify notation. I calibrate the model parameters to match some key target moments in the U.S. taking the SS policy as given. Since calibration of the Pareto weight function depends on the changes in the model parameters during 1977-2018, which I haven't introduced yet, I postpone this part until section 6.

One model period equals to one year. An agent in the model corresponds to a

Model economy in 2018

Since the adoption of the SS Amendments in 1977, the U.S. economy has changed significantly. In particular, earnings inequality has increased sharply, while the population has continued to age. To account for these changes, I feed into the model updated values of the parameters that govern demographics and the earnings process. These changes are assumed to be exogenous in the model. In section 5.1, I discuss each of the changes in detail. In section 5.2, I will assume that the U.S. economy is

Pareto weights in 1977 and 2018

Despite all of the developments in the U.S. economy described in the previous section, the replacement rate policy αt introduced by the SS Amendments of 1977 remained unaltered. The key assumption that I maintain throughout this paper is that it was optimal for the government to do so. This assumption is essential for me to be able to back out the changes in Pareto weights across the old steady state in 1977 and the new steady state in 2018.

For the status-quo (i.e. the actual) replacement rate

Discussion

There are two broad avenues for future research. The first avenue is about the importance of political constraints in shaping the SS policy (and any other government policy). My paper suggests that the observed SS policy might not be compatible with the notion of a utilitarian social planner. Pareto weights is a first approximation of potentially very sophisticated political process. More research needs to be done on understanding and modeling the underlying sources of political inequality and

Acknowledgements

I am indebted to Árpád Ábrahám, Dean Corbae, Andrea Mattozzi and Erwan Quintin. I am thankful for insightful comments to two anonymous referees, Anton Babkin, Christian Bayer, Briana Chang, Piero Gottardi, Emanuel Hansen, Marinacristina De Nardi, Rana Sajedi, John Shea, Matt Weinzierl as well as the seminar participants at the Minneapolis Fed, SAET Meetings in Rio de Janeiro, Econometric Society Meetings in Philadelphia, Midwest Macro in Rochester, XX Workshop on dynamic macroeconomics in Vigo,

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