How Much Retirement Income is Needed to Maintain the Living - PDF document

How Much Retirement Income is Needed to Maintain the Living Standard? Julian Schmied ∗ Christian Dudel † Abstract In light of growing old-age dependency, public pensions are decreasing in many developed countries. As a consequence, private savings and occupational pension schemes have become more important for old age income. But how much income from these sources is needed to compensate for the reduction in public pensions is unclear, as there is no definite standard for how much retirement income individuals actually need. We contribute by estimating constant living standard net replacement rates (CLS-NRRs) based on expenditure data. CLS-NRRs measure how high the ratio of retirement income to pre-retirement income needs to be to keep the living standard unchanged by retirement. We apply modern nonparametric and traditional parametric methods. Using the Income and Expenditure Survey of Germany we show, that these rates mostly exceed 90 %. This is substantially more than a commonly quoted figure in the pension literature. Keywords: replacement rates; pension adequacy; partial identification; semiparametric estimation; nonparametric estimation; JEL Classification: C14 H55 J14 ∗ Max-Planck-Institute for Demographic Research † Max-Planck-Institute for Demographic Research

1 Introduction The proportion of individuals aged 65 and older has been increasing in the majority of developed countries, going along with an increase of the retired population. For the coming decades this process of population aging is expected to continue. This puts social security systems under pressure, and public pension schemes in particular. As a reaction, public pensions have been reduced in many countries, leading to a decrease in pension replacement rates, i.e., retired persons receive a smaller share of their previously earned labor income. For instance, while up to the early 90s the German statutory pension scheme provided average net replacement rates of about 70% (Boersch-Supan and Schnabel 1998), this number has decreased to 53% in 2014 (OECD 2015). Private and occupational schemes have become more important due to this decline in replace- ment rates provided by public pensions. How much individuals need to save in addition to public pensions to compensate for the decrease in replacement rates is unclear, though. The question is how high the replacement rate needs to be. While several heuristics can be found in the literature, usually suggesting replacement rate of around 70% (e.g., Haveman et al. 2007, Benartzi 2012), they lack an empirical basis. Empirical approaches are less common and lead to conflicting results. One example are approaches based on economic life cycle models, which yield a broad range of replacement rates. For instance, Hamermesh (1984) and Mitchell and Moore (1998) report findings for the US between 80% and 90%, while one can derive a replacement rate of 66% from the model of Scholz et al. (2006). This paper contributes to the literature by proposing, applying, and comparing three approaches for the estimation of “optimal” replacement rates. We define “optimal” replacement rates as what we will call “constant living standard net replacement rates” (CLS-NRRs). CLS-NRRs capture how much retirement income is needed to achieve the same living standard as during working life. As such they can be used as a guideline for individual savings and as a reference point for assessing pension adequacy. The three approaches we use vary considerably in complexity and the underlying assumptions. For all of them the basic idea is similar to the estimation of equivalence scales (Dudel et al. 2016). Essentially, given data on one or several welfare indicators, the income levels of retired and pre-retired individuals are sought which give the same values for the welfare indicators. Apart from this basic idea, approaches differ considerably. The first approach is in the spirit of Engel (1857) and fully parametric, the second approach was originally proposed by Pendakur (1999) and is semiparametric, and the third one is nonparametric and based on Dudel (2015). The parametric approach has the virtue that it is easily understood and implemented, but it rests on strong assumptions. The nonparametric approach, on the other hand, is more complex and computationally intensive, but avoids restrictive assumptions of the parametric approach. The semiparametric approach falls in between. The results are based on the German Income and Expenditure Survey (“Einkommens- und Verbrauchsstrichprobe”; EVS). The remainder of this paper is structured as follows. The expenditure based approaches for the estimation of CLS-NRRs are discussed in section 2. Section 3 describes the data. In section 4 we present preliminary results while section 5 concludes. 1

2 Methodology 2.1 Problem description The problem we tackle in this paper can be approached from two perspectives. The first perspective follows economic theory. Let q ( p , y , x ) be a demand function depending on prices p , income y , and socioeconomic characteristics x , where we assume that x includes a dummy variable d capturing whether an individual is retired or not. u ( q , x ) is the utility derived from demand and v ( y , p , x ) is the indirect utility function. Using these functions we define an income function y ( u , p , x ) = min z [ z | v ( z , p , x ) = u ] which returns the smallest possible income which allows a utility level of u given p and x . Now let x 1 and x 0 be two vectors which only differ with respect to d which equals 1 for x 1 and equals 0 for x 0 . Constant living standard net replacement rates (CLS-NRRs) now can be defined as φ ( u , p ) = y ( u , p , x 1 ) (1) y ( u , p , x 0 ) . This means that we are interested in the ratio of incomes before and after retirement which give the same level of welfare, keeping everything else constant. This problem is essentially the same as estimating equivalence scales (Dudel et al. 2016). Throughout we assume that prices are fixed and can safely be ignored, because of which it suffices to write φ ( u ) = y ( u , x 1 )/ y ( u , x 0 ) . Note that φ ( u ) still depends on the level of utility. Equation (1) states the problem from an economic perspective. The second perspective is the estimation problem which follows from this and which can be phrased in terms of the counterfactual approach (Rubin 2005). Let y 1 i ( u ) be the income individual i needs to attain some utility level u when being retired and y 0 i ( u ) is the income level when not being retired. Moreover, let u d i be the utility level the individual achieves depending on whether she is retired or not as captured by d . CLS-NRRs can be defined as y 1 i ( u 0 i ) i ) . (2) y 0 i ( u 0 The problem is that we can either observe y 0 or y 1 and not both. Moreover, y 1 i ( u 1 i ) will be observed and not y 1 i ( u 0 i ) . In the potential outcomes literature, usually three basic assumptions are invoked to overcome problems like the above. First, the unconfoundedness assumption requires that the pair y 1 , y 0 is independent of d conditional on some other covariates x . This requires that selection into retirement can be controlled for. Second, the probability of d = 1 needs to be positive for all values of x (overlap condition). Third, the stable unit treatment value assumption states essentially that observations are independent, i.e., individual i does not influence individual j . Given these three assumptions, usually expectations of quantities of interest are identified. Unfortunately, this is not the case for (2). More specifically, taking expectations we have � y 1 ( u 0 ) � y 1 ( u 0 ) � y 1 ( u 0 ) � � = E � 1 y 0 ( u 0 ) , y 0 ( u 0 ) E � − � Cov (3) . y 0 ( u 0 ) � � y 0 ( u 0 ) y 0 ( u 0 ) E E The first ratio on the right hand side is identified given above assumptions, but the second term is not. This follows from the fact that the joint distribution of y 0 and y 1 is not identified (Dudel 2015). The second term essentially captures how much CLS-NRRs depend on the pre-retirement income. The three approaches we use to estimate CLS-NRRs are all derived from the equivalence scale literature and differ in their assumptions about the second term in (3), among other things. 2