Modelling private wealth accumulation and spend-down in the Italian microsimulation model CAPP_DYN: A life-cycle approach

The Wealth Module starts from the panel dataset produced by the pre-existing blocks of CAPP_DYN, which simulate demographic events, labour incomes and a full range of social security benefits for the period 2008–2050⁴. In keeping with the previous part of the model, the base year population is represented by the 2002 wave of the Bank of Italy’s Survey of Households Income and Wealth (SHIW). As the SHIW suffers from significant financial assets under-estimation due to under-reporting, we use the adjusted wealth data from D’Aurizio et al. (2006) on the same source⁵

Figure 1 summarizes the sequence of processes for the mechanisms of formation, transmission and spend down of household wealth.

Figure 1

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The module adopts the traditional recursive logics of DMSMs, including CAPP_DYN. In addition, some of the simulated processes have a dynamic specification themselves and have been estimated on the panel component of SHIW using the lagged dependent variable⁶ among the covariates. The decision unit for the wealth processes is the household.

For simulation purposes, we adopt a re-coding of SHIW wealth variables into two macro-aggregates: (a) home equity (real wealth) (b) an enlarged financial wealth component, which includes all financial assets plus tangible goods other than real estate (which are assimilated into non-risky assets). Net worth is obtained by subtracting financial debt (if any) from total gross wealth.

As mentioned above, the first simulated events are the intergenerational transfers of wealth between parents and children outside the family of origin (inter vivos and mortis causa). The inter vivos transfers have been modelled by means of a probabilistic approach based on a Heckman two-step procedure in order to account for selection bias. Bequests instead have a mechanical functioning. Due to insufficient information on financial transfers in the SHIW for our purposes, we have used a different micro data source that specifically focuses on this issue: the Survey of Health, Ageing and Retirement in Europe (SHARE). Section 2.4.1 discusses details of the econometrics and the mechanics of this sub-module.

Next, the model updates the wealth stock by assigning a specific return to each asset in order to determine current wealth value (as a random walk with drift based on the mean of the asset return itself). Returns are derived from an iid draw from a specific normal (or Pearson) distribution with constant mean, variance (and kurtosis) derived from available time series for Italy. This step introduces the individual portfolio risk in private accumulation process. The current home equity value of household h, (AH^t) is obtained as⁷

For financial wealth, in order to account for differential returns on the share of risky (φ^t)⁸ and non-risky⁹ assets, we preliminarily estimate financial wealth allocation between these two components with a dynamic model accounting for persistence in attitude toward risk (A static model determines initial conditions for newborn households) and for the role of other observables with a selection model à la Heckman. Since we assume the non risky share of financial wealth accrues a null real return, the weighted rate of return on overall enlarged financial assets amounts to ${\phi }^t{r}_f^t$, where the latter rate is a specific return on financial risky assets obtained as an iid draw from an asset-return-specific distribution¹⁰. The updated value for the enlarged financial aggregate for the household (AF^t) is then determined as: $A{F}^t=\left(A{F}^{t-1}\right)(1+{\phi }^t{r}_f^t)+S^{t-1}\text{where}{r}_f^t\sim iid({\mu }_{AF,}{\sigma }_{AF}^2)$ and S is the flow of yearly household saving. The outstanding debt is obtained by subtracting the capital component of the mortgage instalment paid in the previous period ($R_{cap}^{t-1}$) from its lagged value (B^t-1). Here we adopt the convention that all households repay their mortgage over 20 years (i.e. roughly the average mortgage duration in Italy, according to Rossi, 2008).

We assume the borrowing rate – r_m – normally distributed with mean and standard deviation to be fixed over time once the mortgage has been taken out and the mortgage repayment to be constant. The net wealth is then given by the sum of real and financial wealth minus the outstanding debt (i.e. mortgages being the only form of borrowing we allow in the model).

In the following step the model simulates choices affecting the stock of real estate and the number of dwellings owned by the family.

The decisions to buy or sell a house work on a set of discrete choice models (logit, estimated on the pooling of 1989–2006 waves of SHIW-HA) combined, in simulation, with Monte Carlo techniques. The totals are then calibrated to match an official external source (ISTAT, 2005). First, the model distinguishes between households that already own at least one house, which are allowed to sell a property, and households that do not have housing equity, which are not allowed to sell.

Once the family is selected for the “sale” event, the value of home equity sold AH_s^t is heuristically assumed to be the current value of real wealth divided by the number of houses owned. The new value of household real wealth is the difference between the current real wealth and the value of the sold house.

The financial wealth is assumed to increase by the value of equity that may exceed the existing debt $A{F}^t=A{F}^t+\max \{0,A{H}_s^t-B^t\}$, while the latter (if it exists) falls by the price of equity sold up to its outstanding value $B^t=\max \left\{0,B^t-A{H}_s^t\right\}$; finally, the new mortgage (total and capital) instalment is computed on the new debt (if any):

Next, a similar procedure applies to purchase of houses. When a household is selected for buying a home, the value of the purchased dwelling ($A{H}_b^t$) is estimated using an OLS on a pooling of SHIW cross sections (1989–2006) using the ratio of house value to household net wealth as the dependent variable. The model distinguishes among three cases:

• purchase with down-spending of up to 90% of the enlarged financial wealth; in this case financial wealth decreases by the price of the house bought, real wealth increases by the same amount and any debt does not vary;

• if the price of the house exceeds the 90% threshold, the financial advance can be added to by creating new debt for the difference between the house value and the 90% of financial wealth: ${\widehat{B}}^t=B^t+A{H}_b^t-0.9A{F}^t$; (real and financial wealth are updated accordingly);

• In Italy, private sector employees receive an additional, and sizeable, severance indemnity at retirement (Trattamento di Fine Rapporto, i.e. end-of-service allowance – henceforth ESA). In practice, the ESA is a deferred share of wage, which can also be partially redeemed in some special cases, and in particular for the purchase of the 1^st house or can be fully or partially transferred to complementary pension funds.

Hence, if at least one of the two spouses has an accrued end-of-service allowance (ESA) and the purchase concerns the first house, a 70% redemption of it is allowed as a set-off of debt contracted in ii): ${\widehat{B}}^t=B^t+\max (0,A{H}_b^t-0.7ES{A}_{acc}^t-0.9A{F}^t)$ with any difference exceeding the debt to be added to the financial wealth (decumulated by 90%):

Finally, since the issued debt may be excessively high due to low financial assets relative to the price of the house, we control mortgage sustainability by setting a ceiling to the (total) instalment, as the 40% of the current household net labour and pension income. If the instalment exceeds the threshold, we force the instalment to the ceiling $R_{tot}^t=0.4y^t$ and re-calculate the maximum sustainable debt given current resources: $B_{sust}^t=R_{tot}^t/\left[{(1+r)}^{20}r/\left({\left(1+r\right)}^{20}-1\right)\right]$.

Subtracting the pre-existing debt from this amount, one obtains the maximum amount that can be loaned in the current period to buy the house: $\mathrm{diff}=\max \left(0,\left(B_{sust}^t-B^t\right)\right)$. Finally, the maximum value of the house that can be bought in line with the new stock of debt is recalculated by adding the 90% of financial resources to the maximum amount that can be loaned for the current period ($A{H}_b^t=\mathrm{diff}+0.9A{F}^t$), plus the 70% of the ESA for households which are constrained despite its redemption.

In the last steps of the loop the model predicts household human lifetime resources, which are the present discounted value of labour incomes stream until retirement plus the pension income flows until household extinction (see Section 2.2.1 and 2.2.2 for details). This aggregate is crucial for determining household consumption expenditure.

This latter cannot exceed the sum of all disposable households income and the “liquid” financial wealth [(1- φ^t)AF] net of any mortgage installment.

Finally, yearly household savings are obtained as the difference between disposable labour and pension incomes (net of mortgage instalment) and consumption: $S^t=y^t-R_{tot}^t-C^t$.

The following subsections describe and discuss each sub-module starting, however, from what we conceive as the core of the model, i.e. the consumption rule and the estimation of household lifetime human resources rather than following the order of appearance outlined in Figure 1.

In this section we illustrate the theoretical background of modelling households’ behaviour in allocating resources for consumption over different periods of their life. Our aim is to estimate a general consumption rule in order to capture some possible behavioural reactions related to gradual changes in pension outcome expectations as a consequence of a significant social security reform characterized by a long transition phase.

Assuming a homothetic – non-separable over time – utility function, we can derive a closed-form lifecycle consumption function from the optimization problem as elaborated in Modigliani and Brumberg (1954 and 1979). Hence, our general formulation – in order to get an approximate optimizing model – is given by:

s.t.

Where:

• a = age of household head

• $C_a^t$ = current consumption

• $C_a^{t-1}$ = last period consumption for the same household (internal habit)

• $A_a^t$ = non-human household wealth in year t when the age of the household head is a

• $y_a^t$ = current household disposable income (earnings and pensions) in year t when the age of household head is a

• π = period constant probability of household extinction

• H = household characteristics and type

• r = real interest rate

where, in particular, HR represents the (expected) lifetime human resources (or human wealth) given by the discounted future labour and pension incomes stream. The “structural” element of the equation lies in the introduction of expectations about future income stream, through the role of human resources, as a determinant of household consumption. $C_a^{t-1}$ represents the role of habit in consumption.

For the estimation we choose an empirical specification which well describes the consumption/saving behaviour of Italian households in our sample, summarized in the formula:

The implications of such an empirical specification and the econometric estimation will be discussed in Section 2.3.

In the dynamic simulation program, this equation provides us with a predicted value for the current level of consumption ${\widehat{C}}^t$. To account for the role of liquidity constraints – which should not be neglected in a distributional analysis – we compute current simulated consumption as:

i.e. current household consumption can never exceed the sum of current disposable income plus the liquid share of enlarged financial wealth (non-risky assets), net of the mortgage instalment (if any)

2.2.2 Social security wealth

In order to estimate the expected value of future pension benefits, the model computes the expected value of the first annuity by multiplying the estimated expected replacement rate ${\mathrm{\omega }}_{\mathrm{k},{\mathrm{p}}_{\mathrm{j}}}^{\mathrm{t}}$ by the projection of last labour income (in p_k-1):

(14) $P_{k,p_k}^t={\omega }_{k,p_{kj}}^t{y}_{k,p_k}^t$

The expected present value of future pension flows is obtained as the sum of present values of pension annuities from retirement to the expected age of death (T_k,a+i) (calibrated according to ISTAT projections depending on age, gender and year):

(15) $SS{W}_k^{p_k}=\underset{i=p_k}{\overset{T_{k,a+i}}{{{\displaystyle \sum }}^{\text{}}}}\beta {\delta }^i{P}_{k,i}with\beta =.85and\delta =.985$

where P_k,i is the projected pension for active individuals, and actual simulated pension for retired individuals.

Finally, SSW values are further discounted back to the current period with the βδ¹ quasi-hyperbolic discount factor used for lifetime earnings projections and aggregated for the spouses. By summing the life-time labour incomes component plus the pension component, the model produces an estimate of the expected value of household human resources (HR).

Figure 2

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In this section we discuss the specification and the estimation of the consumption rule, whose parameters are used in the simulation program. As mentioned in the introduction, the idea driving our approach is that the likely impact of structural social security reforms on the consumption/savings age profile of Italian households asks for a step beyond the estimation of a traditional reduced-form Keynesian equation. In fact, looking at the recent past (i.e. our 1989–2008 panel dataset, Figure 3), we notice that the saving propensity profile of Italian households is characterized by a nearly flat pattern from about 35 years on, with pensioners having, on average, a positive propensity to save even at older ages.

Figure 3

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A broad strand of literature has investigated the so called “retirement consumption puzzle” in several countries (Lundberg et al. 2001, Fernandez and Krueger, 2004). For Italy, some authors have explained – at least partially – the high (private) savings propensity of the elderly by the generosity of the social security system (Miniaci et. al, 2003) which, so far, provided pensioners with rather high rate of returns on contributions and high replacement rates. Once social security wealth is included in the total wealth, the savings profile of Italian households turns out to be more consistent with the lifecycle hypothesis, with a positive propensity until retirement and a spend-down phase in the ensuing period¹⁴.

We believe that taking this pattern as given and projecting it into the forthcoming decades – when social security reforms will be fully operational and the generosity of public pensions will be much reduced – would result in missing an important part of the distributional story. In fact, reform especially affects the current young and future workers whose lifecycle consumption is not (or only incompletely) observed and whose expectations have only partially embodied the long-run effects of the reforms themselves. We therefore believe that linking consumption behaviour to a lifecycle theoretical framework, searching for a specification that fits our data more closely, is an appropriate strategy for accounting for such issues. This topic will be further addressed in Section 3.

As mentioned in Section 2.2, the empirical specification is the following:

Such a functional form, where the dependent variable is (the log of the) consumption to HR ratio, proves to better fit our household consumption data across the distribution (which is an attractive feature in a micro simulation distributional model; see Figure 4) at the same time considering the role of habit persistence and the effects of future expectations about incomes and pension outcomes as crucial determinants of current consumption. Moreover, by estimating a propensity rather than a level, in the simulation program we get rid of the necessity to make arbitrary assumptions on dynamics of aggregate consumption due to its non-stationarity in a dynamic economy. In other words, if we simulated in levels, we would need to align consumption in addition to income. On the opposite, we would like consumption to be an endogenous outcome of the model, with respect both to its variance and to the mean itself (i.e. no alignment).

Figure 4

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In order to estimate the dynamic consumption function (10) we use a GMM system estimator (Arellano, Bover, 1995; Blundell, Bond, 1998) with robust standard errors so as to purge the estimations from the bias induced by the endogeneity due to the individual fixed effect.

A consequence of the periodicity of the survey is that the reference consumption propensity is the two-year lag causing a weaker estimated persistence parameter (Lag.ln{C/HR} =0.082) when implemented in the discrete yearly simulation program.

Both the (log of) enlarged financial wealth (af_en) and financial debt (pf) have positive elasticities on the propensity to consume out of human resources while housing equity (ar_h) shows a negative elasticity. This latter, however, has to be evaluated in the light of the interaction with the number of owned dwellings. The positive sign of the interaction coefficient probably indicates a non-linear effect of real wealth on the dependent variable as owners of more than one property often enjoy actual rents (besides imputed rents for owner-occupied dwellings) that represent an extra-source of (capital) income which can be allocated to consumption.

The negative effect of retired household head (hh_retired)¹⁵ confirms the well-known drop in consumption at the time of retirement. Moreover, the household residual life (h_res_life), determined according to the survivor probabilities of the youngest spouses, determines a drop in the consumption propensity. Finally, the effect of household types suggests that nuclear families, i.e. couple with or without non-working children – the reference (omitted) category – are characterized by a lower propensity to consume out of the human life-time resources.

This section describes the functioning of another important block of the Wealth module. This part of the model proves to be of fundamental importance in modelling private wealth within a dynamic microsimulation framework aimed at explicitly accounting – in a probabilistic fashion -for inter-generational links and at assessing the between/cohorts role of private wealth transmission. From a micro perspective, intergenerational transfers may reduce inequality between cohorts but may conversely also increase economic disparities within cohorts. Either way, they may be an important channel for transmitting economic inequalities.

The analysis of such phenomena plays an important role in our study both as the size of the wealth transfers is not negligible, and because intergenerational transfers may support or even substitute for social security transfers, especially when the latter will play a decreasing role in the future. The question is even more crucial when considering three main features of Italy’s demography and economy: the secular decline in fertility, which is greater than in other European countries; the high saving rate of the elderly; the mortgage market imperfections which, causing big borrowing constraints for the young, would even further reduce their consumption capabilities and the possibility to buy a home without substantial private wealth transmission.

Concerning the quantitative evaluation of such a phenomenon, data available for Italy are still narrow. The only two sources are the Bank of Italy’s Survey on Household Income and Wealth (SHIW, 1992 and 2002 waves) and the Survey of Health, Ageing and Retirement in Europe (SHARE), which collects information on a representative sample of individuals over 50. This survey collects richer and more detailed information on wealth intergenerational transfers (and time in the form of reciprocal care) compared with SHIW and allows cross country comparisons. This micro data source has the unusual feature of collecting detailed information on respondents’ children living out of the family of origin, allowing a donor-recipient matching very useful in analyzing determinants of intergenerational transfers.

In order to get a macroeconomic picture of the saving patterns simulated by the model, Figure 5 displays aggregate results in terms of propensity to save out of base income (Y0). In particular, two definitions of savings are adopted: s0, the liquid savings (i.e. base income minus consumption minus the mortgage instalment, if any), and s1, obtained by considering the capital share of mortgage instalment as a form of savings (i.e. base income minus consumption minus annual mortgage interest, if any). As it can be noticed, in a first period, up to nearly 2020, the saving propensity increases, followed by a long period of moderation (more dramatic for the s0 propensity).

Figure 5

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We can identify some forces driving such pattern. Figure 5 (left panel) also plots the share of households whose head is retired. A sharp increase is recorded in this value, which increases from 35% of the population in 2012 to about 47% in 2045. This could be interpreted as first macro-level determinant of the retrenchment of savings in the second spell if we think of retired people in the future decades behaving differently from current Italian pensioners (who are still net savers at the older ages, see Figure 3).

Indeed, given the behavioural hypotheses introduced in the model, households’ life cycle savings patterns will change, presenting features that were missing in the recent past, thus characterized by greater saving just before retirement and more dis-saving after retirement.

These remarks are made explicit by Figure 5 (right panel) which depicts the evolution of saving propensities for households whose head is working, and for households whose head has retired. A clearly diverging pattern can be observed between the two groups. On the other hand, pension expectations are an important parameter of the consumption rule and their evolution determines the initial upward trend in the propensity to save of active households.

Therefore, so far, we have identified two opposite forces affecting saving pattern in the next years. One is a pro-saving effect due to the internalization of expectations of pension reforms by active people; the other is a counter effect – due to the interaction of future pension outcomes with the life-cycle consumption rule – on the behavior of future pensioners, who are expected to become more dis-savers.

Figure 6 shows the average simulated propensity to save age-profile in the two frameworks – LC vs. NS – in three key periods (2012–2020, 2021–2030 and 2036–2045). As it can be noticed, the NS approach tends to reproduce the past average pattern, implying an anomalous flat or moderately-growing profile even after retirement, still consistent with the retirement consumption puzzle particularly marked so far in Italy (right panel). However, this peculiar evidence can be explained by the presence of a pronounced precautionary savings motive (Jappelli et al., 2006; Lusardi, 1997) and a low consumption propensity of elderly, which, despite the generous pension system, reflects a well-rooted habit persistence (Baldini et al., 2002). In fact, although the earning-related Pay-go social security system, introduced in the 1970s, could have produced a ‘free lunch effect’ in the early cohorts of pensioners, increasing their consumption, the parsimonious preference structure of such cohorts, which were active during or just after the WWII, has prevailed on the former effect.

Figure 6

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The second approach displays, on the opposite, a reversal of the above-mentioned profile²¹, which seems more in line with the experience of other western countries.

We conceive this latter scenario as more conceivable in the future due to a significant reduction in future returns on social contributions introduced by the reforms. In addition, radical changes in the socio-institutional environment such as a severe delay both in entry into a stable occupation and child-bearing, are likely to affect individuals’/households’ future life-cycle consumption-savings profiles too. Finally, the habit persistence itself can play a role, as younger cohorts have embodied a significantly higher living standard. Possible reactions in consumption decision can be bounded, but we account for liquidity constraints in determining simulated consumption (see formula 3).

In sum, we conclude the consumption function estimated in the NS approach is hardly conceivable as a steady state relationship Next, we analyze the predicted evolution of private wealth received as a gift or bequest. Figure 7 displays the evolution of the share of recipient families of inter vivos (left) and mortis causa transfers (right) and of the average amount transferred. The share of recipient households decreases from 3.5% in 2008 to 2% in 2050 while the average transfers increases from about 25,000 Euros in 2008 to 240,000 in 2050 (Euros at 2002 prices), according to the benchmark scenario.

Figure 7

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Considering the product of the two dimensions, the mass transferred inter vivos is expected to grow by a factor five in real terms over the next four decades while the mean wage is expected to double in the same period.

Concerning the private wealth transferred mortis causa, the share of heirs’ families in the population is fairly stable between 2% and 2.5%, while the evolution of the average bequest received can be divided into three sub-periods: a steady and consistent growth from 2010 to 2029, an explosion from 2029 to 2042 and, finally, a third period up to 2050, where the amount remains roughly flat.

Multiplying the average amount by the share of population we get a mass of wealth bequeathed in 2050 equal to more than five times the one of 2008.

In terms of average growth, both for inter vivos transfers and bequests, throughout the simulation period the model predicts a noteworthy compound annual growth rate of about 4% (with an acceleration in the central period, i.e. the time when the baby-boom generation is expected to pass away), well above the general growth in wages. Such growth rate is reduced to 3.3% in the low return scenario while it is boosted to more than 4.5% according to the high returns assumptions.

This evidence points out a non-negligible role the intergenerational transmission of private wealth is going to play in the coming decades, both in the dynamics of household accumulation and in wealth distribution, due to its high dispersion.

This section aims at exploring the distributional implications of results provided by our simulations. Figure 8 below depicts the overall evolution in the Gini of projected net wealth among Italian households (left) as well as of equivalent disposable income (Y2) obtained by summing net labour and pension incomes (Y0) with annual rents provided by home equity (net of interests on mortgage, if any), and income from enlarged financial wealth²² (right). The results are plotted both across the two behavioral approaches (LC vs NS) and the three returns scenarios. Difference between thin and thick lines in the figures can be thought of as ‘second order’ effects of assuming a life cycle savings, curbing (yet not reversing) the tendential surge of wealth and disposable income inequality. Although the distributional consequences of a life-cycle consumption structure are minor relative to the first order effects, the impact is not negligible.

Figure 8

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Concerning dynamics, according to the LC approach net wealth inequality is expected to decrease by roughly 38 basis points until about 2025; after that the model predicts a sharp increase in Gini.

Inequality in equivalent overall disposable income is expected to progressively increase all over the simulation period.

As it can be noticed, while assumptions on average returns are roughly neutral in terms of wealth inequality dynamics, whose range of variation among scenarios on returns appears rather thin, they exert a dramatic influence on disposable income. Considering jointly different scenarios on returns and behavioural approaches, at the end of the simulation period the difference in Gini between low returns LC and high returns scenarios NS (lower and upper bounds, respectively) stands to about 60 basis points

The analysis of the contributions of each wealth component in shaping inequality is a specific task of the Wealth module. In order to better disentangle the role of different ‘accumulation channels’, we compute the contributions to variation (i.e. the first difference) in Gini of wealth exerted by the factors at work in the model: intergenerational transfers, savings, capital gains and end-of-service allowance.

In fact, wealth (W) can be conceived as the sum of lagged wealth and current severance indemnity (ESA), savings (S), received net of given transfers (inter vivos and mortis causa, ig_tr), and returns on financial and real assets minus interest on mortgage (capgains):

However, note that lagged wealth is a stock, while other components are flows. This determines a bias in the calculation of the contributions, requiring the following re-specification:

where W₀ is the initial wealth²³.

As our aim is to compute the annual variation in Gini, we first need to decompose this by source.

Following Shorrocks (1982), Lerman and Yitzhaki (1985), Gini can be represented as:

where S_k represents the share of source k in total wealth, G_k is the Gini of source k, and R_k is the Gini correlation of source k with total wealth.

Finally, the contribution of component i to the overall variation of a given variable x is given by:

Therefore, in our framework²⁴,

Figure 9 displays the contributions of different ‘accumulation channels’ to the overall Gini increase/decrease in the LC compared to the NS approach. As it can be noticed, a positive/negative variation emerges depending on the relative strength of opposite effects.

Figure 9

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According to the first approach, the clear reversal of the pattern in wealth dispersion around mid-2020 is mainly driven by a change in the sign of intergenerational transfers impact, which become significantly pro-inequality after 2030. In fact, in the second period, the within age-group pro-inequality effects due to the intergenerational transmission of wealth, which becomes more unevenly distributed, prevails on the between-groups anti-inequality effect related to the reduction of distances between young and elderly average wealth. On the opposite, savings appears mostly inequality-increasing in the previous spell, while inequality-reducing in the latter period. In this case, the between age-group anti-inequality effect related to the spend-down of elderly (placed on average in the right tail of the wealth distribution) replaces the within group pro-inequality impact of savings capacities among active households. Capital gains effects are ambiguous over time, although a slightly higher incidence of negative contributions can be observed. This depends on the non-pure iid nature of overall returns due to the probabilistic model of risk propensity (φ), which is characterized by a non-linear age profile and a non-linear relationship with total wealth.

A similar picture emerges from the non-structural scenario, yet with a clear prevalence of pro-inequality effect of savings, and, to a lesser extent, of intergenerational transfer, capital gains being still slightly inequality-reducing. In fact, looking at Table 5, the main difference between the two approaches in terms of contributions to inequality lies in the different and opposite role of savings, only partially counterbalanced by a difference in terms of intergenerational wealth transmission. The inequality-augmenting role of savings in the NS approach is explained by its peculiar simulated age-profile characterized by the absence of dis-saving in retirement.

Figure 10 shows a similar decomposition of the dynamics of Gini disposable income disentangling the specific role of different income sources – i.e. labour incomes (d_wage), pensions (d_pen), rents on real estate net of negative interests (d_rents) and interests/dividends on financial wealth – in determining its variation.

Figure 10

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In particular, the figure plots the differential contribution of each income source between the higher and lower returns scenarios (both within a common LC approach). Opposite to wealth inequality, in this case it is worth noticing the crucial role of capital incomes; in fact, the dynamics of the Gini in disposable incomes is positively related to the mean returns on private assets (Table A1).

The key ingredient to explain the underlying logics lies in the cumulated difference between the average net returns on private assets and the general growth of earnings (being zero the real growth of pensions), i.e. r-g. Table 6 shows that this latter cumulated difference ranges from 0.13% according to the lower returns assumptions to 1.28% in the higher returns scenario. Such differential mirrors in an increasing share of capital incomes over time, as reported in Table 7. Since capital incomes are assumed to be a fixed proportion of the underlying stocks (a simplifying hypothesis that can be relaxed) and latter is distributed more unevenly than labour and pension incomes, an increasing share of capital income on overall disposable income implies growing inequality. Thus, with r>g (as it is in the present and likely to be in the next years) wealth coming from the past or received as a gift or bequest is going to be compounded faster than earnings growth (see on this topic Piketty, 2011)

Finally, the role of the shares makes also clear the negative contribution to inequality variation of the after-tax earning source despite the future increase in its Gini (not showed here). In fact, the share of labour income on total disposable income is expected to decrease over time, and this fall is stronger the higher the projected returns on wealth due to the increasing relative importance of capital incomes (Table 7).

For an updated overview of pension reforms since 1990s, see T-Dymm final report, Section I, Chapter 4 at http://www.tdymm.eu/sites/default/files/Final-Report.pdf.

See Pensim for US and Sesim for Sweden

For a description of the pre-existing structure of CAPP_DYN, see Mazzaferro and Morciano (2008).

The main implication is that feedbacks from wealth to demographic and occupational decision are not allowed for. A further development of the research will be the sequential integration of the wealth module with pre-existing modules.

D’Aurizio et al. (2006) matched the 2002 SHIW wave with anonymous data from a sample survey of customers of the Unicredit group on the assets actually owned. By using advanced econometric techniques, this procedure determines a substantial correction for private bonds and mutual funds, particularly significant for single household and increasing with age. We do not employ the adjusted data in the econometric stage (except for the estimation of the risk propensity), but we replace them in the initial population (2002) in order to simulate more realistic distributions.

CAPP_DYN is a discrete-time annual model, while our main estimation dataset (the Bank of Italy Survey of Household Income and Wealth) has a two-year frequency. This fact causes an underestimation of persistence in the simulated dynamic models. We are aware of this problem, but, at the state of the art a yearly panel data source is not available for Italy. We thus believe the advantages of fitting a better model (especially for the consumption rule) outweigh the drawback of an underestimated persistence in simulation.

In the benchmark scenario, we have adjusted the average return from Muzzicato et al. (2008) – amounting to about 2.5% over the 1970–2007 period – by imputing a lower (very long run) rate of 1.5%. At the same time we adopt a moderate 8% standard deviation, close to that estimated by Cannari, Faiella (2008) for houses prices in Italy.

This aggregate is composed of stocks, mutual funds, private bonds, foreign government bonds, shares of limited liability companies.

Non-risky assets include bank and postal deposits CDs, PCTs, BFPs and government securities. We also added real (tangible) goods other than real estate.

In the benchmark simulation, we assume real returns of 3% with a standard deviation of 18% and an excess of kurtosis of 2.4% for risky assets. These values amount to a weighted average of short, medium and very long run returns for Italy computed by Dimson et al. (2006).

We tested both a time consistent: β = 1 and δ= 0.971→ i = 3%, and a quasi-hyperbolic framework and decided to adopt this latter scenario as a substantial strand of empirical literature supports this attitude in individuals’/households’ saving decisions (see Thaler, 1990). In fact, it provides simulation results more plausible and consistent with stylized facts. Moreover, it softens the impact of a life-cycle framework making the adjustment process in consumption choices slower, in line with empirical evidence. Presentation and discussion of results under the alternative scenario are available upon request.

The last reform by Monti-Fornero (2012), increased significantly mandatory retirement age, further reducing the flexibility which is a typical feature of the NDC systems. As the paper has mainly a methodological content, the version of CAPP_DYN on which the Wealth module has been applied has not been updated to the last pension reforms.

For an analysis of retirement expectations and pension reforms on SHIW, see Bottazzi et al. (2006).

A drop in consumption after retirement still remains to be clarified. Several theoretical and empirical works propose different explanations for this stylized fact (Hurd & Rohwedder, 2008; Laitner and Silverman 2005; Fernandèz-Villaverde and Krueger, 2005. For Italy, Miniaci et al., 2003).

According to SHIW, household head is defined as the person responsible for the household economic management, irrespective of the gender.

Following Ando and Nicoletti Altimari (2004), we divided the household population in five categories: singles, nuclear families (two spouses plus children, if any), non-nuclear families (households with spouses and active children only, not properly composite non-nuclear families), nuclear single headed and non-nuclear single headed.

Financial wealth includes bank accounts, government and corporate bonds, stocks, mutual funds, individual retirement accounts, contractual savings for housing and life insurance policies.

This is a stronger, less realistic assumption. Nevertheless, only few households are selected for receiving an inter vivos transfer more than once or twice in a life cycle so this implicit assumption should be quite innocuous in distributional terms.

On the opposite, the exclusion of such a covariate (which explains much of the selection/outcome equations) in the recipient equation would have implied a much lower variability in the predicted amount of the received transfers compared to the variance in the predicted amount of given transfers. This fact would have ended up making the transfer sub-module work as a progressive tax-benefit module, with obvious distorting rebounds on the transmission of inequality among generations.

It has to reminded that SHIW micro-data overestimate aggregate households’ savings propensity (as these are obtained residually), compared to National Accounts; thus it has been necessary to calibrate initial aggregate savings to these latter values.

This does not prevent in our simulation households to bequeath even generous amounts of wealth as would be, on the opposite, required by a ‘pure’ life-cycle framework.

In the simulation program we do not explicitly account for the role of capital incomes on the household consumption.

In order to avoid the effects of the other components to be affected by the early distribution of wealth and better analyze the accumulation dynamics underlying the wealth module, we proportionally spread the initial wealth of the base population in the first year of simulation on the remaining components.

These components have been calculated in STATA using descogini (Lopez-Feldman, 2006).

We are grateful to Leandro D’Aurizio, Ivan Faiella, Stefano Iezzi and Andrea Neri for providing us with data adjusted for under-reporting resulting from their work “L’under-reporting della ricchezza finanziaria nell’Indagine sui Bilanci delle Famiglie Italiane”.

We would also like to thank Sergio Nicoletti Altimari for his precious suggestions in the preliminary phase of this work as well as Francesca Gastaldi and Paolo Liberati for their help during the phase of revision.

This work is a synthetic revised version of Simone Tedeschi’s Ph.D thesis. Further details are available upon request.

The opinions expressed here are those of the author and do not reflect the positions of the Bank of Italy.

1. Version of Record published: August 31, 2013 (version 1)

© 2013, Tedeschi et al.

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