Research notes

Microsimulation applied to Pension System: Redistribution effects of Reforms in Italy.

Francesco Marchionne

(June 2007)

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Summary Summary........................................................................................................................... 2 Abstract............................................................................................................................. 2 The Italian Pension System .............................................................................................. 3

Economic Theories and Empirical Evidence................................................................ 3 History of the Pension System in Italy ......................................................................... 4 Goals and Problems...................................................................................................... 6

Microsimulation Model and Redistribution Effects. ........................................................ 9 Microsimulation ........................................................................................................... 9 Model.......................................................................................................................... 10 Hypotheses, Parameters and Scenarios ...................................................................... 15 Demographic Forecasting........................................................................................... 16 Redistributional Effects .............................................................................................. 17

Conclusions .................................................................................................................... 26 Appendix A: Data and Model in Detail.......................................................................... 27 Appendix B: Estimates of Incomes in Detail. ................................................................ 29 Appendix C: Calculation of Pension in Detail. .............................................................. 36 Bibliography ................................................................................................................... 40

Abstract Amato reform (’92), Dini reform (’95), Prodi reform (’98), Maroni-Berlusconi reform (’04): in the last 15 years all governments have modified the Italian pension system. What has changed? What will change? Why? What are the goals? In the chaos of reforms the only certainty for the citizens seems that future pensions will be lower than present ones. But … how lower will they be? Who has really “won” the reform match? In the general reduction in performance, who has “lost less”? And above all, is the era of reforms in Italy over or is it just the first half of a “film”? In the following pages, I will try to answer to all these questions. In the first part, I will analyze the characteristics of the Italian pension system before the 90’s reforms to understand how they have affected the pension system system. In the second part, I will try to foresee the effects these reforms will have in the next decade through a microsimulation model. This model has been created with an innovative procedure based on an integrated (and non sequential) simulation of events. This new approach should guarantee more efficiency with respect to the traditional one even though there are some technical complications in its implementation. Two main results have been obtained. The first one is that actuarial equity is mainly achieved by homogenising regimes and by raising the minimum requisites for being eligible for pension (’92 reform) more than through the introduction of defined contributions (’95 reform). The second result is that excessive lowering of benefits affects negatively on actuarial equity weakening a basic principle established by the reforms themselves. Practically, the non-division of assistance from pension system and the low level of performance determine unhomogeneous benefits. From a pure actuarial defined contribution system point of view, it is unjustified. Without praising how much good has been achieved till date, the new reforms should be aimed at overcoming these precise obstacles.

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The Italian Pension System

Economic Theories and Empirical Evidence Since the postwar period, all industrialized countries have equipped themselves with pension schemes. In Europe, mandatory public pension schemes based on intergenerational solidarity have dominated. These systems that have come up in a very different context, are now in difficulty because of demographic aging and of economic slowing down. For these reasons, the subject of social security has become very relevant in recent studies. In literature, there are different theories on pensions that are very often in disagreement. The main distinction is between “political” theories and theories “of efficiency”. The former look upon the elderly as those leading a winning coalition in a political struggle whose stakes are social security. Among these theories there are those that are based on models of median voting such as Majority Rational Voting [Tabellini 1992] or Once-and-for-all Election [Browing 1975], others on pressure groups such as Time-Intensive Political Competition [Mulligan e Sala-i-Martin 1999] or Taxpayer Protection [Becker and Mulligan 1998]. On the other hand there are theories of efficiency according to which social security eliminates some form of market inefficiency. Among them we have Optimal Redistribution [Mirrlees 1971], Optimal Retirement Insurance [Diamond and Mirrlees 1978] and Optimal Longevity Insurance [Kotlikoff and Spivak 1981]. Slightly different are the theories based on the concept of human capital such as Human Capital Spillovers [Sala-i-Martin 1996] and Return on Human Capital Investment [Pogue and Sgontz 1977, Becker and Murphy 1988]. Alternative approaches have been suggested by Prodigal Father Problem, according to which the elderly, in their haydays, were not enough (Myopic Prodigality) or too (Rational Prodigality) longsighted [Diamond 1977, Laitner 1988], from Keynesian Savings Extraction [Sargent 1998], according to which social security (reducing savings) stimulates consumption and relaunches a stagnant aggregate demand, and from Scale Economies on Administative Costs [Diamond 1993], that sees public social security as a substitute for private plans in virtue of lower administrative costs. Even if the theories of efficiency explain many stylized facts, they do not justify the creation and maintenance of a social security system. Lastly, there are theories that can be defined as “narratives” because they have not been shaped yet. First among them is the one that interprets social security as a chain letter according to the Ponzi–scheme. Another theory that has spread typically in Europe states is that pension system has to reassign work from the elderly to the young when there is involuntary unemployment. Lastly, there are theories that consider public social security as a suboptimal answer to private pensions that for some reason are not chosen as a solution to a problem of optimization as they should be. From a practical point of view, however, literature has precisely classified and analyzed characteristics of pension system distinguishing them between capitalization and PAYGO financing [De Santis 1995, Ceprini and Modigliani 1998, Sabbatini 2003], defined contributions and defined benefits [Samuelson 1958, Amato and Marè 2001], mandatory or voluntary compliance [Kotlikoff, Smetters and Walliser 1998], public or private management [Diamond 1997, Kotlikoff and Sachs 1997] and various forms of guarantee [Vittas 2001]. Due to its typical economic-demographic situation, Italy is among those countries that suffers most from the current crisis of its social security

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system and is therefore a pioneering country in the field of pension reforms. The analysis of the effects of these reforms is therefore not only a case study but also a reference point for every country that has to face this problem.

History of the Pension System in Italy The Italian social security system came into existence at the beginning of the 20th century in the form of private mutualistic associations of solidarity among factory workers from different sectors. They were based on defined contributions operating in capitalization scheme. Between the 50s and 1975, while numerous cohorts of young people, sons of the fascist demographic policy, entered the work force, those born between 1890 and 1915, exterminated by the two World Wars and by transoceanic migrations, retired from working. In this scenario, with a country that was rebuilding itself after a war, the PAYGO system arose as an ideal instrument to guarantee an income to the elderly who had survived. As such the first real social security “system” was founded. From ’45 to ’65, the differentiation between the various categories expanded leading to the creation of an extremely fragmented and generous pension system. It was difficult to keep it running in a steady state with stable contribution and population rates. In 1965-1968, defined benefits and seniority pensions were extended to all occupational categories. Until 1965, in fact, it was an exclusive privilege of public employment. It attenuated fragmentation between categories, but with equalization towards the higher level than towards the lower level as it would have been desirable. Throughout the 70s the law maker did not forego the measures for obtaining consensus, but already since the beginning of the 80s, some new worrying forecasts and the need for corrective intervention were outlined. In the 80s, on one hand measures were taken that eliminated some very evident anomalies of the system, and on the other hand defined benefit regime was extended to self-employed workers despite its already well-known distortions. The system was criticised not only for its overall imbalance but also for its redistributive iniquity. Different situations were generated: i) intra- regimes (ie., differences in the pensionable age and in the requisites necessary for seniority security pension), ii) inter- regimes (ie., differences among individuals in the determination of the pensionable base where the weight of the final earnings favours faster and flying careers, and the distribution of the real pensionable age differs greatly from person to person) [Marchionne 2004]. In the attempt to rebalance the system and to face the depreciation of the Lira, the Amato reform of 1992 (Delegated Legislation of 23 October 1992, n. 421) extended defined benefits of Employed Workers Pension Fund (FPLD) to all regimes and to all new workers. This reform gradually raised not only the elegibility age requirement (from 60 to 65 years for men and from 55 to 60 for women) but also the reference period for calculating pensionable earnings (that went up from 5 to 10 years). It established the incomplete real revalorization of past earnings and limited the automatic appreciation of pensions only to the inflation rate. However, the reform mantained some important distortions such as the difference of 5 years in the age limit between men and women and the threshold of 35 years for seniority pension. These distortions substantially nullified many measures adopted [Fornero and Castellino 2001]. In 1995, under pressure from the stability pact, the Dini reform was created (Law 8 August 1995, n. 335) with the aim to definitely correct the distortions of the system by uniting the regimes and abandoning the defined benefits for the defined contributions

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and the introduction of an actuarial equity in contributions and benefits. The political price paid was high: for safeguarding the expectations of workers, in fact, the transitory provisions were very generous [Franco and Maré 2002]. The social security regulations, even after further “tightening the screw” on the reforms of 1998 (the Prodi government), can be reassumed in this way [Marchionne 2003]:

• Workers with more than 18 years of seniority until 31 December 1995 come totally under the old PAYGO (pension proportionate to the average retributions obtained in the last 10 years, with the coefficient of proportionality equivalent to 2% for each year of contribution for a maximum of 40 years that is re-evaluated on the basis of the consumer price index);

• Defined contrinutions is applied to the newly employed workers from 1 January 1996 ;

• The two schemes are applied pro rata temporis to workers having less than 18 years of seniority;

• Seniority pensions are still accessible but with combined old age-seniority requisites that are always more tightening;

• Defined benefits that were extended to Self-employed workers in 1990, at first in full and later pro rata temporis, are still enjoying it.

The transition leaves open two problems: the financial imbalances (3 or 4 decades) and some distortions that have survived. Since the social security system is not neutral in front of labour market decisions, pension reforms, at least at short term, will not easily accomplish the “magical effect” of reducing contribution rates, guaranteeing good performance, lifting up the labour market again and of creating a financially sustainable pension system [Marano 2002]. For these reasons and for the pressure coming from Brussels to “organize public accounts”, the Berlusconi government in 2004 came back to the question of social security once again and, in particular, encouraged people to extend their working activity. Those who decided to postpone their retirement beyond the official standard retirement age, ceased to contribute to the system and obtained a pay hike which is equivalent to the payments that they would have had to make. The amount of the pension is always calculated after reaching the standard age, but it is obtained only after actual retirement from work (deferment of payment). This is a strong financial incentive to continue working but it can also contribute to the illusion of higher pension benefits. In reality, there is an influence of different factors (kind of job, individual preferences, liquidity constraints, etc.) but, considering strictly from an actuarial point of view, it is convenient to continue working only if the financial incentive is higher than the reduction in the internal rate of return of the system. This estimate is generally complex and an individual often makes his or her decision without rationalizing. Even though the first data are available, a judgement on this last reform appears to be premature. Performing simulations in the absence of liquidity constraints, it is convenient for a worker to take advantage of this possibility only in rare cases. In the end, the other important innovation introduced by the Berlusconi reform regards further rise in the minimum requisites (the so-called “big step”) that surge in 2008. Currently, this is the most important question in political debate.

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Summary – History of Italian Pension System (in brackets, the causes of the reforms)

End XX century : Mutualism essentially based on defined contributions 1945-1964 : PAYGO + Fragmentation of the regimes 1965-1968 : Generalization of the defined benefits to all Employees 1969-1979 : Fragmentation of regimes 1980-1989 : Elimination of some evident distortions 1990 : Extension of the defined benefits to self-employed workers 1992 : Amato Reform (financial crisis) 1995 : Dini Reform (stability pact) 1998 : Prodi Reform (stability pact) 2004 : Berlusconi Reform (stability pact)

Summary – Causes for the crisis in the scheme

Goals and Problems Through the 50s, the Italian pension system followed a tortuous path through different social security schemes. In recent decades, however, the main aim of the reforms has always been to contain the extremely high expenditure on pensions. How come in spite of the continuous European warnings this aim has not yet been reached? The reason is that political costs of these measures, in terms of consensus, is very strong. People consider the promises of the previous regulation as their “acquired rights”: changing these rules is an unpopular action. At the bottom of this problem, however, it should be asked whether there really is a problem of reduction of pension expenditure.

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Expenditure on social protection and social security in EU countries (1995)

Countries Expend. on social Protect. in % of total expend.

Expend. on social protect. in % GDA

Expend. on pensions in %

of total expend.

Expend. on pensions in %

of GDP Austria 55 30 47 14 Belgium 53 30 40 12 Denmark 55 34 37 13 Finland 55 31 41 13 Germany 54 30 41 12 Greece 45 21 n.d. n.d. Ireland 40 20 25 5 Italy 54 25 63 15 Luxemburg 58 25 43 11 Holland 56 32 36 11 Portugal 42 21 39 8 United Kingdom

57 29 38 10

Spain 50 22 44 10 Sweden 49 36 37 13 EU Average 52 28 42 12

Source: Boldrin et al. [1999] The Italian pension system has always taken up the responsibility of social security and, in quite a notable measure, of something that is not social security: assistance. Separating the latter, the defined benefits, in spite of its weaknesses, not only would it not be burdened by such a high debt, but it would still be sustainable (INPS forecast). From a theoretical point of view, the State should take up the responsibility of assistance as it is a support for difficult situations. Disability, minimum pension, early retirement, arduous labour, etc. should be financed through the general tax system and not with the contributions made by workers enrolled on the scheme. In fact, in this way the burden of a social measure of the entire community is made to fall on one single category (even though very wide and variegated) generating a sort of “hidden” tax. In Italy it has been like this: the expenditure on pension covers a part of the social expenditure that is more than double than that in other European countries since, through social security, there has been an attempt to provide for different situations that are often totally outside the system itself, situations that in other countries instead are faced with specific plans. The secondary aim of the reforms of the 90s was that of unifying the regimes. In the course of previous decades, the different occupational categories exerted considerable pressure on the political system in order to obtain a preferential pension deal. The disparities had become too marked and a convergence towards a single regime was a desirable solution from many points of view, first of which was the political acceptability of any other further reform of the system and the second was that of social equity. The measures that were adopted were directed towards a defined contributions that however came across considerable resistance. The variety of regimes that had so much afflicted the defined benefit system did not disappear with the introduction of defined contributions even though it is considerable reduced. The last aim of the reforms, probably the most ambitious one, was that of guaranteeing higher equity. The previous system, by virtue of the fragmentation of the regimes, of its

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operating mechanism and of its elegibility requisites for pension, used to generate negative situations in which instead of providing help to the poorer and precarious workers, offered advantages to people with dynamic and permanent jobs [Marchionne, 2004]. Unifying the regimes and levelling the method of benefit calculation, the law maker clearly gave an indication to go for a system that was not only “financially sustainable” from an aggregate point of view but also “financially equitable” from an individual’s point of view by having a closer tie between contributions and benefits. Whether this result has been achieved, it is difficult to affirm. In fact, many changes in regulations have been introduced in contexts that have remained unchanged (eg. non-separation between assistance and social security) that make it difficult to isolate the impacts of each measure in order to give a right evaluation. In this work, I have tried to assess the efficacy of the reforms since the 90s1 in their reaching the pre-established goals and in particular the goal of a more equitable income redistribution within the pension system. All this will be taken up with a microsimulation model that seems to be most appropriate for a study where individual heterogeneity assumes a determining role and the reference period, covering a transitional phase towards the new regime, is by definition far from a situation of steady state.

1 Berlusconi reform has been excluded because of lack of sufficient data for an analysis like this one. The incentive mechanism to continue working creates complications. From an economic point of view, assuming the hypothesis of perfectly rational agents, the individuals should accept to postpone their retirement only in rare cases even though it is not common behaviour. So the topic should be more deeply analyzed.

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Microsimulation Model and Redistribution Effects.

Microsimulation Often, the study of pension system is taken up from a macroeconomic point of view, with overlapping generational models or more rarely with models of general economic equilibrium. However, both approaches show notable defects. General economic equilibrium models, even when they are well-specified and detailed, are efficacious in the short term but become unreliable very soon when longer time intervals are taken into consideration as in the case of a transition towards the defined contributions regime. Overlapping generation models are excellent at a theoretical level but they come across more difficulties in empirical applications because of their too rigid generational schematization. They turn out to be unsuitable to situations where heterogeneity between individuals is an essential part of the study process. A third approach is microsimulation. It is not so much used due to the difficulty in its implementation and because of the big quantity of data required, but it is more suitable for complex situations like this one. Microsimulation is a technique that uses models developed on a calculator in order to perform analyses and forecasts [Niccodemi 1998]. Its main feature is to use a sample of microdata made out of single economic units (microeconomic panels). Microsimulation offers considerable advantages with respect to a traditional aggregate analysis. The main advantage is the possibility to highlight each effect at the level of individual economic unit. However, there are other elements that make this technique more desirable. First of all, without data aggregation, microsimulation does not suffer from loss of information that afflicts macroeconomic models, and it does not assume restrictive hypotheses on individual behaviour, neither on the distribution of variables of interest. Secondly, it overcomes some difficulties arising by use of macroeconometric equilibrium models or models based on limited groups of “typical” individuals. In fact, macroeconometric models reproduce functional distribution of incomes but not personal distribution; the “typical” unit models, however, cover only a section of the individuals of the economic system limiting to study a restricted part of the entire heterogeneity present in the microdata. Thirdly, microsimulation allows to compare alternative policies within the same demographic and socio-economic scenario or different scenarios for the same economic policy. Fourthly, working with microdata, a better representation of heterogeneity and of the interdependence can be obtained. In the end, the modular structure allows wide flexibility. However, in spite of the powerful calculators, the complexity of the realty makes any virtual copy of the world impossible and therefore simplified hypotheses are always necessary to isolate and focus on the phenomenon that is to be analysed2. Nonetheless, a microsimulation model also has some weak points. First of all, during a simulation, it does not take into account behavioural reactions after modifications of the surrounding environment. Generally, this distorts the estimates as individuals continue to behave in the same way also in the face of significant changes in the context in which they take their decisions. Secondly, the construction of a microsimulation model requires heavy investment in human capital and in calculators as it has to project, program and update the model continually until a malleable and efficient instrument is

2 In general, this happens in a not less significant measure in all economic models.

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obtained. Thirdly, increase in the reliability of a model raises its complexity in an exponential manner. This leads to a considerable waste of energy which is faced with simplified assumptions. These in turn can lead to negative consequences as regards accurancy of results and comparability with other models. Fourthly, being a stochastic procedure, the results obtained are not unambiguous. However, they are more probable than the others and give important indications on the studied phenomena. Finally, last but not least, a big quantity of information is required even though data are often limited in quantity and quality or their use is expensive and inconvenient.

Model The structure of a microsimulation model is modular and divided from a logical-functional point of view into 5 sections: Data, Demography, Income, Pension and Indices. The sources of data are Survey on Householder Income and Wealth (SHIW) from 1993 to 2002 of the Bank of Italy as regards the characteristics of the individuals, and the 2003 yearbook of the Italian National Statistical Institute (ISTAT) as regards demographic variables. The data from the Bank of Italy show various difficulties for this type of analysis, but they remain still the best compromise between completeness, adequateness and representativeness among the different sources of available data (INPS and ISTAT data). A brief description of each module is given below. The data module transforms raw data of the SHIW historical archives of the Bank of Italy 1993-2002 and the ISTAT 2003 mortality and fertility tables, into input for the model. The module is divided into 5 sub-sections: Panel, Net-to-Gross, Transition, Survival and Fertility. The Panel section connects the different years. The Net-to-Gross calculates individual gross incomes starting from net incomes considering the various tax brackets and family/individual detractions of the person through a numerical procedure (Goalseek). After compressing data using the SGEE routine, the third section creates the Transition Matrixes. They are the tables of probabilities of changing status. The last two sections generate Survival Tables (probabilities of remaining still alive the following year for every age and sex) and the Total Fertility Index (average number of children per woman).

Potential � Individual Effects (not only on the whole) � No information loss due to aggregation (no distributive hypotheses) � Personal income distribution (non functional or of typical agents)

� Comparison of scenarios � Heterogeneity

Microsimulation =

a technique that uses models developed on a calculator in order to perform analyses and forecasts [Niccodemi 1998]. Its main feature is to use a sample of microdata made out of single economic units (microeconomic panels)

Limits � Simplification � Constant behaviour of individuals � Heavy investment in human capital and calculators � Reliability-complexity trade-off � Intervalled results not unambiguous � Many detailed data required

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The Demographic module deals with each period (year) to determine new entries in the population (births), the status of each unit (SGEE code) and individuals deceased (deaths). The module is divided into two sub-sections. The first one is a strictly accounting section aimed to determine births and deaths. The second is an evolving section aimed to assign a vector of individual characteristics to each unit according to his specific probabilities (Montecarlo method). The latter section is very complex for two reasons. Firstly, due to scarcely available data in trying to recreate the entire life of an individual so precisely, the more peculiar cases turn out to be difficult to simulate and require correction mechanisms for possible errors that can arise. Secondly, it is necessary to introduce many control procedures aimed to avoid anomalous situations, structural incongruence or unnatural developments (such as pensioners who become students or vice versa, etc.) that are generated by the mechanism of probabilities. Two original solutions are adopted [Marchionne 2007] (see Appendix A). The first one is the Regressive Error Correction Mechanism. It simulates the last “i” periods again when the evolution path of an individual enters an all-zero-row of the transition matrix. This, in fact, generates a loop error in the routine. The second solution is the partial transition matrix closure. Running in an all-zero-row, a positive less-than-one probability of maintaining the same previous characteristics is assumed. In this work, it is 0.5. The Income module deals with estimating individual income on the basis of a group of control variables in order to arrive at an equation that will be used for forecasting purposes. Practically, from the 1993-2002 data, the equation that links an individual’s income to control variables (age, sex, educational qualifications, etc.) will be derived, and later, this relationship will be used to determine future incomes taking the values of the control variables that are generated by the Demography module as reference. In order to be able to reconcile the requirements of implementation with those of precise forecasting, the technique of estimation used is not the most efficient but it is a compromising solution which maintains a certain accuracy without increasing its complexity excessively. This has allowed me not to turn to additional data or to other generally strong hypotheses (see Appendix B). The Pension module deals with annual payments and expected pension on the basis of occupational history according to the laws in force till 2000 (excluding the Berlusconi reform). The aim is to replicate INPS’ (National Institute for Social Security) procedures. As regards contribution payments, the historical tax rates for the past years and those foreseen by the reforms for the future ones have been applied to each category. Establishing contribution rates that are different from those of computation, the system since the Dini Reform is not really contribution-linked: in fact, technically, the amount of benefits is not automatically connected to the contribution history of an individual. As regards pension benefits, overlapping 3 different schemes, it has been divided into 3 parts: quota A for defined benefits on a 5-yearly basis (pre-Amato reform), quota B for defined benefits on the entire working life basis (Amato and Prodi reform), and quota C for defined contributions (Dini reform). Quota A includes the years before 1993, quota B years from 1993 to 1995 and quota C from 1996 onwards. The first two quotas are both defined benefits. The difference is in the reference periods for the determination of pensionable income (see following figures) and in the re-evaluation coefficient of earnings (compound capitalization of inflation rate in A and compound capitalization of inflation rate combined with simple capitalization of 1% in B). The contribution quota C works as a compound capitalization law: the interest rate applied is the average five-year one of GDP growth and the capital is constituted by

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contributions paid. However, the system does not capitalize the contribution payments actually made but those that are accredited every year by Law. This procedure generates a contribution gap that turns out to be economically unjustified in a context of capitalization, and is financially dangerous as regards the sustainability of the system. In quota C, pension is calculated by multiplying the accrued pensionable amount at the time of retirement by the transformation coefficients established in L.333/95, art. 1, commas 6-11. The Legislator has provided for the revision of the transformation coefficients every 10 years “on the basis of demographic surveys and the effective trend of long term GDP with respect to the dynamics of incomes subjected to social security contributions that have been researched by ISTAT” (see Appendix C). Once quotas A, B and C have been defined, the total amount of pension is given by their sum. In the end, the real value of the pension is obtained by applying adjustments to the minimum pension and maximum pensionable earnings.

Reference Periods in Quota A and Quota B

Quota A Pensionable income Seniority time N 1992 T-S T Quota B Pensionable Income Seniority time

Next, the Indices module calculates 5 economic-demographic indicators. The first one is the average Replacement Ratio that is the average ratio of the first pension on one’s last income. The second one is the ratio between average pension and average earning that is the average of all pensions divided by the average of all earnings. These two indices highlight the general trend of the system. The third one indicates the Quota of “Poor” Pensions and includes the percentage of pensioners with a benefit level below 50% of the average income of workers. This wideness shows the efficacy of the system’s fight against poverty. The fourth indicator is the Gini Index that is a measure of concentration or rather, how much the “pension” phenomenon condenses in the hands of the few. This index ranges from 0 to 1 and assumes 0 when the phenomenon is equally distributed (all have the same quantity) and 1 when there is maximum concentration (one person has all and the others nothing). In the end, there is the Internal Rate of Return which is the interest rate produced by an investment where the equivalent of all contributions is paid and the equivalent of all pensions is obtained3. Finally, the Coefficient of Variation has 3 For the tax payers, the pension scheme presents itself as an investment: during one’s working life, he or she accumulates savings that he/she consumes once in pension. It is therefore possible to give an

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been calculated. It is an relative index of dispersion and shows how much a phenomenon moves away from its average. The choice fell on these two last indicators for their simplicity, compactness, clarity, comparableness and relevance. The simulation has been repeated with different demographic hypotheses in order to build scenarios of minimum (where everthing goes wrong) and maximum (where everything goes well) thereby arriving, more than a precise result, at a range of possible solutions.

Summary of the microsimulation modules

0. SOURCES (see Appendix A): a. SHIW (historical) from 1993 to 2002 used by Panel b. ISTAT 2003 c. SHIW (historical) from 1998 to 2002 used by Transition

1. DATA module (see Appendix A): a. Panel (attrition) b. Net-to-Gross by Italian personal income taxation IRPEF (Goalseek) c. Transition (compression SGEE) d. Survival (by sex) e. Fertility (by age)

2. DEMOGRAPHY module (see Appendix A): a. Births (Fertility) b. Deaths (Survival) c. Evolution (Transition)

i. Regressive Error Correction Mechanism ii. Partial Transition Matrix Closure

3. INCOME module (see Appendix B): a. OLS vs FE � Test F b. FE vs RE � BPLM and Hausman c. AB91 + AB95 � AB AR(1) and AB AR(2) d. RE AR(1) � Solution of compromise

4. PENSION module (see Appendix C): a. Earnings Re-evaluation Coefficients Quota A (pre-Amato) and B (Amato) b. Contribution Conversion Coefficients Quota C (Dini) c. Pure calculation of Quotas A, B and C d. Determination of contributions made on the basis of historical rates e. Final calculation of the Pension (Minimum and maximum pension)

5. INDICES module (see above): a. Average Replacement Ratio b. Ratio between average Pension and average earnings c. Quota of Pensions below 50% of the Average Income d. The Gini Index e. Average Internal Rate of Return and Coefficient of Variation (Goalseek)

In conclusion, Microsimulation generates a virtual behaviour of the economic system. The model is developed on the calculator starting from the demographic-economic assessment using the Internal Rate of Return (IRR), as happens in financial markets, that is, the average interest rate that, applied to a cash flow for a given period of time, brings back the income and expenditure to a balance.

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characteristics of an individual sample representative of the entire population. Some indices highlight the performance of the pension system, specially from the aspect of an anti-poverty measure, of rate of return and of equity among individuals. Finally, different demographic hypotheses allow evaluation of the impact of the reforms by considering different future scenarios (refer to next paragraph). This leads to a range of possible results and gives a general idea of the performance of the system more than just a precise definition of its results.

A microsimulation model diagram

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Hypotheses, Parameters and Scenarios The model is supported on many hypotheses even though a limit has been put to their use. As regards the demographic hypotheses, matrixes of transition hide strong assumptions. In fact, in the model they remain constant in T. This means that individuals do not change their behaviour during the simulation period. Temporary changes are imposed by the mechanism of error correction at the time, scaling back to one or more time periods, it redistributes the probability of entering a blind alley among the other possible paths, and by the mechanism of partial transition matrix closure that on the other hand affects directly on the values. Finally, in this work the household structure has been considered only while estimating a individual gross income. For the economic hypotheses, net incomes have been transformed into gross incomes considering only Italian personal income taxation (IRPEF). The earning estimates have been obtained with the RE econometric model with AR(1) errors. This means that the present determinants of the income remain the same in the future. Moreover, the economic development is seen to increase with a growth rate of real GDP by 1.5% with an inflation of 1.5% as assumed by L.335/95.

Summary of the hypotheses and parameters of the model

• HYPOTHESES: o Data:

� No attrition (sample remains representative after elaboration) o Demography:

� No variation in individual behaviour (constant transition matrix) � No distortion in error correction (transition matrix adjustments) � Constant sex and geographical distribution � Non relevance of family structure

o Economy: � No distortion by non-IRPEF taxation � Income forecasts on the basis of RE model with AR(1) errors � No further contribution rate variation with respect to those already foreseen � Indexation of minimum and maximum earnings to inflation � Annual GDP growth and inflation rate equal to 1.5% (see also L.335/95)

o Semplifications: � Exclusion of freelancers and other non INPS categories � Retirement with minimum requisites and absence of survivor’s pension

• PARAMETERS: o Fertility rates o Mortality rates

Lastly, there are some hypotheses to simplify the pension system. It is assumed that the tax rates remain unchanged except for the prescribed normative adjustments, that the highest income limit and the minimum earnings increase only on the basis of inflation as prescribed by law, and that retirement from the labour market takes place depending

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on the “exit window”4 as soon as the minimum requisites are reached. As every freelancer continues to pay in his or her own different fund, they have been excluded. A minimum pension is assigned to self-employed workers of the old regime because it is impossible to rebuild their contribution history (no available data). For their payments, contribution rates assumed by L.233/90 and L.335/95 are hypothesized. They are much below the historical ones. The results for self-employed workers are therefore to be considered rather a low bottom limit. Lastly, survivor’s pension has been excluded. The rates of fertility and death are the “controllable” values, so they have been assumed as parameters of the model 5. The models of simulation are based on the construction of scenarios. One scenario is a possible comprehensive result of the casual variables chosen as control parameters. In these approaches, a range of results creating 3 situations are obtained: one minimum (all wrong), one reasonably probable and one maximum (all good). In this work, given the particular evolution of demographic parameters6, only 2 scenarios are taken into account. In the first one, demographic parameters do not change (Status Quo). In the second one (Steady State) fertility rates increase until they reach a Total Fertility Index of 2.1 while the death rates converge to ISTAT rates (main scenario). The use of scenarios generates not so precise results but a range of possible values. Moreover, adopting the Montecarlo method, the limits of the interval are not unambiguous. Given this aleatoriety each simulation generates situations that are slightly different, even though within the probabilities of every event. To overcome this problem, the results have been rounded off to the last relevant digit that is obtained in 2 subsequent simulations under the same conditions.

Demographic Forecasting According to ISTAT forecasts, the Italian population is ageing. In the next ten years the porportion of the elderly will go up but, it is more worrysome that the proportion of the workers will go down rapidly. This hits the financial foundations of the social security system. If a generous defined benefit plan is added to this phenomenon, the prospects of an explosion of the pension component which is part of the global social expenditure is not so far. However, at the beginning of the 90s, this happened throughout Europe also. In Italy, this phenomenon became bigger because of the strong impact of pension expenditure on social expenditure. Italy’s entry in the European Union and the need to maintain the stability pact forced the Legislator to correct the anomalies. Strong measures were taken, and a containment effect on expenditure, at least in the short term period, was achieved. However, a second reason was called into question many times to justify the need for reforms. The old defined benefit regime was not only generous but also fragmented and distorted from the distribution point of view. The aim of this work is exactly that of analyzing the redistributional effects before and after the reforms in order to establish their efficacy through microsimulation.

4 As opposed to the past situation, after the reforms it is now possible to retire only in certain periods of the year. From the point of view of time, some “windows” are created in order to quit the labour market. 5 Acting on the lifetime of an individual and entering the mechanism of calculation of the coefficients of trasformation of L.335/95, only the death rates have significant effects on its performance. 6 Fertility rates will not so easily go further down after arriving at very low levels. The same concept is also true for death rates: increase in longevity will always be slower.

Microsimulation Model and Redistributive effects

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Source: ISTAT 1990

Source: ISTAT 1990

Redistributional Effects From the results, it comes out that the reforms are able to contain social security expenditure reducing the benefit levels roughly. The below graph shows the coverage provided by the pension system. It is measured by the average Replacement Rate RR that is calculated annually on all workers that quit the labour market. After a short intial phase in which RR falls between 67-70%, the index lowers gradually with intensity going up until 40% and levelling at around 34%. The oscillating trend is due to the sentivity of RR to the cyclical and cohort effects. Since RR has been defined as the ratio between the first pension and the last earning, it is affected by the type of adopted scheme and by the moment a worker retires from work. If he/she had consistent earning increments in the last working period, RR would be lower. In spite of these limits, the trend clearly shows a decrease in the pension level. An indication on the reduction in performance substantially similar to RR, but more in general (as it involves all pensioners), is given by the year by year Ratio between the paid Pension average and the worker Earnings average (RPE). Also in this case, despite

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Microsimulation Model and Redistributive effects

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the indices being different7, the indication that comes out is clear. Dividing the reference period in two, it is possible to distinguish the first phase (until 2015) during which the reduction is still relatively limited, from the second phase (from 2015 onwards) which becomes always wider8 due to the exhaustion of the defined benefit regime and the beginning of the defined contribution regime.

Replacement Ratio and Ratio Pensions/Earnings 2000-2050

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Therefore, financial sustainability of the Italian pension system would be achieved with a strong decrease in social security performance. This reduction would lead to a halving of the pension/earning ratio in the next ten years. However, the long transitory period means that the aggregate effects of the reforms will be seen in many years. We will get them only when defined contributions will be running fully. In the face of such a strong reduction in the performance, the matter is whether these reductions do not call into question the capability of the system to defend its insured people from falling below the poverty line. Obviously, this depends on many other factors such as the household structure and other assistance forms. The following figure shows the trend of the percentage of pensioners whose annual income is below 50% of the average income of workers in the same period. I will call this as “Quota of Poor pensioners” (QP).

7 RR deals only with new annual pensioners while RPE includes all those who get pension at a certain time regardless of the time of retirement. 8 The results obtained are coherent with other models also (eg. RGS 2004, Ferraresi-Fornero 2000, OECD 1998).

Microsimulation Model and Redistributive effects

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Quota of pensions lower than 50% of median work income. 2000-2050

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From less than 41% in 2000, QP rises steadily without reversal of trend until 67% in 2040. The containment of the social security expenditure therefore goes down by over 25 points the capacity of the system to face poverty. Getting into more detail, the next figure shows the RR trend by income groups identified by first, third and fifth quintile calculated on the basis of the distribution of earnings at the time of retirement.

Replacement Ratio by income levels (calcolated on last earning)

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Mean 1° Quintile 3° Quintile 5° Quintile

The 1º quintile (poor subjects) initially undergoes downsizing in the performance almost in the same way as the other groups. Only from 2038 the contraction activates social protection mechanisms that offset the general trend of the system. This brings to light two aspects: on the one hand, the present 1º quintile includes both poor subjects (who continue to be subsidized as shown by the decrease in RR that is less accentuated than the average) as well as non poor subjects (the RR however goes down). This proves that the present system is very generous. On the other hand, in the last period it comes out how minimum pension reduce impoverishment of the group in the face of a general decrease in performance (refer to the other groups). However, the gradual final rise (and the slope that precedes it) is probably due to the different weight of each system.

Microsimulation Model and Redistributive effects

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It is also interesting to note the 5º quintile (rich subjects). Their RR is stationary at the beginning, but goes down after 2017. The phenomenon can be explained by the income ceiling and by the progressiveness of the system. In fact, within the “rich” there will be subjects (“poor” rich) who will have reductions and other individuals for which this phenomenon is not efficacious. In these conditions, less generous formulas are not very significant. Therefore, the group average goes down but more slowly than the general average. However, always fewer individuals have such a high income so as to overcome the pensionable ceiling and therefore RR goes down. The variation in the weights of the regimes justifies the temporary intermediate oscillations. To give a better explanation of the redistributional effects of the system, the trend of the quotas of pensioners according to the different calculation rules have been reported.

Quota of Pensioners by calculus formula for pension. 2000-2050

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Defined Benefits Mixed System Defined Contributions

Moving to redistribution, the Gini index, calculated on “pure” (simple calculation) pension and on the one really paid out (with the maximum and minimum pension applied), highlights a trend that is similar until 2020 and which later goes on in a different way. The widening of the gap shows the importance of the ceilings and thresholds of income and the weakness of the system in pursuing two different (and in certain ways opposing) goals, that is, to fight against poverty and for financial equity.

Gini Index on Pure Pension and Paid Pension. 2000-2050

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The redistribution effects of the reforms are very well highlighted by the comparison of the trend of the Internal Rate of Return IRR with that of the Coefficient of Variation CV considering both Minimum Scenario and Probable Scenario hypotheses.

Total IRR and CV (Minimum Scenario)

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The scenario effect presents itself in two ways. On the one hand, lengthening average life, the IRR level remains slightly higher that the “theoretical” one. But, the increase that comes out of it is only temporary as it is reabsorbed decennially by the realignment of the coefficients themselves. Therefore, a slightly oscillatory level of IRR is seen. On the other hand, the scenario effect influences CV. The convergence of the different regimes towards contribution leads to a reduction in the dispersion of IRR. This can be observed in the first part of the period. In the second period CV remains constant. However, as soon as the system is able to guarantee higher IRR (Probable Scenario) even only temporarily, fewer people are elegible to minimum pension. The integration to the minimum pension is mainly responsible for IRR dispersion, so the CV goes down. The negative correlation between IRR and CV is a further demonstration of the importance of the measures for sustaining pensionable income. There are other 2 factors that explain the level of CV9. The first is the coexistence of pensions paid out with different systems (and therefore IRR) and the mechanism of “exit windows” that forces people to retire only in certain periods of the year10. The second factor is the contrast

9 The hypothesis of retirement at the arrival of the minimum requisites excludes personal decisions from the causes. 10 Obviously, the mechanism of “exit windows” has marginal impact.

Microsimulation Model and Redistributive effects

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between the initial reduction of CV and a substantial unchange in the rest of the period pushes us to make a more detailed analysis. So, for every scenario, the figures that follow report the Internal Rate of Return (IRR) and Mean Square Error (MSE) by occupational categories (private, public employees and self-employed workers).

IRR and MSE by Private Employed (Minimum Scenario)

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IRR and MSE by Private Employed (Probable Scenario)

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IRR and MSE by Public Employed (Minimum Scenario)

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IRR and MSE by Public Employed (Probable Scenario)

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Microsimulation Model and Redistributive effects

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The dotted lines show IRR level added and subtracted 2 times MSE. The two curves are equidistant from the continuous line, and hypothesizing a normal distribution of IRR, they form a range that involves 95% of the cases. For private and public employees, the trend of the two variables is very similar. A slower IRR slope for public employees than for private ones is observed. It is due to the more favourable conditions before. In the end, corresponding figures have been reported for self-employed workers. The IRR starting level is much higher as proof of a particularly favourable situation initially. Since, most of their contributions are largely below than what is required in order to obtain a minimum pension with just pure calculation, their pensions were generally integrated to the minimum. This implies considerably high IRR. Therefore, high dispersion paradoxically indicates a homogeneous benefit condition: everybody was basically assisted even though each one received different benefits.

IRR and MSE by Self-Employed (Minimum Scenario)

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IRR and MSE by Self-Employed (Probable Scenario)

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With the advent of the reforms, this phenomenon becomes smaller even though it still remains quite wide. This, on the one hand, happens due to a technical reason. Under the entry “self-employed workers” there are heterogeneous categories such as direct farmers, tenant farmers, artisans and traders that come together. On the other hand, self-employed workers enjoy more generous transitory measures. In fact, the very low rates and reference to corporate income (in place of gross personal income) lower pension levels so that this category is partially subsidized. Finally, the gap between the computational contribution rate and effectively paid contribution rate that is 1% against 0.3% for public employees and 0.65% for private ones also contributes.

Microsimulation Model and Redistributive effects

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IRR and CV by category (Minimum Scenario)

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In the end, the three job categories are compared. For all of them, the defined contributions indicate a slight decrease in IRR, especially for the self-employed workers that lose some unjustified advantages. There is also a reduction in the dispersion but it seems to be produced more by a tendency within the defined benefits themselves than by the introduction of the defined contributions. In fact, the extension of the reference period to the entire working life in the determination of average income lowers the dispersion well before the Dini reforms start operating fully. Once this phase of reduction of the levels and of the differences between the income rates is over, the period from 2010 to 2030 is characterized by a weaker convergence which later stops

Microsimulation Model and Redistributive effects

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almost completely in the last 20 years. Therefore, financial equity seems to have been achieved only partially, and basically not because of the introduction of the defined contribution method. In fact, on the one hand, homogenisation of the regimes reduces disparities among groups. On the other hand, the raising of minimum requisites for all the regimes leads to a sharp reduction in variability within the groups thereby impeding the individuals to profit from advantageous situations that come up with anticipated retirement. On the contrary, heavy benefit reduction caused by the defined contributions and levelling all towards the bottom, activates social protection mechanisms that raise the level of disparity until substantially compensating the gains generated by the convergence. In the light of this research, the assessment of the reforms can not be totally positive. On the contrary, the behaviour of the Legislator generates a lot of doubts. From a strictly technical point of view, some choices remain unexplained, such as the one that determines computational contribution rates different from the effective ones. As far as efficiency is concerned, if the goal of containing expenditure is attainable, that of achieving equity is much further. The attempts to re-balance the system crashs with the fight against poverty generating distorted situations that put some in a position to take unfair advantage. The most efficient solution would be to pursue different goals with different instruments: to separate social security from assistance would allow the former to allocate services after a working activity (as it should be) covering its burden with social security contribution, and it would allow the latter to intervene only to sustain situations where necessary and financing itself with general taxation. Further reforms should be directed towards achieving this goal that seems to be able to guarantee (or at least to clearly identify how much there is to insure) not only sustainability but also equity of the system. However, political activities (both in discussion and reforms) often concentrate more on marginal topics taking on demagogic-electoral matters instead of substantial-structural matters, and in this way perpetuate dangerous legislative delays that are capable of seriously harming the functional capabilities of the system itself.

Conclusions

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Conclusions In the 90s, the Italian pension system was profoundly reformed with the aim to contain social security expenditure and to guarantee more equity. Concentrating on redistribution effects and starting from the sample data of the Bank of Italy, this work simulates demographic and income development of the present population with the microsimulation model. The approach adopted is innovative with respect to the traditional one, and it is based on integrated and not sequential simulation of events. Even if this is theoretically more efficient, lack of sufficient detailed data has created difficulties to implement it. Once the income profile of an individual was acquired, his pension was calculated according to the regulations in force in 2000. Later, other indicators were created to highlight the redistribution effects. Like any other simulation, in the long term, it loses reliability. The conclusions are not effective guidelines for an economic policy. They are only a mere technical evaluation of the reforms since the 90s till now, under the same hypothesis made by the Legislator (Law has not been “updated” yet) but with newer demographic forecasts. These analyses underline that the failure to reach the established objectives is caused by ad originem reason, that were in “defect” and already known from the beginning (generous transition period, differences between regimes, etc.) and by in itinere reasons, that were “events on the way” more or less foreseeable (economic-demographic trend). The invariance of the transition matrices, the retirement with minimum requisites, the exclusion of some job categories and the abandoning to create a general economic equilibrium model allowed the author to concentrate on the prescriptive aspect of microsimulation in order to emulate the behaviour of INPS and to arrive at a technical outlook of the reforms. Assuming an actuarially impartial system as “fair”, the reforms do not seem to be able to reach the redistribution goals desired. The judgement is obviously technical and does not carry any negative connotations. There are, in fact, many extenuations for the reforms being unsuccessful (fragmentation of the old regimes, generosity in remuneration, lengthening of average life etc.) even if it remains true that the push towards financial equity, shown with some measures (convergence of regimes, raising of age and service requisites, etc.), was definitely blocked by their high political costs (lack of distinction between assistance and social security, long periods of transition, etc.). However, even if all this is taken into, the reforms show many lacunas from the point of view of redistribution. With heavy benefit reduction, many people will get minimum integrated pensions with evident redistribution to their advantage. Moreover, lengthening of average life through coefficients of transformation, benefits those who retire before updating of the coefficients. A certain attention should be given to the mechanism of re-evaluation implicit in the coefficients of the Dini reform as it could generate distortions in the presence of forecast errors. These penalize the oldest and privilege the longeval sex. However, what is more worrying, is the substantial halving of the pension level. Can so restrictive regulations be sustained that generate too wide intergenerational disparities in transition and too low performance? From a financial point of view, lack of moving over to capitalization maintains high the risk of a crisis that is due to a contraction in the base of the demographic pyramid and to the slowing down of economic growth. Supplementary benefits from private penion funds have been indicated as the missing pillar of the Italian pension scheme. Is a reform, that leaned also on this element, capable of sustaining the burden of welfare or is it destined to be transformed into a simple “cut” in the pensions? Many questions still remain open ten years since the beginning of the reforms. In theory, the system could obtain good results, but in the light of this analysis it should be asked whether similar or better results could be not achieved with other measures (re-parameterizing the old system, moving on to total capitalization, creating a mixed financial regime, etc.). Wanting to remain in the field of this work, in the future there will be new necessary interventions to guarantee financial sustainability and more equity to the system. In fact, these aims, with present regulations, seem to be partially achievable not only in transition but also when functioning fully. Therefore, the “film” on the reforms in Italy is not over but has only arrived at the first half.

Appendix A

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Appendix A: Data and Model in Detail. At present there are 3 sources of data suitable for one kind of work like the one done here: the INPS archives, investigation on the labour force from ISTAT and on the budget of Italian families from the Bank of Italy (SHIW). The INPS archives are the biggest in terms of units observed, and are also complete in terms of information on income and occupation. Unfortunately, the data are gathered for bureaucratic purposes and are not scientific. As such, even if they are full of information, they turn out to be inadequate. In particular, there are two flaws that warn us against their use. Firstly, the archives do not cover all people but the job categories managed by INPS (Social Security National Institute). Even if those excluded are few, the data cannot be considered as representative. Moreover, the INPS archives lack information related to the education of an individual. From a theoretical point of view, it is difficult to justify income estimates that are not linked to this variable in any degree. ISTAT’s investigation on the labour force is representative, large and detailed, but does not have information on income. Therefore, using their data could be limited for determining individual characteristics and transition matrices, and in order have income estimates we should turn to other data. SHIW (Survey on the Household’s Income and Wealth) from the Bank of Italy shows information both on the characteristics and on individual income and at the same time it is representative of the population. The SHIW data however show various problems. First of all, they are not a real panel but a pseudo-panel or rather a rotation panel in which, at each wave, only a fraction of the individuals is interviewed again, while the remaining part is substituted by new units in order to maintain the representativeness of the sample. The mechanism of rotation, by construction, amplifies the attrition effect at each wave reducing greatly the number of units useful for the construction of the panel. In order to facilitate the use of the data in the model, the panel has been made in a balanced form as data are also the real starting base for microsimulation. However, this balancing reduction has a marginal impact on the sample. The second problem of SHIW data regards incomes that are measured after contributions and taxes. For every pension system, the principal interest variable is individual income. However, precisely speaking, it is the gross income that is of interest because the contributions are calculated on gross income. This means that SHIW data are re-elaborated with the process of “Net-to-Gross” that transforms net incomes into gross incomes. Net-to-Gross procedure seems theoretically simple but it requires a numerical solution (Goalseek). Moreover, starting from SHIW data, the construction of a panel faces different difficulties regarding connection of the individuals between subsequent waves as the identification code used by the Bank of Italy does not always remain constant. Lastly, the fact that data are gathered bi-annually (on average) creates some difficulties in the making of the transition matrices because some individuals experiments more status between 2 near waves. Having to manage a vast quantity of data, it was decided to reduce the control variables and the their possible values at the minimum. In particular, only income from jobs was taken into account, neglecting completely the financial income as this would have led to a very strong assumption on the wealth distribution of the people and would have introduced considerable arbitrariness with only marginal improvement in the precision of the model. In the end, as regards the model, 3 examples of how they function have been illustrated. The first example deals with the SGEE routine, the second deals with the operation of the transition matrix while the third model concerns the Regressive Error Correction Mechanism. Working example: SGEE Routine

1 3 4 2 0 6 � 1 8 0 6 sex area3 study qualp7n nonoc settp7 sex geocult employment

Appendix A

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Working Example: Transition Matrix Consider a variable with 3 modalities and the its relative transition matrices for ages 1 and 2:

Modality (Age 1) A B C Modality (Age 2) A B C A 0.4 0.7 1 A 0.4 0.8 1 B 0.3 0.6 1 B 0.4 0.7 1 C 0.2 0.9 1 C 0.3 0.8 1

Consider, at time t, a subject of age 1 and modality B. Extraction of a random number x by a uniform rectangular distribution between 0 and 1 is 0.68. Since, on B row in the matrix for age 1, this value is higher than 0.6 (B column) and lower than 1 (C column), the subject moves to modality C in t+1. Similarly, another subject with the same modality B in t and the same extracted value x equal to 0.68, but having an age 2, will still remain in B in t+1 as 0.68 turns out to be higher than 0.4 (A column) but less than 0.7 (B column).

Working example: Error Correction Regressive Mechanism Refer to the transition matrices for age 1 and 2 (on the right). The second matrix has the last row with structural all-zero row. In t, a subject has age 1 and modality B. Random extraction generates an x=0.51 so the modality is the same as the previous period (step 1). If in t+1 the subject has not reached age 2, his transition matrix does not change. x=0.87 is extracted. It determines the move from B to C (step 2). In t+2 the subject attains age 2 and changes the matrix. However, his modality (C row) shows a structural all-zero row. The extraction does not mark an exit modality and the routine generates a error. The correction mechanism is activated. It scales down t by e=1 and repeats the simulation t+1 starting from B and using again the matrix of age 1 (step 3). An extraction of an x=0.97 leads us to the same error (step 4). Time that achieved t+2 is now reduced by e=2 until t

(step 5). Extracting x=0.27 we move to A row (step 6). In t+1, x=0.13 marks only the change in the transition matrix (step 7). In t+2, an x=0.83 leads to a new entry in C row (step 8). An error comes up and the correction mechanism is activated again. Being an error different from the previous one the error counter e is re-initialised at e=1 (step 9). In t+2 an x=0.39 is extracted and the subject lands in t+3 to A row (step 10). In the figure below, capital letters are the modalities and subscripts indicate the

subject’s age. The numbers on the arrows indicate the steps.

t t+1 t+2 t+3

A1 A1 7 A2 10 A2 6 B1 1 B1 B2 B2 8 4 2 C1 C1 C2 C2 3 9 5

Modality (Age 1) A B C A 0.4 0.7 1.0 B 0.3 0.6 1.0 C 0.2 0.9 1.0

Modality (Age 2) A B C A 0.4 0.8 1.0 B 0.4 0.7 1.0 C 0.0 0.0 0.0

Montecarlo Sequence (Start in B1) 01: x = 0.51 B1 02: x = 0.87 C2 03: MRCE e=1 04: x = 0.97 C2 05: MRCE e=2

06 : x = 0.27 A1 07 : x = 0.13 A2 08 : x = 0.83 C2 09 : MRCE e=1 10 : x = 0.39 A2

Appendix B

29

Appendix B: Estimates of Incomes in Detail. Descriptive Statistics --------------------------------------------------- ---------------------------- Variable | Mean Std. Dev. Min Max | Observations -----------------+--------------------------------- -----------+---------------- idkey overall | 1352 780.3177 1 2703 | N = 13515 between | 780.4332 1 2703 | n = 2703 within | 0 1352 1352 | T = 5 | | year overall | 999 1.414266 997 1001 | N = 13515 between | 0 999 999 | n = 2703 within | 1.414266 997 1001 | T = 5 | | gdp overall | 9.63e+11 5.75e+10 8.77e+11 1.03e+12 | N = 13515 between | .0001221 9.63e+11 9.63e+11 | n = 2703 within | 5.75e+10 8.77e+11 1.03e+12 | T = 5 | | ly overall | 10.30545 .5990654 5.908762 13.69284 | N = 7750 between | .5747556 6.208867 12.12798 | n = 1855 within | .3103895 7.502576 12.44289 | T-bar = 4.1779 | | age1 overall | 40.69027 20.72197 0 98 | N = 13515 between | 20.46663 4.6 93.6 | n = 2703 within | 3.262022 36.09027 45.09027 | T = 5 | | age2 overall | 2085.066 1741.609 0 9604 | N = 13515 between | 1716.459 31.8 8771.6 | n = 2703 within | 296.3875 1234.466 2917.466 | T = 5 | | sex1 overall | .5064743 .4999766 0 1 | N = 13515 between | .5000506 0 1 | n = 2703 within | 0 .5064743 .5064743 | T = 5 | | sex2 overall | .4935257 .4999766 0 1 | N = 13515 between | .5000506 0 1 | n = 2703 within | 0 .4935257 .4935257 | T = 5 | | geo1 overall | .4254532 .4944298 0 1 | N = 13515 between | .494503 0 1 | n = 2703 within | 0 .4254532 .4254532 | T = 5 | | geo2 overall | .190529 .3927329 0 1 | N = 13515 between | .392791 0 1 | n = 2703 within | 0 .190529 .190529 | T = 5 | | geo3 overall | .3840178 .4863801 0 1 | N = 13515 between | .4864521 0 1 | n = 2703 within | 0 .3840178 .3840178 | T = 5 | | cult1 overall | .6568257 .4747867 0 1 | N = 13515 between | .4426184 0 1 | n = 2703 within | .1719574 -.1431743 1.456826 | T = 5 | | cult2 overall | .2788013 .4484262 0 1 | N = 13515 between | .4083398 0 1 | n = 2703 within | .1854561 -.5211987 1.078801 | T = 5 | | cult3 overall | .0643729 .2454251 0 1 | N = 13515 between | .2321967 0 1 | n = 2703 within | .0795875 -.7356271 .8643729 | T = 5 | | employ1 overall | .1378468 .3447519 0 1 | N = 13515 between | .3000853 0 1 | n = 2703 within | .1697921 -.6621532 .9378468 | T = 5 | | employ2 overall | .1475398 .3546563 0 1 | N = 13515 between | .2928466 0 1 | n = 2703 within | .2001184 -.6524602 .9475398 | T = 5

Appendix B

30

| | employ3 overall | .0038476 .0619117 0 1 | N = 13515 between | .0482099 0 1 | n = 2703 within | .0388529 -.7961524 .8038476 | T = 5 | | employ4 overall | .0022937 .0478399 0 1 | N = 13515 between | .0299628 0 .8 | n = 2703 within | .0372981 -.7977063 .8022937 | T = 5 | | employ5 overall | .0096929 .097978 0 1 | N = 13515 between | .0750673 0 1 | n = 2703 within | .0629782 -.7903071 .8096929 | T = 5 | | employ6 overall | .0059193 .0767121 0 1 | N = 13515 between | .0627087 0 1 | n = 2703 within | .0441988 -.7940807 .8059193 | T = 5 | | employ7 overall | .0212357 .1441744 0 1 | N = 13515 between | .1146892 0 1 | n = 2703 within | .0873872 -.7787643 .8212357 | T = 5 | | employ8 overall | .0341842 .1817089 0 1 | N = 13515 between | .1474699 0 1 | n = 2703 within | .1061941 -.7658158 .8341842 | T = 5 | | employ9 overall | .0522383 .2225154 0 1 | N = 13515 between | .1487972 0 1 | n = 2703 within | .1654661 -.7477617 .8522383 | T = 5 | | employ10 overall | .2149464 .4108003 0 1 | N = 13515 between | .3614451 0 1 | n = 2703 within | .195328 -.5850536 1.014946 | T = 5 | | employ11 overall | .2227895 .4161336 0 1 | N = 13515 between | .386694 0 1 | n = 2703 within | .1538803 -.5772105 1.022789 | T = 5 | | employ12 overall | .1474658 .3545827 0 1 | N = 13515 between | .3092816 0 1 | n = 2703 within | .1734996 -.6525342 .9474658 | T = 5 --------------------------------------------------- ----------------------------

In the demographic module, the percentage repartitioning of sex and geographical area have been taken out from a long period panel (1977-2002), obtaining, for the sexes, 49.24% for males against 50.76% for females, and for the geographical area, 40.34% for the North, 21.15% for the Centre and 38.51% for the South. As can be noted comparing the figures with those reported above, the mechanism of attrition causes a certain distortion especially in the sexes and between the North and Centre. The averages of the variables employ show the “occupational” structure of the population. The measure that is particularly high in employ12 (“Others”) brings to suspicion a high frequency of missing responses. Therefore, the data seem to suffer from the evils that are typical of micropanels and in particular of attrition and nonresponse. The description of the table concludes by observing that the income figures are deflated and expressed in logarithmic terms and that the structure of the panel is balanced.

Appendix B

31

MODELLO POOLED --------------------------------------------------- --------------------------- Regression with robust standard errors Number of obs = 7750 F( 16, 7732) = . Prob > F = . R-squared = 0.3729 Root MSE = .4749 --------------------------------------------------- --------------------------- | Robust ly | Coef. Std. Err. t P>| t| [95% Conf. Interval] -------------+------------------------------------- --------------------------- age1 | .0375401 .0019859 18.90 0.0 00 .0336472 .041433 age2 | -.0002982 .0000191 -15.58 0.0 00 -.0003357 -.0002606 sex1 | .3796994 .0116031 32.72 0.0 00 .3569542 .4024446 geo1 | .1549614 .0130072 11.91 0.0 00 .1294637 .1804591 geo2 | .1391194 .0159467 8.72 0.0 00 .1078596 .1703792 cult2 | .3193838 .0129645 24.64 0.0 00 .2939698 .3447978 cult3 | .4605837 .0213829 21.54 0.0 00 .4186674 .5025 employ1 | .0056294 .0147929 0.38 0.7 04 -.0233687 .0346275 employ3 | .3320219 .0583663 5.69 0.0 00 .2176082 .4464356 employ4 | .609604 .0694781 8.77 0.0 00 .4734082 .7457999 employ5 | .1646537 .0609903 2.70 0.0 07 .0450963 .2842112 employ6 | -.1958744 .0896301 -2.19 0.0 29 -.3715737 -.020175 employ7 | .2517882 .0464697 5.42 0.0 00 .160695 .3428814 employ8 | .1527456 .0400573 3.81 0.0 00 .0742225 .2312687 employ9 | (dropped) employ10 | (dropped) employ11 | -.2592228 .020967 -12.36 0.0 00 -.3003238 -.2181218 employ12 | -1.781971 .4530157 -3.93 0.0 00 -2.670004 -.8939371 pil | 2.35e-12 9.61e-14 24.44 0.0 00 2.16e-12 2.54e-12 _cons | 11.11694 .1052149 105.66 0.0 00 10.91069 11.32319 --------------------------------------------------- --------------------------- FE MODEL --------------------------------------------------- --------------------------- Fixed-effects (within) regression Num ber of obs = 7750 Group variable (i): idkey Num ber of groups = 1855 R-sq: within = 0.1786 Obs per group: min = 1 between = 0.0262 avg = 4.2 overall = 0.0080 max = 5 F(1 4,5881) = 91.37 corr(u_i, Xb) = -0.4876 Pro b > F = 0.0000 --------------------------------------------------- --------------------------- ly | Coef. Std. Err. t P>| t| [95% Conf. Interval] -------------+------------------------------------- --------------------------- eta1 | -.0127005 .0129382 -0.98 0.3 26 -.0380641 .0126632 eta2 | .000348 .0000413 8.42 0.0 00 .000267 .000429 sex1 | (dropped) geo1 | (dropped) geo2 | (dropped) cult2 | .0973535 .0368974 2.64 0.0 08 .025021 .169686 cult3 | .1298448 .0984271 1.32 0.1 87 -.0631083 .322798 employ1 | .0188143 .0214784 0.88 0.3 81 -.0232912 .0609198 employ3 | .1025256 .0732953 1.40 0.1 62 -.0411602 .2462114 employ4 | .0915888 .0757537 1.21 0.2 27 -.0569162 .2400938 employ5 | .2954979 .059677 4.95 0.0 00 .178509 .4124868 employ6 | .0066192 .0742813 0.09 0.9 29 -.1389995 .1522379 employ7 | .1978347 .0422989 4.68 0.0 00 .1149134 .2807561 employ8 | .2400032 .0369258 6.50 0.0 00 .1676152 .3123913 employ9 | (dropped) employ10 | (dropped) employ11 | -.1461913 .025038 -5.84 0.0 00 -.195275 -.0971075 employ12 | -2.442705 .1762581 -13.86 0.0 00 -2.788236 -2.097174 pil | 3.21e-12 6.86e-13 4.68 0.0 00 1.86e-12 4.55e-12 _cons | 13.05057 .1285068 101.56 0.0 00 12.79865 13.30249 -------------+------------------------------------- --------------------------- sigma_u | .62668847 sigma_e | .32290082 rho | .79021282 (fraction of variance d ue to u_i) --------------------------------------------------- --------------------------- F test that all u_i=0: F(1854, 5881) = 5.85 Prob > F = 0.0000

Appendix B

32

MODELLO RE --------------------------------------------------- --------------------------- Random-effects GLS regression Num ber of obs = 7750 Group variable (i): idkey Num ber of groups = 1855 R-sq: within = 0.1555 Obs per group: min = 1 between = 0.3925 avg = 4.2 overall = 0.3524 max = 5 Random effects u_i ~ Gaussian Wal d chi2(17) = 1345.72 corr(u_i, X) = 0 (assumed) Pro b > chi2 = 0.0000 ------------------- theta -------------------- min 5% median 95% max 0.3639 0.3639 0.6541 0.6541 0.6541 --------------------------------------------------- --------------------------- ly | Coef. Std. Err. z P>| z| [95% Conf. Interval] -------------+------------------------------------- --------------------------- eta1 | .0160723 .0027813 5.78 0.0 00 .0106211 .0215235 eta2 | -.0000827 .0000279 -2.97 0.0 03 -.0001374 -.0000281 sex1 | .4023947 .020627 19.51 0.0 00 .3619664 .4428229 geo1 | .1860222 .0229954 8.09 0.0 00 .1409521 .2310924 geo2 | .1716919 .0288505 5.95 0.0 00 .115146 .2282379 cult2 | .2749432 .0200893 13.69 0.0 00 .235569 .3143175 cult3 | .4457165 .0347159 12.84 0.0 00 .3776747 .5137584 employ1 | .0308236 .0184122 1.67 0.0 94 -.0052636 .0669107 employ3 | .1787553 .0681303 2.62 0.0 09 .0452224 .3122882 employ4 | .1856926 .0736741 2.52 0.0 12 .041294 .3300913 employ5 | .2415076 .0492547 4.90 0.0 00 .1449701 .3380452 employ6 | -.0596803 .0630498 -0.95 0.3 44 -.1832557 .0638951 employ7 | .2149156 .0356701 6.03 0.0 00 .1450036 .2848277 employ8 | .2116516 .0300584 7.04 0.0 00 .1527381 .270565 employ9 | (dropped) employ10 | (dropped) employ11 | -.1945516 .0222952 -8.73 0.0 00 -.2382493 -.1508539 employ12 | -1.902092 .1319174 -14.42 0.0 00 -2.160645 -1.643539 pil | 2.34e-12 7.68e-14 30.48 0.0 00 2.19e-12 2.49e-12 _cons | 11.51312 .0982207 117.22 0.0 00 11.32061 11.70563 -------------+------------------------------------- --------------------------- sigma_u | .39166567 sigma_e | .32290082 rho | .59534995 (fraction of variance d ue to u_i) --------------------------------------------------- --------------------------- --------------------------------------------------- --------------------------- . hausman FE RE ---- Coefficients ---- | (b) (B) (b- B) sqrt(diag(V_b-V_B)) | FE RE Differ ence S.E. -------------+------------------------------------- --------------------------- eta1 | -.0127005 .0160723 -.028 7728 .0126357 eta2 | .000348 -.0000827 .000 4307 .0000305 cult2 | .0973535 .2749432 -.177 5897 .030949 cult3 | .1298448 .4457165 -.315 8717 .0921015 employ1 | .0188143 .0308236 -.012 0093 .0110595 employ3 | .1025256 .1787553 -.076 2297 .0270272 employ4 | .0915888 .1856926 -.094 1038 .0176277 employ5 | .2954979 .2415076 .053 9903 .0336945 employ6 | .0066192 -.0596803 .066 2995 .0392738 employ7 | .1978347 .2149156 -.017 0809 .0227341 employ8 | .2400032 .2116516 .028 3517 .0214476 employ11 | -.1461913 -.1945516 .048 3604 .0113943 employ12 | -2.442705 -1.902092 -.540 6131 .1168962 pil | 3.21e-12 2.34e-12 8.66 e-13 6.82e-13 --------------------------------------------------- --------------------------- b = consistent under Ho and Ha; obtained from xtreg B = inconsistent under Ha, efficient un der Ho; obtained from xtreg Test: Ho: difference in coefficients not syst ematic chi2(13) = (b-B)'[(V_b-V_B)^(-1)]( b-B) = 353.25 Prob>chi2 = 0.0000 --------------------------------------------------- ---------------------------

Appendix B

33

--------------------------------------------------- --------------------------- Breusch and Pagan Lagrangian multiplier test for ra ndom effects: Ly[idkey,t] = Xb + u[idkey] + e[idkey,t] Estimated results: | Var sd = sqrt( Var) ---------+------------------------- ---- ly | .3588793 .599065 4 e | .1042649 .322900 8 u | .153402 .391665 7

Test: Var(u) = 0 chi2(1) = 2400.00 Prob > chi 2 = 0.00 --------------------------------------------------- ---------------------------

Making inference on the 2 models, it comes out that test F, about the nullity of individual effects, is rejected and as such the unrestricted model represented by FEs is better than the Pooled model which is constrained. In order to compare FEs and REs the outputs of BPLM test and Hausman test have been listed. They give out contrasting results. On the one hand, BPLM pushes towards an RE model rejecting the hypothesis of the unvariability in individual effects. On the other hand, the Hausman test pushes towards an FE. Moreover, the estimate of FE shows a no-zero correlation of individual effects with respect to error terms. This is a contradictory situation with the RE hypothesis. Incoherence of the tests is attributable to bad specification and specially to lack of a dynamic variable. In fact, if the model foresaw, for example, lagged income among the explanations, the result for FEs of Hausman test (RE is not unbiased and consistent under H1 therefore the test is wrongly specified) and the result for REs of Breusch-Pagan’s test (however there is positive variance in individual effects) could be justified. ARELLANO-BOND MODEL [1995] --------------------------------------------------- --------------------------- Building GMM instruments: 14 instruments dropped because of collinearity. Arellano-Bond dynamic panel-data estimation, one-st ep system GMM results --------------------------------------------------- --------------------------- Group variable: idkey Num ber of obs = 5543 Time variable : anno Num ber of groups = 1602 Number of instruments = 62 Obs per group: min = 1 F(18, 1601) = 34.49 avg = 3.46 Prob > F = 0.000 max = 4 --------------------------------------------------- --------------------------- | Robust | Coef. Std. Err. z P>| z| [95% Conf. Interval] -------------+------------------------------------- --------------------------- ly[-1] | .2275989 .0350478 6.49 0.0 00 .1589066 .2962913 pil | 3.59e-12 1.73e-13 20.76 0.0 00 3.25e-12 3.93e-12 eta1 | -.0411465 .0064468 -6.38 0.0 00 -.0537819 -.0285111 eta2 | .0005494 .0000676 8.13 0.0 00 .0004169 .0006818 sex2 | -.32934 .0289938 -11.36 0.0 00 -.3861667 -.2725133 geo1 | .1232431 .0283034 4.35 0.0 00 .0677695 .1787168 geo2 | .0898191 .0342257 2.62 0.0 09 .022738 .1569003 cult1 | -.480343 .1186948 -4.05 0.0 00 -.7129804 -.2477055 cult2 | -.1965328 .1124871 -1.75 0.0 81 -.4170035 .0239379 employ1 | 5.407846 2.725201 1.98 0.0 47 .0665511 10.74914 employ2 | 5.426223 2.726184 1.99 0.0 47 .0830002 10.76945 employ3 | 5.637501 2.728081 2.07 0.0 39 .2905603 10.98444 employ4 | 5.795166 2.732972 2.12 0.0 34 .4386401 11.15169 employ5 | 5.850283 2.72979 2.14 0.0 32 .4999933 11.20057 employ6 | 5.710738 2.682919 2.13 0.0 33 .4523141 10.96916 employ7 | 5.913734 2.730054 2.17 0.0 30 .5629263 11.26454 employ8 | 5.954374 2.727975 2.18 0.0 29 .6076411 11.30111 employ11 | 5.437477 2.724013 2.00 0.0 46 .0985091 10.77645 _cons | 6.915754 2.741509 2.52 0.0 12 1.542496 12.28901 --------------------------------------------------- --------------------------- Hansen test of overid. restrictions: chi2(43) = 31 6.06 Prob > chi2 = 0.000 Arellano-Bond test for AR(1) in first differences: z = -8.44 Pr > z = 0.000 Arellano-Bond test for AR(2) in first differences: z = 0.69 Pr > z = 0.488 --------------------------------------------------- ---------------------------

Appendix B

34

Moving to a dynamic panel structure leads to an improvement in estimates, but it also leads to more complexities as can be seen from the output of the Arellano-Bond estimator [1995]11. Regarding this estimate it must be noted that the use of instruments both in the levels and in the differences increases the number of independent variables rapidly. This generates a virtual increase in the fitting measure of the model. The author attempted to limit it as much as possible by cutting down on all unnecessary instruments to evoid false improvements. All dummy variables that were time-invariant, were inserted in the levels only. The other variables were collapsed so as to create a unique instrument for each variable and each amplitude of lag, instead of one instrument for each period, variable and amplitude of lag. Outsiders12 were excluded as they brought about slight distortion in the estimates. As regards inference, the Arellano-Bond Test confirms the presence of serial correlation of 1° order and negates that of the 2° order as hoped for. The coefficients are averagely significant. It is evidenced how the lowering of the original number of instruments from 18713 to 62 has brought about better specification in the model and therefore a clear improvement in the estimates. RE MODEL with AR(1) --------------------------------------------------- --------------------------- RE GLS regression with AR(1) disturbances Num ber of obs = 7750 Group variable (i): idkey Num ber of groups = 1855 R-sq: within = 0.1481 Obs per group: min = 1 between = 0.4069 avg = 4.2 overall = 0.3610 max = 5 Wal d chi2(18) = 1565.38 corr(u_i, Xb) = 0 (assumed) Pro b > chi2 = 0.0000 ------------------- theta -------------------- min 5% median 95% max 0.2692 0.3870 0.5052 0.5052 0.5052 --------------------------------------------------- --------------------------- ly | Coef. Std. Err. z P>| z| [95% Conf. Interval] -------------+------------------------------------- --------------------------- eta1 | .0242296 .0027704 8.75 0.0 00 .0187996 .0296595 eta2 | -.0001619 .0000279 -5.81 0.0 00 -.0002165 -.0001072 sex1 | .4010123 .0187797 21.35 0.0 00 .3642047 .4378199 geo1 | .1817556 .0209212 8.69 0.0 00 .1407507 .2227604 geo2 | .1684787 .0262139 6.43 0.0 00 .1171005 .219857 cult2 | .2903409 .0192509 15.08 0.0 00 .2526099 .328072 cult3 | .4543573 .0323452 14.05 0.0 00 .3909619 .5177528 employ1 | .0248601 .0184242 1.35 0.1 77 -.0112507 .0609709 employ3 | .1942732 .0685771 2.83 0.0 05 .0598644 .3286819 employ4 | .2130514 .0756779 2.82 0.0 05 .0647255 .3613774 employ5 | .2073933 .0485764 4.27 0.0 00 .1121852 .3026014 employ6 | -.0528658 .0629951 -0.84 0.4 01 -.176334 .0706023 employ7 | .2132616 .0356149 5.99 0.0 00 .1434578 .2830655 employ8 | .20887 .0300047 6.96 0.0 00 .1500618 .2676781 employ9 | (dropped) employ10 | (dropped) employ11 | -.2006354 .0231179 -8.68 0.0 00 -.2459457 -.1553252 employ12 | -1.862003 .1300055 -14.32 0.0 00 -2.116809 -1.607197 pil | 2.28e-12 8.41e-14 27.14 0.0 00 2.12e-12 2.45e-12 _cons | 11.26897 .1048993 107.43 0.0 00 11.06338 11.47457 -------------+------------------------------------- --------------------------- rho_ar | .22382739 (estimated autocorrelat ion coefficient) sigma_u | .32733598 sigma_e | .34157908 rho_fov | .47871681 (fraction of variance d ue to u_i) --------------------------------------------------- --------------------------- modified Bhargava et al. Durbin-Watson = 1.5845333 Baltagi-Wu LBI = 2.1906489

11 Number of groups does not correspond to 2703 subjects of the sample because in the estimate only those who have an income are considered. The Arellano–Bond [1991] estimate has not been reported for reasons of space. 12 Outsiders are those subjects with an average income in the period below the 1° and above the 99° percentile (16 units). 13 In the estimates reported here this figure is not visible.

Appendix B

35

In the end, the RE estimate with AR(1) has been reported. Like the previous FE and RE models, the coefficients of FE with AR(1) errors have little relevance14 while those of RE are better. The comeback of the sign coefficients (but not values) and relevance similar to the intial OLS case should be noted. In the choice of the forecast model, computational considerations should also be added to the econometric ones. Using the Arellano-Bond model which is the best, allows us to assign an income to each unit already in the work force, but it leaves open the question of determining gross remuneration of the new entries and of all those subjects who have moved from inactive state to an active state. So, I would need another rule to assign an income to the units for which yi,t-1 = 0. A good compromising solution that maintains a certain dynamism without excessive complexities is an RE model with AR(1) errors. At the time of getting into the job market, the model simulates individual effect αi and assumes a lagged error εi,t-1 null. In subsequent periods the AR(1) structure of errors is used and the model works fully. Therefore, the RE with AR(1) solution is not ideal from an econometric point of view but given the instrumental and functional nature assigned to it in the work, it seems to be a fair compromise between the opposite demands of precise estimates and the ease with which it can be used.

14 Estimate not reported.

Appendix C

36

Appendix C: Calculation of Pension in Detail. Law n.335/95 does not explain the procedure to calculate the coefficients. However, one attachment sent by the Italian Government to OECD in March 2000, on the occasion of the discussion on the report on the economic situation of Italy (Italy’s Survey 2000), expresses the formula in an analytical way. It uses actuarial techniques used by insurance companies for old age and surviving risks with some changes coming from the application of the contribution method to a PAYGO system (i.e. the uniqueness of the transformation coefficients with reference to sex). In this report there are also indications on the parameters and values that are taken on in calculating the transformation coefficients of table A in the law n.335/95. These parameters can be divided into demographic and prescriptive parameters. Demographic parameters are the probability of survival by age and sex, the probabilities of leaving the family by age and sex, and the difference of age between the assignor and survivor by assignor’s age and sex. The prescriptive parameters are the survivor’s rate, the average percentage of reduction of this tax rate in relation to the beneficiary’s income and the difference between the rate of return of the system (assumed as equivalent to the 5-year average of the GDP variation rate) and the indexation rate. Moving over to a formal analysis, here we have a list of the variables with their definitions:

C = transformation coefficient ∆ = divider s = sex (m=male, f=female)

sx

stx

l

l

,

,+ = probabilities of survival between x and age x+t

x = retirement age w = maximum survival age (on the basis of the tables) qx+t,s = probabilities of death between age x+t and age x+t+1 Θx+t,s = probabilities of leaving the family by a subject of age x+t

vedstxl ,+ =probabilities of survival, of not being eliminated by death or another marriage

k = correction in order to keep into account ways of pension distribution (1 month in advance, 2 months in advance, 1 year in advance and so on) by “exit windows” εs = difference between the assignor’s age and that of the spouse η = survivor’s rate δs = percentage of reduction of the survivor’s rate depending on the effect of income requisites r = internal rate of return σ = indexation percentage

−++

11

1

σr

= discount rate

The formula for the calculation of transformation coefficient according to Dini reform is given by:

Cx = x∆

1 with k

Aafms

tvsx

tvsx

x −+

=∆∑=

2,

)(,

)(,

where av(t)

x,s is the average actual value of direct pension given by:

txw

t sx

stxtvsx

r

l

la

−−

=

+

++⋅=∑ σ1

1

0 ,

,)(,

and Av(t)

x,s is the average actual value of the survivor’s pension given by:

Appendix C

37

τε

τ ε

ετ

σδη

σ

−+−−

= −++

−++++

−−

=

+

++⋅⋅⋅⋅Θ⋅⋅

++⋅= ∑∑ 1

1

1

1

1 ,1

,,,

0 ,

,)(,

r

l

lq

r

l

lA

s

s

s

txw

vedstx

vedstx

sstxstx

txw

t sx

stxtvsx

Finacial Survor’s Income Financial Disc. Rate Rate Reducing Disc. Rate Prob. M (o F) Prob. M (o F) Prob. to have Prob. F (o M) lived in t dead in t a family lived in t It is interesting to note that for r = σ e k = 0.5, av(t)

x,s – k coincides with the pensioner’s hope to live till his retirement age. Moreover, this also indicates the number of annual instalments of pension that the pensioner will take. At this point, in order to understand how the Legislator might have arrived at table A of law n. 335/95, it is enough to know the hypotheses made on the parameters that are:

lx,s, qx,s: probabilities of survival and of dying of the year 1990 prepared by ISTAT (source: ISTAT, 1994) lved

x,s: probabilities of survival of the year 1990 prepared by ISTAT and probabilities of another marriage processed by INPS (source: ISTAT, 1994; INPS, 1989) Θx,s: probabilities of leaving the family processed by INPS (source: INPS, 1989) x = 57 – 65 years

=−=+

=fsse

msses 3

3ε

η = 0.6

=−=+

=fsse

msses 7.0

9.0δ

015.111 =

++

δr

=sinstalmentbimonthlyadvanced

sinstalmentannualadvancedk

423.0

0

Appendix C

38

Table 1 – Contribution rates, income ceiling, minimum earnings, minimum earnings for contribution crediting and maximum pension. 1947-2015

TAX RATE (annual average) INCOME CEILING* MONTHLY MINIMUM EARNINGS Min x contrib. crediting Maximum pension YEAR Employee** Farmer*** Artisan*** Trader*** Employee Employee**** Farmer Artisan Trader Farmer-Artisan-Trader All Groups 1947 22,44 L. 3.118.000 L. 3.500 L. 3.500 1948 26,35 L. 5.054.000 L. 3.500 L. 3.500 1949 20,02 L. 5.352.000 L. 3.500 L. 3.500 1950 20,02 L. 5.432.000 L. 3.500 L. 3.500 1951 21,52 L. 5.361.000 L. 3.500 L. 3.500 1952 13,29 L. 5.881.000 L. 3.500 L. 3.500 1953 9,18 L. 6.128.000 L. 3.500 L. 3.500 1954 9,18 L. 6.244.000 L. 3.500 L. 3.500 1955 9,25 L. 6.413.000 L. 3.500 L. 3.500 1956 9,38 L. 6.593.000 L. 3.500 L. 3.500 1957 9,38 14,00 L. 6.923.000 L. 5.000 L. 3.500 1958 11,77 14,00 L. 7.055.000 L. 6.269 L. 3.500 1959 11,76 14,00 12,00 L. 7.394.000 L. 6.500 L. 3.500 1960 15,91 14,00 12,00 L. 7.364.000 L. 6.500 L. 3.500 1961 15,91 14,00 12,00 L. 7.563.000 L. 6.500 L. 3.500 1962 19,28 14,00 12,00 L. 7.782.000 L. 9.462 L. 7.000 1963 22,03 14,00 12,00 L. 8.179.000 L. 12.000 L. 10.000 1964 19,01 14,00 12,00 L. 8.792.000 L. 12.000 L. 10.000 1965 18,71 14,00 12,00 12,00 L. 9.311.000 L. 15.600 L. 12.600 1966 18,56 14,00 12,00 12,00 L. 9.711.000 L. 15.600 L. 12.600 1967 18,91 14,00 12,00 12,00 L. 9.905.000 L. 15.600 L. 12.600 1968 19,60 14,00 12,00 12,00 L. 10.103.000 L. 14.492 L. 13.200 L. 8.191.092 1969 20,56 14,00 12,00 12,00 L. 10.234.000 L. 23.000 L. 18.000 L. 8.191.092 1970 20,56 14,00 12,00 12,00 L. 10.521.000 L. 23.000 L. 18.000 L. 8.191.092 1971 18,91 14,00 12,00 12,00 L. 11.058.000 L. 24.100 L. 18.850 L. 9.735.700 1972 19,01 14,00 12,00 12,00 L. 11.611.000 L. 27.808 L. 22.038 L. 10.156.250 1973 19,01 14,00 12,00 12,00 L. 12.261.000 L. 31.650 L. 25.300 L. 10.669.750 1974 19,95 14,00 12,00 12,00 L. 13.536.000 L. 42.950 L. 34.800 L. 11.629.150 1975 20,73 14,00 12,00 12,00 L. 16.162.000 L. 55.950 L. 52.188 L. 13.018.200 1976 23,31 14,00 12,00 12,00 L. 18.942.000 L. 66.950 L. 66.950 L. 15.133.950 1977 23,31 14,00 12,00 12,00 L. 22.067.000 L. 79.650 L. 76.250 L. 15.052.400 1978 23,31 14,00 12,00 12,00 L. 26.061.000 L. 102.500 L. 91.100 L. 17.741.750 1979 23,31 14,00 12,00 12,00 L. 29.293.000 L. 122.300 L. 103.300 L. 18.489.900 1980 23,89 14,00 12,00 12,00 L. 33.892.000 L. 161.504 L. 136.138 L. 19.386.900 1981 24,01 14,00 12,00 12,00 L. 41.043.000 L. 212.746 L. 177.696 L. 20.827.300 1982 24,16 14,00 12,00 12,00 L. 48.718.000 L. 256.915 L. 208.746 L. 22.163.050 1983 24,51 14,00 12,00 12,00 L. 56.659.000 L. 312.269 L. 245.708 L. 23.564.450 1984 24,51 14,00 12,00 12,00 L. 65.158.000 L. 381.642 L. 277.827 L. 320.200 L. 320.200 L. 4.995.120 L. 24.256.050 1985 24,51 14,00 12,00 12,00 L. 72.065.000 L. 387.712 L. 301.277 L. 345.700 L. 345.700 L. 5.392.920 L. 25.598.950 1986 25,51 14,00 12,00 12,00 L. 78.263.000 L. 409.404 L. 337.323 L. 376.000 L. 376.000 L. 5.865.600 L. 27.844.700 1987 25,51 14,00 12,00 12,00 L. 83.037.000 L. 433.273 L. 355.600 L. 397.400 L. 397.400 L. 6.199.440 L. 29.428.100

Appendix C

39

Table 2 – Contribution rates, income ceiling, minimum earnings, minimum earnings for contribution crediting and maximum pension. 1947-2015

TAX RATE (annual average) INCOME CEILING* MONTHLY MINIMUM EARNINGS Min x contrib. crediting Maximum pension ANNO Employee** Farmer*** Artisan*** Trader*** Employee Employee**** Farmer Artisan Trader Farmer-Artisan-Trader All Groups 1988 25,51 14,00 12,00 12,00 L. 86.857.000 L. 456.115 L. 428.469 L. 418.350 L. 418.350 L. 6.526.260 L. 30.979.988 1989 25,92 14,00 12,00 12,00 L. 91.200.000 L. 497.800 L. 467.669 L. 452.300 L. 452.300 L. 9.407.840 L. 33.492.797 1990 25,92 14,00 12,00 12,00 L. 97.219.000 L. 533.123 L. 500.873 L. 484.500 L. 484.500 L. 10.077.600 L. 35.878.388 1991 26,09 14,75 12,75 12,75 L. 103.149.000 L. 574.127 L. 539.396 L. 519.550 L. 519.550 L. 10.806.640 L. 38.471.186 1992 26,47 15,50 13,75 13,50 L. 109.751.000 L. 610.150 L. 573.242 L. 563.100 L. 563.100 L. 11.712.480 L. 41.695.979 1993 26,97 16,29 14,29 14,29 L. 115.678.000 L. 623.388 L. 585.688 L. 577.750 L. 577.750 L. 12.017.200 L. 42.779.984 1994 26,97 17,00 15,00 15,00 L. 120.536.000 L. 607.912 L. 607.219 L. 602.350 L. 602.350 L. 12.528.880 L. 44.290.402 1995 27,12 17,00 15,00 15,00 L. 125.237.000 L. 626.450 L. 626.450 L. 626.450 L. 626.450 L. 13.030.160 L. 46.062.393 1996 32,70 17,00 15,00 15,00 L. 132.000.000 L. 660.300 L. 660.300 L. 660.300 L. 660.300 L. 13.734.240 L. 48.549.566 1997 32,70 17,20 15,00 15,39 L. 137.148.000 L. 686.050 L. 686.050 L. 686.050 L. 686.050 L. 14.269.840 L. 50.443.159 1998 32,70 17,40 15,80 16,19 L. 139.480.000 L. 697.700 L. 697.700 L. 697.700 L. 697.700 L. 14.512.160 L. 51.300.782 1999 32,70 17,60 16,00 16,39 L. 141.991.000 L. 710.250 L. 710.250 L. 710.250 L. 710.250 L. 14.773.200 L. 52.223.964 2000 32,70 17,80 16,20 16,59 L. 144.263.000 L. 721.600 L. 721.600 L. 721.600 L. 721.600 L. 15.009.280 L. 53.059.162 2001 32,70 18,00 16,40 16,79 L. 148.014.000 L. 740.350 L. 740.350 L. 740.350 L. 740.350 L. 15.399.280 L. 54.438.332 2002 32,70 18,20 16,60 16,99 € 78.507,00 € 392,69 € 392,69 € 392,69 € 392,69 € 8.168,16 € 28.874,56 2003 32,70 18,40 16,80 17,19 € 80.392,00 € 402,12 € 402,11 € 402,12 € 402,12 € 8.364,20 € 29.568,00 2004 32,70 18,60 17,00 17,39 € 81.678,00 € 408,55 € 408,54 € 408,55 € 408,55 € 8.497,84 € 30.040,80 2005 32,70 18,80 17,20 17,59 € 82.985,00 € 415,09 € 415,08 € 415,09 € 415,09 € 8.634,08 € 30.521,60 2006 32,70 19,00 17,40 17,79 € 84.230,00 € 421,32 € 421,31 € 421,32 € 421,32 € 8.763,56 € 30.979,20 2007 32,70 19,00 17,60 17,99 € 85.493,00 € 427,64 € 427,63 € 427,64 € 427,64 € 8.895,12 € 31.444,00 2008 32,70 19,00 17,80 18,19 € 86.775,00 € 434,05 € 434,04 € 434,05 € 434,05 € 9.028,24 € 31.916,00 2009 32,70 19,00 18,00 18,39 € 88.077,00 € 440,56 € 440,55 € 440,56 € 440,56 € 9.163,44 € 32.394,40 2010 32,70 19,00 18,20 18,59 € 89.398,00 € 447,17 € 447,16 € 447,17 € 447,17 € 9.301,24 € 32.880,00 2011 32,70 19,00 18,40 18,79 € 90.739,00 € 453,88 € 453,87 € 453,88 € 453,88 € 9.440,60 € 33.373,60 2012 32,70 19,00 18,60 18,99 € 92.100,00 € 460,69 € 460,68 € 460,69 € 460,69 € 9.582,56 € 33.874,40 2013 32,70 19,00 18,80 19,00 € 93.482,00 € 467,60 € 467,59 € 467,60 € 467,60 € 9.726,08 € 34.382,40 2014 32,70 19,00 19,00 19,00 € 94.884,00 € 474,61 € 474,60 € 474,61 € 474,61 € 9.871,68 € 34.898,40 2015 32,70 19,00 19,00 19,00 € 96.307,00 € 481,73 € 481,72 € 481,73 € 481,73 € 10.019,88 € 35.421,60

Notes * Contribution (Dini) ** Since 1993: +1% above the 1 income range *** Age > 21 years - Before 1990: hypothesis of the law **** Service > 780 weeks

Source Sole24ore Sole24ore Sole24ore Sole24ore INPS Sole24ore Sole24ore Sole24ore Sole24ore Sole24ore INPS

INPS INPS INPS INPS L.335/95 L.485/72 L.485/72 L.335/95 L.335/95 L.638/83 art.7 c1 L. 488/68 L.335/95 L.233/90 L.233/90 L.233/90 L.114/74 L.114/74 L.389/89 art.1 c2 L. 153/69 D.Lgs 207/96 L.160/75 D.P.R.325/72 DPCM 16/12/89 art 2 L.662/96 L.33/80 L.33/80 L.449/97 art.59 L.730/83 art.21 L.730/83 L.67/88 art.21 L.41/86 D.L.384/92 art.2 L140/85 art.7

L.438/92 D.L.384/92 L.544/88 L.438/92 L.388/00

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