Saving Decisions and Fiscal Incentives: ASpanish Panel Based Analysis*

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Economics Working Paper 41

Saving Decisions and Fiscal Incentives: A Spanish Panel Based Analysis*

M~ Antonia Monés t and

Eva Venturat June 21, 1993

Keywords: Savings, Fiscal Incentives, Panel Data.

Journal o/ Economic Literature classification: H31, D91, C33, C34.

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Abstract

The objective oí this papel is to examine the response oí fiscally incentivated savings to income, wealth and a series oí individual characteristics. We use a multiple steps estimation strategy. Our dependent variable is double censored. Thereíore, we first apply a Tobit technique to predict desired savings, real by year. Then we stack these predictions and build a system oí simultaneous equations that is estimated taking into consideration individual effects and cross-equation correlations induced by panel temporal structure and measurement errors in the dependent variables.

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1 Introd uction

Empirical studies of household saving behavior have focused primarily on the total level of savings rather than its allocation among different types of assets. There are, however, a few empirical studies of the composition of household portfolios using individual data. For example, Blume and Friend (1975), Feldstein (1976), and Projector and Weiss (1966) used the 1962 Federal Reserve Board data and Uhler and Cragg (1971) used data from the 1960-62 Michigan Surveys of Consumer Finances. King and Leape (1984) use the 1978 Survey of Consumer Finances De- cisions conducted by SRI International. Also, Venti and Wise (1986) analyze IRA savings with the 1983 Survey of Consumer Finances, and so do Feenberg and Skin- ner (1989), using the IRSjUniversity of Michigan tax payer sample for in come tax returns during 1980-84.

The purpose of this study is to find and quantify the relationship between fiscally incentivated savings and a set of explanatory variables such as disposable income, wealth, marginal tax rates and several household characteristics, for a comparatively large period of time!.

Governments forego an important amount of taxes in arder to stimulate certain types of household savings. In Spain, tax incentives are basically oriented to housing and life and retirement insurance related saving2. If one looks at the characteristics these assets have in common, it becomes clear that the focus of the policy is to encourage people to attain a certain level of income in the future, stimulating them to do Borne precautionary saving to face uncertaintYi or simply to offset the impatience of certain households. The nature of the incentivated assets and particularly their lack of liquidity does not let us consider them as perfect substitutes of other types of assets. Their impact on the supply of loanable funds is also small compared to other assets.

Whether the consequence of tax incentives is simply the substitution between incentivated and non incentivated assets, or whether there is a net increase in total savings is a relevant question that has been addressed in several papers. If evidence is not found in favor of a net increase in savings, then it is possible that the social gains associated to that policy do not compensate for its fiscal cost as well as for the distortions in the asset market that it necessarily implies.

On the other hand, tax deductions on personal savings are meant to offset the negative effect of capital returns taxation on households average propensity to save

1 Most of the studies cited above use cross-section data or short panda. The maximum length is five years in Feenberg and Skinner work.

2The government has also encouraged saving in cert&Ín types of securities, starting in 1987.

More recently, returns from shares on investment funda also receive a special fiscal treatment, since they are taxed only as capital gains and only when they are soldo

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out of disposa.ble income. But the a.va.ila.ble empirica.l evidence is not conclusive a.t this point3.

Our exercise do es not a.llow us to a.ddress some of these questions, but it helps us to study the response of ta.x pa.yers to the incentive, a.nd which of these ta.x pa.yers a.re likely to be the most benefited. -

Although the decisions of how much to sa.ve a.nd which a.ssets to buy a.re simul- ta.neous, it is convenient to think of them a.s two sepa.ra.te questions. Then, we ma.y believe tha.t first the household decides how much to sa.ve. Or wha.t is the sa.me, how much to consume. Second, the choice a.mong different a.ssets ta.kes pla.ce.

According to the life-cyclejperma.nent-income (LCjPI) hypothesis, the first decision will depend on intertempora.l preferences ,huma.n wea.lth (mea.sured a.s the expected present va.lue of current a.nd future a.fter-ta.x la.bor income) a.nd current a.sset wea.lth. The choice of a.ssets ha.s to be ma.de ta.king into considera.tion their differences in returns.

We consider two types of a.ssets (or sa.vings). Once of them entitles fa.milies to a.n in come ta.x reba.te, the other do es noto

The da.ta. used in the estima.tions consists of a. pa.nel of spa.nish income ta.x pa.yers running from 1982 to 1990, a.nd conta.ins informa.tion on income , ta.x ra.tes, a.nd ta.x deductions for severa.l concepts. In pa.rticula.r, we know -to certa.in extent- the a.mount of money a.lloca.ted to some pa.rticula.r types of sa.vings: purcha.ses of houses, life insura.nce contra.cts, certa.in securities a.nd retirement pla.ns.

We ha.ve opted for a.n a.d hoc formula.tion of the tota.l sa.vings function, since the a.ssumptions tha.t would be required to derive a. testa.ble equa.tion ba.sed on the joint LCjPI a.nd ra.tiona.l expecta.tions hypothesis a.re toa restrictive a.nd citen unrea.listic.

In the next section we expla.in how to a.rrive to a. rea.sona.ble model of tota.l consumption (sa.ving). The following section describes how the household discrimina.tes a.mong two types of sa.ving instruments. The fourth section describes the da.ta.

in some deta.il a.nd the fifth one comments on the method used in the estima.tions.

Fina.lly, we report the results a.nd dra.w some conclusions.

2 Modelization of the savings equation

The LC/PI hypothesis is forward-looking in nature. Since future is uncertain, one often requires quite sensible assumptions to be able to estimate the models based on that hypothesis.

3In the spanish case there is Borne evidence or a negative effect or tax ratea on savings. See Zabalsa and Andrés (1991) or Molinu and Taguas (1991) ror evidence on time series data, and Monés, Salas and Ventura (1992) ror panel data evaluation.

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The fact that future labor is stocha.stic, makes not possible to explicitly derive a closed-form solution for the optimal level of consumption, even under rather dema.nding a.ssumptions.

A quite usual starting point is to write the optimal consumption rule for a household as

Ci(t)

= -y(Wi(t) + Hi(t))

₍₁₎

where Ci(t) is total consumption oí household i at time t, Wi(t) is financial wealth (assets) oí household i at time t, and Hi( t) is human wealth (present dis- counted value oí current and íuture after-ta.x labor income) oí household i at time t. The 'Y parameter is the propensity to consume out oí liíetime resources, and will usually depend on preíerences and particularly on the age oí the household head. This consumption íunction can be derived írom a standard deterministic intertemporal utility ma.ximization problem with time-additive preíerences and in- stantaneous utility íunction oí the CRA class. There permanent in come is defined as the interest rate times the liíetime resources (Wi(t) + Hi(t)).

The main problem with this íormulation is that neither human wealth nor permanent income is observable. Since they depend on the household 's expectations about íuture labor income, any variable that helps predict it will show up significant in estimation. One could think oí explicitly íormulating the stochastic process íor labor in come and find a closed íorm representation íor human wealth as a distributed lag oí current and past aíter-ta.x labor income. But with panel data the number oí lags that can be used in estimation is usually very small. On top oí it, ta.xing policies are subject to changes that are difficult to íoresee.

Also, income ta.x is a nonlinear íunction oí the household 's income. In particular , ta.xes paid depend also on capital income, which is a íunction oí past savings.

Thereíore, aíter-ta.x íuture labor income will depend on the time path oí savings.

Human wealth then depends on current and past labor in come (through the explicit íormulation oí an stochastic procesa íor it), and also on assets.

Furthermore, the derivation oí a expression like 1 assumes that the household has no subjective uncertainty about íuture aíter-ta.x labor income. Otherwise it is not possible to obtain a convenient closed solution like equation 1.

Finally, the ratea oí return oí risky assets are stochastic. The derivation oí equation 1 is based on the assumption that interest ratea are fixed. Since this is not the case, the derivation oí a similar closed-íorm solution becomes impossible unless one is willing to impose some extremely restrictive assumptions ayer the interest ratea and labor in come joint distribution.

The íoregoing arguments suggest that any attempt to explicitly íormulate the~

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optimal consumption rule as a íunction oí the variables that are typically available in panel data is a difficult task and is bound to be misspecified. On one hand, is almost impossible to derive a closed íorm solution that takes into consideration the íact that interest ratea are stochastic, that after-tax income is a non-linear íunction oí savings, and that labor in come is alBO uncertain. Add the íact that the liíetime span oí an individual is alBO uncertain, and that utility íunctions can be household specific, depending on íamily composition, age oí the head, and other unobservable variables. On the other hand, even ií we could derive a closed íorm solution (which would require imposing Borne quite unrealistic assumptions), it would be difficult or impossible to find adequate data to estimate it.

At this point, it might be worthy to explore Borne alternative way oí dealing with the problem. In this papel we íollow the lead oí Hayashi (1982) and do not attempt to estimate any "structural" equation íor consumption deriving írom the household 's intertemporal optimization.

The idea consista oí making optimal consumption plana be a íunction oí the variables that are available in our data. The expression should be considered as the least squares projection oí consumption on these variables. We write

c.(t) = X.(t).a + E.(t)

where X,(t) is the matrix of ava.ilable variables and f,(t) is uncorrelated with a.ny predetermined variable in X,(t). The error term summarizes household specific components a.mong other things. Equation 2 can be viewed a.s the reduced form representation of the optima.l consumption for the household's intertempora.l optimization problem. Because of the non-theoretica.l nature of the approach is difficult to give an economic interpretation to each of the regression coefficients. However, one thing is clear: X,(t)/3 is the optima.l consumption for a typica.l household whose o bserved characteristic are summarized by X ,( t).

Once a expression for consumption is found, savings can be obta.ined a.s the difference between disposable in come a.nd consumption. That is

s.(t) = yf(t) - Ci(t) = X.(t)"Y + fi(t)

Here, the 'Y para.meters a.re identical to the (3 ones with the exception oí the coefficient oí disposa.ble income4, which we na.med yt(t).

Next, we will distinguish between two types oí sa.vings a.ccording to whether they are fisca.1ly incentiva.ted or noto

'We implicitly a8sume that disposable income is included in the set oí variables that explain consumption, X¡(t).

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Choosing where to save 3

Once the household has decided how much to consume and how much to save, it has to a.11ocate these savings among several types oí a.ssets. Here we will consider only two kinds: instruments related to the fisca.11y incentiva.ted savings, and the rest oí instruments.

In that section we íollow the standard Capital Asset Pricing Model (CAPM), and we make the decision oí where to save depend on the differentials on returns and riskness oí the two different types oí composite savings.

Let rf(t) denote the risk-íree a.sset return at time t, rl(t) and r2(t) being the returns on two alternative risky assets. Let Pb(t) be the market price oí risk at time t and b1(t) and b2(t) be asset 1 and a.sset 2 mea.sure oí risk, respectively. Under the CAPM assumptions and in a world without ta.xes, we can write

rl(t) - r¡(t) r2(t) - r¡(t)

=

^b1(t)Pb(t)

=

b2(t)Pb(t) (4)

That is, each asset's risk prime (the difference between the risk-free asset return and its own return) is proportional to its riskness.

The model can be relaxed to encompass the fact that the agents may take into consideration other aspects besides returns and riskness when choosing their portfolio. These other characteristics are incorporated in the preferences of the households and will have an additive effect on the above relationship between risk and returns. We now write, for a particular household,

rl(t) - r¡(t) r2(t) - r¡(t)

alí

+ b1(t)Pb(t)

a2í

+ b2(t)Pb(t)

=

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where al, and a2, represent the effect of the agents preferences on the demand for assets 1 and 2 respectively.

Subtracting one equation from the other, we get

Tl(t)

-

^T2(t)

=

^(ali

-

a2i)

+ Pb(t)(bl(t) - b2(t))

₍₆₎

The CAPM says that 6 holds true for each individual. However, it is difficult to

accept that everyone has the same preferences and therefore that the term ali -

a2i

is the same for all households. Furthermore, there are transaction costs associated

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to buying and keeping the portfolio.

In general, the right hand si de of equation 6 will be individual or household specific. Also, the left hand side can be different for each household. Two are the reasons for that assessment. First, it should be written in terms of expectations, and those can be individua.l1y different. Second, we should rea.l1y deal with the after-tax returns, and those certainly are individual specific.

Therefore, a household should be indifferent between the two types of savings if

{rl(t) - r2(t)} {l- T¡(t)} + Ó(t) - K¡(t) = o

where

Ki(t) =

^(ali

-

a2i)

+ Pb(t)(b1(t) - b2(t))

Here T¡(t) represents the marginal ta.x late oí individual i at time tand ó(t) is the ma.ximum ta.x rebate allowed at time t. The return on asset 1 is rl(t)(l-T¡(t))+ó(t), since new purchases oí this asset entitle the owner to a ta.x rebate. The retum oí the other composite asset is simply r2(t)(1 - T¡(t)).

If 7 do es not hold with equality, there is an arbitrage opportunity. Then the household will choose asset 1 when 7 is greater than O and asset 2 ií the relationship is negative.

Summarizing, once total savings have been decided, the choice oí the portíolio depends on their assets relative retumBo We will write

Sl,(t)

= F( {rl(t) - r2(t)} {l - T,(t)} - K,(t) + ó(t), S,(t))

The exact functiona.1 form is given in section 5.

4 Description of the data

We use a data set provided by the Instituto de Estudios Fiscales, a research or- ga.nism dependent from the Spanish Ministry of Finances. It consists of a panel of income ta.x payers running from 1982 to our days and it conta.ins a.l1 the informa.- tion provided in the spa.nish income ta.x summary formo The number of individuals in the original panel is above 100,000 and is growing steadily in accordance to the population to be represented. From a sample of 2100 individuals, we select a subsample of 685 individuals which are observed every year from 1982 to 1990.

One of the advantages of our data set is that the reported income variables are more reliable than in other spanish panel data sets.. Also, we can observe the same

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household through several yea.rs, unlike other da.ta. sets5

On the other ha.nd, given the na.ture oíthe da.ta., we ca.n not observe consumption or total sa.vings like in other pa.nels. We ca.n neither observe the a.ge oí the hea.d oí the household. We a.re nonetheless a.ble to extra.ct a. mea.sure oí fisca.l1y incentiva.ted sa.vings a.nd to discrimina.te between two groups oí a.ge. The a.ge distinction is ba.sed on a. ta.x credit tha.t a.pplies to individuals older tha.n 696.

We now proceed to list a.nd describe the ma.in household iníorma.tion in the pa.nel.

.

Gross and net earned ordinary income, distinguishing among dependent labor, capital, entrepreneurial, proíessional and agricultural sources oí labor income.

There are two types oí capital income: financia! and real state7.

.

Non ordina.ry income. That is, basica.l1y, capital ga.ins or losses indexed by inflation and the number oí years oí ownership oí the asset.

.

Current income, as the sum oí ordinary and non ordina.ry income.

.

Taxa.ble income, which differs from current income beca.use it a.llows tax pa.yers to offset nega.tive income from former exercises.

.

Marginal and average tax rates before tax deductions.

.

Tax deductions. The Spanish system establishes deduction for the following concepts8.

- Income accumulation in the family unit. This deduction applies when there is more than one in come earner in the household9.

- Familiar charges. That includes number oí children, ancestors and disabled persons in charge oí the tu payers.

- Old age. Tu payers over 69 are entitled to this kind oí deduction.

'Such as the "Encuesta. Continua. de Presupuestos FImilia.res" I which is a. pa.nel with repla.ce- ment in which the the sa.me ía.mily is observed a. ma.ximum oí eight qua.rters in which income is measured with a. considera.ble a.mount oí error. Another survey, the "Encuesta. de Presupuestos FImilia.res" is not a. pa.nel.

8This implies tha.t we a.re a.ble to identiíy individuals a.ged 62 a.nd older in 1982

TRea.l sta.te income is either the imputed house rent (in case oí owner occupied houses) or the a.ctual rent perceived.

'We only mention the most importa.nt anea.

DSince 1988 ma.rried couples ca.n fi1l the ta.x íorms sepa.ra.tely (see ta.ble 1). We ha.ve chosen to a.dd the iníorma.tion to maintain the consistency oí the da.ta.. Tha.t required reestima.ting ma.rginal a.nd a.vera.ge ta.x ra.tes a.ccording to the sum oí ta.xa.ble in comes a.nd the ta.x yields oí the members oíthe household.

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-

Dividends. A household that has earned dividend income during the year is a.llowed to subtract a percentage oí this income to reduce double ta.xation.

- Entrepreneurial investment. This is intended to stimulate the reinvest- ment of entrepreneurial profits.

- Savings. The spanish fiscal system currently favor s three types of domes- tic saving instruments: housing, life insurance contracts and retirement planslO. Payment of life insurance premia and purchases oí houses give right to a cut in taxes paidll. The tax incentive on retirement plans has a different nature: in come allocated to these assets is tax free within a limit12. Table 2 shows the tax cuts percentages applied during the nine years of OUT sample.

.

Disposable income. It is defined as the difference between current income and total taxes paid.

.

Wealth. This variable is a proxy we build írom iníormation on capital income.

We have capita.lized net real state income at the rental value oí the property scheduled íor owner occupation1314. OUT estimates oí fixed returns securities holdings are the result oí subtracting earned dividends írom total financia.!

capital income. They have been capita.lized at the yearly current rate oí return on one year maturity government debt. Variable returns income is capita.lized at ha.lf oí the íormer rateo

In a system in which the dependent variable is fiscaliy incentivated savings, disposable income is an endogenous variable since it depends on the amount oí the deduction to which they entitle. Thereíore, it will be necessary to instrument it.

To that purpose, we will use current beíore taxes income -which shows a very high correlation with disposable income- jointly with other exogenous variables included in the specification oí the econometric modelo

Table 4 presents the mean values oí ali these variables, by year. These variables are consistent with the íact that the spanish economy was in a recession up to 1984

l°Retirement pla.ns are a source oí deduction only alter 1987. Beíore that year, holding certain type oí securities alBO gave right to deduction.

11There is a limit on the amount oí the deduction, lee Table 2.

12The tax payment is delayed until the moment oí reception oí retirement íunds, when tax rates will be presumably lower.

13This rental value is estimated by the fiscal authorities as the 3% oí the house value beíore 1987 a.nd 2% thereafter.

l' Although there is a different fiscal treatment oí savings, according to whether they are allocated to ñxed or variable returns securities, we ca.n not observe them separately.

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and that it was íollowed by a strong expansion. The increase in marginal tu rates is explained by increases in real income, fiscal drag15, and severallegal changes. The average tu rate has alBO increased, but leas steadily. This is due to the combined effect oí changes in the marginal tu rate and in the types and percentages oí tu deductions. One can alBO observe an increasing wealth pattern.

The largest volume oí incentivated savings is allocated to housing investment.

Its de crease in the first years oí analysis is due to the íact there was no limit to deduction beíore 1983, while after this date a joint upper limit íor this and other types oí savings was introduced. Its maximum was attained in 1987, when an economic boom that increased housing demand was combined with high tu cuts íor purchases oí non owner occupied houses.

Savings in securities reached their maximum in 1986. The deduction applying to banda holdings disappeared in 1987, while variable returns securities lost the fiscal favor in 1988. Such tu cuts were replaced by an incentive to the purchase oí retirement plans. Table 4 suggests that the new asset has not received much attention by investors.

Our dependent variable is the sum oí the three types oí fiscally incentivated savings: housing, liíe insurance and securities. It is censored upwards, due to the limits imposed by law to the right oí deduction. More important, there is a high percentage oí households with zero observed savings. Table 5 shows the number oí íamily units íor which these limita are effective.

5 Econometric considerations

The system oí equations we want to estimate is:

si(l)

"i(2)

=

^.80

+

(31 [P(1)(1

-

tm¡(1)) + 6(1)] + f32yd¡(1) + (33w.(1) + X.(1)r + v.(1)

=

^.80

+

(31 [P(2)( 1

-

tm¡(2)) + 6(2)] + (3~yd¡(2) + (33w.(2) + X.(2)r + v.(2)

",(T) =

^.80+.81 [P(T)(l - tm¡(T)) + 6(T)] + .82yd¡(T) + .83Wi(T) + Xi(T)r + vi(T) where

S¡(t) p(t)

tm¡( t) ó(t)

represents total fisca.l1y incentivated savings at time t,

represents the difference between real beíore- tax marginal returns oí the two kind oí savings contemplated in this work,

is the marginal tax rate íaced by household i at time t, is the maximum percentual tax-rebate a.l1owed at time t.

15The tariff is not automaticalIy corrected for inflation.

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ydi( t) Wi(t) Xi(t)

is disposable income (including the ta.x-rebate) oí ta.x payer i at time t, is our estímate oí a.sset wea.lth oí household i at time t,

is a vector oí individua.! characteristics oí ta.x payer i at time t

- num-

ber oí children, majar source oí income, entrepreneuria.l investment or old age among others-, a.nd

is a composite error including individua.! and time effects.

That is,

V¡(t)

=

^Q¡

+ v(t) +

U¡(t)

The differentia.ls in returns will be estimated as time varying coefficients. The maximum va.lue oí the allowance parameter ó(t) does not change much ayer the sample time span, and could be jointly estimated with the time dummies ií we choose to treat time effects as fixed effects.

The system becomes

",(1) =.80 + 11(1) + .B16(1) + 6(1)(1 - tm¡(I)) + .B~yd¡(I) + .B3w,(I) + X,(I)r + a, + u¡(I)

8,(2) =.80 + 1/(2) + fJ16(2) + 6(2)(1

-

tTni(2))- + fJ2Yd.:(2) + fJ3w,(2) + X,(2)r + Q, + Ui(2)

"i(T)

=

Po + v(T) +.816(T) +8(T)(1-tTni (T)) +.82y~(T) +.83Wi(T +X¡(T)r+Q¡ +u¡(T) Given that we will never observe negative fisca.l1y incentiva.ted saving (the on1y information ava.ilable in the sample refers to current purchases of these savings instruments) , the dependent variables should be treated as censored variables. Fur- thermore, since there is a.n upper limit to the amount of the deduction for savings, the variable is in fact double censored. That is, let si(t) be the latent variable (desired leve! of savings), a.nd write

+

.Bo + v(l) + .816(1) + 9(1)(1

-

t1ni(I» + .83yd¡(I) + .83U1,(1) + X,(I)r + Q, + u¡(I)

.Bo + v(2) + .816(2) + 9(2)(1 - t1ni(2» + .83yd¡(2) + .83U1,(2) + X,(2)r + Q, + u¡(2)

-+-

Po + II(T) + .816(T) + 8(T)(1

-

t7ni(T)) + .82y~(T) + .83w,(T) + X,(T)r + Q, +

Ui(T) (9)

=

+

with observed savings as

ln

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SiCt)

= o if s:(t) < o

= s:(t) if s:(t) E [O, L¡(t)]

= L¡(t) if s:(t) > L¡(t)t = 1,2, ,T

where L¡(t) is the upper limit for savings and is proportional to taxable income.

Furthermore, individual effects might be important and should be taken care oí.

Ií we could as sume that the system explanatory variables are exogenous16 relative to the composite error a¡+u¡(t), letting U¡ be normally distributed and making use oí 10, our system could be estimated by maximum likelihood. However, evaluation oí the likelihood íunction would require computing multiple integrals oí arder T, which would result in a quite intractable problem17. It would still be possible to consistently estimate the parameters oí interest by using some robust equation by equation method to get T first step estimates. They would then be combined by a minimum distance method in a unique estimator,

In our model, it seems more appropriate to consider that individual effects are not independent oí the explanatory variables. Although a number oí estimation techniques conditional on the individual effect could be tried18, we choose a simpler method which relies on speciíying the conditional distribution oí the individual effects, given the explanatory variables19,

Let 9 and 10 describe the system we want to estimate and assume that

+ ).TZiT]

o.¡IZ¡ '"

N[>'~Z¡l + >'~Z¡2 +

_(11' Assume alBO that 1L¡IZ¡ '"

N(O, n). Here Z¡ includes the variables used to instru-

mentalize disposable income, but not disposable in come itself.

Next, use 11 to write

Si(t)

=

^11"0

+ 1I"~Zil + . . + 'lrTZiT + f¡(t) t = 1,. .., T

18This is not the case in OUt model, since disposable income is endogenous.

17We could restrict the covariance matrix of U¡ and write the likelihood function in a more convenient way, but computation of the solution would still be complicated and is would sensible to the specification of the covariance matrix.

18See for example Neyman and Scott (1948) , Andersen (1973) and Chamberlain (1984) on maximum likelihood estimation, or Mansn (1987) on the method of acotes. The maximum likelihood technique requires finding a sufficient statistic to obtain consistent estimates, and the method of acotes does not allow us to obtain asymptotic standard errara in the usual formo

18See Chamberlain (1980)

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jointly normally distributed. Although efficient estima.tion oí the system is subject to the sa.me computa.tiona.l problems we described beíore, we ca.n find estima.tors oí the {J pa.ra.meters ba.sed on consistent estima.tes oí the 7r pa.ra.meters, obta.ined írom fitting ea.ch period 's censored regression sepa.ra.tely.

One possibility is to use Cha.mberla.in (1980) minimum dista.nce estima.tor. This a.mounts to minimizing

d({3, >')

=

[ir - 11"({3, >')]'V-1[ir - 11"({3, >')]

Rere ir is a consistent estimator oí 'K and the optima.l choice oí y-l is a consistent estimate oí the asymptotic variance oí ir.

Rowever, direct minimization oí the distance íunction presents severa.l disad- vantages. One has to jointly estimate the .8 and >. parameters when we are only interested in the

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ones. Furthermore, we have to impose explicit restrictions on the 'K coefficients, a.nd sometimes these will be nonlinear making necessary to resort to iterative estimation techniques.

An a.lternative approach

,

outlined in Arella.no (1990), consist oí applying the Tobit technique to equation 12

,

year by year. The consistently predicted savings are then used in place oí the censored dependent variable. Next, we ca.lculate each variable's individua.l mea.n and substract it írom the variable to eliminate the individua.l effects. We estimate the resulting individua.l-mea.n corrected system

Si(j)

= ií(j) + .816(j) +

+.b'2Yd,(j) +

.b'3W,(j)

+ X,(j)r + tL,(j) j = 1, . . ., T

which can be rewritten as

=

where

Qo

=

((j) =

íi(1) + .815(1) a.nd

íi(j) + .815(j) -

íi(1) - .815(1)

=

v(j) - v(1)

+ .81(6(j) - 6(1» (13)

12

t*i

(15)

Since disposable in come is an endogenous variable, we need to instrumentalize it. Furthermore, we are substituting the dependent variable by its estimation and this introduces measurement error. Demeaning the variables will then add error correlation across equations.

To account for these two facts, we will use the method of three stages least squares on the differenced variables system. We will alBO compare these estimates with the ones obtained with a method that does not take into consideration the cross equations correlations. To evaluate the importante of individual effects, we alBO present the coefficients of a system for which demeaninJ( does not take place.

6 Resluts

The first stage estimation consists oí cross-section Tobit regressions íor every year oí the sample. We then take the predicted va.lues íor savings and use them as dependent variables in subsequent stages oí the estimation. Due to their merely instrumenta.l character, we do not report the results oí the Tobit regressions20.

Tables 7 and 8 show two a.lternative sets oí system estimates. The first one assumes that there are individua.l effects -correlated with the explanatory variables-, and we subtract individua.l mea.ns írom a.l1 the variables to eliminate them. In Table 8 we do not consider individua.l effects.

Each oí these tables reports a.lso two types oí results. The first two columns correspond to estimates oí the coefficients and their t-statistics, a.nd have been ca.lculated taking into consideration cross-equation correlation. We have used the method oí three stages least squares21 (3SLS). The other two columns are obta.ined a.fter applying an instrumenta.l variables (IV) method that assumes that there is not heteroscedasticity or autocorrelation in the errors.

The intercept coefficient in the individua.l-mean corrected estimations is a mix- ture oí year dummies and ma.ximum deduction differences (see equation 13). It is not significa.nt, as expected.

Fixed annua.l effects have a.lso a very sma.l1 explanatory power. The negative coefficient in 1987 is likely a consequence oí the lose oí the right to deduction on certa.in securities, but it a.lso refiects a de crease in the average propensity oí tota.l (not just the fisca.l1y incentiva.ted) savings to disposable income.

As one could predict, disposable in come shows the most significant coefficient.

2°They ar.. oí courBe available upon requeBt.

21The method iB uymptotically equivalent to íull iníormation maximum likelihood, although iB euier to implemento Satorra and Neudecker (1993) prove that íull iníormation maximum likelihood iB optimal in these nnd oí BetupB.

(16)

The estimated marginal propensity to save out of disposable income is 0,1522.

Wealth accumulation affects savings negatively. The sensitivity is nonetheless small, since an increase in wealth of one million pesetas yields a de crease in savings of less than five thousand pesetas23. This is consistent with the LCjPI hypothesis, which predicts that households will save to hedge themselves from a de crease in labor in come in the last periods of their lives. Wealth therefore will increase until it reaches the desired level, and savings will become negative thereafter.

The LCjPI hypothesis is alBO corroborated by the significantly negative coefficient of the elder group dummy.

The coefficients of the variables labeled MARGINAL82 to MARGINAL90 demand for Borne explanation. Each one of these variables is defined as one minus the marginal tax rate faced by the household. Their coefficients are the product of a parameter and a real before taxes interest rates differential. Since we do not observe the latter, we have to estimate them jointly with the fJ parameter. The estimates have a positive sign (except for 1982), which indicates that for a given difference in return rates in year t, an increase in the marginal tax rate induces a decrease in incentivated savings. To emphasize the importance of these variables in explaining those savings, we have omitted them in the estimations reported in Table 9. The results show a poorer fit and sensible differences in coefficients, thus indicating a significant role of the marginal tax rates on savings decisions.

The dummies that allow us to distinguish among different rnain sources of income are mostly significant. Entrepreneurs, professionals, farmers and earners of housing related renta exhibit a higher propensity to save than the excluded socio- professional category, dependent labor.

The perception of dividends does not help to explain these type of savings, and neither do es entrepreneurial investment. The number of children does not seem to be important either. Having ancestors in charge is responsible for Borne negative effect on the family's saving record. This might be due to an age factor. The period in which most households report children in charge coincides with the one in which labor income is reaching its maximum.

One alBO observes that individual effects are important in arder to explain savings. Looking at tables 7 and 8, we realize Borne differences in the value and significance of the coefficients. The values and t-statistics of variables such as dis- pasable income, wealth , or marginals are larger when no individual effects are considered, but the rest of estimates are very sensible to the specification of the

22 Average propensity to lave out oí disposable income has been a little above 11 % until1986

-

and lower afterwards.

23The values range between 1343 and 4891 pesetas, depending on which estimation method we use.

14

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modelo Basica.l1y, a.l1 the socio-proíessional and ía.mily characteristics change, their sign included.

These two tables a.l1ow us to evaluate the importante oí correcting the estimations íor cross-equation error correlation. An instrumental variables technique wa.s applied with and without correcting íor individual effects. The income, wealth and marginal ta.x rate coefficients are very similar although a little larger in ab- solute value when IV estimation is implemented. Aga.in, some socio-proíessional and ía.mily characteristics dummies change value and even signo Given that our dependent variable is mea.sured with error, cross-equation correlation is present when we use an individual-mean correction to eliminate the individual effects. We per- íormed the íollowing test: we calculated the individual effects íor each household as average predicted savings minus the average explanatory variables vector times the estimated coefficients oí Table 7. Then we did a regression oí these individual effects on a.l1 the explanatory variables oí the system and tested the null hypothesis that the coefficients oí that regression

were a.l1 O. The hypothesis wa.s ea.sily rejected24. Table 6 shows the correla...

tion matrix that results írom applying two stages lea.st squares to each equation separately. It can be observed that correlation is present and quite strong, specia.l1y a.mong the la.st years equation errors.

7 Concluding Remarks

Our resulta show that for a given value of disposable income, higher marginal ta.x ratea or higher wealth levels reduce ta.x incentiva.ted savings.

The former result might seem counterintuitive at first. One would believe that the ta.x incentive should operate more strongly at higher marginal ta.x ratea.

However, we should realize that this is not the correct interpretation. Higher dis- pasable income is a.ssociated to higher marginal ta.x ratea. But once the disposable income effect is ta.ken care off, the positive coefficient on marginal ratea could be refiecting the fact that at Borne point households are interested in diversifying their portfolios, and fiscally incentiva.ted saving looses part of its initial attractiveness.

Wealth accumulation playa a negative role on incentiva.ted savings. The result can be understood a.s a corroboration of the LC/PI hypothesis. Nonetheless

,

it is alBO plausible that rich people savings are allocated preferably to non incentiva.ted saving. In fact, wealthy people alrea.dy own a house, and do es not have that much need for life or retirement insurance.

Older households show alower saving profile than the rest of the sample. Aga.in,

2tThe F statistic was 1327 with 595 degrees oí freedom.

(18)

this result is conditioned by the type of savings being examined. Particularly, it is sensible to expect that people ayer 62 of age are not oriented into buying a house or a retirement plan.

Additional variables included in the system have little explanatory power, except for the main sources of income dummies. Entrepreneurs and professionals show a higher propensity to save on incentivated assets than the employees. One possible interpretation relies on the fact that entrepreneurs and professionals are subject to more uncertainty about future labor income.

In summary, the marginal propensity to save on incentivated assets out of dis- pasable in come is high, but the nature of these assets puts a limit on the amount of savings devoted to them. Once a household owns a house and pays a reasonable annual premium for life and retirement insurance, extra savings are going to be oriented to the purchase of more liquid assets to adjust to a more diversified portfolio composition. This argument would explain the negative sign of both variables WEALTH and ELDER.

Also, we should take into account that individual preferences play an important role since people may have different feelings about these particular types of assets.

Regarding the methodology used in estimation, we have presented Borne evidence in favor of considering individual effects that are correlated with the explanatory variables and of correcting for cross-equation correlations.

16

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References

ANDERSEN, E. B. (1973). "Condicional inference and models for measuring. Men.

talhygiejnisk Forsknings Institut. Copenhagen.

ARELLANO, M. (1989), ClOn the efficient estimation ofsimultaneous equations with covariance restrictions," Journal o/ Econometrics, 42:247-265.

ARELLANO,

M.

^AND

O.

BOVER (1990), "La econometria de los datos de panel,"

IntJestigaciones Económicas, 1:3-45, (Segunda época).

BLUNE, M. AND l. FRIEND (1975), "The a.sset structure oí individual portíolios and Borne irnplications íor utility íunctions," Joumal o/ Finance, 30:585-603.

CHAMBERLAIN, G. (1980), "Ana.lysis oí covariance with qua.litative data," Review o/ Economic Studies, 47:225-238.

- (1984). "Panel data, " in Griliches, Z. and M.D. Intrilligator, editors, Handbook of Econometrics. EIsevier Science. vol. n.

FEENBERG,

D.

AND J. SKINNER (1989). "Sources ofIRA saving," Working Papel 2845, NBER.

FELDSTEIN, M. S. (1976), "Personalta.xationandportfoliocomposition: Anecono- metric analysis," Econometrica, 44:631-650.

HAYASHI, F. (1982). "The effect oí liquidity constraints on consumption: A crasa sectional analysis, " Working Papel 882, NBER.

KING, M. A. AND J. l. LEAPE (1984). "Wea.1th and portfolio composition: Theory and evidence, " Working Papel 1468, NBER.

MANSKI, C. (1987), "Semiparametric analysis oí random effects linear models írom binary panel data," Econometrica,55:357-362.

MOLINAS, C. AND D. TAGUAS (1991), "La tasa de ahorro de las familias y la fiscalidad: un enfoque estructural," Moneda y Crédito, 192.

MONÉS M.A., R. SALAS AND E. VENTURA (1992). "Consumption, real after ta.x interest rates and income innovations, " Working Papel 18, Universitat Pompeu Fabra.

NEYMAN, J. AND E. L. SCOTT (1948), "Consistent estimates based on partia1ly consistent observations," Econometrica, 16:1-32.

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SATORRA,

A.

AND

H. NEUDECKER (1993). ,cOn the a.symptotic optimality oí

a.lterna.tive minimum-dista.nce estima.tors in linea.r la.tent-va.ria.ble models, "

Working Pa.per 35, Universita.t Pompeu Fa.bra..

UHLER, R. S. AND J. G. CRAGG (1971), "The structure ofthe asset portfolios of households," Review o/ Economic Studies, 38:341-357.

ZABALZA,

A.

^AND L. ANDRES (1991), "¿afecta la fiscalidad al ahorro? ," Moneda y Crédito, 192.

18

(21)

(22)

Table 2: Table oí Legal Deductions

-

Concept 82183"--1 84 I 85 I 86 I 87 I 88 I 89 90

.15 .15 .15

.15 .15 .15 .15

.15 .17 .15 .17 .15

.15 .17

.10 .10

.15 .10 .10 .10

.15 .10 .10 .10 Current housei

Other houses3

Fixed returns securities2 Variable returns securities.

Life Insurance _.10

N ates:

1. In 1982 there is no limit the the amount oí housing deduction practiced. The limit on deductions based on the securities concept was a 25 % oí taxable income. The limit on liíe insurance based deductions was 45,000 pesetas.

This last limit holds alBO in 1983 and 1984, but the joint limit on housing (both types) and securities (also both types) is equal to the 30 % oí taxable income.

2. Aíter 1985, the deductions ba.sed on the concepts oí this ta.ble ha.d a. joint limit oí a. 30 % oí ta.xa.ble income.

3. Between 1985 and 1987, the 17 % percentage oí deduction is applied not only to non current houses, but alBO to newly purchased current houses.

4. Aíter 1987, this deduction is mea.nt íor Retirement Plans. Variable returns securities are no longer a source oí tax rebates. Retirement plans entitle to another type oí rebate. They are considered a earning income related expenditure and they are not part oí taxable income.

20

(23)

Table 3: Definition oí Variables

Variable Name Variable Description

D83 to D90 MARGINAL82 to MARGINAL90 DISP. INCOME WEALTH

ENTREPRENEURIAL AGRICULTURAL PROFESSIONAL SECURITIES HOUSING DIVIDENDS

ENT.INVESTMENT CHILDREN

OLD IN CHARGE EARNEDINCOME AGE701

DEPENDENTLABOR INCENTIVATED SAVING SECURITIES SAVING HOUSING SAVING

LIFE INSURANCE SAVING SECURITIES INCOME HOUSING INCOME

ELDER

-- -

Time dummy variables.

Defined as 1 minus the marginal tax rate, from 1982 to 1990.

Disposable Income Computed wealth

Dummy variable for majar source of income Dummy variable for majar source of income Dummy variable for majar source of income Dummy variable for majar source of income Dummy variable for majar source of income Dummy variable for earners of dividends

Dummy variable for investment by entrepreneurs Number of children in the household

Number of low-income ancestors in the household Total net income before taxes

Dummy variable for households older than 70 in 1987 Dummy variable for majar source of in come

Sum of deduction entitling savings Saving in fixed and variable securities2 Saving in housing assets

Saving through life insurance instruments Financial capital income

Home imputed value and other real estate capital income

Dummy variable that identifies heads of household that were older than 69 in 1990

1. The proportion oí members belonging to that group is 16.9% in OUT sample.

2. It includes retirement plans savings aíter 1987.

(24)

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(25)

Ta.ble 5: Saving Intervals Distribution

Table 6: Cross Model Correlation, from 2SLS Individual-mean corrected estimations

Corr 82 83 84 85 86 87 88 89 90

1 -0.303 -0.077 -0.047 0.0563

-0.419

-0.326 -0.229 -0.469

-0.303 1 0.492 -0.150 -0.365 0.290 0.141 -0.024 0.405

-0.077 0.492

1 0.019 -0.301 -0.069 0.003 -0.123 0.245

-0.047 -0.150 0.019

1 0.042 -0.103 -0.250 0.081 -0.166

0.056 -0.365 -0.301 0.042

1 -0.47 -0.562

-0.58 -0.584

-0.419 0.290 -0.069 -0.103 -0.478 8 1 0.629 O 0.442

0.554

-0.326 0.141 0.003 -0.250 -0.562 0.629

1 0.638 0.641

-0.229 -0.024 -0.123 0.081 -0.580

0.442 0.638

1 0.624

-0.469 0.405 0.245 -0.166 -0.584 0.554 0.641 0.624

1

(26)

=

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Name EPT'

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I

7

J.

Table 7: Individual-mean corrected regression model

24

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(27)

Table 8: Reg on model with no individual-mean correction

(28)

Table 9: No individual-mean correction. Differential rates omitted

26