The influence of income uncertainty on saving
behaviour
X.A. van den Berg Amsterdam, March 16, 2014
E-mail: xander.vandenberg@student.uva.nl
Supervisor: J.C.M. van Ophem
Second Marker: M.J.G. Bun
Master’s thesis of Econometrics
Faculty of Economics and Business, University of Amsterdam
Contents
1 Introduction 3 2 Theory 4 2.1 Theoretical model . . . 4 2.2 Literature . . . 6 3 Empirical model 7 3.1 Panel estimator . . . 8 4 The dataset 9 4.1 Dependent variable . . . 10 4.2 Risk perception . . . 11 4.3 Explanatory variables . . . 14 5 Results 15 5.1 Ordered probit . . . 15 5.2 Random effects ordered probit . . . 18 5.3 Linear panel regression . . . 206 Conclusion 22
References 23
Appendix A The DHS survey 26
Appendix B Variables of the DHS survey 27
1
Introduction
In periods when unemployment is rising, income uncertainty rises due to a perception of increased risk (Curtin, 2003). One option to negate this perceived increased risk is to reduce spending and increase savings with the idea that e.g. a period of unemployment would not lead to financial problems.
After the credit crunch in 2007, businesses were more eager to cut costs, leading to a decreased job certainty. The Netherlands, like most countries in the Eurozone, is still facing the consequences of the financial crisis of 2007. Since then, unemployment rose from 4% to 8,2%1 and is expected to
keep rising until at least 20142. Furthermore, the number of employees who are enjoying their fixed contracts for a undetermined amount of time have been declining since 2002, thus creating additional uncertainty in the labour market.
The aim of this thesis is to investigate empirically the relationship be-tween household saving and their perception of their income risk in The Netherlands. A couple of characteristics make The Netherlands an interest-ing example for a closer study on savinterest-ings behaviour. The Dutch financial sector is relatively large as it contributes 6,8% to GDP as opposed to an average of 5.3% for the EU-15 (Schoenmaker & Werkhoven, 2012). Further-more, several nationalisations and bankruptcy’s of Dutch banks generated high amounts of media attention and strengthened the idea that banks, and thus savings accounts, and other financial investments were not necessarily without risk.
Studies into income uncertainty and precautionary savings by Leland (1968) and Sandmo (1970) stated the theoretical conditions for increases in income risk to results in increased saving behavior. Further research based on simulations for this effect has been done by Zeldes (1989) and Caballero (1991) and found that income uncertainty can indeed contribute to the amount of saving.
Empirical research on time series relies on proxies that reflect aggregate risk and as noted by Guiso et al. (1992) and Kimball (1990), the individual effects tend to be washed out in the process of aggregation. Proxies used in cross section regressions as measurements for income risk, such as job sector, tend to be correlated with other attributes. Moreover these proxies tend to be a result of self selection, a risk seeking individual will tend to select himself into cases that are risky in nature.
The data used in this thesis will be the DNB Household Survey (DHS)
1 http://www.cbs.nl/nl-NL/menu/themas/arbeid-sociale-zekerheid/publicaties/artikelen/archief/2013/2013-079-pb.htm 2 http://www.cpb.nl/cijfer/kortetermijnraming-maart-2013 3 http://www.cbs.nl/nl-NL/menu/themas/arbeid-sociale-zekerheid/publicaties/artikelen/archief/2012/2012-3743-wm.htm
which is a internet-based survey available on a year to year basis by Cen-tERdata (University of Tilburg), which collects data on 2,000 households. This survey has been held yearly since 1993 and the composition of the respondents reflects the Dutch-speaking population. The questions asked cover a range of topics such as income, health and economical/psychological concepts. Since there is no way to directly observe a households perceived earnings risk, several questions posed to the respondents do grant an esti-mate for the households perceived risk. Such a method results in a more direct measure for risk instead of a proxy or aggregate.
This thesis is organised as follows. Section 2 provides the theory on income risk and consumption and background on previous research on this subject. Section 3 will focus on the empirical model followed by section 4 where the empirical dataset is discussed. Section 5 presents the results and section 6 will contain the conclusion and presents an outlook for future work.
2
Theory
2.1 Theoretical model
In this section the theoretical model for consumer saving and their income risk is revisited as introduced by Leland (1968) and has been examined further by Caballero (1990), Weil (1993) and Guiso et al. (1992). The model assumes an infinitely lived consumer who takes decisions in discrete time and maximizes a time separable utility function. This consumer faces the following maximization problem
max ct+i Et ∞ X i=0 (1 + δ)−iU (ct+i) ! (2.1)
The consumer works a fixed amount of hours per period t + i for which he receives labour income. The mean and variance of the income are the only sources of uncertainty considered. This consumer can lend and borrow at a risk free interest rate 1 + δ = R > 1 and and receives a random non-interest income ytevery period t. Assuming that the after-tax labor income
yt follows a autoregressive process, it is defined by
yt= γyt−1+ (1 − γ)ˆy + t (2.2)
where yt is the income in period t, 0 < γ < 1 is a constant and a positive
deterministic component ˆy. The stochastic component tare identically and
independently distributed and have a constant mean of 0 and a variance σ2. Letting the wealth of the consumer be zero at t = 0 with wealth at time t equal to wtand individual consumption ct, at time t, the budget constraint
for the consumer becomes
wt= Rwt−1+ yt− ct. (2.3)
Assuming that the consumer has an exponential utility function (Caballero, 1990), which is increasing for the consumption ct, the maximisation problem
of the consumer in 2.1 becomes max ct+i −1 θ ∞ X i=0 βiexp(−θct+i), (2.4) subject to constraints yt= γyt−1+ (1 − γ)ˆy + t, wt= Rwt−1+ yt− ct (2.5)
where β is the discount rate and θ is the (constant) degree of absolute prudence.
In the case where the interest rate is equal to the discount rate, βR = 1, solving for ct yields
ct= R − 1 R − γ(yt+ 1 − γ R − 1y + wˆ t) − Πt R (2.6) where Πt= R − γ θR log E exp − θR R − γt . (2.7)
For the general case, where βR = 1 does not necessarily hold, please refer to Caballero (1990).
Assuming that the income shock is normally distributed, equation 2.7 reduces to
Π = θR
R − γσ
2. (2.8)
The first part of 2.6 is, given the restrictions on the parameters, positive and increasing for yt and ˆy. Equation 2.8 is increasing for the risk prudence θ,
the persistence of income γ and the income shock variance σ2. Thus the op-timal consumption for the consumer is decreasing when income uncertainty rises and, depending on income parameters, the consumer will increase their wealth by lowering consumption. Or in other words, an increase in perceived risk will lead to an increase in savings.
For computational purposes the model assumes an infinitely lived con-sumer, but this of course presents problems for the elderly and retired. Receiving pension and social security benefits that come with retirement present different income risk considerations as opposed to labour income. Unemployment is then no longer an issue but other income risks arise such as uncertain life expectancy and (a lack of) inflation corrections by pen-sion funds. The general assumption is that a person’s accumulates wealth
throughout their life until their retirement at which point they start de-cumulating wealth. The life-cycle hypothesis as introduced by Modigliani (1966) even goes as far as stating that this decumulation of wealth reaches zero at the end of a consumers’ life. However, research (Hurd, 1987) shows that this rate is significantly smaller mostly due to uncertainty of their life expectancy as well as bequests motives.
2.2 Literature
Several studies have been done on precautionary savings by modelling and simulating this effect. Caballero (1991) and Zeldes (1989), amongst others1, show in their simulations and modelling that large parts of savings can be attributed to precautionary savings.
Unlike the evidence from the simulation- and model studies however, the empirical findings are mixed on the subject of precautionary saving. The problem mostly lies in identifying an exogenous risk measure so that it captures an individuals’ or households’ uncertainty and is uncorrelated with other effects that influence saving. Direct risk measures are generally not available and hard to measure, and tend to be substituted by proxies and aggregates which tend to have their own problems.
Empirical research on the subject has shown, if present, the effect of perceived risk on savings to be significant. Papers finding an insignificant effect tended to use proxies as a risk measure such as Skinner (1988) who used occupation as a risk measure, which he acknowledges is subject to self-selection as people who are risky in nature tend to find riskier occupations. Other empirical findings by Lusardi (1998) show a significant effect for risk perception, however she notes that this did not provide a rationale for large accumulations of wealth. The risk measure used for her findings was derived from job loss probability, which was given by the respondent, as a proxy for income risk. This measure however poses problems for self-employed and temporary workers. Research done by Carroll et al. (1994) uses an aggregate proxy for risk, lagged consumer sentiment, but finds no effect of precautionary saving. Engen & Gruber (2001) on the other hand use unemployment insurance as a proxy and finds the consumption to increase when the insurance is more generous.
Other research takes an alternative and more direct approach for risk measuring. Guiso et al. (1992) uses self reported uncertainty and finds a small but significant effect, noting that their method fails to explain a large fraction of savings and wealth accumulation. Kazarosian (1997) uses the variance of a household income to describe savings behaviour over 15 years and concludes that his results show that a strong precautionary motive exists for savings.
1
3
Empirical model
Several estimations done in this thesis rely on a dependant variable, dis-cussed in 4.1, which is discretely ordered in four categories. The use of a multinomial model is possible but doing so would mean the information about the ordering of the variable would be lost in the regression. A more suitable approach can be done using an ordered response model. Consider the following function
y∗i = x0iβ + i, E[i|xi] = 0, (3.1)
for i = 1, ..., N , where xi is the vector of observations, β is the vector of
unknown variables and the values i which are i.i.d. with some cumulative
distribution function F .
The value of y∗i is not observed but instead the value yi= j is measured
when the value of yi∗ falls between two threshold values, τj−1 and τj. Using
this, the observed variable yi can be defined by the following equation
yi = 1 if − ∞ < yi∗≤ τ1, j if τj−1< y∗i ≤ τj, j = 2, ..., M − 1, M if τM −1< yi∗< ∞. (3.2)
Thus the unknown parameters in equation 3.1 are β and (M − 1) threshold values. Note that no constant is present as it’s effect would be absorbed in the threshold values. With F as the cumulative distribution function of i,
the marginal effects become
pij = P [yi = j] = P [τj−1 < yi∗≤ τj] = P [yi∗≤ τj] − P [yi∗≤ τj−1]
= F (τj− x0iβ) − F (τj−1− x0iβ), j = 1, ..., M
(3.3) The function F has to be specified for estimation where usually the normal and logistic distributions are taken, thus resulting respectively in the or-dered probit and oror-dered logit models. The oror-dered probit regression used in this thesis, which was introduced by Aitchinson & Silvey (1957), assumes i∼N (0, σ2). Parameters can be estimated using maximum likelihood. The
log-likelihood for this estimation is then defined by
log(L(β, τ1, ..., τM −1)) = N X i=1 M X j=1 yijlog(pij) = N X i=1 log(pij). (3.4)
By using the scale normalisation σ = 1 (Allison, 1999) the probabilities are given by
As stated, the ordered probit regression is done assuming i∼N (0, 1) in
the statistical software1 package. But since the variance is normalized, i.e. σ = 1, the following relation exists
βm= αm/σ, k = 1, ..., K (3.6)
where K is the number of exogenous variables. When there is a no presence of heteroskedasticity in the model, the assumption σ = 1 holds leading to an unbiased and consistent estimator. In the case that heteroskedasticity does exist in the model, the assumption no longer holds, thus resulting in an inconsistent estimator. Testing procedures like those for linear regres-sions are not suited for use on ordered probit regresregres-sions as, if present, the coefficients are scaled so that the residual variance is the same for all groups though the scaling will differ per group. In order to test for heteroskedastic-ity, a heterogeneous choice model is instead used as introduced by Williams (2010). This model is similar to the probit model with the exception that the standard deviation is now allowed to be individual specific,
σi= exp(
X
j
zijγj), (3.7)
where zi is a vector of variables, either discrete or continuous, assumed to
be able to identify heteroskedasticity, e.g. a set of dummy variables. As op-posed to other tests for heteroskedasticity, one cannot generally test for the presence of this effect in the case of an ordered probit estimation. However, by explicitly specifying the determinants of heteroskedasticity, the hetero-geneous choice model can be used to correct and/or test the significance of these determinants. Note that for z = 0, the above equation leads to σi = 1.
3.1 Panel estimator
CentERdata provides annual surveys but the aforementioned ordered probit model will in general be unfit for regressions on panel data. A more sensi-ble approach is using panel estimation techniques such as a fixed-effects or random-effects model. Adjusting for fixed-effects however, requires a trans-formation to remove the individual specific effects. Unlike the linear model a simple transformation, such as the within-transformation, is not readily available. An extension of fixed effects to the ordered probit estimator would be complex and not very straightforward. The case for a random-effects model however is more promising. Consider the following equation
y∗i,t= x0i,tβ + νi+ i,t, E[i] = 0, (3.8)
1
StataCorp. 2013. Stata Statistical Software: Release 13. College Station, TX: Stata-Corp LP.
where t = 1, ...., ni and νi are the i.i.d. panel-level random effects which are
distributed N (0, σν2). Again the values of yi,t∗ are not observed but instead the latent variables yi,t are, analog to equation 3.2, observed with unknown
cutoff points τ1, τ2, ..., τM −1. Thus the probability of observing outcome j
for observation yi,t becomes
pi,t,j = P [yi,t = j] = P [τj−1< yi,t∗ ≤ τj] = P [yi,t∗ ≤ τj] − P [y∗i,t≤ τj−1]
= F (τj− x0i,tβ − νi) − F (τj−1− x0i,tβ − νi), j = 1, ..., M
(3.9) Defining the conditional distribution for response of yi,t as
f (yi,t, τ, xi,tβ + νi) = M Y m=1 pIi,t,mm(yi,t) = exp M X m=1
(Im(yi,t)log(pi,t,m))
(3.10) where Im(yi,t) = ( 1 if yi,t = m 0 otherwise. (3.11)
For observations i, i = 1, ..., N , the conditional distribution of yi= (yi,1, ..., yi,ni)
0,
where ni is the number of observations for panel i, is ni
Y
t=1
f (yi,t, τ, xi,t, νi). (3.12)
Assuming again that i∼N (0, 1), the likelihood for case i, li, can then be
defined as li(β, τ, σν2) = Z ∞ −∞ e−νi2/2σ2ν √ 2πσν ( ni Y t=1 f (yi,t, τ, xi,t|νi))dνi (3.13)
4
The dataset
In this chapter the datafile is described along with the variables used. The data used for this thesis is the DNB Household Survey (DHS) which is an internet-based survey available on a year to year basis by CentERdata (University of Tilburg), and has been available since 1993. The aim of the survey is, amongst others, to provide information on both economical as well as psychological aspects of financial behaviour. This thesis will focus on the annual datasets of 2008-2012 as datasets for the period 2007 and earlier do not contain some of the necessary variables and questions as described
below. The dataset represents the Dutch population as shown in Appendix A in which a comparison of characteristics of the dataset and the population can be found. Definitions of variables and more of the dataset can be found in Appendix B. The annual amount of household observations for the period 2008-2012 ranges between 1660 and 1885.
Some questions answered by the respondents were not on an individual level but on a household level. Since there can be multiple entries in the dataset for one household, one entry per household member, performing a regression without accounting for this might introduce sampling bias. There-fore regressions will be done on households rather than persons. In order to find the associated variables for the household such as age but also for fi-nancials, only information from the head of the household will be taken into account as the assumption is that he/she will know the household situation best. This approach has no effect on households consisting of one individual but otherwise adds the assumption that the variables calculated and used for the head of the household, e.g. income risk and savings expectations, are representative for the household itself.
4.1 Dependent variable
To answer the question what influences saving behaviour, a dependent vari-able is needed describing saving behaviour of an individual. The respondents in the survey faced several questions about personal wealth, such as savings accounts and various types of investments. On top of that, more psycholog-ical concepts such as their perception of their savings behaviour last year were also asked. Of particular interest is what respondents answered to what the likelihood for the household is to be saving in the next 12 months, with possible answers ordered in four categories ranging from not likely to very likely. This variable, the savings intent, will be considered as a de-pendent variable for regressions in order to find out how it is affected by risk perception. The hypothesis is that a positive relation exists between this individuals’ savings intent variable and their future income uncertainty. Figure 1 shows the composition of household savings intentions of the DHS data survey for the available five years. The composition itself doesn’t vary greatly over the shown period but the households who are at least inclined to save are consistently in the majority at around 80%.
Since the DHS survey provides detailed information on a household’s as-sets and liabilities, the households’ total savings can be calculated which will be defined as the total amount of money in saving- and checking accounts as well as the households’ valuation of their positions in three financial in-struments: bonds, stocks and mutual funds. A variable for total savings growth, or decline, is not available in the dataset but differencing the total savings will give the same result at the cost of decreasing the periods avail-able by one. Moreover, not all households have their savings information
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 2008 2009 2010 2011 2012 Yes, certainly Yes, perhaps Probably not Certainly not
Figure 1: Household Savings Intent
available for every year thus a regression on this difference would mean a further reduction in available quantity of observations.
The savings intent is assumed to be a good estimator for actual savings behaviour, i.e. a household intending to save is more likely to have a larger observed savings after 12 months. However this might not necessarily be true due to changing circumstances or even simply failing to succeed in ”self-improvement”. An analysis on this subject is found in section 5.3.
The hypothesis that savings are positively correlated with perceived risk assumes that people are able to make the choice to save. One issue with both identifiers of savings however is that households willing to save, but cannot do so due to their financial situation, will report it unlikely for them to save and/or no savings will be observed even though they could be perceiving high risks. For these cases there will be no precautionary savings effect. As the dataset does not provide enough information to accurately identify1 those who have the opportunity to save and those who do not, both are used for the estimations.
4.2 Risk perception
In order to find a good measure for income risk, the variable(s) preferably need to be unaffected by sample bias, making e.g. the employment sector or occupation unfit for use as a risk measure. Another approach might be using a person’s belief about their personal job loss probability, but this method ignores income variation and sources of income other than employment. Perhaps more importantly this does not fully contain all information about
1
A less accurate approach would, for example, be separating groups based on their income but this does not lead to conclusions other than those found in this thesis.
income risk, e.g. a contract ending in three months gives a loss probability of 100% but the respondent might already have another job opportunity waiting for him, i.e. the respondent might have more information than the data suggests.
A more fit approach of measuring a households’ risk might be its per-ception of changes in their real income. The DHS survey includes a set of questions to assess the respondents perception of uncertainty. The partic-ipant was first asked to give the lowest estimation of their net income for the next year followed by the same question but for the highest income. After this a set of five intervals were defined for possible net incomes for the next year, based on the participants given lowest and highest estimations, for which the respondent was asked to assign probabilities to each interval. These probabilities should sum up to 1, thus yielding an approximation of a person’s belief about their income probability distribution.
In a follow up set of questions, participants were asked to assess what the most likely (consumer) prices increase would be for the next year. The answer to this questions was used to construct yet again five intervals of probabilities of consumer price index increases for which the participant was asked to assign probabilities to each interval. The choices presented to participants and how variables were defined can be found in Appendix B.
One problem with this self reported measure of income risk is that some respondents unfortunately did not answer with probabilities in line with probability theory, e.g. the sum of probabilities does not equal to 1. The persons more prone to such errors are also more likely to be lower educated than those who are able to answer correctly. Incorrect answers lead to the corresponding household observation being excluded from further analysis, making this method prone to selection bias. A further analysis on this subject is found in Appendix B.
The two probability distributions yield a persons expected values and variances for their nominal income for the next 12 months as well as their expectations for the inflation for the next 12 months. These variances are respectively defined as σi and σπ. Following Guiso et al. (1992) the risk
measure is expressed in real terms, where it is assumed that a households’ expectations for real income growth has the following relation1
i = r + π, (4.1)
where i denotes the nominal income growth rate, r denotes the real growth rate and π denotes the inflation rate. The variable of interest is r and, more importantly, it’s variance σr. Using 4.1, the following equation is obtained
σ2i = σr2+ σ2π+ 2ρσrσπ, (4.2)
1This can be considered as a simplification of 1 + r = (1 + i)/(1 + π) and is similar to
where ρ is the correlation between r and π. Solving 4.2 for σr yields
σr= −ρσπ±
q σ2
i + (ρ2− 1)σ2π (4.3)
As seen, σr is dependent on 2 known factors, σi and σπ, and one unknown,
ρ. Thus to obtain σr, additional assumptions need to be made analogous
to Guiso et al. (1992). As standard deviations are either positive or zero, roots cannot be taken from negative numbers and using 4.3, information about the value of ρ can be retrieved. In order to find this value of ρ, the assumption is made that the correlation is equal for all households.
Table 4.1 shows that some respondents do not expect their income to change in the next 12 months. Setting σi to zero reduces equation 4.3 to
σr= −ρσπ±
p
(ρ2− 1)σ2
π. (4.4)
The only value ρ can take for equation 4.4 to ensure non-negativity is -1 which reduces the equation to σr= σπ. Obviously the value of σr reduces to
zero when the beliefs about inflation and the nominal income rate are both fixed.
In contrast, if their beliefs about inflation are fixed but their income beliefs are not than, regardless of the value ρ, equation 4.3 reduces to σr=
σπ.
The last possibility is that both standard deviations are larger than zero. Assuming that the correlation is the same for all households, ρ must satisfy the value found above, the coefficient used for computations is set at -1.1 Evidence found by Guiso et al. (1992) supports the use of this value.
Equation 4.3 thus simplifies to
σr= σπ± σi. (4.5)
In order to ensure non-negativity of the standard deviation, equation 4.5 is reduced to σr = σπ + σi for computations. This value is regarded as the
measure for risk perception.
Table B.7 shows the distribution of the generated values of σifor the year
2012. The median for the values lies at 2,6%. Note that about 15% does not believe that their income will change in the next 12 months, essentially perceiving a riskless income stream.
The mean for the calculated expected inflation for the year 2012 lies at 3,4%, 0,9%2 higher than the actual inflation numbers for the years 2012 and
2013 in The Netherlands3.
1
Note that this value implies that a perfect negative correlation exists between real earnings and inflation. This, however, does not imply a causality and does not seem an unreasonable assumption given the implications of equation 4.1.
2
The actual inflation numbers in The Netherlands for the years 2012 and 2013 were both the same at around 2,5%. Source: http://www.cbs.nl/nl-NL/menu/themas/prijzen/cijfers/kerncijfers/inflatie.htm.
Table 4.1: Beliefs about nominal income (2012 survey) σi N Frequency 0% 215 14,8% 0%-0.5% 102 7,0% 0.5%-1% 106 7,3% 1%-2% 208 14,3% 2%-3% 158 10,9% 3%-5% 185 12,7% 5%-10% 266 18,3% 10%-15% 98 6,7% ≥ 15% 116 8,0% Mean: 2,01% 1454 100% 4.3 Explanatory variables
A total of more than 1800 variables are available every year in the DNB Household Survey. Since not all households answered the questions of in-terest, such as those for future savings behaviour and risk perception, the amount of useable observations decreases. In order to keep the quantity of observations for analysis as large as possible, the explanatory variables will consist mostly out of variables which are generally available.
The survey provides detailed information on the background of a re-spondent, which is used to construct control variables. One of the control variables used is age. According to economic theory, as the life-cycle hy-pothesis introduced by Modigliani (1966), it is expected that as people grow older their necessity for saving decreases. Though there are several reasons for this effect, the main argument is that older people have had more chances to build up capital as opposed to e.g. starters on the labour market.
Figure 2 shows the composition of the dataset for savings. There seems to be a steady 70% percentage of the households saving, though this percentage is lower than the amount intending to save in the coming year as shown in figure 1.
Furthermore a dummy variable is generated based on if households indi-cated that they saved last year, equalling 1 if this is true and zero otherwise. Note that the question itself does not ask whether the total savings increased last year or that it increased for a given period in the last year. As the vari-able might incorporate some savings persistence, it is expected that the value positively correlates with the dependent variable.
Also included is a dummy variable for gender. In this case the value equals to one for males, zero for females. Furthermore a dummy for edu-cation is added as a control variable. This equals to 1 of the respondent has completed a higher vocational education or has an academic degree, and equals zero otherwise. Both dummy’s are computed for the head of the
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 2008 2009 2010 2011 2012 yes no
Figure 2: Households Saved Last Year
household.
Other variables included are gross wages and total savings. The defini-tions of these variables can be found in Appendix B.
People aged above the retirement age (> 65) arguably have a different income risk as well as different saving behaviour compared to the country’s labour force. Performing a regression without taking this group into account might distort the computed parameters though. On the other hand, these increase the quantity of observations and might provide information other-wise left out when discarding this group, therefore a separate regression will be done with a dummy which equals to one if the age is larger or equal to 65.
As the dataset only consists of respondents aged 16 and above, there is no need to consider the group aged ≤ 15. Further data description and analysis can be found in Appendix B.
5
Results
5.1 Ordered probit
The original sample of the 2012 DHS survey included 1830 households. As noted earlier, only the heads of the households are taken into account. Most households reported the usual variables of interest such as education and gender but unfortunately a large portion did not (correctly) provide info on other explanatory variables. The total amount of usable observations
Table 5.1: Ordered probit regression
(1) (2) (3) (4) (5)
Sample All Age < 65 Age ≥ 65 All All
Age -0.0104∗∗ -0.0166∗ -0.0156 -0.0148∗ -0.0157∗ (-2.72) (-2.31) (-1.20) (-2.42) (-2.48) Sex -0.190 -0.425∗∗ 0.101 -0.189 -0.223 (-1.54) (-2.60) (0.51) (-1.54) (-1.73) Higher educated 0.109 0.000493 0.152 0.0995 0.0954 (1.05) (0.00) (0.95) (0.95) (0.86) Risk perception -1.368∗ -1.990∗ -0.00156 -1.364∗ -1.378∗ (-2.04) (-2.42) (-0.00) (-2.03) (-1.99)
Saved last year 1.783∗∗∗ 1.948∗∗∗ 1.628∗∗∗ 1.781∗∗∗ 1.924∗∗∗
(15.58) (12.23) (9.70) (15.55) (13.82)
Total gross income 0.00000539∗ 0.00000832∗∗ 0.00000216 0.00000568∗ 0.00000715∗∗
(2.27) (2.62) (0.57) (2.36) (2.65) Total savings -0.000000192 -0.000000202 -0.000000159 -0.000000180 -0.000000211 (-0.85) (-0.71) (-0.40) (-0.79) (-0.85) Age ≥ 65 0.150 0.242 (0.92) (1.34) cut1 Constant -1.527∗∗∗ -1.926∗∗∗ -1.794 -1.719∗∗∗ -1.761∗∗∗ (-5.21) (-4.40) (-1.83) (-4.76) (-4.69) cut2 Constant -0.461 -0.846∗ -0.739 -0.652 -0.623 (-1.60) (-1.97) (-0.76) (-1.83) (-1.69) cut3 Constant 0.778∗∗ 0.467 0.456 0.588 0.715 (2.68) (1.08) (0.47) (1.64) (1.91) lnsigma d65btot 0.00000397∗ (2.01) Observations 600 357 243 600 600 Pseudo R2 0.219 0.254 0.180 0.220 0.223 t statistics in parentheses ∗ p < 0.05,∗∗ p < 0.01,∗∗∗p < 0.001
decreases to 600 and further decreases to 357 if the group aged 65 and over is not taken into account. Retirees have different risk and consumption profiles than those in the labour force, though this group can increase the statistical significance of the regression and therefore separate regressions were done with respect to the inclusion or not of this group.
The results of the ordered probit regressions on the dependent variable, the savings intent, can be found in table 5.1. Column 1 describes the initial regression and shows age, risk perception, the dummy for savings last year and total gross income to differ significantly from zero. By including the group aged 65 and older might introduce heteroskedasticity due to a differ-ence in earnings and expenditure. Columns 2 and 3 show regressions done on the group aged 16-65 and 65 and older respectively. Column 4 introduces a dummy for that second group. Quadratic terms variants of the variables, where applicable, were found to be insignificant and are therefore not used in the estimations.
All regression estimations show that the risk perception, as defined in section 4.2, is significant but the negative sign indicates that increased risk corresponds with a decreased likelihood of saving which is the opposite of what the theory suggests. Note that the values of risk perception are in the order of percentages, the marginal probability effect for an individual would thus be significantly smaller than for example the variable Saved last year.
The table shows that the sign for the age variable is in line with the theory of the life-cycle hypothesis that a persons’ consumption increases with their age. The significance of the gross total income variable suggests that the higher the income, the more likely a person is willing to save. Furthermore it seems that total savings itself is not significantly different to zero indicating that the total amount of savings do not impact short-term savings behaviour.
The evidence from the regressions in column 2 and 3, as well as eco-nomic theory, suggests that the group aged 65 or older expresses a differ-ence1in saving behaviour due to a difference in earnings and expenditures, however performing a Chow-test on both groups does not indicate that these groups are statistically different and another regression with a dummy for this group, shown in column 4 of the same table, shows that the latter is also not significant.
Several variables however differ significantly for both groups, such as risk perception and gross income. In order to test2, and possibly correct, for het-eroskedasticity, a source for this problem has to be specified. Assuming that
1
In a similar fashion it can also be argued that the self-employed have different risk profiles and might also affect the results. Similar testing as done for the group aged > 65 however does not lead to conclude that this group is statistically different.
2Note that the assumption is made that the error terms are normally distributed.
Using semi-nonparametric estimation techniques, as introduced by Stewart (2004), did not provide a better alternative than the standard normal distribution.
a persons’ income risk variance rises with their income, a dummy variable1 d65btot is generated as follows
d65btot = (
0 if age < 65
Total Gross Income last year if age ≥ 65. (5.1) The fifth column shows the results from an ordered probit regression with a variable used for controlling for the aforementioned heteroskedasticity. The variable d65btot, which is assumed to be a source of heteroskedasticity and is shown in column five of table 5.1, does indeed signal a presence of heteroskedasticity in the model. Though the evidence is significant at the 5% level, it is not strong.
The sign for the risk perception variable is again significantly different from zero but has a negative sign here as well. This suggests that a person who perceives a higher risk is less inclined to save, which is the contrary of what theory suggests. Other income risk measures, such as the chance of one losing their job, and risk factors, such as houses being ”underwater” for home owners and the relative level of income on savings, were also tested for but found to be insignificant.
5.2 Random effects ordered probit
A possibility for these conflicting results, i.e. the sign of the risk perception is not in line with the hypothesis, is that the amount of observations are too low, increasing the amount of observations is possible but only by using panel estimation. The DHS data is available for every year since ’93 but only the period 2008-2012 is included as the questions for the risk perception variable were not available in the periods prior to 2008. Since the regression is a panel regression and the dependent variable is ordered, a random effects ordered probit estimation is done as described in section 3.1. Unfortunately, not all households provided (valid) answers for each question every year nor were all households included in the every yearly dataset. The panel estimation was unbalanced with an average of 2.0 observations out of 5 per household for the final regression.
Table 5.2 shows the regression output. The first two columns show the separate regressions on the the labor force and the group aged > 65, the third column shows the results for the entire population. The conclusion remains the same for all groups, the risk perception, when significant, shows a negative relationship with savings intent. Other results strengthen what was seen earlier such as the significance of values as age and total gross income. Note that a direct comparison of the value sizes, aside from com-parison issues with an ordered probit estimation, is however less obvious as
1Several possible sources of heteroskedasticity were tested for which only the variable
Table 5.2: Random effects ordered probit regression
(1) (2) (3)
Sample Age < 65 Age ≥ 65 All
Age -0.0290∗∗∗ -0.0219∗ -0.0222∗∗∗ (-4.76) (-2.08) (-6.93) Sex -0.292∗ 0.0948 -0.134 (-2.25) (0.56) (-1.32) Education 0.0676 0.286∗ 0.187∗ (0.58) (2.08) (2.15) Risk perception -1.584∗∗ -0.229 -1.336∗∗ (-2.81) (-0.20) (-2.68)
Saved last year 2.082∗∗∗ 2.123∗∗∗ 2.097∗∗∗
(18.12) (16.73) (24.73)
Total Gross Income 0.00000983∗∗∗ 0.00000211 0.00000621∗∗
(3.62) (0.67) (3.10)
Total Savings 7.88e-08 7.37e-08 8.24e-08
(0.27) (0.25) (0.40) cut1 Constant -3.468∗∗∗ -3.013∗∗∗ -3.105∗∗∗ (-9.16) (-3.75) (-12.39) cut2 Constant -1.676∗∗∗ -1.162 -1.290∗∗∗ (-4.74) (-1.47) (-5.55) cut3 Constant 0.215 0.746 0.600∗∗ (0.63) (0.95) (2.64) Observations 1515 1054 2569 t statistics in parentheses ∗ p < 0.05,∗∗ p < 0.01,∗∗∗ p < 0.001
the cutoff points have changed as well. 5.3 Linear panel regression
The previous regressions and conclusions indicate that there is some incon-sistency between the theory on precautionary savings, as described in earlier sections, and what is found in the results. This gives reason to believe that a significant discrepancy might exist between what the households perceive as their risk and what is computed. Note that, as mentioned earlier, other used measures of risk were found to be statistically insignificant.
Another conclusion might be that the model specification is wrong, or more specifically that respondents their indication for their saving might not necessarily translate to a likewise positive or negative amount of savings, thus making the dependent variable misleading. An explanation for this might be either that households are unable to adequately estimate their savings behaviour or that the question posed, ”Is your household planning to put money aside in the next 12 months?”, leaves room for interpretation. E.g. it is ambiguous what someone has answered who is planning to save for one month, but plans to consume from his wealth for the other eleven months.
In order to test if the dependent variable is a good estimator for savings behaviour, a regression is done using the equation below
yi,t+1− yi,t = αi+ x0i,tβ + i,t (5.2)
where yi,t is the individuals’ savings at time t and xi,t the variable vector at
time t. The term yi,t+1− yi,t thus indicates the difference in savings between
years, the savings growth. A household indicating that they intend to save at time t would mean an increased likelihood that the observed savings at time t + 1 have increased, assuming that the savings are observed correctly. Note that by taking differences for the savings, the periods available for a panel regression decrease by 1. In order to test this hypothesis a regression is done using a random effects1 panel estimator for the period 2008-2011. The panel is unbalanced, with an average of 2,9 out of 4 observations, as again not all variables used are available for every household for each year. The results for this estimation can be found in column 1 of table 5.3. The explanatory variables are defined the same as in for the ordered probit regression with the addition of two savings intent dummy variables2. Of importance in the results is the lack of significance, at a level of 10%, for the last two dummy variables which leads to believe that there is indeed
1The choice for a random effects model is made as it is assumed that the individual
effects are randomly distributed. Furthermore this keeps the assumptions equal to those for the results in section 5.2. A Hausman test does not indicate the need for a fixed effects estimator.
2
Table 5.3: Panel regression on Total Savings (1) (2) Age 264.5∗ 427.4∗∗ (2.29) (2.76) Gender dummy 1918.3 2850.7 (0.52) (0.68)
Higher education dummy 1167.9 3848.2
(0.36) (1.10)
Saved last year 5474.9 4048.6
(1.33) (1.16)
Total Gross Income 0.102 0.219∗
(1.28) (2.55)
Total Savings -0.198∗∗∗ -0.241∗∗∗
(-18.29) (-25.96)
Planning to save -723.6
(-0.05) Not planning to save -2386.7 (-0.18) Risk perception 65125.8∗ (2.08) Constant -15607.0 -33050.8∗∗ (-1.03) (-2.85) Observations 3208 1968 t statistics in parentheses ∗ p < 0.05,∗∗ p < 0.01,∗∗∗ p < 0.001
reason to believe that a discrepancy between the savings intent and the actual savings exists.
The ordered probit regressions were done on an ex ante premise, meaning that the assumption was that the given information was able to give an accurate description about current and future behaviour. As shown above, the savings intent does not seem to be a strong predictor for the actual future savings behaviour. By doing a similar regression as above with risk perception added as a variable, i.e. again an unbalanced random effects panel regression, an alternative approach to the ordered probit regressions is done but at the cost of less available periods for a regression. Moreover, as the explanatory variables are (partly) lagged with respect to the dependent variable, it is more susceptible to exogenous variables not found in the model. For the unbalanced random effects panel regression, equation 5.2 is again used with the totalsavings as the dependent variable y. The estimation is similar to that in table 5.2 with only the dependent variable changed, and thus the observations and model type, and the risk perception has been set to zero for people aged≥65. The results of this regression can be found in column 2 of table 5.3. Note that the dependent variable is denominated in euro’s and the risk perception in the order of percentages.
The linear panel estimation shows a different relation than the ordered probit regressions between savings and risk perception. Assuming that the risk measure and linear panel model used are correct, the results suggests that a positive relation does exist between actual savings and risk perception. However, even though the evidence found for the sign is significant at a level of 5%, little can be said about the actual size of the parameter for risk perception given the large size of the confidence interval1.
6
Conclusion
This thesis considers the impact of a households’ risk perception on its sav-ings behaviour. Theoretical research shows that the risk perception has a positive influence on the savings of the household. Previous empirical re-search done has shown that the influence of precautionary savings, if found present, does indeed show such a relation though the effects are generally not found to be large. A sidenote for these results is that most studies use proxies that do not fully capture an individuals risk (perception). The research for this thesis uses a different approach where risk is individually calculated using data from the DHS made available by CentERdata. In-dividuals implicitly supplied probability distribution for their income and inflation expectations which were used to assess their risk perception.
The results can be divided in two parts, the ordered probit results and the linear panel estimation results. The first is an ex ante analysis which
1
surprisingly showed a significant negative relationship between savings intent and risk perception. Further analysis showed that savings intent might not be a good estimator for actual future savings, after which the linear panel estimation was done where, opposed to the first part, the savings intent was replaced by actual savings. This second part, which was thus done on an ex post premise, shows a positive relationship between actual savings and a households’ perceived risk.
Some larger shortcomings exist in the approach of this thesis, one of which is that households must have a certain opportunity to save. Those who want to save, but can’t due to their financial situation, might skew the results. Another problem is that the current approach for assessing risk perception is subject to self-selection. Respondents might have had trouble answering the questions, which was indicated by the reasonably large amount of observations excluded due to incorrect answers. Those who have trouble with these questions regarding probabilities also tend to be lower educated. Lastly, some of the questions posed leave room for interpretation such as the basis for the savings intent.
Possible improvements for future research can be found in a refinement of the questions posed in the dataset, where currently some might leave a room for interpretation. Furthermore, adding questions on the subject of savings opportunity might help correcting for this problem. Lastly, not all sources of risk are accounted for. Besides income and inflation risk, health risk might also be a factor and might further increase understanding of savings behaviour.
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Appendix A
The DHS survey
The DNB Household Survey (DHS) is a survey done annually by CentER-data, part of the CentER Group, which is closely linked to Tilburg Uni-versity and is sponsored by De Nederlandsche Bank. The survey is done annually since 1993 and collects data from over 2000 households partici-pating in the CentERPanel. The CentERpanel is a internetpanel which is representative for the Dutch speaking population. Participants without an internet connection are also able to participate through equipment supplied by CentERdata, allowing internet access via the television. Questions are asked and stored digitally without the presence of a physical interviewer. In 2012, a total of 1830 different households have responded though not all are present in previous years. A comparison between population data and general statistics of the dataset is given in Table A.1. These statistics are comparable to others years.
Table A.1: General properties of dataset
Variable Population DHS 2012 Males 49,5% 49,3% Females 50.5% 50,7% Age <20 23,3% 16,5% 20-40 24,8% 18,0% 40-65 35,7% 43,1% 65-80 12,1% 19,3% >80 4,1% 3,2% Average (years) 40,6 46,6
Average household size 2,2 2,38
Income (in thousands per household)
Average gross income 33,0 32,1
Average net income 22,3 24,2
Data for the dutch population is made available by the Cen-traal Bureau voor de Statistiek (CBS) at http://www.cbs.nl/nl-NL/menu/themas/bevolking/cijfers/kerncijfers/bevolking-kc.htm.
Average gross income data can be found at
http://www.cpb.nl/cijfer/kortetermijnraming-september-2012 and http://www.cbs.nl/nl-NL/menu/themas/inkomen-bestedingen/cijfers/kerncijfers/inkomen-van-personen-kc.htm.
Appendix B
Variables of the DHS survey
Definitions and statistics for various elements of the DHS survey are pre-sented in this section. Unless specified otherwise, these represent the survey of 2012.
Gross total income is calculated by CentERdata and is defined by the fol-lowing equation
btot = loon + vut + pens + wao + ww + wg + aow + aww + abw + waz +wajong + ioaw + alim + max(winst, 0) + hprem + hwf,
(B.1) where btot is the gross total income and the other variables are defined as follows
Table B.1: Gross total income composition Variable name Description
loon pay/salary
vut early retirement benefits
pens retirement pension/annuity
wao disability benefits
ww unemployment benefits
wg unemployment benefits civil servants
aow general old-age pension
aww general windows’ and orphans’ pension
abw social assistence/benefits for self-employed waz disability benefits for self-employed
wajong disability benefits for persons disabled at the age of 17 ioaw benefits for elderly and other partly disabled
alim alimony to/from spouse
winst profits
hprem premium for subsidised purchase of house
hwf rateable value of accommodation
Note that those with a higher income also have a larger opportunity to save. Separate analysis’s however did not provide other conclusions or insight than what is found in the results.
Expected savings behaviour Question: Is your household planning to put money aside in the next 12 months?
Table B.2 shows the possible answers and statistics. For table 5.3 the first two of table B.2’s answers were pooled together as well as answers three
Table B.2: Expected savings behaviour
Available answer N Frequency(%)
Yes, certainly 961 47,0% Yes, perhaps 650 31,8% Probably not 313 15,3% Certainly not 86 4,2% Don’t know 36 1,8% Total 2046 100%
and four in order to increase statistical significance. These pooled variables are referred to as Planning to save and Not planning to save respectively.
Savings
As described in section 4.3, savings are considered to be the total amount of money in saving- and checking accounts as well as the households’ positions in three types of financial instruments: bonds, stocks and mutual funds. Table B shows the percentages of the observations participating in such saving methods per year since 2008 as well as the homeownership percentage amongst respondents. Curiously enough the homeownership rate for 2009 seems substantially lower though no reason was found as to why.
Table B.3: Household savings composition
Checking and/or savings accounts Bonds Stocks Mutual funds Houseowner
2008 98.6% 3.8% 9.6% 15.6% 60.3% 2009 98.5% 3.6% 9.9% 19.7% 52.6% 2010 97.5% 3.1% 10.3% 18.1% 60.4% 2011 97.3% 3.6% 9.6% 17.5% 62.9% 2012 95.8% 4.3% 9.6% 17.0% 62.5% Importance of saving
Respondents were asked about their saving motives with possible answers ranging, if applicable, from 1 to 7. These questions and the household answers can be found in table B.4. Some respondents answered, for various reasons, ”not applicable” to some of the questions, therefore these were not taken into account for the table.
Note that these questions do not necessarily reflect risk such as income uncertainty, e.g. a household finding precautionary saving important but not experiencing high uncertainty is not more likely to save due to this effect. Though initially accounted for, these were found to be insignificant and were dropped following the Bayes Information Criterion.
Table B.4: Importance of saving
How important is it to you to have some money saved? N Mean Std. Dev.
to leave a house and/or other valuable assets to your children 1063 3.36 1.89
to help your children if they have financial difficulties 1084 4.83 1.76
to supplement your general old-age pension 1158 5.14 1.63
in order to cover future (high) expenses 1372 5.47 1.37
so that you do not ever need to ask other people for financial help 1366 5.72 1.43 so you can buy a (different) apartment or house in the future 1106 3.15 1.88
to generate income from interests or dividends 1227 3.26 1.83
to increase your freedom so you can do what you want 1357 5.34 1.48
to leave money to your children (or other relatives) 1169 3.40 1.92
to have some savings to cover unforeseen expenses 1391 5.93 1.11
to have some extra money to spend when you are retired 1311 5.12 1.56
to give presents or gifts to your children and/or grandchildren 1125 4.28 1.78 to have enough money in your bank account to
be sure you will be able to meet your financial liabilities 1380 6.06 1.16 to buy durable goods (such as furniture,
electrical equipment or bikes) in the future 1363 4.94 1.56
for a better future 1311 4.75 1.52
N=1412
Table B.5: Highest completed education composition
Type of education 2008 2009 2010 2011 2012
Primary 9% 9% 9% 10% 9%
Pre-vocational 22% 22% 23% 23% 23%
Pre-university 10% 10% 9% 10% 10%
Senior vocational training 15% 15% 15% 14% 14%
Vocational colleges 18% 18% 20% 20% 20%
University 8% 9% 9% 10% 10%
No education (yet) 16% 16% 14% 12% 13%
Education
The DHS survey contains information about the respondents highest level of education completed, which is summarized for the period 2008-2012 in table B. As opposed to 2008 it seems that the relative amount of people without education has dropped while those with a higher education has risen.
Earnings uncertainty
LOW Question: What do you expect to be the lowest total net annual in-come your household may realize in the next 12 months? Please use digits only, no dots or comma.
HIGH Question: What do you expect to be the highest total net yearly income your household may realize in the next 12 months?
If HIGH − LOW > 5 then the following four questions were posed, other-wise these were skipped.
Below, we will show you a number of amounts that could theoretically be the total net income of your household. Please indicate with each amount what you think is the probability (in percentages (or how many cases out of 100)) that the total net yearly income of your household will be less than this amount in the next 12 months
PRO1 What do you think is the probability (in percent) that the net yearly income of your household will be less than [LOW+((HIGH-LOW)*2)/10] in the next 12 months?
PRO2 What do you think is the probability (in percent) that the net yearly income of your household will be less than [LOW+((HIGH-LOW)*4)/10] in the next 12 months?
PRO3 What do you think is the probability (in percent) that the total net yearly income of your household will be less than [LOW+((HIGH-LOW)*6)/10] in the next 12 months?
PRO4 What do you think is the probability (in percent) that the total net yearly income of your household will be less than [LOW+((HIGH-LOW)*8)/10] in the next 12 months?
Let the points calculated be {x1, x2, x3, x4}. The four questions above yield
four points of a cdf function, {P RO1, P RO2, P RO3, P RO4}, and define
{P RO1, P RO2−P RO1, P RO3−P RO2, P RO4−P RO3} as {pro1, pro2, pro3, pro4}.
Assuming that the probabilities of points within an interval are uniformly distributed over said interval, this yields the following probability density function
f (x) = 0 if x < LOW, x ≥ HIGH pro1 x1−LOW if LOW ≤ x < x1 pro2 x2−x1 if x1 ≤ x < x2 pro3 x3−x2 if x2 ≤ x < x3 pro4 x4−x3 if x3 ≤ x < x4 1−P4 i=1proi HIGH−x4 if x4 ≤ x < HIGH (B.2)
As explained in section 4, the variable desired is σi. Taking the variance of
the above function yields the variance in terms of a currency whereas the required variable is the variance of the nominal change in income in percent-ages. To achieve this, the variance of the above function is divided by the total income.A table depicting the distribution of the standard deviations can be found in table 4.1.
As noted in section 4.2, not all observations included valid probabilities as answers. The amount of excluded observations differs each year but lies in the range 23%-26%. Manually fixing these distributions, e.g. by scaling, would only add the assumption that the households which did not manage to produce correct probabilities are (in relative terms) capable of correctly estimating their income and inflation beliefs. Moreover, more problems exist in the wrongly answered probabilities for which the respondents intent is less apparent. The group whose probabilities could be fixed by scaling was considered too small and as a result these were not used.
Inflation uncertainty
PR0 Question: What is the most likely (consumer)prices increase over the next twelve months, do you think? Available answers: 1%,2%...,10%. Given the answer to PR0 the participant was asked to assign probabili-ties to four intervals, constructed as follows
if pr0=1 or pr0=2 Y1:=’1’ Y2:=’2’ Y3:=’3’ Y4:=’4’ if pr0=3
Y1:=’1’ Y2:=’2’ Y3:=’4’ Y4:=’5’ if pr0=4
Y1:=’2’ Y2:=’3’ Y3:=’5’ Y4:=’6’ if pr0=5
Y1:=’2’ Y2:=’4’ Y3:=’6’ Y4:=’8’ if pr0=6
Y1:=’3’ Y2:=’5’ Y3:=’7’ Y4:=’9’ if pr0=7
Y1:=’3’ Y2:=’6’ Y3:=’8’ Y4:=’11’ if pr0=8
Y1:=’4’ Y2:=’7’ Y3:=’9’ Y4:=’12’ if pr0=9
Y1:=’5’ Y2:=’8’ Y3:=’10’ Y4:=’13’ if pr0=10
Y1:=’5’ Y2:=’8’ Y3:=’12’ Y4:=’15’
PR1a Of course it is difficult to predict on forehand how much (consumer)prices will increase.Therefore we would like to ask you how sure you are about your prediction. How likely do you think that it is that the increase (in percent) in prices in the next twelve months will be less than [Y1]%?
PR2a How likely do you think that it is that the increase (in percent) in prices in the next twelve months will be less than [Y2]%?
PR3a How likely do you think that it is that the increase (in percent) in prices in the next twelve months will be more than [Y3]%?
PR4a How likely do you think that it is that the increase (in percent) in prices in the next twelve months will be more than [Y4]%?
Analog to the income certainty questions, the above questions yield five intervals, though in this case no upper boundary is defined but let’s assume there exists such a boundary and define it as y5 which is solved by the
equa-tion y5− y4= y4− y3. Also let’s define {P R1a, P R2a − P R1a, 1 − P R2a −
P R3a, , P R3a − P R4, P R4} as {pro1, pro2, pro3, pro4, pro5}. Assuming that
the probabilities of points within an interval are uniformly distributed over said interval, this gives the following probability density function
f (x) = pro1 y1 if 0 ≤ x < y1 pro2 y2−y1 if y1 ≤ x < y2 pro3 y3−y2 if y2 ≤ x < y3 pro4 y4−y3 if y3 ≤ x < y4 pro5 y5−y4 if y4 ≤ x < y5 0 otherwise (B.3)
As before, taking moments is an integration over five continuous uniform distributions: pro1∗ U (0, y1) +P4i=1proi+1∗ U (yi, yi+1).
For the year 2012, the mean of the expected inflation was 3,4%, for which the distribution can be found in table B.6. The average standard deviation is 1,3% and is distributed as shown in table B.7. A total of 1.918 observations were made regarding inflation probabilities of which 524 observations, or 27,3% were discarded for violation of probability theory.
The total percentage of observations that are left out for violations of probability theory for income and/or inflation beliefs, is 44,5% and as noted in section 4.2, this method might be prone to self-selection as the assumption is that higher educated have a higher likelihood of understanding probability theory. In order to see if any factors increase the likelihood of one being
Table B.6: Beliefs about inflation (2012 survey) Eπ N Frequency 0%-1% 4 0,3% 1%-2% 132 9,5% 2%-3% 577 41,4% 3%-4% 346 24,8% 4%-5% 159 11,4% 5%-7% 110 7,9% ≥7% 66 4,7% Mean: 3,4% 1394 100%
Table B.7: Beliefs about inflation (2012 survey)
σπ N Frequency 0%-0,25% 83 6,0% 0,25%-0,5% 157 11,3% 0,5%-0,75% 260 18,7% 0,75%-1% 309 22,2% 1%-1,25% 226 16,2% 1,25%-1,5% 124 8,9% 1,5%-1,75% 74 5,3% 1,75%-2% 51 3,7% ≥ 2% 110 7,9% Mean: 1,31% 1394 100%
excluded, a dummy is created equalling 1 if excluded and 0 for the opposite. A probit estimation can be done on this dummy. To keep the model simple, a regression is done for the year 2012. Note that the probit model is essentially a special case for the ordered probit model, which is defined in section 3, with only one cutoff point.
Table B.8: Probit regression on exclusion dummy (1) Age -0.00586 (-0.49) Age squared 0.0000481 (0.43) Gender dummy 0.0720 (1.03)
Total Gross Income -0.00000683∗
(-2.40) Total Gross Income squared 4.75e-11∗
(2.07)
Degree of urbanisation 0.0161
(0.69) Higher education dummy -0.351∗∗∗
(-5.17) Constant 0.190 (0.60) Observations 1721 Pseudo R2 0.021 t statistics in parentheses ∗ p < 0.05,∗∗ p < 0.01,∗∗∗p < 0.001
Table B.8 shows the estimation results of a probit regression on the exclusion dummy. Note that in contrast to other estimations, this is done on an individual level. Firstly, the pseudo R2 shows the model to have a low explanatory power. Secondly, there is significance for the gross total income variable and its squared terms. But more importantly the variable sign for higher education shows strong significance.
but possible. For a probit model the following probabilities exist
P (yi = 1) = P (yi > 0) = Φ(x0iβ) (B.4)
P (yi= 0) = P (yi ≤ 0) = 1 − Φ(x0iβ) (B.5)
The value of the marginal probability effect for βj, and thus xi,j, depends
on the other values of xi, making the interpretation difficult. Defining the
following
xi,1= a vector of values where xi,j = 1
xi,0= the same vector of values as above but where xi,j = 0,
the marginal probability effect can be defined as
Φ(x0i,1β) − Φ(x0i,0β). (B.6)
By using means for the values of xi, but varying the education dummy, table
B.9 is be generated based on the estimation results and properties seen in table B.8.
Table B.9: Chance of being excluded
Education Dummy P Std. error. 95% Confidence interval
0 ,4896 ,0162 ,4578 - ,5214
1 ,3532 ,0190 ,3159 - ,3905
Where the education dummy equals 1 if the respondent enjoyed a higher education and zero otherwise. Assuming that the model is correct and keep-ing all other variables at their mean leads to a 13,6% lower chance for a respondent to be excluded if having enjoyed a higher education. In other words, there is strong evidence that a subpopulation is more pronounced than the other. This is not necessarily worrisome as the regressions found in section 5 control for the education variable on the right hand side, but it does raise questions on other unobserved and uncontrolled characteristics such as savings opportunity. However since there is no correct information for this group on the excluded probabilities, the (non-testable) assumption is made that this does not impact the results.
Appendix C
Risk perception computation
The DHS data files supplied have been modified in SPSS and the variables generated and/or transformed were done so using the programming lan-guage of SPSS, SPSS Syntax. The following code was used for this thesis to generate the variables for risk perception as discussed in Appendix B. if (pr0=1) y1=1. if (pr0=2) y1=1. if (pr0=3) y1=1. if (pr0=4) y1=2. if (pr0=5) y1=2. if (pr0=6) y1=3. if (pr0=7) y1=3. if (pr0=8) y1=4. if (pr0=9) y1=5. if (pr0=10) y1=5. if (pr0=1) y2=2. if (pr0=2) y2=2. if (pr0=3) y2=2. if (pr0=4) y2=3. if (pr0=5) y2=4. if (pr0=6) y2=5. if (pr0=7) y2=6. if (pr0=8) y2=7. if (pr0=9) y2=8. if (pr0=10) y2=8. if (pr0=1) y3=3. if (pr0=2) y3=3. if (pr0=3) y3=4. if (pr0=4) y3=5. if (pr0=5) y3=6. if (pr0=6) y3=7. if (pr0=7) y3=8. if (pr0=8) y3=9. if (pr0=9) y3=10. if (pr0=10) y3=12. if (pr0=1) y4=4. if (pr0=2) y4=4. if (pr0=3) y4=5. if (pr0=4) y4=6. if (pr0=5) y4=8. if (pr0=6) y4=9. if (pr0=7) y4=11.
if (pr0=8) y4=12. if (pr0=9) y4=13. if (pr0=10) y4=15. execute. compute pr5a=pr1a/100. compute pr6a=(pr2a-pr1a)/100. compute pr7a=(100-pr2a-pr3a)/100. compute pr8a=(pr3a-pr4a)/100. compute pr9a=pr4a/100. compute y5=y4+(y4-y3). compute Einfl=1/2*(pr5a*(y1)+pr6a*(y1+y2)+pr7a*(y2+y3)+pr8a*(y3+y4)+pr9a*(y4+y5))/100. execute.
if (pr6a<0 | pr7a<0 | pr8a<0 | pr9a<0) Einfl=0.
RECODE Einfl (0=SYSMIS).
execute.
COMPUTE Vinfl=1/10000*1/3*(pr5a * (y1 ** 2)+pr6a*(y1 ** 2+y2 ** 2+y1*y2)+pr7a*(y2 ** 2+y3 ** 2+y2*y3)+pr8a*(y3 ** 2+y4 ** 2+y3*y4)+pro9*(y4 ** 2+y5 ** 2+y5*y4))-Einfl**2. COMPUTE STDinfl=Vinfl**.5. EXECUTE. COMPUTE x1=laag+((hoog-laag)*2)/10. EXECUTE. COMPUTE x2=laag+((hoog-laag)*4)/10. EXECUTE. COMPUTE x3=laag+((hoog-laag)*6)/10. EXECUTE. COMPUTE x4=laag+((hoog-laag)*8)/10. EXECUTE. COMPUTE pro5=number(pro1, F3)/100. EXECUTE.
COMPUTE pro6=(number(pro2, F3)-number(pro1, F3))/100. EXECUTE.
COMPUTE pro7=(number(pro3, F3)-number(pro2, F3))/100. EXECUTE.
COMPUTE pro8=(number(pro4, F3)-number(pro3, F3))/100. EXECUTE.
COMPUTE pro9=(100-number(pro4, F3))/100.
COMPUTE Eink=1/2*(pro5 * (laag+x1)+pro6 * (x1+x2)+pro7 * (x2+x3)+pro8 * (x3+x4)+pro9 * (x4+hoog)). EXECUTE.
if (pro6<0 | pro7<0 | pro8<0 | pro9 <0) Eink=0.
RECODE Eink (0=SYSMIS).
if ((hoog-laag)<5 & (hoog-laag)>=0 & laag>0) Eink=(hoog+laag)/2. execute.
COMPUTE Vink=1/3*(pro5 * (x1 ** 2+laag ** 2+x1*laag)+pro6*(x1 ** 2+x2 ** 2+x1*x2)+pro7*(x2 ** 2+x3 ** 2+x2*x3)+pro8*(x3 ** 2+x4 ** 2+x3*x4)+pro9*(x4 ** 2+hoog ** 2+hoog*x4))-Eink**2. EXECUTE.
COMPUTE STDink=Vink**.5. EXECUTE.
compute NSTDink=STDink/Eink.
if ((hoog-laag)<5 & (hoog-laag)>=0 & laag>0) stdink=0. if ((hoog-laag)<5 & (hoog-laag)>=0 & laag>0) nstdink=0. execute.
