Jurgen Polling
s2240629 – MSc. Finance – MSc. Economics University of Groningen
22-06-2017
Abstract
This study examines household investments over time, when facing different deposit interest rates. Moreover, it examines the effect of the (declining) deposit interest rates on the amount invested in risky assets; stocks and bonds, with the use of random effects models and Tobit models. Additionally, the decision whether to invest in one or both asset markets was tested through binary choice probit models. The data used to test these models was obtained from the Survey of Health, Ageing and Retirement in Europe. Overall, the deposit interest rate has a negative influence on the amount invested by households; this holds for stocks, bonds and total investments. Moreover, a positive influence of the deposit interest rate was found regarding the investment decision of households. However, this effect was not significant for the investments in bonds. The results remain similar after the conduction of a sensitivity analysis on assumptions made to obtain useful data.
Key words: Portfolio structure; deposit interest rates; stocks; bonds JEL classification: D14, G11
Thesis supervisor: Dr. S. J. Drijver
2 1. Introduction
It is commonly known from textbooks and previous literature that diversification should occur when constructing a portfolio (Campbell, 2006). However, this is not observed in the real world, as most household do not construct a portfolio that includes any form of risky assets, but they rely solely on the deposit interest income obtained from their safe investment on a bank account (Bertraut and Starr-McCluer, 2001). As will be discussed in the next chapter, there are several reasons for individuals and households to have investments (or the absence of them). Moreover, previous literature has thoroughly analyzed the effect of the characteristics of individuals on one’s portfolio allocation and participation in the markets of risky assets. Lately, several studies have been conducted that observe external influences on the portfolio allocation decisions households make (i.e. tax structure and inflation rate)( Hochguertel, Alessie and van Soest, 1997; Poterba, 2001).. This research will contribute to these studies about external effects on portfolio structure decisions.
Based on panel data obtained from the Survey of Health, Ageing and Retirement in Europe (SHARE), this research will analyze the effect of the deposit interest rate received on a (assumed to be) safe bank account on the investment decisions made by households. As one could observe a trend of decreasing deposit interest rates, the return obtained on the wealth1 of individuals is under pressure, as most households have their wealth partly stored on a bank account. The reasoning behind this study is that households wish to obtain a certain amount or percentage of revenue on their wealth. With declining deposit interest rates, the alternative, investing in risky assets against a higher return, becomes more tempting to maintain a certain revenue level.
This study found a significant and negative relation between the deposit interest rate a household receives at their bank account and the amount invested in stocks, the amount invested in bonds, and the total amount invested in risky assets. On the contrary, the deposit interest rate has a significant and positive influence on the decision to participate in the market of risky assets and on the decision to participate in the stock market. An insignificant result was found for the participation in the bond market.
The rest of this paper will be structured as follows. Section two will discuss the relevant existing literature about asset allocation and household portfolios. Thereafter, based
1 This study defines wealth as the investment made in liquid assets (i.e. bank account, stocks and bonds) and
3 on this literature and the reasoning given before, the hypotheses of this study will be given. Section three will describe the data collected and gives an overview of the modification made to obtain useful and interpretable data. Subsequently, the methods used in this study to analyze the hypotheses will be discussed in the fourth section. The results from these models are evaluated in section five, followed by some discussion point about the data and models in section six. Based on the discussion, a sensitivity analysis has been performed, which will be discussed in section seven. Lastly, section eight will give an overall conclusion regarding this study.
2. Literature
In this second chapter, existing relevant literature written on household asset allocation will be discussed. The main theme in these articles is the influence of demographic characteristics on the asset allocation of a household. However, more recent studies have also conducted research about other, external, influences. Both these types of influences will be discussed later. First of all, the framework of household asset allocation in theory will be set. Thereafter, this theory will be compared with the household portfolios observed in the real world. Finally, the hypotheses of the research will be expounded.
2.1 Asset allocation models over time
4 will be dynamic and influenced by the market, contrary with short term models, in which the risk free interest rate is often assumed to be fixed. Bodie, Merton and Samuelson (1992) adjusted the model by adding one more variable: the hours of work people choose to exchange for their leisure time. With this adjustment, the model became even more realistic.
The general result from the model is that the relative amount of wealth invested in equity, which is a risky asset, should decline during a lifetime. Bodie, Merton and Samuelson (1992) give two reasons for this phenomenon. First, human capital can be seen as a safe asset which is a relatively high proportion of wealth when younger and declines during one’s life. Therefore, a younger person should invest more in risky assets to create a portfolio with sufficient risk. On the other hand, this human capital also brings some risk, especially for young people, with less or no work experience. However, when entering prime-age (around 30 years), uncertainty about life-time income will decrease, implying that this group is able to take on more financial risk (Gollier, 1999). Moreover, when approaching retirement, older people exhibit less labor flexibility. When faced with disappointing investment income, they are not able to work additional hours or more years in total. Therefore, it is reasoned that the fraction of risky assets will decline after the prime-age. Even though there will be variation in size throughout a lifetime, all the models predict (or advise) households to hold part of their wealth invested in risky assets to optimize lifetime utility. Or as stated in Campbell (2006) in the textbook model of household asset allocation, no matter how risk averse, all households should hold some equities when there exists a positive equity premium, which is commonly accepted.
5 rich”. One of the main findings was, as confirmed by Campbell four years later, that rich households are more likely to own every kind of asset. This rich segment of households owns in particular more equity in privately held businesses, 75 percent of the rich households versus 13 percent of the rest of the population. The second biggest gap is stock ownership, where the difference is 74 percent compared to 16 percent. Another study performed by McCarthy (2004) found similar results. McCarthy stated that the majority of households will not have a complex portfolio structure, but rather store their wealth solely into their savings account. This even holds in the UK and US where stockholding is traditionally high. A second problem observed from empirical evidence is that households, when investing, do not diversify but only hold a portfolio that contains a few different assets (Hochguertel et al. 1997). A later study of Bertraut and Starr-McCluer (2001) reported a modal number of household assets of three.
2.2 Evidence of internal and external influences on assets allocation
As mentioned before, various studies have been conducted to explain the difference between the theoretical model of Merton and the derogating households portfolios observed in the real world. These influences can broadly be categorized in internal and external influences. Examples of internal influences are demographic characteristics, health status and risk aversion. Moreover, examples of external influences are the effective tax rate and the inflation rate.
6 increases when a household is headed by a college graduate and lower for those without any high school degree. This result can be supported by earlier findings from Hubbard, Skinner and Zeldes (1995) stating that this group has lower background income risk. Moreover, according to Haliassos and Bertraut (1995) these households may obtain an informational advantage, which creates an opportunity to invest in an easier and less time consuming manner. A last comparison Bertraut and Starr-McCluer did, was between the marital states. Results conclude that unmarried men have a lower probability of owning risky financial assets compared to married couples or female-headed households. However, this contradicts earlier research done by others (i.e. Jianakoplos and Bernasek, 1998). Many of the findings above have been confirmed through other researches, both before and after Bertraut and Starr-McCluer (i.e. Mankiw and Zeldes (1991); Campbell (2006)). Besides these well researched influences (age; wealth; education; gender) numerous studies have been conducted about various other household characteristics (race; number of children; pension structure etc.) which will not be discussed here, as these are not specifically relevant.
In the next section, the influences of several external factors on household asset allocation will be discussed. However, these influences are not studied as frequently as the household characteristics. One of the most important external factors for a household is the marginal tax rate, which is researched by Hochguertel, Alessie and van Soest (1997). Their research was conducted in the Netherlands, with data of more than 3000 households. As stated in their study, the theory provides little guidance on the matter. Because of the complex tax structure, it seemed impossible to work with a theoretical model. Therefore Hochguertel et al. worked with the empirical evidence to describe the effect of taxation on asset allocation. Their study showed that “the marginal tax rate on income is highly significant”; households hold more financial wealth when they are subjected to a larger marginal tax rate. This can be explained by the tax-free allowances on both returns from savings and on dividend income. Due to the structure, the tax advantage grows when household face a higher marginal tax rate. Moreover, it was found that people invest more risky when facing a higher marginal tax rate.
7 research points out six main aspects of portfolio behavior that are influenced by the tax structure, namely: asset selection, asset allocation, borrowing, asset location in taxable and tax-deferred account, asset turnover and whether to hold assets directly or through financial intermediaries. Several reasons for the investigation of the taxation are given by Poterba. One of the most important reasons regards the empirical problem mentioned above: the significant difference between the theoretical models and the real world empirical data regarding household asset allocation. It is stated that tax expenses lead to an increase the other transaction costs, which could be a reason for the low diversification observed in household portfolios. Moreover, Poterba states that the tax structure faced by households could explain the patterns that are found in the empirical studies. The study concludes with several general patterns. The first conclusion Poterba founds is that the tax structure clearly influences the choice of households whether or not to acquire an asset. However, the influence on the amount invested in a certain asset is weaker. Secondly, from the data observed, there appears to be a connection between asset trading and the tax rules. However, it is ambiguous whether the change in trading is the result of re-timing of trades that would otherwise been made on another point in time or the result of ‘new’ trades, or how these two are divided. Although there is limited evidence, the data suggest that only a few investors in the U.S. choose their portfolio allocation based on their taxable and tax-deferred accounts.
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2.3 Hypotheses
This research will focus on the gap that is described by Brennan and Xia. The leading hypothesis will analyze the relationship between the deposit interest rate and the amount invested in financial assets. The psychological idea leading to the reasoning behind this hypothesis, will be that the returns on savings are decreasing if the deposit interest rates decrease and therefore households will shift their focus to the financial market, with risky assets, to achieve comparable returns as before the decline in the deposit interest rate. This reasoning leads to the first hypothesis:
Hypothesis 1: The deposit interest rate observed on a household’s savings account is
negatively correlated with the amount invested in risky assets.
Furthermore, the risky assets, mentioned in the first hypothesis, will be divided in two groups, namely stock and bonds. The reasoning behind these hypotheses is equivalent of the reasoning behind the first hypothesis. Therefore, the next hypotheses are constructed:
Hypothesis 2a: The deposit interest rate observed on a household’s savings account is
negatively correlated with the amount invested in stocks.
Hypothesis 2b: The deposit interest rate observed on a household’s savings account is
negatively correlated with the amount invested in bonds.
Besides testing for the amount invested in stocks, bonds and both, the effect of the deposit interest rate on the participation in stocks and bonds markets will be evaluated with the use of a dummy variable (own assets / do not own assets). The expected correlations are similar to the hypotheses stated above. Therefore the corresponding hypotheses are expressed as:
Hypothesis 3a: The deposit interest rate observed on a household’s savings account is
negatively correlated with the participation in either the stock market and / or bond market.
Hypothesis 3b: The deposit interest rate observed on a household’s savings account is
negatively correlated with the participation in the stock market.
Hypothesis 3c: The deposit interest rate observed on a household’s savings account is
9 3. Data
The first part of this chapter will describe the raw data that is collected. Subsequently, the second part will clarify the modifications that have been performed to optimize the data for analysis. Lastly, there will be some descriptive statistics about the main variables used in this research.
3.1 Data Collection and Descriptives
The data used in this paper origins from the SHARE-database2. The SHARE project consists of several waves in more than thirty countries, each wave with roughly three years interval3. The first wave (2004/05) started with approximately 30,000 observations, while in the last wave (2015) almost 70,000 observations were included. The SHARE project targets a population of inhabitants, living in the respective country and aged fifty years and over. Additionally, the partners of the target population, at the moment of conducting the interviews, were also interviewed, regardless of their age. However, this will still cause the average age to be higher than it is in a normal population. This higher average age could result in an age-bias, as stated in the previous chapter; a higher age tends to result in higher amounts invested in risky assets. However, this connection is not considered a problem in this research, because this target population will be appealing to investigate just for that reason.
All the data collected by the SHARE-project is collected through personal face-to-face interviews, with additional computer software; computer-assisted personal interviewing (CAPI). These personal interviews were required to perform physical tests and analysis. However, these physical test results will not be used in this research.
The data is divided in different modules, which are bundles of related questions. There exist, along with others, a demographics module, physical health module and mental health module. Within all participating households, three specific types of respondents were selected
2 This paper uses data from SHARE Waves 1, 2, 4, 5 and 6
DOIs: 10.6103/SHARE.w1.600, 10.6103/SHARE.w2.600, 10.6103/SHARE.w4.600, 10.6103/SHARE.w5.600, 10. 6103/SHARE.w6.600), see Börsch-Supan et al. (2013) for methodological details. (1)
The SHARE data collection has been primarily funded by the European Commission through FP5 (QLK6-CT-2001-00360), FP6 (SHARE-I3: RII-CT-2006-062193, COMPARE: CIT5-CT-2005-028857, SHARELIFE: CIT4-CT-2006-028812) and FP7 (SHARE-PREP: N°211909, SHARE-LEAP: N°227822, SHARE M4: N°261982). Additional funding from the German Ministry of Education and Research, the Max Planck Society for the Advancement of Science, the U.S. National Institute on Aging (U01_AG09740-13S2, P01_AG005842, P01_AG08291, P30_AG12815, R21_AG025169, Y1-AG-4553-01, IAG_BSR06-11, OGHA_04-064,
HHSN271201300071C) and from various national funding sources is gratefully acknowledged (see www.share-project.org).
10 to answer specific modules about the household. These are additional questions on top of the basic questions asked to all respondents. The household respondent answered the questions about housing, household income and household consumption. The family respondent answered the questions about the children living in the household. At last, the financial respondent answered the questions about financial transfers and household assets. Being a specific respondent does not exclude a participant to become a secondary specific respondent; when the household consists of a single person, this person will be the household, family and financial respondent. The financial respondents are the leading respondents for this research, as the asset allocation of the household portfolio is given by the financial respondent. Therefore, one observation in the dataset will represent a complete household. Moreover, the demographics used as control variables (age, years of education) are specified to the financial respondent. With the use of three dummy variables, the financial, family and household respondents are marked in the data.
The research will mainly be based on the asset module. Within this module, the questions needed for this research are regarding the amount of investments the respondents had in specific financial instruments at the time of the interview. Additional to the questions, short explanations about the financial instruments were given to the respondents. As stated before, the financial respondent answers these questions as a representative of the whole household. The questions are set up in two steps; first, the respondent is asked about the amount they have invested in a specific financial instrument. Only when the answer is unknown or the respondent refuses to answer the respondent will advance to the second step. The second step will be to give an indication based on three boundary values; a lower, middle and higher value. This technique is called the “unfolding brackets” and will yield answers in terms of “around lower value” or “between middle value and higher value”. The recoding of these answers will be discussed later. All the amounts refer to Euro values; foreign values were converted with the proper exchange rate at the time of the interview.
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3.2 Deposit interest rates
A first remark regarding the collection of the deposit interest rates is about the overall availability of these rates. As these are not publicly available for all the countries and all the specific years, predictions have been made. These predictions are based on two elements. The first element is the short-term interest rates per country per year, which were obtained from the OECD. These are the rates at which short-term borrowing occurs between financial institutions or the rates of short-term government paper. Moreover, limited data on deposit interest rates was obtained from the World Bank database. These deposit rates are the rates paid by commercial banks on savings deposits of households or individuals.
With these short-term interest rates and data on 103 observation points over time for several countries, a regression model was estimated to fill the remaining missing values of deposit rates4, a total of 157 observations have been predicted. As the short-term interest rates are country specific, it is assumed that these rates reflect the economic states of each country. Therefore, it is not required to apply control dummies regarding country. This assumption has been confirmed after conducting an analysis on the data set, with and without control dummies regarding countries. However, time dummies have been used to control for time. Moreover, several model estimations have been conducted (OLS, robust standard errors, panel data) to find the best fitting values, based on (adjusted) R-squares and residuals, and therefore the best estimations of the deposit rates. When estimating the model of this research, the observed deposit rates will be applied, if available. For the remaining observations the predicted deposit rates will be used. A dummy variable (observed or predicted) has been created to control for this difference in a later stage of the research.
3.3 Data Modification and Generation
The last part of this chapter describes the modifications made to the data obtained from SHARE. Moreover, it provides a brief summary of the generation of the new variables that will be used to obtain the data that can be analyzed.
As stated before, every person has a unique ID. Combined with the wave in which this person is participating, this will yield a unique combination in every time wave. This attribute is used to merge five different time waves into one panel dataset. As a result of the panel data structure, the models automatically control for unobservable factors such as risk aversion,
12 cultural background or country-specific policies. Every person participated at least once and a maximum of five times in this dataset. Moreover, the participations are not necessarily consecutive; one could neglect to participate due to illness of absence during a time wave. This caused the panel data to be unbalanced.
After the merging the separate waves, the variables not needed for this research were dropped from the dataset. Moreover, some missing age values are generated for the sixth wave, as there is information available on year of birth from earlier waves. The financial respondent dummy is used to keep the observations related to the household assets and to drop the rest of the observations. Furthermore, some impossible or illogical values have been removed from the dataset; examples are negative ages or education years. Finally, to be able to control for country effects in the subsequent stage of this research, country dummies have been created. Germany is used as the benchmark, as it one of the countries that participated in every time wave.
This research will focus on the incentive to invest actively in financial instruments, rather than storing money on a bank account for a safe deposit interest rate. Moreover, to measure this incentive and to keep the research confined, only the amount invested in stock and bonds will be measured. Therefore, the amount invested in mutual funds will be divided between these two variables. Moreover, a total amount invested variable will be generated by using the sum of the amount invested in stocks and bonds. Respondents had the opportunity to indicate in which proportions their mutual funds are divided between stocks and bonds. For the respondents who answered with “mostly bonds/stocks”, a ratio of ninety percent is used5. For the respondents who answered with equally divided, a ratio of fifty percent is used. Moreover, to divide the amount of mutual funds if the ratio is not known or rejected to answer, the average proportions of the other respondents is used, which accounts for forty-four percent in bonds and fifty-six percent in stocks.
As explained before, the dataset could provide two types of values for every financial instrument; precise self-reported amounts and imprecise answers based on the unfolding brackets. For the purpose of this research, the answers received from the unfolding brackets have been translated into money values. To achieve consistent values, some assumptions have been made, as there is no additional data available that could specify these answers. It is assumed that the “below lower bound” value has half the lower bound value as best estimate;
13 the “around lower/middle/higher bound” value has the lower/middle/higher bound value as best estimate; the “between lower/middle and middle/higher bound” value has the average of the lower/middle or middle/higher bounds as best estimate; and the “higher than the higher bound” value has a best estimate of one and a half times the higher bound. The money values received from these assumptions were combined with the self-reported amounts into a new variable. This method has been performed on several variables. To correct for potential outliers and incorrect values, the top and bottom one percent of the observations have been cropped.
Additionally, for each of these instruments, dummy variables have been generated. These dummy variables are constructed in two layers. The first is instrument specific; “did the respondent possess stocks, yes or no”. The second layer is an overall view on risky assets. For the purpose of this study, any active investment in a financial instrument is seen as a risky investment. Therefore, the dummy variable is positive when the respondent possesses at least one of the risky instruments, where the bank account variable is seen as a risk free investment. 3.4 Descriptive Statistics
Below in Table 1, the descriptive statistics of the control, dependent and independent variables are given. As stated before, the average age of the respondents is relatively high, almost 67 years. Furthermore, the average years of education lies around 10 years and the distribution between men and women is quite equal, with 43% men and 57% women. The number of observations used in the financial variables is heavily reduced. This is due to the fact that the group of respondents who are investing in the financial market is limited. Moreover, as can be seen from the relatively large standard deviations, the differences between separate observations are enormous. As this research uses panel data, every respondent will be analyzed separately.
Table 1. Descriptive Statistics
In this table the descriptive statistics are reported. The descriptive statistics consist of the number of observations, the mean, the standard deviation and the minimum and maximum for the control, dependent and independent variable.
Control, dependent and independent variables Number of
observations Mean
Standard
Deviation Min Max
Age 178,242 66.96 10.57 23 111.6
Years of education 178,242 9.60 5.36 0 25
14 Prediction dummy – Predicted(1), Observed (0) 178,242 0.631 0.483 0 1
Amount in bank account 110,108* 16,424 29,781 0 248,055
Amount in stocks 26,804* 39,460 72,578 0 616,903
Amount in bonds 21,105* 31,628 50,858 0 362,827
Total amount invested 30,346* 56,852 92,307 0 912,921
Has bank account – Yes(1), No(0) 178,242 0.617 0.486 0 1
Has stocks – Yes(1), No(0) 178,242 0.150 0.357 0 1
Has bonds – Yes(1), No(0) 178,242 0.118 0.323 0 1
Has any risky assets – Yes(1), No(0) 178,242 0.170 0.376 0 1
Deposit interest rate 178,242 0.012 0.012 -0.002 0.062
*Only observations with self-reported amounts have been used.
4. Methodology
As stated before, the data consist of (unbalanced) panel data. Within the dataset there are three variables of interest; the amount invested in stocks, bonds and total investments. Moreover, these variables have also been translated into corresponding dummy variables representing the possession per investment. Therefore, a continuous regression model will be used to estimate the first set of variables. Moreover, a binary choice model will be used to estimate the probabilities regarding the dummy variables. Lastly, the data of the amount and the dummy variables will be combined into a new variable: when a person has no investments, stocks and bonds, it will be reported as 0 instead of a missing value in the amount variables. Afterwards, these values will be tested in a Tobit model as these newly created variables will have a natural boundary at 0 (negative investments are not considered feasible).
4.1 Fixed Effects Model vs. Random Effects Model
15 (Verbeek, 2012). The Hausman test has been conducted for all three dependent variables. All three tests returned with a chi-square probability of 0.0006, which indicates that the null hypothesis is rejected. Therefore, the fixed effects model is a viable option. However, as discussed below, other elements influence the choice between the fixed effects and random effects model.
As this research tries to explain the investment decisions of households, based on the deposit interest rate it faces, the fixed effects model is a valid model. With this model, the differences between the waves ‘within’ households are estimated. While it controls for personal characteristics, it measures the effect of the deposit interest rate for every household over the years. However, as discussed before, the data is obtained from several countries with each a distinctive economy, taxation system, inflation rate and other different influences. Moreover, under the fixed effects model, it is assumed that the unobserved abilities of a household (financial respondent) are constant. However, it is safe to say that a major event, like the crisis in 2007/08, could affect a household’s risk aversion and knowledge about risky investments, and therefore influences the investment decisions of households. As stated by Torres-Reyna (2007) “if you have reason to believe that differences across entities have some influence on your dependent variable then you should use random effect”. Moreover, as suggested by Torres-Reyna, the Breusch and Pagan Lagrangian multiplier test for random effects has been conducted7. This test provided a significant result with a probability of 0.0000 on random effects. Therefore, this research will conduct the random effects model, conditional on the goodness-of-fit of the model, which will be observed alongside with the results.
4.2 Construction of the Random effects model
The standard linear regression model (not controlling for random effects) used when testing the variables with panel data can be written as (Verbeek, 2012):
𝑦𝑖𝑡 = 𝛽0+ 𝑥′𝑖𝑡𝛽 + 𝜀𝑖𝑡. 𝑖 = 1, 2, … , 𝑁, (1) Opposite to the fixed effects model, the random effects model assumes that the error term
observed in the formula above consists of two distinctive parts. Firstly, it has a household
6 The complete results of the Hausman test can be found in appendix C
7
16 specific component (𝛼𝑖), which remains constant over time. Secondly, there is the remaining component of the error term (𝑢𝑖𝑡), which is assumed to be uncorrelated over time (Verbeek 2012). Therefore, the random effects model can be written as:
𝑦𝑖𝑡 = 𝛽0 + 𝑥′𝑖𝑡𝛽 + 𝛼𝑖+ 𝑢𝑖𝑡 𝑖 = 1, 2, … , 𝑁. (2) Where the 𝑦𝑖𝑡 stands for the dependent variables of household (respondent) i in time (wave) t;
the amounts invested in the financial instruments, converted to natural logarithms to obtain coefficients that represent a marginal effect in percentages. Moreover, 𝑥′𝑖𝑡 will reflect the independent variable, for household (respondent) i in time (wave) t, the deposit interest rate, and several control variables; the amount on a household’s bank account, age, years of education of the financial respondent, a set of country dummies (with Germany as the benchmark, as they participated in every wave) and the prediction dummy. The independent and control variables have a similar construction of i and t as the dependent variable. Lastly, 𝛽0 represents the constant and 𝛽 represent the coefficients of interest corresponding to the independent and control variables.
4.3 Construction of the Binary Choice Probit Model
As the variables “has investments, stocks and bonds” are designed to distinguish between two discrete alternatives (0 or 1), a binary choice model is used to describe the data. The coefficients of these models will predict the probability that 𝑦𝑖𝑡 = 1| 𝑥′𝑖𝑡. The preferred model with the field of economics is the probit model. Moreover, the probit and logit models typically yield very similar results in empirical work (Verbeek, 2012). This is especially the case when the econometric model is straightforward, as in this research. Therefore, the probit model, with the standard normal distribution function, will be used as binary choice model to estimate the dummy variables. The probit model is fully described by
𝑦𝑖𝑡∗ = 𝛽0+ 𝑥′𝑖𝑡 𝛽 + 𝜀𝑖, 𝜀𝑖 ~ 𝑁𝐼𝐷 (0, 1), 𝑖 = 1, 2, … , 𝑁, (3) 𝑦𝑖𝑡 = 1 𝑖𝑓 𝑦𝑖𝑡∗ > 0, (4)
17 variables based on the investment decisions. After estimating the model, the effects of the variables will be evaluated at the mean, as is conventional when conducting a probit model. 4.4 Construction of the Tobit model
When the dummy variable is combined with the amount of investments a household has, a variable with a natural boundary at zero is created. Therefore, a Tobit model is used to analyze these variables. As stated by McDonald and Moffitt (1980) the model devised by Tobin (1958) is a model in which it is assumed that the dependent variable has a number of its values clustered at a limiting value, usually zero. The Tobit model uses all the observations8, as opposite of the standard random effects model, where the non-responsive answers were treated as a missing value and therefore not used in the estimation of the model. Moreover, the Tobit model is generally preferred over alternative techniques which conduct the analysis solely on data above the natural boundary (McDonald & Moffitt, 1980). The standard Tobit model can be described by several equations with estimation conditions. These equations are similar to those of the probit model seen before. The formalized model looks like:
𝑦𝑖∗ = 𝛽0+ 𝑥′𝑖𝛽 + 𝜀𝑖, 𝑖 = 1, 2, … , 𝑁, (6) 𝑦𝑖 = 𝑦𝑖∗ 𝑖𝑓 𝑦𝑖∗> 0, (7) 𝑦𝑖 = 0 𝑖𝑓 𝑦𝑖∗≤ 0. (8) Similar to the probit model, the εis are assumed independent of all xi (Verbeek, 2012). The construction of the model will be identical to the variables used in the previous models. However, there will be a single difference regarding the dependent variables, as this will be the amount of investments, stocks and bonds without missing values. Moreover, the variables will not be transformed in their natural logarithm, as zero has no natural logarithm and this will lead to a skewed distribution.
5. Results
This chapter will present and discuss the results obtained from the models explained in the last chapter. Moreover, it will review the hypotheses that were constructed based on earlier research. The results and corresponding hypotheses will be evaluated per model. As the dataset contained many observations, the majority of the results are significant at the one
8 It is assumed that the majority of non-responsive answers are households (financial respondents) without any
18 percent level. Per model the coefficients, standard errors between parentheses, and some model specifications are reported.
5.1 Random Effects Model
For the random effects model, the marginal effects are displayed in Table 2. The specific results regarding the hypotheses are shown in the second row in Table 2. These effects should be read as percentages change, as the dependent variable was converted to the natural logarithm. Therefore, a one unit change (one percent change in deposit interest rate) in the independent variable, will result in a percentage change of the respectively observed effect in Table 2 (times hundred percent) in the dependent variable. The random effect model evaluates the first three hypotheses stated in the second chapter of this research. Firstly, the model specifications will be evaluated. Secondly, with the results the hypotheses will be tested. Thereafter, several interesting results from the remaining variables will be evaluated.
At the bottom of Table 2, the model specifications have been reported. As can be seen from the Wald chi-square and the corresponding probabilities, all of three random effect models have their joined coefficients significant different from zero (Torres-Reyna, 2007). Therefore, the models are appropriate to analyze. The R-squared of the models are 0.18 (total investments), 0.16 (stocks) and 0.25 (bonds).
5.1.1 Amount invested in risky assets – hypothesis 1
The marginal effect of a percent change (increase of 100 basis point) in the deposit interest rate, which corresponds to one unit, has an considerable negative effect on the amount invested, namely -565.6%. This means a marginal effect of -5.7% per basis point. This effect is significant on a one percent level. Therefore the first hypothesis is accepted: the deposit interest rate negatively affects the amount invested in risky assets.
5.1.2 Amount invested in stocks – hypothesis 2a
19
5.1.3 Amount invested in bonds – hypothesis 2b
The last hypothesis evaluated by the random effects model is regarding the amount invested in bonds. The influence of the deposit interest rate is again considerable; however it is less than the amounts reported before. The marginal effect of the deposit interest rate is -379.1% per 100 basis point, or -3.79% per basis point. This estimation is also significant at the one percent level. Therefore it is concluded that the third hypothesis is accepted. The deposit interest rate negatively affects the amount invested in bonds.
5.1.4 Control variables – Random effects model
As stated before, the majority of the coefficients are significant at the one percent level due to the substantially amount of observations. As expected for the age and years of education, the coefficients are positive and significant for every model estimated. Moreover, the effect of being male is also positive and significant at the one percent level in the first two models and five percent level in the third model. This is consistent with the expectation received from existing literature (Barber and Odean, 2001). The amount on a household’s bank account, the variable used to control for wealth, is measured in thousands of Euros. The significant coefficient shows a positive influence between wealth and amount invested in all three models. Lastly, the country dummies that compare the specific countries with the benchmark, Germany, will be discussed. Belgium, Switzerland, Ireland, Italy, Israel and Luxembourg, differ significantly with Germany in a positive sense in all three models. Several countries display different signs per model, for example Denmark, Sweden and the Netherlands. It can be seen that the Eastern European countries (i.e. Czech Republic, Estonia, Hungary, and Slovenia) have negative coefficients compared to Germany in all three models.
Table 2. Random effects model
This table presents the coefficients obtained by estimating the three random effects model. It displays the marginal effects in percentage change of the dependent variable. The standard error is given between parentheses. Moreover, the significance level of the coefficients are reported by *, ** and *** for the 10 percent level, the 5 percent level and the 1 percent level, respectively.
Independent variable Amount Invested Amount of Stocks Amount of Bonds
20 (0.002) (0.002) (0.002) Male 0.194*** (0.022) 0.267*** (0.024) 0.048* (0.026) Amount on bank account 0.005***
(0.000)
0.005*** (0.000)
0.005*** (0.000) Predicted interest rate 0.1328 ***
21 Portugal -0.581*** (0.148) -0.380** (0.177) -0.295* (0.177) Sweden -0.095** (0.044) 0.322*** (0.051) -0.834*** (0.050) Slovenia -1.732*** (0.092) -1.102*** (0.100) -1.887*** (0.153) Constant 8.198*** (0.089) 7.669*** (0.100) 7.184*** (0.107) Wald Chi-squared 4,693.46 3,442.70 5,173.87 Probability Chi-squared 0.0000 0.0000 0.0000 Within R-squared 0.0078 0.0055 0.0202 Between R-squared 0.2191 0.1886 0.2800 Overall R-squared 0.1874 0.1605 0.2589 Number of observations 26,894 23,817 18,832
5.2 Binary choice probit model
The binary choice probit model is conducted to estimate results for the last three hypotheses, regarding the participation in the stock and bond market. After estimating the models, the margins are calculated per variable at the mean of each variable, as is common with the probit model estimations. These marginal effects are shown in Table 3. Before evaluating the hypotheses, the model specifications will be examined. As before, each model has a Wald chi-square that results in a probability of 0.0000, therefore these models are also appropriate to analyze.
5.2.1 Participation in risky assets – Hypothesis 3a
As can be seen in Table 3, the deposit interest rate has a strong marginal effect, 0.854. Moreover, this effect is positive and significant at the one percent level. As stated before, these effects are calculated at the mean and predict the chance that a household has investments (𝑦 = 1) . With this marginal effect, hypothesis 3a is rejected. However, a contradicting correlation is observed from these results. Therefore, it can be concluded that the deposit interest rate positively affects the participation in either the stock and/or the bond market in risky assets.
22 In the second model, as with the previous model, the coefficient has a positive effect, 0.255, and is significant at the five percent level. This contradicts the expected effect and therefore rejects the hypothesis about the participation in the stock market. Based on the results it is concluded that the deposit interest rate positively affects the participation in the stock market.
5.2.3 Participation in bonds – hypothesis 3c
In the third model estimated, a negative marginal effect at the mean is observed. However, this effect is not significant on any level. Therefore, it is not possible to either accept or reject the hypothesis regarding a positive or negative effect of the deposit interest rate on participation in the bonds market as the model cannot prove a significant coefficient different from zero. The deposit interest rate does not affect the participation in the bond market.
5.2.4 Control variables – Probit model
As seen in the three random effect models discussed earlier, years of education, being a male and the amount in a household’s bank account (measured in thousands of Euros) have a significant and positive influence on the participation decision, in both stocks and bonds. The effect of age is ambiguous when compared between the three probit models. For the total participation it is significant on the one percent level and positive. However, for participation on the separated assets, it is both negative and significant at the one percent level. The country dummies show a similar pattern as seen in Table 3. Within the Eastern European countries the participation decision is significantly lower when compared to Germany. Moreover, this negative effect occurs also in countries with major economic downturns, with Greece and Spain as examples.
5.2.5 Implications
23 could be an incentive to invest these additional incomes and diversify between safe and risky assets.
Table 3. Binary Choice Probit Model
This table presents the coefficients obtained by estimating the three binary choice probit models. The coefficients are displayed as the effect on the probability that the household has the dependent variable as investment; these coefficients are evaluated at the means. The standard error is given between parentheses. Moreover, the significance level of the coefficients are reported by *, ** and *** for the 10 percent level, the 5 percent level and the 1 percent level, respectively.
Independent variable Has Investments Has Stocks Has Bonds
Deposit interest rate 0.854*** (0.121) 0.255** (0.114) -0.046 (0.102) Control variables Age 0.002*** (0.000) -0.002*** (0.000) -0.001*** (0.000) Years of education 0.009*** (0.000) 0.009*** (0.000) 0.006*** (0.000) Male 0.069*** (0.003) 0.066*** (0.003) 0.040*** (0.002) Amount on bank account 0.001***
(0.000)
0.001*** (0.000)
0.000*** (0.000) Predicted interest rate -0.049***
24 Hungary -0.282*** (0.022) -0.240*** (0.022) -0.190*** (0.018) Ireland -0.092*** (0.020) -0.046** (0.019) -0.103*** (0.018) Italy 0.006 (0.007) -0.080*** (0.008) 0.026*** (0.006) Israel -0.095*** (0.013) -0.049*** (0.012) -0.089*** (0.010) Luxembourg -0.024* (0.013) 0.008 (0.012) -0.011 (0.010) The Netherlands -0.107*** (0.009) -0.059*** (0.009) -0.117*** (0.008) Poland -0.296*** (0.021) -0.233*** (0.020) -0.229*** (0.019) Portugal -0.154*** (0.015) -0.135*** (0.015) -0.123*** (0.013) Sweden 0.272*** (0.007) 0.271*** (0.006) 0.161*** (0.005) Slovenia -0.117*** (0.010) -0.073*** (0.010) -0.182*** (0.010) Log likelihood -46,496.99 -43,446.17 -40,626.01 Wald Chi-squared 7,185.22 6,849.64 5,881.10 Probability Chi-squared 0.0000 0.0000 0.0000 Number of observations 110,108 110,108 110,108 5.3 Tobit model
25
5.3.1 Amount invested in risky assets – Hypotheses 1
When evaluating the estimations of the Tobit model, it can be seen that the deposit interest rate has a strong negative influence of -84,770 Euros per 100 basis points or -847 Euros per basis point. Moreover, this effect is significant at the one percent level. This is consistent with the results found in the random effects model and the hypothesis constructed at the beginning of this study. Therefore, the hypothesis is accepted: the deposit interest rate negatively affects the amount invested in risky assets.
5.3.2 Amount invested in stocks – Hypothesis 2a
The second coefficient shows similar results as observed at the random effects model, this is corresponding with the second hypothesis. The effect is strongly negative and significant at the one percent level. A change in the deposit interest rate of 100 basis points will cause a -44,915 Euros change in the amount invested in stocks, or a -449 Euros change per basis point. Therefore, the hypothesis is accepted: the deposit interest rate negatively affects the amount invested in stocks.
5.3.3 Amount invested in bonds – Hypothesis 2b
The third coefficient that is evaluated, also confirms the results obtained from the random effects model, which is corresponding with the third hypothesis. The effect is strongly negative and significant at the one percent level. A change of 100 basis points leads to a change of -40,865 Euros in the amount invested in bonds, or a -409 Euros change per basis point. As these results are consistent with the hypothesis stated before, it is accepted that the deposit interest rate negatively affects the amount invested in bonds.
5.3.4 Control variables – Tobit model
26 observed before. However, a similar pattern as before is still in place. The Eastern European countries have fewer investments in assets, in all three models. This difference is also observed for the countries that had an unhealthy economy during this time period (Greece and Spain). Moreover, some countries have no significant difference in the amount invested, but prefer to invest in stocks over bonds compared to Germany. This is true for households from the Netherlands, as the coefficient of the amount invested is not significant, the coefficient of amount invested in stocks is positive and significant at the one percent level and the coefficient of amount invested in bonds is negative and significant at the one percent level.
Table 4. Tobit Model
This table presents the coefficients obtained by estimating the three Tobit models. The coefficients represent the marginal effect on the dependent variables in Euros. The standard error is given between parentheses. Moreover, the significance level of the coefficients are reported by *, ** and *** for the 10 percent level, the 5 percent level and the 1 percent level, respectively.
Independent variable Amount Invested Amount of Stocks Amount of Bonds
Deposit interest rate -84,770*** (14,410) -44,915*** (10,630) -40,865*** (7,151) Control variables Age 96*** (16) 29** (12) 66*** (8) Years of education 712*** (33) 444*** (24) 270*** (15) Male 6,138*** (340) 440*** (247) 1,746*** (157) Amount on bank account 234***
(5)
161*** (4)
83*** (3) Predicted interest rate 1,341**
27 Spain -4,778*** (882) -1,504** (641) -3,223*** (409) France -3,128*** (885) 309 (645) -3,454*** (414) Greece -5,036*** (1,238) -1,769** (902) -3,286*** (581) Hungary -1,379 (2,111) 583 (1,545) -1,843* (1,012) Ireland -698 (2,401) 1,277 (1,755) -2,067* (1,144) Italy 2,516*** (889) -1,284** (646) 3,896*** (412) Israel 6,627*** (1,489) 3,773*** (1,088) 2,891*** (705) Luxembourg 4,018*** (1,502) 2,081* (1,094) 1,818* (702) The Netherlands 204 (1,094) 2,730*** (800) -2,666*** (520) Poland -4,561*** (1684) -1,441 (1,277) -3,022*** (791) Portugal -5,049*** (1495) -2,366** (1,090) -2,663*** (702) Sweden 16,892*** (857) 16,268*** (623) 517 (396) Slovenia -6,654*** (1,103) -2,432*** (803) -4,170*** (515) Constant -9,428*** (1,452) -6,338*** (1,060) -3,147*** (687) Log likelihood -1,336,608.3 -1,302,630.8 -1,257,335.8 Wald Chi-squared 8,132.80 6,942.34 5,177.29 Probability Chi-squared 0.0000 0.0000 0.0000 Number of observations 110,108 110,108 110,108 6. Discussion
Before continuing with the robustness checks, the design of the models will be discussed. Firstly, the model used to predict the deposit interest rates9 will be discussed. There
28 are several points of discussion and attention. A strong point about the model is regarding the (adjusted) R-squared value, which is relatively high. This suggests that the prediction made based on the model, are indeed acceptable values. However, the time dummy variables used in the model to control for different economic states are not all significant. Moreover, the financial crisis could have had a significant influence on the data obtained from both the World Bank and the OECD, as the government actively changed the interest rates to help restore the economy in Europe and therefore weakened the connection between the separate rates.
As stated before, the deposit interest rates were partly observed and partly predicted by the model, as the complete set of deposit interest rates could not be obtained from a dataset with observed rates. Moreover, after the prediction, a dummy variable has been created and used to control for the difference between observed and predicted deposit interest rates. As observed in Tables 2, 3 and 4, the prediction dummy is mostly significant at the one percent level, with the exception of the third estimation in the Tobit model, the effect on amount invested in bonds. Moreover, it seems that the sign of the coefficient of the prediction dummy is the opposite of the sign of the corresponding coefficient of the deposit interest rate. Because the variables are opposed, the influences will counter each other. This results in a smaller effect of the deposit interest rate if this rate is predicted, ceteris paribus. As a stronger effect of the deposit interest rate would not change the outcome of the correlations, only the magnitude of the coefficient, this will not influence the conclusions of this research. However, as the deposit interest rates are the leading independent variables, further research with solely observed deposit interest rates is preferred and should be conducted to confirm the results found in this study.
29 time and therefore most influences will be controlled for, as the research is based on panel data.
As stated in the second chapter, respondents who could not answer the investment questions with a specific value, had the option, the unfolding brackets option, to choose an indication based on three given values. These answers were structured as “around lower value, between middle value and higher value”. In order to use these answers in the models, assumptions have been made about the values that correspond with the answers. As most of the answers point to a specific value, “around middle value, between middle and higher value”, it is assumed that the generated values from these answers are appropriate to use. However, as stated before, it is preferred to obtain values that are directly observed and not obtained through self-reporting or the unfolding brackets technique.
A third point of critique is about the interpretation of the results. From the previous tables strong significant results with a major impact have been observed. However, the data underlying these results was obtained during uncommon times. Since the majority of the data was obtained during and around the recession with extreme economic states. During this period the interest rates were overall rapidly declining. Moreover, the stock and bond market collapsed and investor’s trust diminished. The decline of stocks and bonds values could have two different influences on the data. Firstly, during this time, investment values declined as a result of the financial crisis. Therefore, all investments made before the crisis, declined in value. Moreover, as the prices of investments were at an all time low rate, this could have been an incentive to invest more than under normal circumstances after the financial crisis. Either way, it is beyond dispute that the financial crisis has influenced the data and the investment behavior of households. Therefore, when interpreting the results it should be kept in mind that this data reflects a time period including an uncommon and weak economic state.
30 other distributions will be used as a sensitivity analysis. This analysis will be discussed in the next chapter.
7. Robustness checks
As stated above, a sensitivity analysis has been conducted to control for the assumption that was made to divide the mutual funds. As the fifty/fifty ratio will be correct on average, only the ratio of ninety/ten and ten/ninety will be tested. Moreover, the analysis will test two different ratios, one in both “directions”. The first ratio will be hundred/zero (and zero/hundred), or in other words, the complete value of mutual funds will be allocated to stocks (bonds) if the respondent answered with “mostly stocks (bonds)”. This method will allow for increased differences between the amount of stocks and amount of bonds. Moreover, the second ratio will lessen these differences by equalizing the original ratio to seventy-five/twenty-five, or in other words, three quarters of the mutual fund value will be allocated to stocks (bonds) if the answer of the respondent was “mostly stocks (bonds)”. When analyzing this ratio, the binary choice probit models will not be estimated again, as the change in ratio will not affect the participation in the stocks or bond market compared to the original model. Furthermore, the ratio will not influence the total amount invested, as this is the sum of amount invested in stocks and the amount invested in bonds. Therefore, these models will also not be estimated again. The results on the sensitivity analysis can be found below in Table 5, where solely the results of the deposit interest rate will be shown. The ratios in brackets indicate which assumption is made when the respondents answers with “mostly stocks/bonds”. The full results from the models can be found in appendix D till F.
Table 5. Results from sensitivity analysis
This table presents the results from the sensitivity analysis and the original results for all the three models. The ratio between parentheses represents the ratio used to divide the mutual funds. The original ratio used is (90/10). The coefficients are reported in a similar form as in the previous tables; the random effects model presents the marginal effect in percentages, the Tobit model presents the marginal effect in Euros and the probit model presents the marginal effects in percentage chance of possessing the investment. The standard errors are given between parentheses. Moreover, the significance level of the coefficients are reported by *, ** and *** for the 10 percent level, the 5 percent level and the 1 percent level, respectively.
The deposit interest rate
Stocks (90/10) Stocks (75/25) Stocks (100/0) Bonds (90/10) Bonds (75/25) Bonds (100/0) The random effects model -5.611***
(0.922) -5.867*** (0.871) -5.320*** (0.918) -3.791*** (1.067) -4.956*** (0.942) -8.368*** (1.014)
31 (14,410) (10,392) (11,084) (10,630) (6,960) (7,619) The probit model 0.255**
(0.121) - - 0.418*** (0.109) -0.046 (0.114) - - 0.335*** (0.090)
As can been seen above in the results of the sensitivity analysis, most of the coefficients do not differ in sign and significance. However, when evaluating the probit model, coefficients significant at the one percent level are found in the results from the 100/0 model. This is on the contrary with the results found before, that were not significant at the one percent level (five percent level for possession of stocks and no significant level for possession of bonds). However, the 100/0 ratio is the extreme case, especially when evaluating the possession of stocks and bonds, as in these cases the “mostly stocks/bonds” answers will dedicate the complete amount of mutual funds to either stocks or bonds. Since every other ratio, from 99/1 to 50/50, will lead to the same results when observing the possession of stocks and bonds. Therefore, before interpreting these probit results within a region or country, the available mutual funds in this specific region or country should be evaluated, based on their structure (i.e. solely one type of investment, or mostly a combination of the both).
8. Conclusion
This paper studies the effect of the deposit interest rate on the investment decisions made by households, either in stocks or in bonds or a combination of both. These investments are evaluated at two levels, with a variable that contains the precise amount invested in stocks and bonds and with a dummy variable that presents the choice whether to invest at all (or not). The data used to analyze the hypotheses was obtained from the Survey of Health, Ageing and Retirement in Europe (SHARE). This database contains panel data regarding several European countries from 2004 till 2015, including the financial crisis in 2007/08, observed with intervals of three years. The deposit rates were partly obtained from observed data, and partly, with the use of the observed rates, predicted using regression estimations. Three kinds of models were used to test the hypotheses; the random effects model, the probit model and the Tobit model.
32 amount invested in bonds. With the use of the probit model, the participation in the stock and/or bond market is tested. This study found a positive effect of the deposit interest rate on the decision to participate on the stock market and investing overall. This could be evidence of diversification between safe and risky assets when households receive additional income through deposit interest. However, the effect found for the participation on the bond market is negative and not significant. The results obtained from the Tobit model confirm the results from the random effects model; the deposit interest rate has a negative and significant effect on the amount a household invests in stocks, bonds or a combination of both risky assets.
To strengthen these results, a sensitivity analysis has been conducted on the assumption made to obtain useful data from the SHARE database. The results regarding the random effects model and the Tobit model are in line with the results found in the original models. Moreover, the probit model gives results that are expected from the first estimation of the model; these results are significant at a lower level.
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35 Appendices
Appendix A - Participating countries and their corresponding wave years
Country ID Country Wave 1 Wave 2 Wave 4 Wave 5 Wave 6
11 Austria 2004 2006/07 2011 2013 2015
12 Germany 2004 2006/07 2011/12 2013 2015
13 Sweden 2004 2006/07 2011 2013 2015
14 Netherlands 2004 2007 2011 2013 -
15 Spain (Castilian) 2004 2006/07 2011 2013 2015
15 Spain/Girona (Castilian or Catalan) - - - 2013 2015
15 Spain/Girona (Catalan) - - - 2013 2015 15 Spain/Girona (Castilian) - - - 2013 2015 16 Italy 2004 2006/07 2011 2013 2015 17 France 2004/05 2006/07 2011 2013 2015 18 Denmark 2004 2006/07 2011 2013 2015 19 Greece 2004/05 2007 - - 2015 20 Switzerland (German) 2004 2006/07 2011 2013 2015 20 Switzerland (French) 2004 2006/07 2011 2013 2015 20 Switzerland (Italian) 2004 2006/07 2011 2013 2015 23 Belgium (French) 2004/05 2006/07 2011 2013 2015 23 Belgium (Flemish) 2004/05 2006/07 2011 2013 2015 25 Israel (Hebrew) 2005/06 2009/10 - 2013 2015 25 Israel (Arabic) 2005/06 2009/10 - 2013 2015 25 Israel (Russian) 2005/06 2009/10 - 2013 2015 28 Czech Republic - 2006/07 2011 2013 2015 29 Poland - 2006/07 2011/12 - 2015 30 Ireland - 2007 - - - 31 Luxembourg (French) - - - 2013 2015 31 Luxembourg (German) - - - 2013 2015 32 Hungary - - 2011 - - 33 Portugal - - 2011 - 2015 34 Slovenia - - 2011 2013 2015
35 Estonia (Estonian or Russian) - - 2010/11 2013 2015
35 Estonia (Estonian) - - - 2013 2015
35 Estonia (Russian) - - - 2013 2015
36 Appendix B – Deposit interest rate regression
The deposit interest rates are partly the true, observed rates and partly predicted based on the short term interest rates on government bonds per country. The observed deposit interest rates are obtained from the World Bank database. Moreover, the short term interest rates are obtained from the OECD database. It is assumed that these rates are country specific and will influence the local banks when setting their deposit interest rate. With these two rates, combined with time dummy variables (with 2015 as benchmark) and an Eastern European dummy variable (1 if the country lies in Eastern Europe, 0 otherwise), a regression has been performed to obtain an estimation for the remaining deposit interest rates. Several models have been tested and, based on the residuals and (adjusted) R-squared, the model presented below has been used to perform the prediction. This is a normal linear regression model. As stated before, the preference goes to the observed rates. Therefore, these are used when available and when not, the predicted rates are used. To control for these rates, the prediction dummy has been created.
The standard error is reported between the parentheses. Moreover, the significance level of the coefficients are reported by *, ** and *** for the 10 percent level, the 5 percent level and the 1 percent level, respectively.
Independent variable Deposit interest rate
