Risky Asset Holding and Labour Income Risk: Evidence from Italian Households

Transcription

1 Risky Asset Holding and Labour Income Risk: Evidence from Italian Households Thesis for Master in Finance Haiyue Dong and Junjie Jiang Supervisor: Professor Hossein Asgharian Lund University School of Economics and Management May 25th, 2016

2 Abstract Household portfolio choice problem has been in debate for a long time, and it becomes more relevant nowadays. Substantial works have been done to understand the relationship between labour income risk and risky asset holding, despite that inconsistent empirical relationships are revealed. In this paper, we investigate the age-variant e ects of labour income risk on households participation decision and risky asset share with data from the Italian Survey on Household Income and Wealth (SHIW). The results under the narrow definition of risky assets suggest that the risky asset share of the middle-aged households are less influenced by labour income risk, compared to the young and the elderly households. These results are robust to alternative measure of labour income risk. Keywords: Permanent income risk, Transitory income risk, Age-variant e ect, Households risky asset holding. We would first like to thank our thesis supervisor Professor Hossein Asgharian at the Department of Economics of Lund University. We are gratefully indebted to his enlightening comments and patient guidance. We would also like to thank our discussants at the mid-term seminar for their valuable suggestion. Haiyue Dong and Junjie Jiang i

3 Contents 1 Introduction 1 2 Literature Review Household Portfolio Choice Problem Risky Asset Holding and Labour Income Risk Measures of Labour Income Risk Data 12 4 Methodology Step One: Income Risk Measuring Step Two: Risky Asset Holding Empirical Results Step One: Income Risk Measuring Step Two: Risky Asset Holding Descriptive Statistics Market Participation Risky Asset Share Robustness Check Conclusion 39 Reference 41 Appendix 45 ii

4 List of Tables 1 Frequencies and Number of Sample Households Variable Explanation Labour Income Regression Results Cross-sectional Covariance Matrix of Unpredictable Labour Income Growth Average Income Risk by Industry-Education Group Risky Asset Holding of Households in Comparison between Participants and Non-participants Participation Decision and Labour Income Risk Narrow Definition Risky Asset Share and Labour Income Risk Narrow Definition Breusch and Pagan Lagrangian multiplier test for random e ects Correlation Between Participation Decision and Explanatory Variables Correlation Between Risky Asset Share and Explanatory Variables Participation and Risky Asset Share and Total Inocme Risk Participation Decision and Labour Income Risk Broad Definition Risky Asset Share and Labour Income Risk Broad Definition List of Figures 1 Participation Rate and Italian GDP Growth Scatter Plot of Transitory and Permanent Risk iii

5 1 Introduction Household portfolio choice problem has been the subject of contentious debate in both theoretical and empirical research. Given the increasing financial sophistication and life expectancy of households, this problem is even more relevant nowadays. Among all the topics covered in this realm, how households should invest in risky assets 1 and what they actually do are of particular interests to many, and yet remain challenging. An important feature that makes these issues di cult to study is that households possess a significant amount of non-tradable assets human capital, the risk of which represents a notable source of background risk. Substantial works have been done to uncover the relationship between labour income risk and risky asset holding. Theoretical works on portfolio choice problems invariably point to the negative e ect of labour income risk on risky asset share (Bodie, Merton & Samuelson, 1992; Viceira, 2001; Gomes & Michaelides, 2005), On the other hand, empirical works show rather mixed evidence on the influence of income risk. For instance, Angerer and LAM (2009) and Guiso, Jappelli and Terlizzese (1996) find strong evidence that labour income risk reduces households market participation and risky asset share, corroborating the implications of the theoretical models, whereas Bertaut (1998) and Arrondel, Pardo and Oliver (2010) document that the e ect is only negative under certain specifications, providing very limited support for the theoretical predictions. Despite the well-explored e ect of labour income risk, it has never been investigated if such e ect di ers for households within di erent age groups. As households grow older, they display inconstant risk aversion (Harrison, Lau, & Rutström, 2007) and experience changes in several other aspects, such as health status. These changes could potentially influence how households perceive labour income risk, and thus further influence how they incorporate labour income risk into their risky asset holding decisions. If this is the case, previous mixed evidence on the role of labour income risk may simply be the result of ignoring such disparity between households in di erent life stages. 1 Risky assets are defined as financial assets that carry significant price volatilities, such as shares and bonds. 1

6 The purpose of this study is thus to investigate the age-variant relationship between labour income risk and risky asset holding. This study di ers from previous studies in that the e ect of labour income risk is allowed to vary for households within di erent age groups through the inclusion of interaction terms between income risk measures and age group dummies. Furthermore, this study distinguishes between permanent and transitory risk components and examines how these two risk componentsdi er in roles in the portfolio choice problems of Italian households. To the best of our knowledge, previous studies on Italian households portfolio choice problem (Guiso et al. 1996; Grande & Ventura, 2002) have not employed the permanenttransitory risk framework. Such separation between permanent and transitory risk components has two favourable features that entail the re-evaluation of the relationship of interest on Italian households. First of all, the permanent-transitory risk framework is congruous with the modelling of labour income process in most theoretical works (e.g. Cocco, Gomes & Maenhout, 2005) where agents are assumed to be exposed to both permanent and transitory income risks. In this sense, the separation of permanent and transitory risks enables direct test of the implications of these works. Previously, labour income risk is either approximated with realised income variability, as in Heaton and Lucas (2000), or with subjective risk measures, as in Guiso et al. (1996). These two income risk measures, while meaningful in their own ways, are incongruous with the ones normally used in theoretical literature. Secondly, permanent and transitory components represent labour income risks of di erent durabilities, and it is then expected that permanent component has larger influence compared to transitory component, due to the high persistence of permanent shocks. Previous studies that distinguish between these two risk components have proved their di erent roles, and thus the significance of such separation (Angerer & LAM, 2009; Calvet & Sodini, 2014; and Blundell, Pistaferri & Preston, 2008). Given these two features, it could provide more insight to treat the income risk as partitioned into two components, the permanent and the transitory, in the evaluation of their respective roles in households risky asset holding. Our study has two distinct contributions. Most importantly, it is the first study to investigate the age-variant e ect of income risk on risky asset holding. We find some evidence that the e ect of labour income risk on risky asset share is smaller for the middle-aged households, compared with that of the young and the elderly 2

7 households. If labour income risk is approximated with permanent risk component, 1% increase in permanent risk significantly decreases the risky asset share by 0.8% for the young and the elderly participants, while by only 0.2% for the middle-aged participants. This di erence also holds for alternative measure of labour income risk. However, this di erence disappears under other specifications. In addition, our study contributes to the understanding of Italian households risky asset holding decisions and allows for international comparison. The separation of permanent and transitory risks has not been employed in the study of Italian household data. Our results suggest that neither permanent nor transitory risk is the primary reason that prevents Italian households from participating in the market, whereas the fixed cost of entry, education, and residential areas are. As to risky asset share, both risks are found to have significant impacts, and the impact of permanent risk is more robust. Moreover, the estimated coe cients predict that the permanent and transitory risks have opposite roles in deciding risky asset share, which di ers from the result of Angerer and LAM (2009) where transitory risk is found to have negative and insignificant impact. The paper is organised as follows. Section 2 reviews literature closely related to the topic of interest. Section 3 presents the dataset employed and restrictions imposed on the selected samples. Section 4 is the methodology part where the construction of labour income risk measures is elaborated and the model specification for risky asset holding is presented. Section 5 shows empirical results and discussions of these results. In the final section, limitations of this work are discussed and concluding remarks are drawn. 3

8 2 Literature Review In this section, existing literature related to our study are reviewed in three parts. In the first part, basic models and extensions on household portfolio choice problems are reviewed in general. In the second part, theoretical and empirical studies on the relationship between labour income uncertainty and portfolio choice are scrutinized. In the third part, measures of labour income risk in previous studies are reviewed with a focus on the permanent-transitory risk framework. 2.1 Household Portfolio Choice Problem Households encounter the problem of allocating their wealth to consumption, savings and investments throughout the whole life cycle, and they occasionally rebalance their portfolios in order to achieve larger utility when faced with changes of interest rate, income, and other factors that influence their well-being. Therefore the portfolio choice problem of households cannot be simply addressed by the one-period optimization solutions (e.g. Markowitz, 1952) commonly employed by financial practitioners. Rather, the problem is normally formulated with an intertemporal consumption-investment model (e.g. Viceira, 2001) and is evaluated under both the discrete- and continuous-time framework. The articles of Samuelson (1969) and Merton (1969) are pioneering works on the multi-period optimization problem. In the seminal paper of Samuelson (1969), the multi-period consumption-investment problem is formulated in discrete time. It is assumed that agents derive utility from current consumption, and that the amount available to consume is constrained by the wealth function where risky asset returns influences the amount of wealth. The problem is solved with dynamic programming approach and Samuelson shows that the multi-period portfolio problem can be easily reduced to the single-period problem if certain conditions are posited. The result states that for an agent with constant relative risk aversion, the optimal fraction of wealth invested in risky assets is constant during the life-cycle. In the companion papers of Merton (1969 & 1971), the same problem is evaluated in the continuoustime framework and similar conclusions are drawn. Building upon these works, Merton (1973) o ers the first major extension of equilibrium capital asset pricing theory to a multi-period setting where a state variable 4

9 is introduced, allowing for changing investment opportunities (Du e, 1998). This leads to the three fund theorem, which states that each agent should hold three funds, the risk-free asset, a myopic portfolio and a hedging portfolio, and that the combination of them are determined by the agent s preferences and hedging demands. These fundamental models in Samuelson (1969) and Merton (1969, 1971 & 1973) suggest that all agents should hold risky assets, despite that the share and combination of risky assets vary with the agents risk attitudes and hedging demands. Whilst these models provide rather tractable and elegant solutions to the multi-period portfolio choice problem, the assumptions of hyperbolic absolute risk aversion and frictionless market, and the absence of background risks make these theories vulnerable to some prevailing facts, e.g. the limited participation in the stock market, thus necessitating more general extensions. The first thread of studies attempts to formulate behavioural anomalies observed from experiments (e.g. Camerer, 1992) that cannot reconcile with the axioms of expected utility theory which is commonly relied on in the theoretical research. Several non-expected utility preference formulation are proposed and applied to the modelling of portfolio choice problems (Brandt, 2009). For example, the prospect theory proposed by Kahneman and Tversky (1979) incorporates the anomaly that agents are relatively more responsive to losses than to gains, and introduces the concept of reference point and formulates the value function as concave for gains while convex for losses. The theory is later applied to the formulation of portfolio choice problem by Berkelaar, Kouwenberg and Post (2004). Unlike the first thread of studies that pursues explanations from the behavioural side, the second thread of studies seeks to capture the influence of real-life market features, the most important of which are market frictions and background risks. According to Brandt (2009), studies on market frictions, especially on fixed entry costs, transaction costs and capital gains taxation, are extensive and ongoing because of practical relevance. For example, Balduzzi and Lynch (1999) are the first to consider the situation when the agent is faced with transaction costs and return predictability simultaneously. The numerical solution suggests that the inclusion of transaction costs induces a wider no-trade zone, and the agent rebalances more frequently in the presence of return predictability, and the utility cost of ignoring 5

10 transaction costs can be substantial. Background risks are firstly formally considered by Pratt and Zeckhauser (1987). Kimball (1993) introduces the concept of prudence, that agents will hold precautionary savings in expectations of risks. Kimball (1993) further generalizes their framework to evaluate the interaction between background risks and the unfavourable risk. Both these works imply that bearing one risk would make the agent unwilling to take another, even if the two risks are statistically independent. Heaton and Lucas (2000) calibrate a model with background risks. Their results imply that higher background risk reduces risky asset share. The studies that followed normally consider three specific kinds of background risks: housing risk, health risk and labour income risk. One of the most prominent papers considering housing risk is the work of Cocco (2005). In that paper, Cocco (2005) assumes that the agent s consumption utility from housing is related to the house size. He further assumes perfectly positive correlation between the cyclical housing price fluctuations and aggregate labour income shocks and imperfect correlation between housing price fluctuations and temporary labour income shocks. After the model is calibrated to match the variation in the American households panel data, it predicts that when financial net worth is low, a high-level real estate keeps household liquid assets at a low level and prevents households from participating in the stock market. Compatibly, empirical works find consistent evidence on the crowding-out e ects of housing (Arrondel & Savignac, 2009; Heaton & Lucas, 2000). Studies on the relationship between health risk and risky asset holding are mostly empirical. Christelis, Georgarakos and Sanz-de-Galdeano (2014) find that the reduction in health-related risk induces stock holding for those with college education using a regression discontinuity design to exploit the fact that the onset of Medicare is at the age of 65 in the America. Cardak and Wilkins (2008) use Australian household survey data and find a significant negative e ect of poor health status on the risky asset ratio for employed households. 6

11 2.2 Risky Asset Holding and Labour Income Risk For an average agent, human capital is an asset of paramount importance, and the realisation of it, as represented by labour income streams, is subject to risks of job shifts, unemployment and wage changes. Such risks are almost uninsurable and labour income is non-tradable due to moral hazard problem that restrains agents from trading against their future income (Viceira, 2001). As labour income risk is not possible to insure or hedge against, it is an important source of background risks for an agent to consider when making consumption-investment choices. Bodie et al. (1992) incorporate non-tradable labour income into the intertemporal model in the continuous-time framework. They characterise the wage dynamics and the risky asset return dynamics as given by the same Wiener process, and further assume perfect positive correlation between these two processes. They show that if the second-order partial derivative of the value function with regard to wealth and wage is negative, the presence of wage risk decreases optimal risky asset share, and vice versa. This result, as they argue, involves both wealth and substitution e ects: while the agent s asset demand is dependent on total wealth, his optimal exposure from risky assets is the di erence between his desired total exposure and the wage risk. In discrete time, Viceira (2001), Cocco et al. (2005) and Gomes and Michaelides (2005) draw upon the permanent-transitory risk framework presented in Carroll (1997) to formulate the labour income process. Viceira (2001) considers the case where labour income and stock returns can be imperfectly correlated, and models the labour income as subject to permanent income shocks. 2 His approximate solution to the optimal policy for an employed agent has several implications. Firstly, the optimal share is positively related to the risk premium of the risky asset, and negatively related to the relative risk aversion of the value function. Secondly, the optimal share decrease as the agent grows older and his human capital diminishes. Thirdly, it is optimal for the agent to invest more in risky assets if his labour income innovation and stock return innovation are negatively correlated, and vice versa. Similar conclusion can be seen in Cocco et al. (2005). In that paper, a slightly more 2 The author explains that the assumption of zero transitory risk follows from the results of his previous theoretical work, Viceira (1998), where transitory risk is found to have very little impact. 7

12 complicated income process is assumed, where the permanent risk is further decomposed into an aggregate component and an idiosyncratic component, but the risk is only estimated at the permanent risk level. Given that the estimated correlation between income risk and return risk is insignificantly positive, the calibrated model suggests that labour income represents an implicit holding of risk-free assets, and that risky asset share declines as income risk increases and vice versa. While the formulation of Viceira (2001) ignores transitory income risk and assumes constant relative risk aversion, the model of Gomes and Michaelides (2005) takes into account both permanent and transitory risks and assumes Epstein Zin preferences, enabling the separation of risk aversion from the elasticity of intertemporal substitution. Moreover, Gomes and Michaelides (2005) attempt to simultaneously match the participation rate and the risky asset share conditional on participation. Their numerical solution delivers two important implications. Firstly, participation rate increases in risk aversion, leading to the result that market participants are on average more risk averse than nonparticipants. They argue that the e ect of wealth accumulation motive dominates that of risk aversion, and consequently those with higher risk aversion (and thus higher prudence) is more motivated to pay the fixed cost of entry and to accumulate wealth through participating in the stock market. Secondly, since the market participants are more risk averse, they do not invest fully in equities. To evaluate the influence of income risk in particular, they increase the variance of transitory shocks by a factor of three from that in the baseline model where the variance of the transitory risk is set to They find that such increase reduces risky asset share, but induces higher market participation rate, following from the dominant e ect of wealth accumulation motive for the more risk averse agents. Taken together, these studies suggest that higher labour income risk reduces optimal allocation to risky assets if labour income innovation and stock market innovation is either independent or positively correlated. As to market participation, Bodie et al. (1992), Viceira (2001) and Cocco et al. (2005) imply that all agents should hold risky assets regardless of their exposure to labour income risk, while Gomes et al. (2005) implies that higher income risk can stimulates higher market participation rate, provided that the wealth accumulation motive is stronger for more risk averse agents. Empirical works attempting to evaluate these relationships give somewhat mixed evidence which could be attributable to the diverse labour income risk mea- 8

13 sures employed in these studies. Guiso et al. (1996) and Cardak and Wilkins (2009) find strong evidence that labour income risk impinges on demand for risky assets. Guiso et al. (1996) are among the first to empirically test the implications of previous theoretical works on background risks (e.g. Pratt & Zeckhauser, 1987; Kimball, 1993). They construct an objective labour income risk measure based on households self-reported expectations on inflation and income growth from the Italian household survey data. They find that higher labour income risk significantly reduces risky asset share and this result is robust under both the narrow and broad definitions of risky assets. Cardak and Wilkins (2009), applying the variance of realised income change as income risk proxy, find that labour income risk significantly reduces risky asset share for Australian households. On the other hand, limited evidence is documented in Bertaut (1998) and Arrondel et al. (2010) that labour income risk discourages participation. Arrondel et al. (2010) adopt the same specification as that of Guiso et al. (1996) and control for the correlation between income risk and stock return risk using the self-perceived relationship between income risk and return risk as a proxy for the correlation. 3 They find that labour income risk has no significant impact on participation when the correlation is not controlled for. However, controlling for the correlation greatly shifts the results: the impact is significant and negative for those perceiving a non-positive correlation, consistent with theoretical predictions. Bertaut (1998) investigates the determinants of stock market participation decisions of American households using data from the Survey of Consumer Finance of year 1983 and Two dummy variables are used to indicate if the household is enrolled in jobs with above or below average unemployment risk. He finds that the sign of the estimated coe cients for income risk proxies are not steady, thus providing limited support for the argument that labour income risk makes households unwilling to hold risky assets. Angerer and LAM (2009) and Calvet and Sodini (2014) distinguish between permanent and transitory income risk components, but contrary conclusions are drawn in these papers about the roles of these two risk components. Angerer and LAM 3 According to Arrondel et al. (2010), the explicit question in the DELTA-TNS 2002 asks interviewees the reason that may lead big firms to downsize the labour force. The correlation is assessed to be positive for interviewees with the answer a binding bankruptcy constraint, and negative with the expectation of a positive price impact on the firm s listed stocks. 9

14 (2009) construct measures for these two components using data from the National Longitudinal Survey of Youth 1979 (NLSY79). They find that the estimated permanent risk, although significantly smaller than the transitory risk for all households, is relatively more important, accordant with the implications in Viceira (2001). It is estimated that 1% increase in permanent risk reduces risky asset share by more than 1%, and the e ect is found to be statistically significant, while the e ect of transitory risk is smaller and insignificant. Calvet and Sodini (2014) estimate the transitory and permanent components in the same way as Cocco et al. (2005). By exploiting a panel of Swedish twins with twin-pair fixed e ects, they find that transitory income risk reduces risky asset share at 10% significance level, while permanent income risk has no significant e ect. 2.3 Measures of Labour Income Risk As can been seen from the previous section, the theoretical modelling of labour income risk employs the identical permanent-transitory risk framework which dates back to the permanent income hypothesis of Friedman (1957) who proposes that the observed income is the sum of a permanent component and a transitory component. The former reflects the influence of factors that determining the agent s capital value or wealth (e.g. education, ability and location) and thus decides the mean value of the observed income; while the latter reflects e ects of accidental occurrences and thus hardly has persistent impacts on the observed income. 4 Carroll (1997) formulates the income turbulences as partitioned into the permanent and the transitory components. In that paper, it is assumed that the log current income is the sum of the log permanent income and the transitory shock, with the log permanent income following a random walk and the transitory shock being a white noise. This assumed labour income process provides a variance structure that can be exploited to separate the permanent and transitory risks, which are measured as the standard deviations of the permanent shock and the transitory shock, respectively. 5 In contrast, the empirical researches utilise a variety of labour income risk proxies. If we are to classify these proxies according to the time reference and the data required, two basic categories can be identified. The first is derived from ex 4 However, under certain circumstances the transitory component can have a non-zero mean as argued in Friedman (1957). 5 The detailed steps can be found in Carroll and Samwick (1997). Our paper uses a similar measure that based on this variance structure and variance ratios of di erent horizons. 10

15 ante information on occupation and self-reported job expectations, and requires only cross-sectional data or a short panel. Bertaut (1998) and Cardak and Wilkins (2009) use occupation-related dummies in their regression as income risk measures. Guiso et al. (1996) derive a measure of subjective income risk from self-reported expectations on income and inflation. Arrondel et al. (2010) derives a similar measure using two years self-assessed income growth of survey recipients. The second category of income risk proxies is obtained from ex post information on realised labour income variability, and thus requires a dataset of both longitudinal and cross-sectional dimensions. The construction of such proxy involves firstly removing the e ects of the predictable parts due to life-cycle ageing and other household characteristics (e.g. age, age-squared and education) from the realised labour income, and then using the unpredictable parts, the residuals, to compose the risk measure. For example, Cardak and Wilkins (2009) measure the income risk as the 5-year sample variance of the unpredictable income growth from Australian household survey data. The income risk proxies applied in Angerer and LAM (2009) and Calvet and Sodini (2014) fall into this category as well, and the risk is further decomposed into permanent and transitory components, as accordant with the theoretical modelling. The significance of such separation of permanent and transitory risk components is that it distinguishes between labour income shocks of di erent persistence, which has been proved advantageous in previous studies on consumption-saving choice and portfolio choice problems. For example, it has been documented in Blundell et al. (2008) and Carroll (2009) that these two risks of di erent durability di er in their e ects on consumption: permanent shocks significantly a ects consumption, whereas transitory shocks have little impacts since they are insured against through saving. Angerer and LAM (2009) and Calvet and Sodini (2014) distinguish between the permanent and transitory components and find contrary evidence on the roles of these two risk components on risky asset demand. 11

16 3 Data The data used in this study is from the Survey on Household Income and Wealth (SHIW), an Italian survey operated by the Bank of Italy from the 1960s to the present. The survey asks questions on selected households demographic characteristics, employment status, incomes from various sources, financial assets, and other aspects relevant to social and economic research. Besides the broad range of information, it revisits a portion of households from the previous survey year since 1989, thus providing data of these households in a panel structure. Given these features of the survey, the database is especially suitable for the chosen methodology and is desirable to address the research question presented in this paper. Above all, the broad time span and the panel structure makes it feasible to more accurately identify the income risk components for each household. Equally important is that information on both income and risky assets is available simultaneously, which is not very common, since previously studies on households mainly focus on their consumption-savings behaviour. Many new databases focusing on household finance are established recently, such as the China Household Finance Survey, but these databases do not contain time dimensions of desirable length. Several restrictions are imposed on the selected sample due to the focus of this study and the requirements of the methodology. First of all, only households whose heads are considered to be exposed to labour income risk are included, since the purpose of the study is to investigate the influence of labour income risk. As a result, households whose heads are below 20 (for below college education level) or 22 (for college and above college education level) years old are excluded from the sample, as well as households whose heads are above 67 years old. Households whose heads are not employed during the whole time period, e.g. retirees, non-respondents, students, homemakers, are also left out. Secondly, following Campbell, Cocco, Gomes and Maenhout (1999) and Cocco et al. (2005), we define labour income in a broad sense as the sum of wages and salaries, self-employed income, welfare income and transfers of the household head and, if present, his (or her) spouse. Extreme values of labour income (below the 1% quantile or above the 99% quantile) are adjusted to the 1% or 99% quantile to reduce the possible influence of outliers. Thirdly, the methodology used to construct labour income risk measures requires the time dimension 12

17 of the panel data to have even intervals, for example, annual or biennial data, and consequently only data collected during 1998 to 2014 are utilised. This is due to the fact that the SHIW is conducted on odd years from 1989 to 1995 and on even years from 1998 to 2014, and the methodology cannot deal with the three-year interval between 1995 to Finally, to more accurately measure the income variability of di erent horizons, we limit the sample households to those showing up at least six consecutive times in the data by excluding households who were not interviewed consecutively. As a result of these restrictions, the number of selected households is reduced to 1215, and the number of observations is Table 1 reports the average frequencies of sample households and the number of sample households included in each year. The average frequency means that the sample households are interviewed in 7.33 waves of the SHIW, which is equivalent to a time span of approximately 14 years. All 1215 household samples are included in year 2004, 2006 and Table 1: Frequencies and Number of Sample Households Mean Std. dev. Min Max Frequencies Year # of households

18 4 Methodology To determine the influence of income risk on risky asset share, a two-step approach is employed. In the first step, the transitory and permanent components of labour income risk are estimated for each household. In the second step, their influence on risky asset holding decision and risky asset share is evaluated. 4.1 Step One: Income Risk Measuring Following Carroll (1997), we assume that the logarithmic of labour income is a combination of predictable part and unpredictable part. The unpredictable part has two components, permanent and transitory, with the former a random walk process with a zero-mean shock and the latter a zero-mean shock. By regressing the logarithmic labour income on a set of observable variables (e.g. age, education), the unpredictable part, as represented by the residual u it from the regression, is attained. The model is specified as follows: lny it = Constant + Male it + Educ it + Mar it + Area it + Age it + Size it + T t + u it (1) u it = µ it + v it with v it N(0, µ it = µ i,t 1 + " it with " it N(0, 2 iv) 2 i") (2) In Equation (1), the control variables are gender of household head, education level, marital status, area, third-order polynomial of age, family size and time trend. The detailed definitions of these control variables are shown in Table 2 and the construction of these variables from the original data is shown in Appendix A. In Equation (2), u it is the unpredictable labour income, and µ it is its permanent part and follows a random walk. The unpredictable income innovation is thus comprised of two components, " it and v it. The former is the permanent shock and is 2 independently and identically distributed with mean zero and variance i",andthe latter is the transitory shock and is independently and identically distributed with 2 mean zero and variance iv. i" and iv are our measures of permanent risk and transitory risk, respectively. After obtaining the residuals from Regression (1), the variance ratio technique bor- 14

19 Table 2: Variable Explanation Variables Ln(income) Male Age Family size College (Above college ) Married (Single/Divorced) North (Center) Time trend Net wealth Explanation The natural logarithm of labour income, including wages and salaries, self-employed income, welfare income and transfers of the head and, if present, his or her spouse. Dummy variable that takes on the value of 1 if the household head is male and 0 otherwise. Age of the household head. In the labour income regression, the participation model and the risky asset share model, age, age-squared and age-cubed are included as control variables. Numerical variable representing the number of members in the household. Dummy variable that takes on the value of 1 if the household head s highest education level is college (above college), and 0 otherwise. Dummy variable that takes on the value of 1 if the household head is married (single/divorced), and 0 otherwise. Dummy variable that takes on the value of 1 if the household lives in the north (center) of Italy, and 0 otherwise. The time trend variable that captures any time trends during year 1998 to Numerical value of the net wealth of the household. 15

20 rowed from Carroll (1997) and Angerer and LAM (2009) is applied to estimate the permanent and transitory risk measures. To do this, define the k year growth of unpredictable labour income as ku it = u it u i,t k, and then the variance of the k year growth is k i" 2 +2 iv. 2 To work with the SHIW data, similar expressions for biennial data are derived. Define the 2k year growth of stochastic labour income as 2ku it = u it u i,t 2k, and then the variance of the 2k year growth is 2k i"+2 2 iv. 2 6 In order to measure permanent risk and transitory risk with the method presented in Angerer and LAM (2009), we further split household samples into subgroups according to the head s industry and highest education level. 7 That is, households whose heads share the same industry and highest education level belong to the same group. If one group contains less than 30 households, it is combined with the other group in the same industry. It is then assumed that the ratio of permanent risk to transitory risk is constant for households in the same group. That is, where j represents the industry-education group. 2 i" 2 iv = r j, This method is similar to that in Angerer and LAM (2009), where households are divided into groups based on highest education level and occupation. In the SHIW data, however, there are only three kinds of occupations, blue-collar, white-collar and self-employed. We consider this categorisation too coarse to make accurate estimates. Instead, we utilise information on industry and education. This categorisation is also employed by Carroll and Samwick (1997) who report that income shock is statistically di erent in means for employees in di erent industries at 2% significance level. Given the assumption of group-identical ratio of permanent risk to transitory risk, the 2k year growth of unpredictable labour income can be rewritten as a function of the ratio r j, horizon k and the transitory risk 2 iv as in Equation (3). And the biennial variance ratio of horizon 2k can be written as a function of r j and k as in Equation (4). var( 2ku it )=2 2 iv(kr j +1) (3) 6 Steps on how the expressions are derived from the assumed labour income process are shown in Appendix B. 7 Detailed information on how we divide the samples are shown in Appendix A. 16

21 VR(2k) i = var( 2ku it ) var( 2u it ) 1 = r j +1 + r j r j +1 k (4) With the relationship in Equation (4), we estimate the group ratio r j using restricted OLS. After obtaining r j, we use the relationship in Equation (3) and estimate the transitory component for each household. The variances are approximated with sample variances. Combining the estimated r j and b 2 iv we get the estimated permanent risk b 2 i". By taking the square roots of them we get the permanent and transitory risk measures, b i" and b iv, for use in the next step. 4.2 Step Two: Risky Asset Holding In this paper, households risky asset holding choices are modelled as two separate decisions. Households firstly decide whether or not to enter the risky asset market, and then decide the amount of financial assets allocated to risky assets. Subsequently, two regressions are estimated regarding households risky asset holding: the first considering households decisions to participate in the market or not, and the second the share of risky assets conditional on participation. We assume that these two dependent variables are determined by a set of household demographic characteristics, labour income risk, an unobservable household-specific error, and a white noise. The household-specific error and the white noise are both independently and identically distributed. In addition, we allow the e ects of labour income risk to vary for households within di erent age groups to more accurately gauge the e ect of labour income risk. The two models are thus: P it = a 0 + a 1 b i" + a 2 b iv + a 3 b i" AgeGroup2 it + a 4 b iv AgeGroup2 it + a 5 b i" AgeGroup3 it + a 6 b iv AgeGroup3 it + a 7 i (5) + a 8 X it + i + it with i N(0, it N(0, 2 ) 2 ) 17

22 RAS it = b 0 + b 1 b i" + b 2 b iv + b 3 b i" AgeGroup2 it + b 4 b iv AgeGroup2 it + b 5 b i" AgeGroup3 it + b 6 b iv AgeGroup3 it + b 7 i (6) + b 8 X it + i +! it with i N(0,! it N(0, 2 ) 2!) P it is a binary variable that takes on the value 1 if household i holds risky assets in year t, and otherwise 0. RAS it is the ratio of risky assets to total financial wealth. The two dummy variables, AgeGroup2 it and AgeGroup3 it are used to indicate if the age of the household head falls into the interval and 57 67, respectively. b i" and b iv represent the estimated permanent and transitory risk components from the previous section. X it is a vector of control variables including gender, marital status, age, family size, education, current-year net wealth, and year dummies. The detailed explanation and construction of these variables are included in Table 2 and Appendix A. To control for the covariance between labour income innovation and stock return innovation, the covariance dummy,, is introduced. Households with heads employed in manufacturing, construction and public administration industries have the covariance dummy equal to 1 to indicate that their income innovations are positively related to excess stock returns. The covariance control used in this paper is based on the paper of Campbell et al. (1999) where it is found that on the aggregate level, employees in manufacturing, construction and public administration industries experience permanent shock significantly positively related to lagged excess stock returns. The two models are then estimated with random e ect OLS. The underlying assumption for the random e ect estimators to be consistent is that the unobserved household-idiosyncratic characteristics do not embody any elements correlated with the observed regressors. In other words, it has to be satisfied that cov( i,x it )=0 for Regression (5) and cov( i,x it )=0forRegression(6). 8 We choose random ef- 8 The X it here denotes all the other explanatory variables, including income risk measures, in the two regressions. 18

23 fect model for two reasons. First of all, random e ect model allows us to explore the influence of labour income risks, which is time-invariant for each household. The permanent and transitory risk components are, by assumption and by construction, household-specific and unchangeable, thus restraining us from using fixed e ect model which is accepted as a more convincing tool than random e ect model. Secondly, the Breusch-Pagan Lagrange multiplier test favours random e ect model to pooled OLS regression as can be seen from Table 10 in Appendix D that the null hypothesis of no significant di erence across households is rejected at 1% significance level. 19

24 5 Empirical Results This section is composed of two parts. In the first part, results from step one are shown, including outputs from the labour income regression and summary statistics on the permanent and transitory risks for each industry-education group. In the second part, results from step two are shown, including outputs from the participation model and the risky asset share model under both narrow and broad definitions of risky assets. 5.1 Step One: Income Risk Measuring Table 3 presents results of the labour income regression. R-squared value equals and most demographic variables are significant at 1% significance level except single. The estimates are in accordance with other studies on the labour income determinants (e.g. Carroll, 1997). For instances, a marital status of married positively influences labour income while single impinges on labour income. Italians living in the north areas tend to have higher total labour income than those living in the south. And education is a positive predictor of labour income. The residuals from this regression represent the unpredictable part of labour income. Table 4 shows the cross-sectional covariance and autocovariance matrix of the unpredictable income growth, as represented by 2u it, between year 1998 and The first-order autocovariances (reported in shaded cells) are all negative and significant, while the second-order autocovariances and the higher-order autocovariances are mostly insignificant. The negative first-order autocovariances imply that two consecutive income growth observations move in the opposite direction, and the income growth process is thus mean-reverting. 9 Overall, Table 4 suggests that the random walk assumption of the permanent income component is a good representation of the SHIW data. Table 5 presents statistics of permanent and transitory income risk estimates for the 12 industry-education groups. The primary intention is to separate households according to both industry and education to estimate the group-identical ratio of permanent risk to transitory risk. If one group contains less than 30 households, 9 The results could be inferred from the assumed unpredictable income process. Appendix B shows the details. 20

25 it is combined with the other group in the same industry. As a result, the average permanent and transitory risk estimates are only reported at industry level for households whose heads are employed in agriculture, transport and communication, credit and insurance institutions, and real estate and renting services. The permanent and transitory risks reported in Table 5 are consistent with previous literature (e.g. Angerer & LAM, 2009; Blundell et al. 2008) in that the permanent risk is smaller than the transitory, which follows from the unit root assumption of permanent risk. However, compared with estimates from the U.S. households, the permanent risk estimates are typically smaller in scale, while the transitory are larger in scale. Cocco et al. (2005) report that the standard deviation of permanent income shock ranges from 0.08 to 0.12 and that of the transitory ranges from 0.1 to 0.35 for the U.S. households. At industry level, households in credit and insurance services, and government and other private and public services experience the lowest permanent and transitory income risks, while people in building and construction, and manufacturing industries have the highest permanent and transitory risks. At education level, more highly educated households are, on average, have lower permanent risk and transitory risk, except individuals in the manufacturing industry. The estimated household-specific and time-invariant permanent and transitory risks are then used in the next step in the evaluation of their respective roles in households risky asset holding. 21

26 Table 3: Labour Income Regression Results Variables # of obs. Mean Std. Dev. Log Income Regression Results Age *** (0.0294) Age *** ( ) Age e-05*** (4.46e-06) College degree *** (0.0123) Above College Degree *** (0.0170) Married *** (0.0284) Single (0.0377) Divorced or Separated *** (0.0348) North *** (0.0135) Center *** (0.0156) Male *** (0.0135) Family Size *** ( ) Time Trend *** ( ) Constant 10.74*** (0.447) R-squared Notes: The dependent variable is log labour income. Robust standard errors are reported in parentheses. ***, **, and * indicate significance levels of 0.01, 0.05, and 0.1 respectively. 22

27 Table 4: Cross-sectional Covariance Matrix of Unpredictable Labour Income Growth 2u i, u i, u i, u i, u i, u i, u i, u i,2014 2u i, u i, u i, u i, u i, u i, u i, u i, Notes: 2u i,t equal to u i,t u i,t 2, is the two-year di erence of unpredictable labour income. The unpredictable labour income is the residual from the labour income regression. Each cell in the matrix reports two statistics, the first being the variance of 2u i,t or the autocovariance between 2u i,t and 2u i,t 2k, and the second being the p-value of the autocovariance. 23

28 Table 5: Average Income Risk by Industry-Education Group Occupation Group Education Group Mean of Income Risk Measure # of households Permanent, b " Transitory, b v Agriculture All level (0.0532) (0.2130) Manufacturing High school and below (0.0407) (0.1650) College and above (0.0412) (0.2033) Building and High school construction and below Whole sale and retail trade Transport and communication Credit and insurance institutions Real estate and renting services General government and other private and public services College and above High school and below College and above (0.1135) (0.3517) (0.0824) (0.1737) (0.0577) (0.2508) (0.0481) (0.2191) All level (0.0348) (0.1511) All level (0.0216) (0.1141) All level High school and below (0.0415) (0.2143) (0.0401) (0.2039) College and above (0.0333) (0.1517) Total sample All (0.0553) (0.2077) Notes: Standard deviations are reported in parenthesis. 24

29 5.2 Step Two: Risky Asset Holding This section starts with descriptive statistics on households market participation rate and a T-test on di erence in means between characteristics of participants and non-participants. It then proceeds with regression results of the participation model and the risky asset share model. These results are discussed with regard to predications of standard theoretical models and findings from previous empirical works. At last, robustness of estimates from the baseline models is checked in three aspects Descriptive Statistics Table 6 shows statistics on households participation rate in di erent types of assets and the average amount invested in each asset class in year 2006 for all the interviewees and the sample households respectively. Two definitions of risky assets are used. The narrowly defined risky assets include corporate bonds, mutual funds, shares and managed savings, and the broadly defined risky assets include government bonds of di erent maturities and loans to cooperatives in addition to the narrowly defined risky assets. The participation rate of Italian households is approximately 23% under the broad definition, much lower than the 50% participation rate of the U.S. households as reported by Guiso, Haliassos and Jappelli (2002). Among all the risky assets, mutual funds, corporate bonds, equity shares and Treasury bills are the four most popular financial assets among Italian households. The last two columns report average share of risky assets relative to total financial wealth for households who hold risky assets. The comparison between the entire interviewees and our sample households suggests that the sample households are, in general, more active in the market, as evidenced by the higher participation rate and average investment amount. Table 7 reports mean values of several characteristics of market participants and non-participants of the sample households, and a T-test is conducted to compare the di erences in means. As expected, the non-participants, on average, undergoes significantly higher permanent and transitory income risks, and their income innovations are more positively related to stock return innovations. Moreover, these two groups also di er significantly in means in other aspects. However, the T-test is insu cient for causal inference, and control strategies are used in the next step to evaluate the e ects of these characteristics. 25

30 Table 6: Risky Asset Holding of Households in 2006 Participation rate Average amount Average share for participants All Selected samples All Selected samples Corporate bonds 6.35% 8.72% Mutual funds 8.24% 13.99% Shares 6.50% 11.03% Foreign shares 0.85% 1.15% Managed savings 1.49% 1.65% T-bills 7.31% 7.16% T-certificates 2.48% 2.55% T-bonds 1.69% 2.30% Zero coupon 0.18% 0.33% Other government securities 0.42% 0.41% Loans to cooperatives 2.23% 2.80% All Selected samples Total risky assets Narrow definition 16.41% 24.20% % 55.44% Broad definition 23.19% 30.37% % 61.38% Notes: The narrowly defined risky assets include corporate bonds, mutual funds, domestic and foreign shares, and managed savings. The broadly defined risky assets include T-bills, T-certificates, T-bonds, zero coupons, other government securities, and loans to cooperatives in addition to the narrowly defined risky assets. 26

31 Table 7: Comparison between Participants and Non-participants Characteristics Participants Non-participants T-test of di erence in means Mean Std. Dev. Mean Std. Dev. t-statistics p-value Income risk Permanent Transitory Covariance dummy Controls Age Net wealth Male Married College Above college North Center Family size #ofobservations Notes: The participants are households in possession of risky assets, and the risky assets include equity shares and cooperate bonds, following the narrow definition. The null hypothesis is that the di erence between means is 0. 27

32 5.2.2 Market Participation In order to delineate the influence of labour income risk and the interaction terms between income risk and age, five versions of the participation model are considered, and their results are reported in Table 8. As can be seen from the first two columns, both permanent and transitory risks discourage market participation if they are respectively included in the regression. When they are considered together as shown in Column 3, however, only permanent risk remains to significantly reduce propensity to hold risky assets. Additionally, the magnitude of the coe cient of permanent risk is nearly four times that of the coe cient of transitory risk, which might suggest that permanent income risk is more important in determining households participation in the market. 10 The last two columns present results of the multivariate regressions. In Column 4, when interactions and covariance dummy are not included, the e ect of permanent risk is still significant but only at 10% significance level, whereas that of transitory risk is insignificant. 1% increase in permanent income risk reduces the likelihood of participating by 0.645%, while 1% increase in transitory income risk increases the likelihood of participating by 0.08%. Adding interactions and covariance dummy yields no material change to the results as can be seen is Column 5, and all interaction terms are insignificant. Results in Table 8 reveal some interesting observations. Firstly, the e ect of transitory risk is not stable. The coe cient of transitory risk becomes positive and insignificant when it is considered together with permanent risk. It is thus highly possible that transitory income risk is not the primary cause that discourages participation, but rather it captures the e ect of other variables. Secondly, permanent risk and transitory risk tend to have opposite roles in determining risky asset market participation, as indicated by their respective negative and positive coe cients in column 3 and 4. This result is consistent with that of Angerer and LAM (2009) in that the permanent risk significantly impinges on market participation. However, the role of transitory risk clearly contradicts the prediction of Viceira (2001) and the empirical findings of Angerer and LAM (2009), but corroborates the calibrated example of Gomes and Michaelides (2005) where it is found that increase in transi- 10 However, this could also follow from the high correlation between these two risk components. We discuss the problem in Appendix F. 28

33 tory risk encourages market participation. Last but not least, the magnitude of the permanent risk coe cient is larger than that of transitory risk coe cient, showing that permanent risk is relatively more important, especially given the smaller scale of permanent risk compared to transitory risk. As to the relative importance of labour income risk and control variables, it seems that the propensity to hold risky assets is more a ected by net wealth, education, residential area and year dummies than labour income risk proxies, as shown in Column 4 and 5. The e ect of net wealth is positive and pronounced, supporting the theory of fixed costs of transactions (Brandt, 2009). Higher educated people and male heads are more likely to participate risky asset markets. The positive e ect of education is documented in Van Rooij et al. (2011), and empirical studies have uncovered the gender di erence in risk attitude and find that females are more risk averse (Fellner & Maciejovsky, 2007; Rosen et al. 2003). Households in northern and central Italy are more active due to the fact that these two areas are more developed than the rest. In addition, several year e ects are found to be significant, which could be attributed to the macroeconomic conditions of Italy. Guiso and Jappelli (2002) have documented that certain macroeconomic factors (e.g. reform of social security system) contribute to the change of market participation rate of Italy households. Figure 2 also shows that participation rate and Italian GDP growth rate share a mutual trend, to some degree. Equally noticeable is the negative e ect of the covariance dummy, which is significant at 10% significance level, meaning that those whose labour income innovation positively correlates with stock return innovation are more conservative about holding risky assets. This supports the implication of the theoretical model that households with labour income innovation positively related to stock return innovation should avoid market participation. Taken together, the results suggest the limited influence of income risk components on households propensities to hold risky assets, and the rather dominant e ects of several control variables. In the next step when the roles of these variables are evaluated with regard to risky asset share conditional on participation, it can be seen that the relative importance of them shifts. 29

34 Table 8: Participation Decision and Labour Income Risk Narrow Definition Explanatory Variables (1) (2) (3) (4) (5) permanent, b " *** *** * * (0.144) (0.400) (0.334) (0.445) transitory, b v *** (0.040) (0.112) (0.091) (0.128) * (0.017) b " AgeGroup (0.562) b v AgeGroup (0.151) b " AgeGroup (0.919) b v AgeGroup (0.221) Controls Age 0.044* (0.024) (0.024) Age * (0.001) (0.001) Age (0.000) (0.000) Net wealth (in 10,000 euro) 0.001*** 0.001*** (0.000) (0.000) College 0.109*** 0.110*** (0.016) (0.016) Above College 0.149*** 0.151*** (0.026) (0.026) Married (0.030) (0.030) Single (0.036) (0.036) Divorced (0.035) (0.035) North 0.247*** 0.247*** (0.017) (0.017) Center 0.172*** 0.170*** (0.021) (0.021) Male 0.030** 0.030** (0.014) (0.014) Family size (0.006) (0.006) Year ** 0.035** (0.017) (0.017) Year (0.017) (0.017) Year (0.018) (0.018) Continued on the next page. 30

35 Continuation of Table 8 Explanatory Variables (1) (2) (3) (4) (5) Year * (0.018) (0.018) Year ** ** (0.019) (0.019) Year (0.020) (0.020) Year * * (0.021) (0.021) Year * * (0.023) (0.023) Constant 0.314*** 0.317*** 0.312*** ** * (0.014) (0.015) (0.312) (0.354) (0.359) Observations 8,909 8,909 8,909 8,909 8,909 # of households 1,215 1,215 1,215 1,215 1,215 Between R-squared Overall R-squared Notes: The dependent variable in this table is a binary variable that takes on the value of 1 if households i invests in risky assets in year t and 0 otherwise. The risky assets follow the narrow definition and include corporate bonds, mutual funds, shares and managed savings. All regressions are estimated with random e ect OLS. Robust standard errors are clustered by households and reported in parenthesis. ***, **, and * indicate significance levels of 0.01, 0.05, and 0.1 respectively. 31

36 5.2.3 Risky Asset Share Table 9 presents the results of the risky asset share model, with risky assets following the narrow definition. The first two columns present results of the univariate regressions. The estimated coe cient of permanent risk is 0.41%, meaning that risky asset share decreases by 0.41% in response to 1% increase in the standard deviation of permanent shock. This e ect is significant at 5% significance level. In contrast, the estimated coe cient of transitory risk is negative and insignificant. This result suggests that transitory income risk solely cannot account for households portfolio allocation to risky assets. When permanent and transitory risks are included simultaneously as in Column 3, it appears that permanent risk discourages allocation to risky assets whereas transitory risk promotes allocation to risky assets. However, the robust standard errors shoot up to as high as almost three times the robust standard errors in the univariate regressions. Column 4 reports results from the multivariate regression where demographic characteristics, interactions and the covariance dummy are included as additional regressors. As before, permanent risk and transitory risk have opposite e ects, but the e ect of transitory risk becomes insignificant. Although the value of transitory risk is larger than that of the permanent risk as shown in Table 5, this di erence in values is outweighed by the large gap between the magnitudes of their e ects. Therefore the combined influence of the unpredictable income risk on risky asset share is negative as can be seen in Table 13 in Appendix G where the unpredictable labour income risk is measured with standard deviations of the unpredictable income shock. Moreover, all the interactions included have little significant impacts on risky asset share. The e ect of permanent risk keeps in high significance level and is negative under all specifications, while that of transitory risk changes a lot. The magnitude of the coe cient of permanent risk falls in the range predicted by the calibrated model of Viceira (2001). Viceira (2001) shows that when relative risk aversion is set to 3, risky asset share reduces by approximately 1% in response to 1% increase in permanent risk, and when relative risk aversion is set to 8, risky asset share reduces by 2.4%. Hence, the estimated e ect of permanent risk is in line with theoretical predictions presented in Viceira (2001) and the empirical results of Angerer and LAM (2009). However, no previous studies have documented the positive e ect of transitory risk on risky asset share, and we are inclined to interpret it as consequence of the mul- 32

37 ticollinearity problem. 11 Because of the instability of transitory risk e ect and the concern of the high correlation between the two risk measures, we only include permanent risk and its corresponding interactions with other demographic controls in the last specification, and the results are shown in Column 5. Permanent risk significantly discourages allocation to risky assets, although the magnitude becomes 0.8%, much smaller than in previous cases. Remarkably, the interaction between permanent risk and AgeGroup2 is positive and significant at 5% significance level, meaning that 1% increase of permanent risk only reduces risky asset share by approximately 0.2% for households aged 44 to 57 years old, which is a quarter of that for the young and elderly households. Such disparity in e ect for di erent age groups could be possibly accounted for by several factors that change the groups perception of and thus the reaction to labour income risk, which cannot be directly tested with the data at hand. These factors, including home ownership, health status, risk aversion and some other unobservable factors, have di erent e ects on households perception of labour income risk, and combined together, they cause the e ect of labour income risk to be di erent for di erent age groups. On the one hand, the middle-aged and the elderly households own house property while the young are still saving for housing. 12 According to Banks, Blundell, Oldfield, and Smith (2004) and Sinai and Souleles (2003), home ownership provides insurance against risks related to housing services, such as rent risk. It can follow that the young exposed to such risks perceive labour income risks as more severe and tend to invest less in risky assets to reduce their total exposure to risks. On the other hand, younger households are less likely to encounter health problems compared to older households and they display lower relative risk aversion than the older households as documented in Harrison et al. (2007). It then follows that the young households should demonstrate less aversion toward the same level of labour income risk compared to the older households, which should be further translated to smaller e ect of the labour incomer risk on risky asset holding. Moreover, there are unobservable factors that may also contribute to the disparities between age groups. Combined together, these factors distinguish the middle-aged 11 Due to the method used to separate these two risk components, the estimated risk components are highly correlated. We discuss this problem in Appendix F. 12 It is documented in Jappelli and Pagano (1994) that the average age of Italian buying their first house property is around 44, and savings peak before the purchase of the property. 33

38 households as less sensitive to marginal changes of labour income risk, compared with the young and the elderly households, in determining risky asset share. As to the impacts of control variables, it can be seen from the last two columns of Table 9 that some of them also contribute to households allocation of financial wealth to risky assets. Firstly, the third-order polynomial of age is found to have significant influence, and it suggests a positive relationship between age and risky asset share when age ranges from 20 to 67, consistent with the model implications presented in Wachter and Yogo (2010) and Campanale et al. (2015). More educated households also tend to invest more in risky assets. The estimated positive e ects of age and education are consistent with the argument that financial literacy improves slowly through life-time learning, and it is the channel through which education a ects risky asset share (King & Leape, 1984; Lusardi & Mitchell, 2006; Lusardi &Mitchell,2007). Secondly,theestimatedcoe cient of net wealth is negative, meaning that the portfolio share falls in response to increase in net wealth, consistent with the findings of Wachter and Yogo (2010) and Heaton and Lucas (2000), who emphasise the negative e ect of private proprieties for the rich in determining risky asset share. Leaving out transitory risk and its interactions yields qualitatively and quantitatively similar results as shown in Column 5. 34

39 Table 9: Risky Asset Share and Labour Income Risk Narrow Definition Explanatory Variables (1) (2) (3) (4) (5) permanent, b " ** *** *** *** (0.160) (0.445) (0.591) (0.255) transitory, b v *** (0.040) (0.111) (0.166) (0.016) (0.016) b " AgeGroup ** (0.800) (0.263) b v AgeGroup (0.211) b " AgeGroup (0.898) (0.342) b v AgeGroup (0.244) Controls Age 0.120*** 0.120*** (0.039) (0.039) Age *** *** (0.001) (0.001) Age *** 0.000*** (0.000) (0.000) Net wealth (in 10,000 euro) (0.000) (0.000) College (0.016) (0.016) Above college 0.053** 0.053** (0.021) (0.021) Married (0.036) (0.037) Single (0.044) (0.045) Divorced (0.042) (0.043) North (0.022) (0.022) Center (0.026) (0.026) Male (0.017) (0.017) Family size * (0.008) (0.008) Year *** 0.063*** (0.024) (0.023) Year (0.024) (0.024) Year ** 0.059** (0.024) (0.024) Continued on the next page. 35

40 Continuation of Table 9 Explanatory Variables (1) (2) (3) (4) (5) Year (0.025) (0.025) Year (0.026) (0.026) Year (0.026) (0.026) Year (0.028) (0.028) Year (0.033) (0.033) Constant 0.561*** 0.552*** 0.549** ** ** (0.012) (0.012) (0.012) (0.587) (0.584) Observations 2,245 2,245 2,245 2,245 2,245 # of households Between R-squared Overall R-squared Note: The dependent variable in this table is the risky asset share conditional on participation. The risky assets follow the narrow definition and include corporate bonds, mutual funds, shares and managed savings. All regressions are estimated with random e ect model. Robust standard errors are clustered by households and reported in parenthesis. ***, **, and * indicate significance levels of 0.01, 0.05, and 0.1 respectively. 36

41 5.3 Robustness Check There are several reasons that our baseline models may not accurately capture the relationship between labour income risk and household risky asset holding: it is possible that the estimated parameters are sensitive to how the risky assets are defined or the inclusion of more covariates, and the method to disentangle the two income risk components causes the two components to be highly correlated. In this section, two separate robustness checks are conducted to address these two potential problems. Firstly, it is tested if the estimates are robust under the broad definition of risky assets. The broadly defined risky assets include government bonds of various maturities and loans to cooperatives in addition to the narrowly defined risky assets. As in the case of the narrowly defined risky assets, we regress four times with di erent predictors for the participation model and the risky asset share model respectively. The results are shown in Table 14 and Table 15. The results of the participation model are rather similar to those of the baseline model, despite that the e ect of permanent risk is reduced to insignificant as shown in the last two columns of Table 14. As to the risky asset share model, one noticeable disparity from the baseline model is that transitory risk significantly increases risky asset share regardless of the inclusion of the covariance dummy and the interactions as shown in the last two columns of Table 15. This positive e ect of transitory income is di erent from that in Table 9. Secondly, it is tested if the estimates are robust under alternative measure of labour income risk and inclusion of more control variables. Instead of permanent and transitory risk components, the standard deviation of unpredictable biennial labour income growth 13 is employed as the income risk proxy. In addition, current and previous year incomes and previous year net wealth are included as control variables. For both the participation model and the risky asset share model, the results are rather similar to those of the baseline models as can be seen from Table 13. Noticeably, the coe cient of the interaction between income risk and AgeGroup2is significant at 1% level, in accordance with the results of Column 5 in Table 9 when only permanent income risk is considered. 13 The unpredictable biennial labour income growth is 2u it, and u it is the residual from Regression 1. The standard deviation of 2u it is the square root of sample variance, p var( 2u it ). 37

42 In summary, the influence of permanent risk is robust and keeps its dominant role even though the definition of risky assets is extended to include government bonds and loans to cooperatives, whereas the role of transitory risk changes a lot when it is used to determine participation propensity and risky asset share of Italian households. In addition, the age-variant e ect of labour income risk is also identified with alternative proxy of income risk. Finally, the estimated parameters for other covariates are quantitatively and qualitatively similar to those in the baseline model. 38

43 6 Conclusion It is well-documented in the theoretical literature that labour income risk has a negative impact on households risky asset share, but previous empirical findings provide mixed evidence on the role of labour income risk, which could be attributable to the failure of considering the age-variant influence of labour income risk. In this study, the age-variant influence of labour income risk on risky asset holding is investigated, and some evidence is found that the risky asset share of the middle-aged market participants is less a ected by labour income risk compared to the young and the elderly participants. Another question this study seeks to address is how permanent and transitory risk components influence Italian households risky asset holding. The permanent and transitory risks represent income risks of di erent durabilities, but previous studies on Italian households portfolio choice problem have not distinguished between these two risk components (Guiso et al. 1996; Grande & Ventura, 2002). And hence it is expected that these two risks have dissimilar roles in determining households risky asset holding. The risk measures are constructed by exploiting the variance structure of the unpredictable labour income, the same way as Angerer and LAM(2009). Our findings suggest that neither permanent nor transitory risk is the primary reason why Italian households avoid participating in the stock market, but the fixed cost of entry, education and residential areas are the most significant factors that influence households propensities to hold risky assets. However, the picture shifts when it comes to risky asset share conditional on participation. Permanent risk is found to have pronounced and negative e ect on risky asset share, consistent with the implication of Viceira (2001) and the empirical findings on the U.S. households by Angerer et al. (2009), but inconsistent with the findings on Swedish households by Calvet et al. (2014). Contrary to the role of permanent risk, transitory risk is found to encourage allocation of financial wealth to risky assets, which is not documented in previous studies. However, the positive e ect of transitory risk has to be interpreted with caution since it is not significant under several specifications. Several limitations should be acknowledged since they could possibly impair the validity of our results. Firstly, the income risk measures based on sample variances can 39

44 be inaccurate proxies for labour income risk. Despite that the households can underor wrongly report the values of income and risky assets, the average number of observations for each household is only Therefore, the calculated sample variances could be imprecise, especially those for unpredictable labour income growth of long horizons. Secondly, the prerequisite for random e ect estimators to be consistent is usually hard to fulfil. Thirdly, the biennial data could leave out important information of the interval years. Finally, the method used to construct permanent risk and transitory risk causes high correlation between these two variables, which could possibly a ect the results. Given these drawbacks of the methodology and the data, future empirical studies could improve the work in two aspects. Firstly, alternative dataset that contains longer time span and more cross-sectional units can be employed, and o cial records are usually more reliable than survey data. Secondly, more reliable tools can be adopted to reduce bias from unobserved factors. For instance, twin fixed e ect model can be applied to eliminate influence of genetic features shared by the twin. Finally, future theoretical works could incorporate the evidence that households in di erent life stages perceive labour income risk dissimilarly in their portfolio choice decisions. 40

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49 Appendix Appendix A Constructing Variables from SHIW The composed history dataset of SHIW is used. It is available online at the Bank of Italy website (click to access). How the variables are constructed from the original dataset is explained as follows. Household Id and Year Name in the original dataset: nquest, anno The variable nquest is the unique id assigned to each household. anno identifies the year of the interview. Household Head Name in the original dataset: nord The household head is identified if the nord of a person equals 1. The SHIW questionnaire assigns the person as household head who is responsible for the household budget, or who is primarily responsible for or most knowledgeable about the household budget. 14 This assignment is directly adopted by us since it serves our purpose well. Labour Income, LnY Name in the original dataset: yl, yt, ym Labour income is constructed in a broad sense following Campbell et al. (2001) and Cocco et al. (2005). We include wages and salaries, self-employed income, welfare income and transfers of both head and, if present, his or her spouse. Welfare income and transfers are included because they serve as natural insurance against unfavourable wage risk and are highly relevant to households choices of consumption and savings. Other control variables Other control variables, including net wealth, age, gender, industry, education, family size, residential area, and marital status, are either directly adopted or adapted 14 Quoted from the 2014 SHIW questionnaire. 45

50 from the original dataset. For instance, residential area is originally included as acategoricalvariablethattakeson1to3toindicateresidentialareasofnorth, center or south respectively. Three dummy variables are constructed based on this categorical variable, and only two of them are included in the model to avoid the dummy variable trap. 46

51 Appendix B Deriving Variance for Labour Income Shock Equation (2) in Section 4 specifies the assumed process of stochastic labour income: u it = µ it + v it with v it N(0, 2 iv) µ it = µ i,t 1 + " it with " it N(0, " 2 i") (A1) The variance of 2k-year stochastic labour income growth is thus: var( 2ku it )=var(u it u i,t 2k ) = var(µ it + v it µ i,t 2k v i,t 2k ) = var((" it + " i,t " {z i,t 2k+1 )+v } it v i,t 2k ) 2k (A2) =2k i" +2 iv =2 2 iv(kr j +1) The variance ratio of horizon 2k is then: VR(2k) i = var( 2ku it ) var( 2u it ) = 2k i" +2 iv 2 i" +2 iv = 2 iv(kr 2 j +1) 2 iv 2 (r j +1) = 1 r j +1 + r j r j +1 k (A3) The empirical counterpart for (A3) is as follows, and is estimated with restricted OLS for each group j: d VR(2k) ij = j + j k ij + ij subject to j + j =1 (A4) The variances are approximated with sample variances. For example, d var( 2u it )= 47

52 T 2 t=1 ( 2u it 2 u it ) 2 T 2 1 horizon k is thus t=1 2u it and 2u it = T 2 T 2 var( d 2ku it ) var( d 2u it ). d VR(2k)i =. The estimated variance ratio of Covariance Structure of Stochastic Labour Income Growth To see why the cross-sectional autocovariance matrix in Table X evidences the hypothesised stochastic labour income process in (A1), construct the covariance between two consecutive observations of stochastic labour income growth: cov( 2u it, 2u i,t 2 )=cov(u it u i,t 2,u i,t 2 u i,t 4 ) = cov(µ it + v it µ i,t 2 v i,t 2,µ i,t 2 + v i,t 2 µ i,t 4 v i,t 4 ) = cov(" it + " i,t 1 + v it v i,t 2, " i,t 2 + " i,t 3 + v i,t 2 v i,t 4 ) = cov( v i,t 2,v i,t 2 ) = 2 iv (A5) As shown above, the covariance is negative for all T, corroborated by the negative shaded cells in Table4. 48

53 Appendix C 0,35 0,3 0,25 0,2 0,15 0,2686 0,1847 0,2922 0,214 0,2591 0,1901 0,245 0,1795 0,232 0,1641 0,2256 0,1494 0,2446 0,171 0,2111 0,2114 0,1575 0,1491 0,1 0,05 0-0,05 0,037 0,016 0,016 0,02 0,017 0,003-0, ,028-0,04-0,1 Narrow Broad GDP growth Figure 1: Participation Rate and Italian GDP Growth Italian GDP growth data adapted from the World Bank Statistics

54 Appendix D Table 10: Breusch and Pagan Lagrangian multiplier test for random e ects Participation model P = Xb + u[households]+ e[households, t] Estimated results: Var sd=sqrt(var) P e u Null hypothesis Var(u)=0 P-value Risky asset share model RAS = Xb+ u[households]+e[households, t] Estimated results Var sd=sqrt(var) RAS e u Null hypothesis Var(u)=0 P-value Notes: Thetestisrunaftertheregressionwithrandome ect model. The test. on participation model is run after the regression in Column (4) Table 8. The test on risky asset share model is run after the regression in Column (4) Table 9 50

55 Appendix E Table 11: Correlation Between Participation Decision and Explanatory Variables P b" bav Age Age 2 Age 3 College Above college Married Single Divorced Net wealth North Center Male Family size P b" bv Age Age Age College Above college Married Single Divorced Net wealth North Center Male Family size Notes: P stands for the participation dummy. Risky asset follows the narrow definition. b" and bv stand for the estimated permanent and transitory risks, respectively. In each cell two statistics are reported, the Pearson correlation coe cient and the significance level. All interaction terms are omitted. 51

56 Table 12: Correlation Between Risky Asset Share and Explanatory Variables RAS b" bv Age Age 2 Age 3 College Above college Married Single Divorced Net wealth North Center Male Family size RAS b" bv Age Age Age College Above college Married Single Divorced Net wealth North Center Male Family size Notes: RAS stands for risky asset share. Risky assets follow the narrow definition. b" and bv stand for the estimated permanent and transitory risks, respectively. In each cell two statistics are reported, the Pearson correlation coe cient and the significance level. All interaction terms are omitted. 52

57 Appendix F Figure 2: Scatter Plot of Transitory and Permanent Risk As can be seen in Figure 2, the constructed permanent and transitory risk components are highly correlated, and the Pearson correlation coe cient between them is as high as 0.94 as shown in Table 11. This is a drawback of the method that arises from our assumption: to disentangle these two risk components, it is assumed that the ratio of the permanent risk to transitory risk is identical within each industry-education group. Therefore it is not surprising to see that the estimated risk components plot as several straight lines. Such high correlation causes several problems and we choose to address the multicollinearity problem or not in di erent situations. Firstly, for the participation model, Column 2 and 3 in Table 8 clearly shows that including both permanent and transitory risks into the regression makes the coe cient of the transitory risk to be insignificant. Instead of interpreting this as evidence of the more important role of permanent risk, we prefer to think of it as the consequence of the multicollinear- 53