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Tilburg University Ownership of Stocks and Mutual Funds Alessie, R.J.M.; Hochgürtel, S.; van Soest, Arthur Publication date: 2001 Link to publication Citation for published version (APA): Alessie, R. J.

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Tilburg University Ownership of Stocks and Mutual Funds Alessie, R.J.M.; Hochgürtel, S.; van Soest, Arthur Publication date: 2001 Link to publication Citation for published version (APA): Alessie, R. J. M., Hochgürtel, S., & van Soest, A. H. O. (2001). Ownership of Stocks and Mutual Funds: A Panel Data Analysis. (CentER Discussion Paper; Vol ). Tilburg: Econometrics. 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Download date: 16. mrt. 2017 No OWNERSHIP OF STOCKS AND MUTUAL FUNDS: A PANEL DATA ANALYSIS By Rob Alessie, Stefan Hochguertel and Arthur van Soest December 2001 ISSN Ownership of Stocks and Mutual Funds: A Panel Data Analysis Rob Alessie Free University Amsterdam, Tinbergen Institute Stefan Hochguertel European University Institute Arthur van Soest Tilburg University This version: November 29, 2001 Abstract In many industrial countries, ownership rates of risky assets have risen substantially over the past decade. This trend has potentially wide ranging implications for the intertemporal and cross sectional allocation of risk, and for the macro economy, establishing the need for understanding ownership dynamics at the micro level. This paper offers one of the first such analyses using representative panel survey data. We focus on the two main types of risky financial assets, mutual funds and individual stocks. We extend existing univariate dynamic binary choice models to the multivariate case and take account of interactions between the two types of assets. The models are estimated on data from the waves of the Dutch CentER Savings Survey. We find that both unobserved heterogeneity and state dependence play a large role for both types of assets. Most of the positive relation between ownership of mutual funds in one period and ownership of individual stocks in the next period or vice versa, is explained by unobserved heterogeneity: if we account for correlation between the household specific effects in the two binary choice equations, we find a negative effect of lagged ownership of stocks on the ownership of mutual funds. These findings can be explained by adjustment costs that make it optimal to stick to one type of asset. Keywords: household portfolio choice, panel data JEL classification: C33, C35, D12, D91 This paper has greatly benefited from useful comments by Richard Blundell, other participants of the TMR Conference on Savings, Pensions, and Portfolio Choice, Paris, the 2001 Annual Meeting of the European Economic Association, Lausanne, and seminar participants at the European University Institute, Free University Amsterdam, Tilburg University, University of Groningen and University of Cyprus. Financial support from the TMR network on Savings and Pensions (grant number: FMRXCT960016) is gratefully acknowledged. Correspondence to: Arthur van Soest, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands, e mail: 1 1 Introduction In many industrialized countries including the Netherlands, the percentage of private households that own some type of risky financial assets has increased substantially during the nineties. In the US for example, the fraction of households owning some risky financial assets increased from 31.9% in 1989 to 49.2% in In Italy, the ownership rate increased from 12.0% to 22.1% in the same time period. 1 Similar trends exist in many other countries. To quote The Economist of March, 2001: Wider share ownership is profoundly important. It spreads wealth, changes attitudes to economic freedom and lowering business taxes, and leads to greater shareholder activism. This puts pressure on managers to improve their performance and promises to raise productivity and economic growth. Household stock ownership becomes more and more important with all kinds of implications for financial markets and macro-economic policy. According to the Financial Times of August , the wider share ownership has reversed the public opinion on the US Federal Reserve s policy of cutting interest rates: while in the past, the majority of the public would be concerned about lower returns to their savings accounts, most households will now applaud an interest rate cut since it increases the expected returns to their shares portfolio. On the other hand, the same Financial Times article states, referring to the group of retail investors in risky assets, that one problem for policy makers analyzing this growing group of Americans is that useful data on the identity of the average investor is hard to come by. This illustrates the need for empirical work on portfolio choice at the level of the individual households. The forthcoming volume by Guiso et al. (2001) provides an overview of the current state of the art in this field. This volume links portfolio choice theory to empirical research and contains empirical studies for several countries. While many countries have some survey data on ownership and amounts invested for several types of assets, this data is often limited to one or more cross sections. Though useful for many purposes, such data is insufficient to analyze the dynamics of portfolio choice behavior. This requires panel 1 These numbers are taken from Guiso et al. (2001), Table 3. 2 data. Household panels with information on portfolio composition are currently available for Italy and the Netherlands only. Existing empirical studies typically focus on broadly defined asset groups, including all risky financial assets as one category. Important differences between various risky financial assets, however, will not be revealed in an analysis at this high level of aggregation. Although it is infeasible to use survey data to analyze ownership of every single financial product in the market, it seems worthwhile to distinguish a few subcategories of risky financial assets and to investigate the dynamics in the ownership patterns of these categories as well as the interactions between these patterns. In particular, we think it is useful to consider the two largest categories, individual stocks and mutual funds. The theoretical argument to treat these separately is that one mutual fund can provide the level of diversification which would require a large number of different stocks. Thus mutual funds seem very attractive for the small, non expert investor who wants to invest a limited amount with relatively low transaction costs. On the other hand, since transaction costs for stocks will be less than proportional with the amounts held, holding individual stocks may be more attractive for the large investors. An empirical argument to distinguish between the two types of risky assets is that in many countries including the Netherlands, the mutual funds market has grown even more than the market for individual stocks. In this paper, we use dynamic binary choice panel data models to explain the dynamics of the ownership structure of asset portfolios. Existing univariate random effects panel data models are extended to the bivariate case, accounting for interactions between two types of assets. One of the main features of the univariate dynamic binary choice model with random effects is that it can distinguish between unobserved heterogeneity and genuine state dependence. In addition, the bivariate model can explain correlation between ownership of one type of asset and lagged ownership of the other type of asset from correlated unobserved heterogeneity as well as from state dependence across assets. The correlation between random effects in the ownership equations captures correlated unobserved heterogeneity. Dummies for lagged ownership of each asset type in each equation capture genuine state dependence effects. To investigate the sensitivity of the results for the random effects assumption, we compare our model with a fixed effects dynamic 3 linear probability model. The empirical analysis considers ownership of stocks and mutual funds, using the waves of the CentER Savings panel survey of Dutch households. This is one of the few existing household panel surveys with detailed information on ownership of many types of assets and debts. The sample consists of a sub-sample designed to be representative for the Dutch population, and of a (smaller) sub-sample from the highest income decile. Since ownership of risky assets is much more common among the rich than among others, this makes the data particularly useful for our purposes.the estimation sample is an unbalanced panel with 2861 households who, on average, participate in 3.4 waves. Our aim is to increase insight in how households adjust the structure of their asset portfolios, addressing questions such as the following. Who are the people who have invested in mutual funds or stocks? Do background variables such as income, age, education level, and labor market status affect ownership rates of the two types of assets in the same way? Can changes in these background variables explain the increasing trends in the ownership rates? Why has the ownership rate of individual stocks increased less than the ownership rate of mutual funds? Have most new investors gone into mutual funds, or have people replaced individual stocks by mutual funds? If people hold mutual funds to diversify their risk, there seems no reason to hold individual stocks in addition. Still, the raw data show a positive correlation between ownership of mutual funds and ownership of individual stocks. Is this spurious correlation, or is there genuine state dependence across asset types, which could, for instance, be due to learning effects? Or is it because the new mutual funds owners simply keep their individual stocks? The remainder of this paper is organized as follows. In the next section, the econometric models are presented. The data are described in Section 3. Section 4 contains estimation results. Section 5 concludes. Appendix A contains some additional estimation results. More details on the model and the estimation procedure are given in Appendix B. 4 2 Models Following Hyslop (1999), we use two kinds of models. In Subsection 2.1, the random effects probit model is presented. This model explicitly incorporates the binary nature of the dependent variables and produces predicted ownership probabilities between zero and one. On the other hand, it relies on the assumption that individual effects are uncorrelated with regressors. Since this assumption is hard to relax in a discrete choice framework, in Subsection 2.2 a linear probability model is presented that allows for fixed effects, but has the drawback that predicted ownership probabilities may be outside the zero/one interval. 2.1 Random Effects Probit Model In this subsection we introduce a multivariate discrete choice model for panel data, to explain ownership of different types of assets. For the sake of notational convenience, we present the bivariate case, but the generalization to the case of more than two asset types is straightforward. Since we will apply the model to ownership of stocks and mutual funds, we will refer to asset type 1 as stocks and to asset type 2 as mutual funds. We use the following notation, where the index for the household is suppressed. y jt : dependent variables; ownership dummies for stocks (y 1t = 1 if the household owns stocks in year t, y 1t = 0 otherwise) and mutual funds (y 2t = 1 if the household owns mutual funds in year t, y 2t = 0 otherwise); t = 1,..., T. x t : vector of independent variables, assumed to be strictly exogenous. The same independent variables are used in the two ownership equations. α j : random individual effects (j = 1, 2); (α 1, α 2 ) is assumed to be bivariate normal with variances σα 2 1 and σα 2 2 and covariance σ α1 σ α2 ρ α. u jt : error terms (j = 1, 2; t = 1,..., T ); (u 1t, u 2t ) are assumed to be bivariate standard normal with covariance ρ and to be independent over time. 2 2 We have estimated specifications allowing for first order autocorrelation in the u jt but found insignificant values of the autocorrelation coefficient for both assets. 5 We assume that (α 1, α 2 ), {u jt ; j = 1, 2; t = 1,..., T } and {x t ; t = 1,..., T } are independent (which implies that x t is strictly exogenous). The following specification will be used in the sequel. 3 y 1t = x tβ 1 + y 1,t 1 γ 11 + y 2,t 1 γ 12 + α 1 + u 1t (1) y2t = x tβ 2 + y 1,t 1 γ 21 + y 2,t 1 γ 22 + α 2 + u 2t (2) 1 if yjt 0 y jt = j = 1, 2; t = 1,..., T (3) 0 else Some special cases are worth mentioning. If γ 12 = 0, the equation for stocks (1) does not contain the lagged mutual funds ownership dummy. In that case, the parameters β 1, γ 11 and σ 2 α 1 can be estimated consistently by considering only equation (1). This would be the standard univariate panel data probit model for binary choice, with state dependence (y 1,t 1 is included) as well as unobserved heterogeneity (the random effect α 1 ). See Heckman (1981a) for a discussion of this model. Similarly, the equation for mutual funds (2) can be estimated as a univariate model if γ 21 = 0. If y 2,t 1 enters the first equation but error terms and random effects in the first equation are independent of error terms and random effects in the second equation, then y 2,t 1 is weakly exogenous in the equation for y 1t. In this case the first equation could be treated as a univariate model with (weakly) exogenous regressors only. One of the main issues in the univariate version of this dynamic model, is the distinction between unobserved heterogeneity (random effects) and state dependence (the lagged dependent variable). Both phenomena can explain why ownership of stocks in period t is positively correlated with ownership of stocks in period t + 1 (conditional on observed background variables x t and x t+1 ). The model estimates will tell us to which extent the correlation is due to either of the two. In the bivariate model, a similar issue can be addressed, concerning the spill over effects from one asset type on the other. If ownership 3 Adding interactions of the two lagged dependent variables or of lagged dependent variables with x t would make the model as flexible as a transition model with four different ownership states (both assets owned, stocks only, mutual funds only, neither of the two; the standard transition model would not include the random effects, however). We experimented with interaction terms but found they did not change the qualitative conclusions and were mostly insignificant. 6 of stocks in period t + 1 is correlated to ownership of mutual funds in period t, this can be due to correlated unobserved heterogeneity (i.e., a non zero covariance between α 1 and α 2 ) or due to state dependence across asset types, i.e., a non zero value of γ 12. This is important for understanding the dynamics of the asset ownership decisions. For example, a positive value of γ 12 could mean that mutual funds which are easily accessible and advertised on a large scale may have a learning effect in the sense that their acquisition changes people s attitudes to holding risky assets in general. People may then be induced to start buying individual stocks. On the other hand, a positive correlation between the random effects would simply mean that the same people who find it attractive to hold stocks in general also have a preference for holding mutual funds. Initial Conditions and Estimation This subsection is an informal discussion of how to estimate the model. Details can be found in Appendix B. In a short panel, there is a problem with the initial conditions (cf. Heckman (1981a)). One way to deal with this problem is to add static ( reduced form ) equations for the first time period similar to the dynamic equations, but without the lagged dependent variables. The coefficients are allowed to be different from the coefficients in the dynamic equations, the random effects are linear combinations of the random effects in the dynamic equations, and the error terms are allowed to have a different covariance structure. This is the straightforward generalization of the solution that was given by Heckman (1981b) for the univariate case. In principle, the static equations can be seen as linearized approximations of the true reduced form (obtained by recursively eliminating y t 1 until t = ). Heckman s simulations suggest that the procedure already works well in short panels, i.e. the approximation error does not lead to a large bias on the parameter estimates. 4 4 An alternative solution is explored by Lee (1997), who treats the initial values as fixed. Lee s simulation evidence suggests that this does not lead to any serious bias if the panel consists of 20 waves, but it does if the panel has only eight waves. It therefore seems less appropriate for our panel of six waves. Chay and Hyslop (2000) compare various ways to deal with the initial conditions problem in logit and probit models. They find that the probit model with the Heckman procedure performs better than other random effects models. 7 The complete model can then be estimated by Maximum Likelihood (ML), including the nuisance parameters of the static equations. Conditional on the random effects, the likelihood contribution of a given household can be written as a product of bivariate normal probabilities for all time periods. Each bivariate normal probability is then the probability of the observed ownership state, conditional on the ownership state in the previous year (t 2) or unconditional (t = 1). Since random effects are unobserved, the actual likelihood contribution is the expected value of the conditional likelihood contribution, with the expected value taken over the two individual effects. This is a two-dimensional integral. It can be approximated numerically using, for example, Gauss Hermite quadrature. Instead, we use simulated ML: bivariate errors are drawn from N(0, I 2 ), they are transformed into draws of the random effects using the parameters of the random effects distribution, the conditional likelihood contribution is computed for each draw, and the mean across R independent draws is computed. If R with the number of observations, this gives a consistent estimator; if draws are independent across households and R faster than N, then the estimator is asymptotically equivalent to exact ML (see Hajivassiliou and Ruud (1994), for example). 5 In practice, the data at hand are an unbalanced panel, due to attrition, non response, and refreshment. We assume that attrition and item non response are random. We will use the complete unbalanced sub panel. This is more efficient than using the balanced panel only Linear Probability Model This subsection presents standard linear dynamic panel data models as discussed in numerous places. See, for example, Verbeek (2000, Section 10.4) for an accessible overview. To formulate the linear probability model, two types of covariates are distinguished: x t = (x 1 t, x 2 ), where covariates in x 1 t are time varying and (strictly) exogenous, and 5 In the application, we found R = 100 to be sufficiently large in the sense that results did not change if R was increased further. 6 There are some observations with gaps (observed for t = 1, 2, 4, 5, 6 for example). For computational convenience

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