2.1 Data

This study draws from the 2011 Survey of Knowledge and Attitudes on Elderly Issues. Based on a three-stage stratified sampling design, the survey was jointly conducted by the National Statistical Office, the College of Population Studies at Chulalongkorn University, and the Ministry of Social Development and Human Security. After removing observations with inconsistent responses (99 observations), the final sample contains 8,901 observations. It constitutes a nationally representative sample of the Thai working-age population (defined as individuals aged between 18 and 59).

2.2 Measures

The outcome variable is pre-retirement savings, denoted by SAV _i. It is based on the question: ‘Have you prepared yourself financially, including saving money and accumulating assets, for old age?’. The variable SAV _i takes the value of 1 if individual i responded yes to the question and 0 otherwise.

The main explanatory variables are twofold. Denoted by NSelf _i, financial non-self-reliance is based on the question: ‘Which of the following financial sources do you think you could rely on when you become old?’. Respondents were allowed to identify one or more of the eight possible responses: own income, spouse's income, children, grandchildren, relatives, own wealth (savings or assets), own pension, and the government. Four of the responses, including own income, spouse's income, own wealth, and own pension, are deemed to be indicative of ‘self-reliance’ in old age.Footnote ¹ The variable NSelf _i is assigned the value of 1 if none of the self-reliance responses was selected (and one or more of the remaining possible responses were selected), and the value of 0 if individual i chose any of the four self-reliance responses.

The distinction between ‘non-self-reliance’ (NSelf _i = 1) and ‘self-reliance’ (NSelf _i = 0) can be alternatively explained. While ‘non-self-reliance’ refers to the expectation that none (0%) of the required financial resources in old age would come from oneself, ‘self-reliance’ does not necessarily imply the extreme opposite, that is, total self-dependence (100%). Instead, it represents the expectation that some or all (>0%) of the financial resources needed in old age would be provided by oneself.

The other main explanatory variable is the identification of the most important source of old-age financial security. It is based on the question: ‘Which of the following financial sources do you think would be most important to you when you become old?’. The same possible responses described in the preceding paragraph applied and respondents were required to choose only one. In the empirical strategy, the possible responses are categorized into three non-overlapping groups. The omitted group includes respondents who chose any of the self-reliance responses as their most important source of old-age financial security. The other two groups represent those who considered family support and government support to be their most important financial source in old age, denoted by $Fam\_M_i$ and $Gov\_M_i$, respectively. The variable $Fam\_M_i$ takes the value of 1 if individual i identified his/her children, grandchildren, or relatives to be the most important financial source in old age, and 0 otherwise. The variables $Gov\_M_i$ are assigned the value of 1 if individual i identified the government as his/her most important source of old-age financial security.

The interaction terms between the two main explanatory variables are also explored. Since there are two categories for non-self-reliance (i.e., NSelf _i  = 0 and NSelf _i = 1) and three categories for the most important source of old-age financial security (i.e., $Fam\_M_i$ = 1, $\;Gov\_M_i$ = 1, and the omitted category of self-reliance), on the surface, it would seem feasible to create 3 × 2 = 6 mutually exclusive interaction terms. However, the interaction term between NSelf _i = 1 and the omitted category of self-reliance as the most important financial source is unattainable – practically because its construction yields no observations, and intuitively because it would refer to the presence of an individual who does not think of him/herself as a reliable source of old-age finances yet identifies him/herself as the most important financial source in old age. Therefore, there are only five interaction terms. The variable $SF\_M_i$ takes the value of 1 if individual i expected to be self-reliant and identified the family as the most important financial source in old age. The variable $SG\_M_i$ takes the value of 1 if individual i expected to be self-reliant and identified the government as the most important financial source in old age. The variables $NSF\_M_i$ and $NSG\_M_i$ are assigned the value of 1 if individual i expected to be non-self-reliant and identified the family and the government to be the most important financial source in old age, respectively. The fifth interaction term is the omitted category, including individuals who expected to be self-reliant and identified themselves as the most important financial source in old age.

2.3 Empirical Model

To examine the relationship between the decision to save for retirement during the working ages and expected sources of post-retirement financial security, three regression specifications are used. Based on a probit model, the first specification takes the following form:

(Spec. 1)$$SAV_i^\ast = \alpha NSelf_i + {\boldsymbol x}_{\boldsymbol i}^{\bi{\prime}} \zeta + e_i.$$

$\hskip-1pcSAV_i^\ast$ denotes the latent variable of pre-retirement savings, SAV _i. The explanatory variable of interest is NSelf _i, referring to the expectation for financial non-self-reliance in old age. It is hypothesized that α be negative, consistent with the fact that pre-retirement savings and sources of old-age financial security other than oneself have been shown to be substitutable (Lee et al., Reference Lee, Mason and Miller2003; Schultz, Reference Schultz2005; Galasso et al., Reference Galasso, Gatti and Profeta2009; Choukhmane et al., Reference Choukhmane, Coeurdacier and Jin2013).

Vector x_i represents a deliberately chosen set of individual/household characteristics. It includes variables that have been shown to be statistically important in explaining saving behaviors, including gender, age, education, marital status, income, and household structure (Binswanger and Carman, Reference Binswanger and Carman2012; van Rooij et al., Reference van Rooij, Lusardi and Alessie2012; Finke and Huston, Reference Finke and Huston2013; Nosi et al., Reference Nosi, d'Agostino, Pagliuca and Pratesi2014; Alan et al., Reference Alan, Atalay and Crossley2015). It also includes whether the individual worked in the formal or the informal sector, as the variable indicates the potential existence of an old-age pension in Thailand. Altogether, the vector captures each individual's constraint as well as their ability to predict future consumption trajectories and foresee how much they need to save today in order to optimize their lifetime living standards.

The second probit regression specification is given by:

(Spec. 2)$$SAV_i^\ast = \beta _1Fam\_M_i + \beta _2Gov\_M_i + {\boldsymbol x}_{\boldsymbol i}^{\boldsymbol {\prime}} \eta + u_i.$$

The variables $SAV_i^\ast$ and x_i are similarly defined. The variable NSelf _i is replaced by $Fam\_M_i$ and $Gov\_M_i$, which represent whether individual i expected family support and government support to be their most important financial source in old age, respectively. The reference category is self-support as the most important financial source in post-retirement years. It is hypothesized that both β ₁ and β ₂ be negative; the probability of saving for retirement is likely to be lower among individuals who expect their family and the government to be more important than themselves as a source of old-age financial security.

The third specification is given by:

(Spec. 3)$$SAV_i^\ast = \gamma _1SF\_M_i + \gamma _2SG\_M_i + \gamma _3NSF\_M_i + \gamma _4NSG\_M_i + {\boldsymbol x}_{\boldsymbol i}^{\boldsymbol {\prime}} \theta + v_i.$$

The variables of interest are $SF\_M_i$, $SG\_M_i$, $NSF\_M_i$, and $NSG\_M_i$. Defined in the ‘Measures’ sub-section, they represent the interaction terms between NSelf _i, on the one hand, and $Fam\_M_i$ and $Gov\_M_i$, on the other. The omitted category is when the individual expected to be self-reliant and identified themselves as the most important financial source in old age. Consistent with the discussion for Specifications 1–2, the coefficients γ ₁ − γ ₄ are hypothesized to be negative.

The main explanatory variables in Specifications 1–3 are potentially endogenous. In addition to the problem of reverse causality, the presence of common unobserved heterogeneity represents another source of estimation bias. The literature suggests that time and risk preferences (Bernheim et al., Reference Bernheim, Skinner and Weinberg2001; Binswanger and Carman, Reference Binswanger and Carman2012; van Rooij et al., Reference van Rooij, Lusardi and Alessie2012; Finke and Huston, Reference Finke and Huston2013) as well as personality traits (Hurd et al., Reference Hurd, Duckworth, Rohwedder and Weir2012) determine pre-retirement decisions and may contemporaneously influence how individuals identify their source of financial security in the future. Nevertheless, these variables are difficult to measure in a national survey and are missing in the data used in this study.

Recursive multivariate probit modeling is used to account for potential endogeneity bias in all of the above specifications. For illustration purposes, based on Specification 3, the model jointly estimates the following five probit equations:

(1)$$SAV_i^\ast = \gamma _1SF\_M_i + \gamma _2SG\_M_i + \gamma _3NSF\_M_i + \gamma _4NSG\_M_i + {\boldsymbol x}_{\boldsymbol i}^{\boldsymbol {\prime}} \theta + e\_SAV_i; \;$$

(2)$$SF\_M_i^\ast = {\boldsymbol x}_{\boldsymbol i}^{\boldsymbol {\prime}} \lambda _{SF\_M} + {\boldsymbol z}_{\boldsymbol i}^{\boldsymbol {\prime}} \mu _{SF\_M} + e\_SF\_M_i; \;$$

(3)$$SG\_M_i^\ast = {\boldsymbol x}_{\boldsymbol i}^{\boldsymbol {\prime}} \lambda _{SG\_M} + {\boldsymbol z}_{\boldsymbol i}^{\boldsymbol {\prime}} \mu _{SG\_M} + e\_SG\_M_i; \;$$

(4)$$NSF\_M_i^\ast = {\boldsymbol x}_{\boldsymbol i}^{\boldsymbol {\prime}} \lambda _{NSF\_M} + {\boldsymbol z}_{\boldsymbol i}^{\boldsymbol {\prime}} \mu _{NSF\_M} + e\_NSF\_M_i; \;$$

(5)$$NSG\_M_i^\ast = {\boldsymbol x}_{\boldsymbol i}^{\boldsymbol {\prime}} \lambda _{NSG\_M} + {\boldsymbol z}_{\boldsymbol i}^{\boldsymbol {\prime}} \mu _{NSG\_M} + e\_NSG\_M_i, \;$$

where

$$\left[{\matrix{ {e\_SAV_i} \cr {e\_SF\_M_i} \cr {e\_SG\_M_i} \cr {e\_NSF\_M_i} \cr {e\_NSG\_M_i} \cr } } \right]\sim N\left[{\left[{\matrix{ 0 \cr 0 \cr 0 \cr 0 \cr 0 \cr } } \right], \;\left[{\matrix{ 1 & {\rho_{12}} & {\rho_{13}} & {\rho_{14}} & {\rho_{15}} \cr {\rho_{12}} & 1 & {\rho_{23}} & {\rho_{24}} & {\rho_{25}} \cr {\rho_{13}} & {\rho_{23}} & 1 & { \rho_{34}} & {\rho_{35}} \cr {\rho_{14}} & {\rho_{24}} & {\rho_{34}} & 1 & {\;\;\;\rho_{45}} \cr {\rho_{15}} & {\rho_{25}} & {\rho_{35}} & {\rho_{45}} & 1 \cr } } \right]} \right].$$

Vector z _i represents instrumental variables (IVs). It is included in the equations for the ‘endogenous’ regressors (i.e., equations (2–5)) but excluded in the main regression (i.e., equation (1)). The error terms are assumed to follow a five-dimensional standard normal distribution. The expected value and the variance for each error term are 0 and 1, respectively. As shown in the variance-covariance matrix, there are 10 unique covariances (ρ), one for each pair of the error terms. Given the joint probability density function, the model is estimated using a simulated maximum likelihood estimator (MLE).

The validity of the IVs is tested with a simple over-identification test. Endogeneity bias is assessed through tests of the covariance between the error terms in equations (1) and (2) (ρ ₁₂), between equations (1) and (3) (ρ ₁₃), between equations (1) and (4) (ρ ₁₄), and between equations (1) and (5) (ρ ₁₅). Assuming that the IVs are valid, statistical insignificance of the covariances would indicate the lack of evidence supporting the presence of unobserved common factors and endogeneity bias in the system of equations (Monfardini and Radice, Reference Monfardini and Radice2008).

The recursive multivariate probit approach is chosen deliberately. Lewbel et al. (Reference Lewbel, Dong and Yang2012) identify four ‘convenient’ (i.e., readily implementable) estimators that can be used to measure the effect of endogenous regressors in binary choice models: two-stage least squares linear probability models (2SLS-LPM), MLE, control function estimators, and special regressor models. Recursive multivariate probit modeling falls within the MLE category. The control function and the special regressor approaches are not applicable to this study. The identification of the former relies on specific functional forms and requires that the endogenous regressors be continuously distributed, which stands in contrast with the discrete nature of the endogenous regressors here. The identification of the latter requires the existence of an exogenous regressor that is continuous with a large support and preferably a thick-tailed distribution. As shown in Table 1 below, it is not possible to identify such regressor in the data; most of the regressors are discrete and the support of the few continuous regressors that are available is limited, having small variances.

Table 1. Descriptive statistics and tests of equality of pre-retirement saving proportions (N = 8,901)

Notes: [Ref.] = Reference category; ***^, **^, * = 1, 5, and 10% of level of significance respectively; test statistics in column III refer to χ² tests for equality of proportions, unless otherwise stated.

Source: Authors' calculation from the 2011 Survey of Knowledge and Attitudes on Elderly Issues.

The other two estimators, including 2SLS-LPM and MLE, can be used. In reference to Specification 3, the 2SLS-LPM approach treats the main discrete variables as if they were linear, using actual (instead of latent) variables of SAV _i, $SF\_M_i$, $SG\_M_i$, $NSF\_M_i$, and $NSG\_M_i$. In the first stage, equations (2–5) are (separately) estimated with IVs z_i. In the second stage, equation (1) is estimated, with the first-stage predicted values being used in place of the endogenous regressors. The approach does not use information in the first-stage error terms, assuming that they are unrelated to the error term in the second stage. An important disadvantage of the approach is that fitted probabilities may be below 0 or above 1.

It is argued that the MLE approach, which encompasses recursive multivariate probit modeling, is more appropriate than 2SLS-LPM. It estimates equations (1–5) simultaneously through a known joint distribution of the error terms. The method is considered more efficient than 2SLS-LPM as it requires more information (Lewbel et al., Reference Lewbel, Dong and Yang2012), exploiting the covariances of the error terms to obtain more precise estimates. Also, unlike 2SLS-LPM, it does not produce out-of-range probability values. It should be noted that the identification of the MLE approach is derived from two sources: the use of IVs and the functional form. With regard to the latter, Wilde (Reference Wilde2000) argues that, as long as there is a varying exogenous regressor in all equations of the model (i.e., there is sufficient variation in the data), the nonlinearity of the model alone is sufficient for identification and no exclusion restrictions are needed. A more recent article by Li et al. (Reference Li, Poskitt and Zhao2019) elaborates on the issue by specifying the conditions under which identification by functional form is appropriate.