DIAGRAMA DE CONTROL

2.4.1 Introduction to Unordered Multiple Choice Models

The purpose of this chapter is to investigate the changing influence of socio-economic background and ability on the educational aspirations and choices of young individuals. Empirical models for educational aspirations and choices are estimated using two different datasets and controlling separately for parents’ education and parents’ occupation in order to avoid multicollinearity among the independent variables.

The dependent variables which estimated educational aspirations and choices are unordered, having no natural ranking across the alternatives. Unordered choice models are motivated by a random utility model. All alternative choices are labelled arbitrarily and each individual chooses only one of the possible options. For each individual iand possible alternativekthere is an unobserved random variable defined as a continuous latent variable y_i,k∗ . This latent variabley∗_i,k conditional on a set of independent and control variables,x, is distributed for theith individual who has to choose betweenj= 1,2...k choices. Utility, conditional on the set of the independent and control variables is specified as:

y_i,k∗ =βk‘xi+i,k

The empirical model is driven by the probability that choice j is made meaning that if individuali makes choicej then one assumes that y∗i,k is the maximum utility among the

j options.

2.4.2 The Multinomial Logit Model

The technique that has been used for the three outcome unordered models is the Multinomial Logistic regression using Maximum Likelihood (ML) estimation techniques to estimate the parameters that best fit the data. The dependent variable is a categorical variable with individuali’s chosen educational alternative kand although the independent variables do not vary across alternatives, the parameterβj differs across them (Schmidheiny, 2007). In the method of ML, the parameter values which maximise the likelihood, or equivalently the log-likelihood, are picked and estimated using the Newton-Raphson iterative method

(Czepiel, 2012).

In Multinomial Logit Models (MLM), choice is a function of the characteristics of the individual making the choice and the explanatory variables remain constant over the alternative choices. For the specific MLM and particularly for the interpretation of the marginal effects which will be explained in detail below, for each educational alternative k the non-educational alternativek has been chosen as the reference category. As a result, the estimation procedure for aspirations allowed us to model the factors that affect the probability of aspiring academic education rather than not aspiring academic education, aspiring vocational education rather than not aspiring vocational education and not aspiring any post-compulsory education rather than aspiring post-compulsory education. Similarly, the estimation procedure for choices allowed us to model the factors that affect the probability of choosing academic education rather than not choosing academic education, choosing vocational education rather than not choosing vocational education and not choosing any post-compulsory education rather than choosing post-compulsory education. The MLM analyses individual choice among discrete alternatives with the assumption that each individuali chooses the alternative that yields higher utility or satisfaction. For this specific estimation the following data model is estimated for the ith individual for educational choice k:

Y_i,k∗ =β0+β1,kSESi+β2,kAbilityi+γk‘Xi0+i,k where the variables are:

• Y_i,k∗ : the latent variable corresponding to educational aspiration or choice k of individual i

• β0: the intercept parameter (constant).

• SESi: the socio-economic component of individual iincluding occupation of both parents or highest educational achievement of both parents.

• Abilityi: the ability component of individuali.

• Xi: a vector of several controls for individual iincluding gender, ethnicity, parents’ age, number of children in the household and whether living in an urban area. The controls include binary, categorical and continuous variables.

fork indicating academic, vocational and no post-compulsory qualifications.

The latent variableY_i,k∗ can be thought of as the utility associated with individualichoosing educational alternativek where there is some randomness in the actual amount of utility obtained which accounts for other unobserved factors that go into the choice. The value of the actual variable Yi is then determined non-randomly from these latent variables as the randomness has been moved from the observed outcomes into the latent variables. Educational outcome kis then chosen if only the associated utility which is determined by the value ofYi,k is found to be greater than the utilities of all the other alternatives. That is:

P r(Yi = 1) =P r(max(Yi,1, Yi,2, Yi,3) =Yi,1)

P r(Yi = 2) =P r(max(Yi,1, Yi,2, Yi,3) =Yi,2)

P r(Yi = 3) =P r(max(Yi,1, Yi,2, Yi,3) =Yi,3)

The dependent variable distinguishes how the likelihood of the educational aspiration or choice of an individual varies as the independent variables vary. The error component, i,k, represents any other unobserved factors that have an effect on educational choices. Table 2.3 below summarises the dependent and key variables used in each estimated model. As mentioned above, the estimated regression models include a number of other control variables apart from the socio-economic background and ability component. The same control variables among the two datasets have been used in order to make their results comparable. The ability component differs among the two datasets but in both cases represents the level of cognitive ability developed in early ages.

Table 2.3: Summary of estimated models

Model Age Dependent Variable SES component Ability component BCS

1 16 Educational aspirations Parents’ occupation Friendly Maths Test (age 10) 2 16 Educational aspirations Parents’ education Friendly Maths Test (age 10) 3 26 Educational choices Parents’ occupation Friendly Maths Test (age 10) 4 26 Educational choices Parents’ education Friendly Maths Test (age 10) LSYPE

5 16 Educational aspirations Parents’ occupation KS2 Maths (age 10-11) 6 16 Educational aspirations Parents’ education KS2 Maths (age 10-11) 7 25 Educational choices Parents’ occupation KS2 Maths (age 10-11) 8 25 Educational choices Parents’ education KS2 Maths (age 10-11)

2.4.3 Marginal Effects

In a MLM the sign and value of an estimated coefficient determines a log-odds ratio and when in that form is not as clear in determining the relationship between an independent variable and a dependent variable. For clear interpretations about the direction and magnitude of the relationship between an independent and a dependent variable in a MLM, marginal effects should be calculated and their standard errors (Bowen and Wiersema, 2004). The marginal effects are defined as the slope of the prediction function at a given value of the explanatory variables and thus inform us about the change in predicted probabilities due to a change in a particular predictor (Wulff, 2015). There are two different approaches of measuring marginal effects. The first is to set all of the predictors to their mean values resulting in marginal effects at the mean (MEM). The disadvantage of using this approach is that it is unlikely that there is a unit in the sample that is average on all model variables. In order to avoid this, the marginal effects have been estimated using average marginal effects (AME) which relies on actual values of the independent variables. The marginal effect is calculated for each individual according to their characteristics, and then averaged across all individuals.

The estimated marginal effects are surrounded by 95% confidence intervals. As referred above, the marginal effect shows the outcome of a unit change in each variable on the probability of choosing each educational alternative and in the specific case it is not interpreted relative to a reference category. In other words, the marginal effect for each of the regressors is examined on the probability of observing each of the three alternative outcomes, including the choice between academic, vocational and no post-compulsory qualifications. All categorical variables fitting in the model have been treated as factor variables and the marginal effect has been computed as a discrete change in the probability of having each characteristic rather than having the omitted category characteristic.

2.4.4 Selection in educational alternatives and omitted variable bias

Making use of the longitudinal nature of both datasets the chapter includes rich control variables that allowed to take into account a large number of exogenous factors as required to identify only a ceteris paribus link from socio-economic background and cognitive skills to educational aspirations and choices. These specific control variables could have a direct or an indirect impact on educational aspirations and choices and have been selected to be

used in the estimation as they can be considered exogenous to the individuals’ aspirations and choices but are still likely to be highly associated with educational decisions. The set of explanatory variables includes family characteristics (number of children in the household and parents’ age), individuals’ demographic characteristics (gender, ethnicity) and a description of the area of residence (urban or rural). These variables remain the same in all models and for both surveys. Positive values in the marginal effect of each variable indicate that the probability of attending each type of education (or not attending any education) increases when an individual has that specific characteristic whereas negative values indicate that attendance to that type of education is reduced with that covariate. It is widely acknowledged that the educational aspirations and choices of students can be influenced by a myriad of factors. For example the role of peers in influencing educational aspirations and choices, which is extensively examined in the next chapter, or the role of the school, which is discussed in more detail in Chapter 4, are not considered in this analysis. Further, selection in each educational alternative is one of the main econometric issues associated with causal estimations. It is possible that part of the estimated socio-economic and ability effect could be capturing other unobserved characteristics of the individual, different from those that are included in the set of control variables. As identified in previous analyses following a similar approach, by “simply including additional observed variables cannot definitely eliminate omitted variable bias arising from unobservable factors and in the absence of a randomized experiment, there is a limit to how far this study can go in establishing causal relationships” (Vignoles et al., 2011, p. 5).

To identify the causal effect of socio-economic background and ability on educational aspirations and choices is beyond the scope of this chapter. The chapter follows a strongly comparative approach to examine, between cohorts, the change in the importance of socio-economic background and ability in influencing educational attainment andwithin

cohorts, the difference in the effect of these inputs between aspirations and choices. To the extent that biases are the same across the compared models, they will cancel out when looking at these differences.