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«SCHOOL CHOICE AND SWITCHING COSTS ABSTRACT Voucher systems in education firmly rely on the parent´s ability to choose their child´s school at any ...»

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In our case, we understand , as the cost a student must face when (s) he decides to change the chosen school for another which reports a greater level of utility. Also, in (1) it is observed that in order for a student to switch to the better option, the benefit must outweigh said cost. If this occurs, then the benefits of competition will be observed. In our case, switching costs are measured according to a group of appropriately weighted attributes and the level of utility reported by the chosen provider facing each new market proposal in the market. Therefore, this can be expressed as in (2).

, ℎ ℎ + = ,ℎ ℎ + (2) Therefore, we suppose that the probability of changing the original school depends on , as in (3).

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Following with (3), we hope that in the absence of switching costs, our model suggests that a positive value of should induce parents to change the school previously chosen.


Using an identification code for each student, we followed this cohort of students who were in fourth grade in 2000, and we went back to observe then in their eighth grade in 2004, so we were able to verify if they changed schools. Thus, we can compare the expected utility associated with the chosen school and that associated with a new school that was not available when they were in 4th grade, but that was available when they were in the 8th grade, as in (1).

To this end, we merged a number of databases. The first data base is SIMCE that allows identifying students, the school they attended, and number of socio- demographic characteristics. The second is the database of students applying to universities in 2009 (i.e., those who were in their 12th grade in 2008) to get their addresses at the moment they applied to the university. Assuming the address didn’t change in the period considered, we georeferenced each home and school with digital maps, and we determined the Euclidian distance from each student´s home to every school and we get the parameters associated with distance, price and quality, and hence, the empirical tradeoffs into the indirect utility function. 3 To estimate the parameters associated with the probability that parents decide to keep the child in the original school, we consider the model (3). The general empirical versions of (3) first directly estimate the probability in terms of S, and second decompose the effect of each variable on the probability of changing school over the period considered as in (4) to estimate a possible differentiated effect.

, = ( ; ; , ; , ; ) (4) Where , is a binary variable for that chooses ℎ in the year 2000, and takes the value 1, when the student remains in the same school in 2004 and 0 if they moved to another school. is the difference in the SIMCE (standardized test score) between the originally

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between the chosen school and the best new option (in US$), , is the difference in the distance between home to the chosen school and home to the best new option; , is the student’s academic performance when he/she was in the 4th year and is a dummy variable that is 1 if the student is male. However, this increase of probability may not be linear, and in particular, can rise sharply once the benefit of the change outweighs its cost. Figure N°1 illustrates this possibility in which two regimes exist. The existence of a non-linear probability is explained by the families’ degree of sensitivity facing the change in wellbeing created by new schools, which translates to families not switching their children’s schools for small changes in levels of utility, or changing schools when said level reaches a threshold that depends on their preferences. Therefore, we estimate a threshold for each student and reWe tested our model using the residuals of an equation that considered SIMCE as dependent variable, and socio demographic variables as independent ones, to adjust for the influence of the family. The endogeneity problem arising from the endogenous nature of school location, as treated in that paper was addressed by using as instrument the number of schools in the county and in given ratio around each school. We pursue using SIMCE because the choice predictions were better, and an adjusted quality metric assumes particularly highly sophisticated parents.

calculate the probability of remaining in the chosen school despite the fact that there are better alternatives available Hasen (2000).

Figure 1. Probability of changing school with switching costs.

Probability of changing school.

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As a first analysis we tested whether helps to explain the switches and how, we define = 1, when a student switches schools and = 0 otherwise. The sample correlation between and is 0.05 and is statistically significant, unlike 0, and we found that, is statistically larger in cases in which a student switched schools, which would indicate that the changes in the function of utility by the entrance of new schools affect the decision of remaining in the chosen school (see table N°5) Table N°5: Is s statistically different when = 0 or = 1?

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Given what is presented in this paper, it is plausible to maintain that when people experience marginal changes in their levels of utility, they do not change providers, rather they will when this change is sufficiently significant to make such a decision and these changes allow for identifying an eventual threshold, which is unknown, ∗. We found three possible thresholds for performance: approximately 33.5 SIMCE points, (2/3 of a standard deviation), 2.8 kms (Euclidian distance), and about US$48 in price. Also, the table N°6, presents the probability of staying at the originally chosen school, evaluating possible thresholds for each one of the attributes. The models explain a small percentage of the total variance, but on a whole, it is significant and the variables considered are also significant and economically relevant. Overall, the probability, to remain in the original school decreases when the new school’s performance is better, when it is cheaper and when the student is female. For example, the results for the attribute tuition is illustrated in figure N°2, where the results are easier to interpret, and it is observed that the probability of staying at the chosen school decreases as the chosen school is more expensive than the new entries, more so when it surpasses the threshold of US $ 48.25, when the new school is best alternative and is much cheaper. As observed in figure N°2, the probability of staying in the same school increases when the chosen school is the better alternative to the new schools, that is to say, it is less expensive. The found results are coherent, but that there is a “jump”; a particularly huge reduction appears when the new best alternative is much cheaper (over US$48). It is also observed that the probability of staying in the same school decreases with the entrance of new schools that are a better option than the chosen school.

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Figure N° 2. Probability of remaining in the chosen school facing changes in Price.

Probability staying school 83.03 82.83 82.63 82.26 76.50 76.07 75.76

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We proposed an approach to measure switching costs in a context of consumers that value different characteristics simultaneously, and we apply it to the case of education in Chile, where a voucher system covers over 90% of the population. The voucher system in education firmly relies on parents having the possibility to choose their children´s school, and that parents actually make use of that choice. The economic theory suggests the effect of competition on school performance is positive, but it may be small when choice is limited. The speed in which parents respond to quality signals depends on whether they can reverse a previous decision.

Thus, the natural concern regarding parents’ capacity to react is given by the existence of switching costs. If they are substantial, the impact competition could have on academic performance would only occur through the effect of new students and the short run impact on quality would be very weak. Switching costs would dissuade parents from changing children to a different school once they are already enrolled in a school. Whilst our findings must be taken carefully, as other attributes that allow for more completely estimating a function of utility are missing, the results do illustrate that switching costs exist and they significantly impact the decision to stay or to change schools. Still, we found that the probability that parents change their children from the original school increases with the presence of new schools and better opportunities. The existence of switching costs, however, may help to solve a main puzzle regarding the contradictory results in different waves of studies. In particular, that the most recent evaluations of the voucher system, focusing on longer periods, are showing a higher impact on results.


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