Last week, I met a student who wanted to seek some advice on behalf of his sister.

She had just graduated with a diploma in hospitality and tourism management and planned initially to enrol in a Bachelor of Arts in Tourism course offered by a private school in Singapore next year.

But she was now having second thoughts. "Is there any value in a private degree?," my student asked.

His question was with reference to results from the inaugural employment survey for private school graduates, released on Nov 15. The survey showed that only 60.1 per cent of private school students found full-time permanent work within six months of graduation and their median starting pay was $2,550 a month. These statistics paled in comparison to the 79.9 per cent and $3,325 per month employment figures for graduates from the autonomous universities.

There are at least two reasons to be wary when using these results to evaluate the performance of private schools and the value of a private school degree.

First, the response rates from the survey were low. Of the graduates surveyed, only 32 per cent responded to it. In contrast, the response rates from the employment surveys conducted at the autonomous universities were much higher, at 70 per cent.

If those who responded were more likely to be unemployed, then the figures may have underestimated the salaries and the percentage of students from private schools that actually found employment.

Is it plausible that graduates who responded were more likely to be unemployed? Yes. Because such graduates would have more free time to do the survey.

On the other hand, those who found employment would probably have had less time for it.

Second, while some of the employment and salary difference between private and autonomous university graduates may indeed reflect employers' preference for autonomous university-trained graduates, at least part of the difference is also due to differences in the characteristics of students attending both types of universities.

We can use a simple comparison of employment outcomes between private and autonomous university graduates to infer the value of a private school degree (relative to an autonomous university degree) only if students entering both types of universities were, on average, the same - in all respects, such as incoming A-level or polytechnic academic results, parental income, age, ethnicity, gender, innate ability, level of motivation, and communication skills.

However, those who enrol in private universities and those who enrol in autonomous universities are likely to differ in other areas, not just school choice.

For instance, since autonomous universities in Singapore are well ranked globally, and are known to be selective, students who enrol in private universities might tend, on average, to have scored lower in their A-level or polytechnic exams.

Since employers are likely to select candidates based on a package of qualities, including past academic performance - that is, A-level or polytechnic performance - part of the difference in labour market outcomes between both groups of graduates might actually be reflecting employers' weaker preference for people with poorer A-level or polytechnic grades, not so much university type.

As such, simply attributing the entire difference in salary and employment rates to differences in university type would be naive.

Of course, one could restrict comparisons so that we only compare the employment outcomes of private and autonomous university students with the same observed characteristics - for instance, the students with the same incoming A-level or polytechnic academic results, parental income, age, ethnicity, gender. This would help to make the comparison more "apples to apples".

But even such a comparison could still produce an unreliable estimate of the value of having a private degree - relative to an autonomous university degree - if in addition to observable characteristics, private and autonomous university students differ along unobserved dimensions - such as communication skills or how hardworking they are, which are unobserved by the researcher. Since we cannot measure such unobserved characteristics, we cannot hope to control them in a statistical setting.

How, then, can we get an accurate estimate of the value of a private university degree?

In practice, this can be done if we restrict comparisons to students who fall at the thresholds of attending both types of universities.

To illustrate, suppose we have a group of students who have applied to study at two universities - one private and the other autonomous. Further, suppose that the autonomous university has a more stringent entry requirement.

Then a good way to estimate the value of the autonomous university degree - relative to the private school degree - is to compare the employment outcomes of graduates who are immediately on both sides of the fence.

In other words, we compare the outcomes for those people who just narrowly pass the threshold incoming test score requirement of the autonomous university - and so narrowly succeed in entering the autonomous university - and the outcomes of people whose incoming academic results narrowly fall short of the requirement - so narrowly fail to make it to the autonomous university and, therefore, enter the private university.

As long as there is nothing special about the threshold entry requirement, other than its use in assigning students to the different types of universities, we can reasonably attribute any difference in labour market outcomes at the threshold to the effect of university choice. This is because students immediately on both sides of the threshold are likely to be similar.

Before such an exercise is done, it would be premature to sound the death knell for private schools.

• The writer is a lecturer in the Department of Economics, National University of Singapore, and a Research Affiliate at the Institute of Labor Economics in Bonn, Germany. His research focuses on the Economics of Education.