Sex, Drugs and Economics

Tuesday, 4 April 2023

Understanding lower domestic university enrolments

North Island universities are blaming high employment and a drop in school-leavers with University Entrance for a big fall in enrolments by New Zealand students.

All five North Island universities told RNZ they had started the year with fewer full-time-equivalent domestic students than the same time last year.

The drop was trivial at Waikato, but significant at the remaining four institutions.

The two South Island institutions that shared their figures with RNZ, Canterbury and Lincoln, reported increased domestic enrolments...

The University of Auckland said it had been expecting a fall in domestic enrolments this year, but the actual result was lower than expected due to "the relatively low numbers achieving University Entrance"...

Massey University described its eight percent drop in domestic FTE students as slight and said [it] was prone to labour market shifts...

Victoria University said its enrolments "have been affected over the past few years by the intersection of changes in student demand, the growth of new areas of study and the waning of others, demographic changes, unique economic conditions (i.e., low unemployment and growing cost of living), closed borders, and the broader impacts of Covid-19".

To understand what's going on, it is worthwhile to unpack the things that contribute to domestic school-leaver university enrolments. I focus on domestic school-leavers, as they make up the majority of new university enrolments, and it turns out that the changes are mostly predictable.

Take this simple identity:

E = P * [S/P] * [U/S] * [E/U]

E is the number of domestic school-leaver enrolments. P is the total population (of New Zealand). S/P is the proportion of the population who are school-leavers. U/S is the proportion of school-leavers who achieve university entrance. E/U is the proportion of those who achieve university entrance who ultimately enrol at university.

This identity essentially describes where domestic school-leaver enrolments come from, and understanding each component of the identity, and changes in each component, will give us a good understanding of what is happening with enrolments (and what is likely to happen in the future).

Let's start with P, the population of New Zealand. The population is growing, at about 0.7 percent per year. As for S/P, the proportion of the population who are school-leavers, this is shrinking slowly over time. This is obvious when you look at a population pyramid for New Zealand (like this one). The age cohorts at the bottom of the pyramid are smaller than those above them. That also means that when you combine P and S/P, the number of school leavers is declining, and likely to continue to decline in the future.

Moving on to U/S, the proportion of school-leavers who achieve university entrance, we know that this was artificially inflated during the pandemic, as NZQA gave away lots of bonus NCEA credits (e.g. see here for 2021). Those bonus credits came to an end this year, and there were fewer credits available in 2022. This means that we should expect a smaller proportion of school leavers to achieve university entrance from 2022, compared with 2021 or 2020. There may be a small decrease in 2023 again, and then beyond that the proportion of school leavers achieving university entrance will probably return to its long-run flat trend (see page 2 of this document).

Finally, E/U is the most uncertain component. The proportion of those who achieve university entrance who ultimately enrol at university depends on labour market conditions, as the statements from Massey University and Victoria University note. When the economy is doing well, and jobs for school leavers are relatively plentiful, more school leavers will opt to go straight into the workforce, rather than to university. Right now, at 3.4 percent, the unemployment rate is close to the lowest it has been over the last 15 years. Even the youth unemployment rate (for those aged 15 to 24 years) is very low, at 9.6 percent. However, the economy may tip into recession later this year (or at least, that is what is expected by many economists - see here and here). If the economy slows, there will be fewer jobs for school leavers (and for everyone else), and enrolments might start to pick up.

When we put this all together, we realise that the demographic trends (P and S/P) together contribute to lower enrolments, and student achievement (U/S) will lead to lower enrolments this year and next year (after a temporary increase over the last two years). Finally, economic conditions (E/U) will likely increase enrolments later this year, and perhaps into next year.

Overall, it probably isn't all bad news for universities as a whole in the short term, but only if the expected recession comes to pass. Longer term, the demographic changes weigh more heavily, and domestic enrolments are likely to decline over time as a result. Of course, the universities are busy competing for those declining enrolments, and that competition will no doubt heat up as the declining total enrolments start to eat into university budgets.

Sunday, 2 April 2023

How not to strategise for penalty kicks

In game theory, a pure strategy is an unconditional choice of strategy for a player. In other words, the player chooses that strategy for sure. That distinguishes it from mixed strategy, where the player randomises their actions, choosing each of the possible strategies with some probability (which might be zero). There are lots of examples of mixed strategies. One that I use in my ECONS101 class is the choice for a tennis player over whether to serve down the middle, into the body, or out wide. If they chose one strategy for sure, they would reduce their chances of winning. Instead, they should randomise - sometimes choosing the first strategy, sometimes the second, and sometimes the third.

Another example from sports is the penalty kick in football (or soccer, if you prefer). The penalty taker must choose which side to kick towards, and the goalkeeper must choose which way to defend. I've discussed this game and the mixed strategy equilibrium before (see here and here).

The key problem with mixed strategy is that it genuinely involves randomisation. You cannot reason a pure strategy solution to a mixed strategy game. If you do, you end up with something like this:

I'm not sure where the video comes from (TV or movies, or something else), but it is very similar to a story related in the book Soccernomics, by Simon Kuper and Stefan Szymanski (as Robbie Butler notes here). The solution to mixed strategy games is not to try and solve them with pure strategy, but to randomise.

[HT: Jadrian Wooten at Critical Commons, via the Economics Media Library]

The employment effects of the minimum wage, from American Community Survey data

The minimum wage in New Zealand goes up tomorrow, from $21.20 to $22.70 per hour. At times like this, it is worth considering what impacts increasing the minimum wage will have. In terms of the effects of increasing the minimum wage on employment, the literature is not settled. It does appear that the effect depends a lot on context (see the links at the end of this post for more, as well as how the minimum wage affects a lot of things other than employment). However, my reading of the literature does suggest that increasing the minimum wage reduces employment, and that reduction in employment is concentrated among young and less educated workers (see my most recent post on that point here).

That most recent post drew on three articles, one of which was by Jeffrey Clemens (University of California, San Diego) and Michael Strain (American Enterprise Institute). I've now gone back read some of their earlier research (which had been sitting in my to-be-read pile), published in 2018 in the journal Contemporary Economic Policy (ungated version here). Like their more recent research, this paper uses data from the American Community Survey, and compares four groups of states:

States that increased their minimum wage by more than $1 between January 2013 and January 2015;
States that increased their minimum wage, but by less than $1, between January 2013 and January 2015;
States that indexed their minimum wage to inflation between January 2013 and January 2015; and
States that did none of those things (as a control group).

Those are quite similar to the 'policy groups' of states that Clemens and Strain looked at in their more recent research. They then apply a difference-in-differences strategy, comparing the difference in employment rates (separately for people under 25 with less than a high school education, people aged 16-21 years, and teenagers) between states in each group, before and after 2013. Their dataset covers the period from 2011 to 2015. Importantly, they control for a number of economic variables that may affect employment, including median house prices, state income per capita, and employment among higher skilled population groups. Clemens and Strain find that:

...minimum wage increases exceeding $1 reduced employment by just over 1 percentage point among groups including teenagers, individuals ages 16-21, and individuals ages 16-25 with less than a completed high school education. By contrast, smaller minimum wage increases (including those linked to inflation indexation provisions) appear to have had much smaller (and possibly positive) effects on employment.

In other words, the results are consistent with large minimum wages changes leading to disemployment. However, there is reason for caution with interpreting these results, because they didn't test for pre-trends between the policy group states. Clemens and Strain do note that:

...economic conditions were moderately stronger in states that enacted minimum wage increases relative to other states. Prime age employment, for example, grew by an average of 2.3 percentage points in states that either enacted minimum-wage changes exceeding $1 or that index their minimum wage rates for inflation. Across states that enacted no minimum wage increases, prime age employment increased by a more modest average of 1.6 percentage points.

However, that difference is evaluated across the entire period of the data. Looking at the time from 2011 to 2013 would be more helpful. Eyeballing Figure 3 from the paper does make it seem like the pre-trend for large statutory increases in the minimum wage (more than $1) is flatter than for the other groups (compare the bottom line with the top three lines, for the period from 2011 to 2013):

So maybe we should expect the group of states with large minimum wages not to experience as big an increase in employment as other states after 2013, because they weren't experiencing as big an increase in employment as other states before 2013. Clemens and Strain do report some additional analyses in the supplementary materials to the paper that they claim account for pre-trends, but I don't think that the approach that they report there really does account for pre-trends. That should temper any enthusiasm we have for these particular results, and given that they have been supplanted by more recent results from the same authors using similar data, we should discount them somewhat. Nevertheless, they do make a small contribution to the side of the evidence that supports the disemployment effects of the minimum wage.

Why Teslas are like paperback books

Tesla has lowered the price of its cars. This New Zealand Herald article from earlier this month asks whether it is because of flagging demand or a tactic to boost sales:

In explaining why Tesla Inc keeps cutting prices on its electric vehicles, the auto industry is pretty much divided into two camps.

On one side are analysts who see an aggressive move by the leading manufacturer of EVs to gobble up sales and market share from its competitors just as they’re beginning to bring more vehicles to market.

On the other side are critics who argue that with demand for Tesla’s older vehicles beginning to wane, the company feels forced to slash prices to attract buyers.

Over the weekend, Tesla cut the prices of its two costliest vehicles by between US$5000 and $10,000, or 4.3 per cent to just over 9 per cent. A Model S two-motor sedan now starts at US$89,990, with the Plaid “performance” version beginning at US$109,990. A Model X SUV dual motor starts at $99,990, the performance version at $109,990.

Chances are, it is neither of those explanations (but, if anything, it is closer to the second). To see why, we need to recognise that this is a form of price discrimination. Price discrimination occurs when a firm charges different prices to different groups of consumers for the same product or service, and where the difference in price does not arise from a difference in costs to the firm.

In order for a firm to practice price discrimination, it needs to meet three conditions:

Groups of consumers that have different price elasticities of demand (heterogeneous demand);
Different groups of customers can be identified; and
No transfers across submarkets.

Let's think about Tesla's situation. Do they have different groups of consumers with different price elasticities of demand? I would say yes. When Teslas were first released, many consumers were excited and anxious to buy a shiny new-release Tesla. The waitlists were long, but those consumers didn't care. For those consumers who wanted a newly released Tesla, there were few substitutes. They didn't want just any old car. They wanted a shiny new-release Tesla. The consumers on the waitlist for a new-release Tesla had demand that was relatively inelastic, meaning that they were not very responsive to a change in price (when a good has few substitutes, it has more demand that is relatively more inelastic). With relatively inelastic demand, Tesla could charge a high price, and it wouldn't cause those consumers to walk away. Prices of new-release Teslas were high.

Fast-forward to now, and those first consumers' demand for a Tesla has been satisfied. The remaining customers aren't nearly as keen on a Tesla. For current consumers, the choice isn't a Tesla or nothing at all. There are many other EVs that would be as good as, or nearly as good as, having a Tesla. The current consumers' demand is more elastic, meaning that they are more responsive to a change in price (when a good has more substitutes, it has more demand that is relatively more elastic). Tesla cannot charge as high a price without those consumers going somewhere else for a car. Prices of Teslas should fall, which is exactly what we are seeing.

What about the other two conditions? Tesla can tell which consumers are in which group. The consumers who sign up to the waitlist before a new car is released are clearly signalling to Tesla that they have relatively inelastic demand, and are willing to pay a higher price. Consumers who are willing to wait until later have more elastic demand, and are willing to pay a lower price.

What about no transfers across submarkets? Clearly, a Tesla owner can sell their Tesla second-hand to another buyer. However, the purpose of the this condition is so that consumers who buy at a low price don't turn around and sell to consumers who would otherwise buy at a high price. That isn't possible in this case, since Tesla sells first at the high price, to the consumers with more inelastic demand. Those consumers can resell their Tesla, but the remaining consumers are only willing to pay a lower price.

Tesla isn't alone in adopting this strategy for price discrimination. There are lots of similar examples. New season fashion clothing is sold at a high price, to consumers with relatively inelastic demand, and then is sold at a lower price at the end of the season to consumers with relatively elastic demand. Books are initially released in hardcover, and sold at a high price to consumers with relatively inelastic demand, before being released as paperbacks and sold at a low price to consumers with relatively elastic demand. When a new musical is released, tickets for the musical are initially sold at a high price, to consumers with relatively inelastic demand, and then when the musical is older, tickets are sold at a lower price to consumers with relatively elastic demand. And so on. All of these are examples where the first consumers believe that there are few substitutes for the good or service, so their demand is more inelastic, while later consumers believe that there are more substitutes, so their demand is more elastic.

Price discrimination is everywhere, once you know what to look for. Tesla is selling its cars in much the same way that publishers sell books. And in the same way as for new release books, when Tesla releases a new model car, it can restart the process for that new model from a high initial price.