Exam Prep

There isn't much here you don't already know, but I would advise having a quick read through of these slides before each exam to remind you of good exam technique.With 3 weeks to go till your first exam, just make sure you're chipping away each day. Like I've said to you countless times now, you're way better off doing 20 hours of revision in five days than doing it in 2. When you hit a wall and you can go no further, go do something else. You'd be amazed at how it all just falls into place when you just go for a walk or something. This doesn't work if you're cramming and scared to leave your desk.

That aside, if you have any other questions, be sure to e-mail me.Exam prep

All models are wrong, but some are useful.

Economists are often mocked for the assumptions we make in our models. People accuse of us surging ahead with elegant computations, forgetting that our entire analysis rests on some wholly implausible assumptions. Well, yes, these assumptions are often totally ridiculous. And yes, given their general contribution to the financial crisis, the macroeconomists of the last 20 years have got a hell of a lot to answer for. But, a good model, humbly deployed, can still be useful despite it's implausible assumptions.


A model is just a system of hypothetical propositions. A model is to Economics what the word 'if' is to Philosophy. Imagine if every time a philosopher said 'if' they were shouted down by everyone else because their 'if' simply wasn't true. 'If' is a bloody useful concept. "All models are wrong, but some are useful", said the statistician George Box. We know the assumptions we make are frequently implausible, but that doesn't make the results of our models useless. The tedious stereotype implies we economists believe these assumptions to be true, or will assume anything to reach some predetermined conclusion. I would suggest the opposite, that economists deliberately propose false assumptions in order to try and prove their theories to be false.


Take the following statement:


"Grammar schools and selection on ability only benefits the children of the wealthiest families because ability is so highly correlated with SES (socioeconomic status)."


You might agree or disagree with this statement and God knows plenty of people have a view. But to actually know whether this is true requires the analysis of several phenomena at once. Grammar schools likely increase the access to quality schooling for high ability children in poor neighbourhoods. They also probably harm the children remaining in those poor neighbourhoods as their more able peers leave them behind. Then again, schools in poorer neighbourhoods might be able to better target their teaching at their remaining students, so this segregation by ability could help the less able and so on.


Proper, objective analysis of this issue becomes very complicated very quickly using language alone (or as an economist would say, both the first and second derivatives of complexity with respect to language used are positive). Each of the statements I made in the previous paragraph can be articulated more precisely with algebra. You can sit in the pub all day long and argue about which of the above effects is the strongest, but persuasive anecdotes skilfully delivered with elegant rhetoric can't deal with internal theoretical inconsistencies in the way maths can. For this reason, the evolutionary biologist J. B. S. Haldane said "an ounce of algebra is worth a ton of verbal argument". Words can paint a picture and give you the perspective of the artist, maths can build a 3D (or more) model that can be manipulated and examined from any angle we like.


With this example, a mathematical model could articulate the conditions that would have to be true for selection on ability to benefit children from poorer families. Say we assumed, for the sake of computational simplicity, that all parents were aware of all possible schools they could send their children to. Ignore, just for the moment, the likely scenario that high SES parents will be more informed of their choices. Now let us suppose show that even if this assumption were true, our model showed that allowing all schools to select on ability would cause such strong social segregation that the implied necessary improvement in teaching quality for less able pupils in poorer areas was implausibly large.


The initial implausible assumption was there to provide the ideal scenario for some hypothesis to be true, just as engineers initially simulate plane designs in frictionless skies. If, given that ‘ideal world’ assumption, that plane doesn’t fly, or the theoretical model generates implausible results, then we can probably ditch that design or rule out that hypothesis altogether. The model was wrong, but it was also useful.

A first look at Game Theory: Prisoner's Dilemma

I think I've asked a few of you which courses you will be doing next year. I would recommend Intermediate Micro, you will be taught some very interesting stuff, especially Game Theory.

The first game you will be shown is the Prisoner's Dilemma, nicely summarized in this post. Lots of people don't like the PD story, mainly because they do not understand it. The point of this story is not that people are selfish or not to be trusted. Rather, the point is that given these payoffs, the equilibrium shown is the only one possible.

As I said in my last post, you are being taught how to get from X, a set of assumptions, to Y, an equilibrium given those assumptions. The PD is a nice introduction to Game Theory because it has a simple solution and an easy to understand narrative.

Other games could just as easily have an equilibrium where it makes sense for everyone to co-operate and there are very simple revisions to the basic PD setup which lead to that outcome. See if you can come up with them yourselves.

Social Welfare Functions

Here's an entertaining post on Social Welfare Functions written by my colleague Michael Sanders.

As Economics students, you will frequently hear others claim that the we economists assume all people to be machines, much like Spock. Generally speaking, these people will be dreadlocked Sociology students wearing God-awful hemp jumpers that stink of rolling tobacco, even if they don't smoke. These people misunderstand what Economics does.

Get a philosopher to state their normative assumptions about what is best for society and an economist will show you, using some maths, the implications of those assumptions. The Economics you learn at undergraduate level rarely has much to say about those assumptions themselves, we generally leave that normative stuff to others.

Most models you will learn are generally based on the "If X, then Y" principle. Don't worry too much about the X, the assumptions, worry about the analysis that takes us from X to Y, the equilibrium.

A Great Summary of the Austerity Debate

There was a fantastic discussion on the impact of cutting government spending on the radio this morning, here is the transcript. I would urge you to read this and make sure you understand it. E-mail me if you have any questions.

Also, think about how the pro-austerity view could be expressed mathematically. The Keynesian model you have studied would unequivocally recommend increasing government spending (G) or cutting taxes (T) to stimulate Aggregate Demand. What, according to those who support austerity, is missing from that model?

I will post again in a few weeks and give you my own thoughts, but you should have a think about it yourself first.

Khan Academy... and how to get better at Maths.

I'm sure I have already told you all that if you're having trouble with any of the Maths, you should definitely buy this book. It is only £6 and it takes you through most of the calculus you will need to do in your degree, but starts at a really nice and gentle introductory level.

If you're still struggling with a problem and you've tried going through your notes, I'm sure many of you will already be browsing the internet, which is fine. This is exactly what you should be doing. Wikipedia is always a good place to start, but their explanations can be somewhat technical. I have only just discovered Khan Academy and I think it is brilliant. Scroll down the page and you will find hundreds of short clips, taking you through the various mathematical techniques you will need. I like the way he presents the material, he tries to make it as intuitive as possible and he gives plenty of examples.

There was one other thing I wanted to say. Occasionally, I hear students saying, in a tone of resignation, that they are just no good at maths. Well, my response is to tell you that you aren't yet in the position to know if you're good at it or not. You might find it difficult and frustrating, but just because you've spent two hours working on something and gotten nowhere doesn't mean you have wasted your time. These exercises are exactly that, exercises. You won't know if you're any good at economics until the end of your second year. Until then, you shouldn't be too certain you're going to get a first or fail, you just don't know.

You're not supposed to be able to do everything yourself, first time, all the time. But what you are supposed to do is keep on trying, a little bit every day, because these ideas take time to make sense to most people. So, if you have an exercise due Thursday (which you do), it's best to take a look at it on the Friday before and start thinking about it, even if that's just a read through the questions and your notes. Then when you're sitting about on Saturday thinking about something completely different, you might have a little epiphany. Then you can take a look at it Sunday, understand a little more and so on. But what is less likely to work is sitting down to look at it on the Wednesday before. Even if you put six hours into it that day, it won't be as productive as looking at it for one hour for each of the previous six days.

As an economist would put it, your marginal productivity is likely to diminish quite rapidly each day, so it makes sense to work for an hour on three or four consecutive days than for four hours on one day.

Exogenous changes in G

Here's an example of the Keynesian Multiplier being used to analyze real world problems. Right now, governments are trying to cut their spending on goods and services (G), or at least, restrict G's growth. Stiglitz says that given stagnant growth, governments should be doing the opposite. You will also hear similar arguments from Paul Krugman, which he makes pretty much every minute of every day on his blog or Twitter.

Also consider the current government's plans to spend £30bn on a new High Speed Rail Network (HS2) and their consideration of a new airport for London. These are all 'pro-growth' policies, partly because of the Keynesian Multiplier. The government will pay construction companies who will receive income, they will spend some proportion of that income on other goods and services, that spending will be received by others as income, those people will then spend a proportion of that money on goods and services etc etc etc

You shouldn't necessarily take this as proof that Krugman, Stiglitz or Keynes are correct. I'm posting this so you can see that what you are learning right now has a direct application to real world problems and so that you can see the sort of language that economists use when discussing these models.