Good and old advice to young economists

Almost every econ PhD student knows the following two articles, but one more hyperlink in the vast ocean of the internet cannot harm. These are pieces of advice to young economists that come from two academics that are probably at rather opposite ends of the spectrum, both in terms of political views and in terms of writing style. Classic read.


John Cochrane: "Writing Tips for Ph. D. Students"
Paul Krugman: "How I Work."

Bill Evans - Here's That Rainy Day

Evans' richly stacked chords are just great.

Wouter den Haan on the state of modern macro

This Wednesday, my advisor Wouter den Haan gave a public lecture at the LSE titled "Is Everything You Hear About Macroeconomics True?". It was very stimulating. While I disagreed on some points (on which possibly more later), I was impressed by the earnesty with which he criticised the profession and his own work, and at the same time sharply drew the line to unwarranted criticism often heard from journalists and politicans.

Excerpt:

Often we get accused of not being open to alternative approaches. I think that's somewhat true. I think people are always somewhat defensive of things which are new. Especially things that are going to threaten your human capital. If you put a lot of effort into building up this human capital to be able to work with these mathematical [DSGE] models, you're not that happy if the new guy says: "No, let's do it another way." But I also think that these alternative approaches would get a lot more attention if they used the same language as the dominant paradigm (for example things like "efficient markets") and if they also understood better what the challenges are.

In particular, the challenges are not so much to generate a crash - our models can do that, too - or to generate volatile asset prices, or to have models that are better than these protoypes [RBC and New-Keynesian models]. The hard part is, if you discipline yourself by choosing parameters, to then get interesting action. There is a bunch of PhD students here, and they know that the hardest part is not to have an idea. The hardest part is to have an idea that is actually going to be quantitatively important if you discipline yourself in choosing things like preferences, technology and market structure.

You can listen to the whole thing here and also download the slides.

Fallacy of the week: higher risk implies higher return

I remember a conversation at my local bank branch when I wanted to open a small securities account. Their financial advisor asked me what assets I wanted to invest in and offered advice in allocating the portfolio. Most of what she said sounded extremely sensible, but that was mainly because she was a good saleswoman and I hadn't prepared myself well for the meeting.

One part of her advice was that I could choose to invest in equity mutual funds or individual stocks. While the latter would be much more risky, it would also offer the chance of a much higher return.

Over the years, I have heard this argument time and again. In it's general form, it goes somewhat like this:

"Here's an investment opportunity. It's quite risky, but as you know, people who only accept low risk only get low returns. So if you want a high return, invest now!"

The argument sounds somewhat intuitive to me. After all, it's just a description of risk premia, right? Markets reward high risk strategies with high returns. But just as this argument is intuitive, it is also dangerously wrong. Why? Because if you believe it, you will put your hard-earned savings at unnecessary risk by not sufficiently diversifying your portfolio.

This post does not contain any deep thoughts about economics. But I write it because my personal observation suggests that many small individual investors run more or less unconsciously into this simple fallacy.

To illustrate it a little more, suppose you are indeed a small individual investor (if you bother to read this far then you almost certainly are). You can invest money into two stocks, Coca-Cola and Pepsi. You expect both to yield an average return of 4% over the next year. But being stocks, they're both risky: You think that 90% of the time, the return of each stock will fluctuate between 0% and 8%. Now, you could invest all your money in either Coke or Pepsi. Or you can invest half the money in each. If you do the latter, your return will be within 0% and 8% less than 90% of the time, because in order for the return to fall below 0% you need both companies to do badly instead of just one. So this reduces your risk. And what's your expected return? It's the average of 4% and 4%, in other words... still 4%!

You can go ahead and go stockpicking here, and expose yourself to higher risk. Will it earn you higher returns? Sometimes, but on average: not at all. So sober up and stop gambling with your savings.

And what I say does not only apply to stockpicking. It also applies to pouring a lot of money into the purchase of real estate, or putting it all into an equity stake of that tech/green/tax-evading start-up company. Yes, this is very risky because if that one asset implodes your money is gone. But at the same time, you will often also not get a higher return for taking that risk.

Here's a slightly more technical version of the argument. Asset pricing theory tells us that it is not variance which markets compensate with high returns, but covariance with the discount factor: $$ E[R_i]=R_0 (1 - Cov(Q,R_i))$$ where \(R_0\) is the (hypothetical, if you wish) risk-free rate. In the special case of quadratic utility of an investor with a fixed sum to invest over one period, we get the CAPM formula $$ E[R_i]-R_0=\beta_i (E[R^m]-R_0) \text{ with }\beta_i=\frac{Cov(R^m,R_i)}{Var(R^m)}$$ where \( R^m\) is the return on the "market portfolio", the asset allocation of the marginal investor. Now let's rewrite the return on security i as \( R_i = ( R_i - \beta_i R^m) + \beta_i R^m = R_i^d + R_i^{nd}\). Clearly we have $$ E[R^d_i]=R_0 \text{ and } E[R^{nd}_i]=E[R_i]$$ So the market compensates only the risk of the non-diversifiable component \(R^{nd}_i\), but not that of the diversifiable component \(R^d_i\): We have $$\beta_i=\frac{Var[R^{nd}_i]}{Var[R^m]} \neq \frac{Var[R_i]}{Var[R^m]}$$ The fallacy is to put an "=" sign in the last line. Do you think nobody in his right mind would make that mistake? Well, the German Wikipedia does, stating that \(\beta_i \) would be the relative volatility of an asset relative to the market... I would bet that a lot of people read this or similar expositions and then go on picking their favourite stocks instead of just buying the bloody ETF.

Now you might say: "Wait, I still want to buy Google instead of Apple stock because I know that that company is better. I got business sense!" Except this is not about business sense. This is not about knowing which company has a good business model and which doesn't. This is about figuring out which securities are under- or overvalued relative to where they will be in the future. Can you analyse this while working a full-time non-finance job and taking care of the kids on the weekends?

There is one potent argument against diversification of course: costs. Actively managed mutual funds take hefty management fees, so with that strategy you might really need to trade off significantly lower returns in exchange for lower risk. With the rise of ETFs and online brokerage accounts, however, it is nowadays very cheap to buy diversified securities or just build your own diversified portfolio. The case is probably less clear for investing in real estate or non-public companies. Real estate and private equity funds for small individual investors do exist, but here the fees are still pretty high. Still, just because it is costly for you to diversify a risky investment strategy doesn't mean that it is also costly for more sophisticated investors. And if these guys are pricing your strategy, then you will still not earn higher returns by taking higher risk.

Every time you do optimal policy, Hayek sends you a greeting card

Whether you work as an economist, a management consultant, a computer scientist, an engineer, or indeed in any other profession in which you have to build some sort of mathematical model and solve some kind of optimality problem, you are often running into a very basic tradeoff. If you make a model that captures your object of study very realistically and in detail, you have a hard time figuring out how to optimise it. And if you make a model that you know to optimise, it is often in some important aspects oversimplified. So if you're an economist, you will be hopeless finding optimal policies in large-scale models of the macroeconomy, while nobody will believe the small-scale models you build to think about optimal policy. If you're a management consultant, you can fit some nonlinear model to explain your customer data very well, but good luck communicating a non-linear business strategy to the CEO of your client. If you're a computer scientist, you know the tradeoff as the curse of dimensionality. If you are an engineer, you know that versatility and precision of a machine usually run in opposite directions.

Essentially, we're facing a tradeoff between calibration and optimisation: models that fit the data or process we're looking at very well are hard to optimise well, and models that are easy to optimise usually don't fit the data well.

While this tradeoff exists almost anywhere, and is really just a consequence of the complexity of the world relative to the cognitive capacity of the human mind, I think it is carries a particular meaning in economics.

We know that under the standard assumptions we make (which are satisfied for example by the RBC model), the first welfare theorem holds. That's great, because the question of what the government should do is clear: nothing. The market allocates all resources efficiently. Okay, but that all markets are efficient is such an old joke that you can't even impress your grandmother with it. The world abounds with physical or pecuniary externalities, asymmetric information, bounded rationality or contract enforceability problems, and economics has demonstrated their existence both theoretically and empirically.

In principle, such market failures open the possibility of corrective government intervention. As economists, we often ask: What would an optimal policy intervention look like? As long as policy is not able to restore market efficiency completely (attaining the "first-best", as we say), this becomes quite a difficult problem. The computational complexity of solving a Ramsey problem is much higher than that of calculating a competitive equilibrium.

The reason that is so, at least in macroeconomics, is Hayek's insight that the market is successful because it distributes information decentrally. In the market, every individual need not know all the circumstances of some change which led to resources being allocated differently, as long as they see the prices in the market. I don't need to know that the implementation of some useful technological discovery requires extentive use of tin in order to give up some consumption of it to make room for that discovery; all I need to know is that the price of tin has gone up. By contrast, a central economic planner would need to aggregate all the dispersed information in the economy in order to know how resources should be allocated optimally. Collecting this dispersed information is very problematic, especially when it is about characteristics such as preferences, which are almost impossible to measure.

When we solve a competitive market equilibrium, we take the same position: we only need to solve optimisation problems for agents taking prices as given. Then we can solve for prices using resource constraints in a final step. By contrast, the Ramsey central planner takes into account the impact of policy on prices, and it is this which makes the Ramsey problem difficult. Now, of course solving for prices is also not always easy, especially with heterogenous agents such as in Krusell and Smith. But try to solve a Ramsey problem in the Krusell-Smith model!

And again, while we can calculate optimal policies elegantly in some models, those particular models are often so simplistic that, at least by my impression, people are more often than not very sceptical about the conclusions.

So every time you despair about a Ramsey or other optimal policy problem in economics, and you find yourself faced with a tradeoff of building a simple model nobody believes or not being able to calculate the optimal policy, Hayek is sending you a greeting card from the past: "Remember that the information contained in prices is difficult to centralise".